Transformer (deep learning architecture)

6838: 5063: 6822: 6814: 5137:, and each layer in a transformer model has multiple attention heads. While each attention head attends to the tokens that are relevant to each token, multiple attention heads allow the model to do this for different definitions of "relevance". In addition, the influence field representing relevance can become progressively dilated in successive layers. Many transformer attention heads encode relevance relations that are meaningful to humans. For example, some attention heads can attend mostly to the next word, while others mainly attend from verbs to their direct objects. The computations for each attention head can be performed in 3497: 3164: 3156: 3489: 5055: 3200: 6802: 6830: 971: 6580: 6169: 6445: 8151: 16430: 15506: 2161: 16410: 6183: 7768: 6087: 11425: 15516: 8940: 6440:{\displaystyle {\begin{aligned}{\text{given input vectors }}&h_{0},h_{1},\dots \\{\text{combine them into a matrix }}H&={\begin{bmatrix}h_{0}\\h_{1}\\\vdots \end{bmatrix}}\\{\text{EncoderLayer}}(H)&={\begin{bmatrix}{\text{FFN}}({\text{MultiheadedAttention}}(H,H,H)_{0})\\{\text{FFN}}({\text{MultiheadedAttention}}(H,H,H)_{1})\\\vdots \end{bmatrix}}\\\end{aligned}}} 5897: 11117: 8146:{\displaystyle {\text{RoPE}}{\big (}x_{m}^{(1)},x_{m}^{(2)},m{\big )}={\begin{pmatrix}\cos m\theta &-\sin m\theta \\\sin m\theta &\cos m\theta \end{pmatrix}}{\begin{pmatrix}x_{m}^{(1)}\\x_{m}^{(2)}\\\end{pmatrix}}={\begin{pmatrix}x_{m}^{(1)}\cos m\theta -x_{m}^{(2)}\sin m\theta \\x_{m}^{(2)}\cos m\theta +x_{m}^{(1)}\sin m\theta \\\end{pmatrix}}} 1201:(Luong et al, 2015) compared the relative performance of global (that of (Bahdanau et al, 2014)) and local (sliding window) attention model architectures for machine translation, and found that a mixed attention architecture had higher quality than global attention, while the use of a local attention architecture reduced translation time. 6755: 8757: 1133:. LSTM became the standard architecture for long sequence modelling until the 2017 publication of Transformers. However, LSTM still used sequential processing, like most other RNNs. Specifically, RNNs operate one token at a time from first to last; they cannot operate in parallel over all tokens in a sequence. 11112: 14263:

Chowdhery, Aakanksha; Narang, Sharan; Devlin, Jacob; Bosma, Maarten; Mishra, Gaurav; Roberts, Adam; Barham, Paul; Chung, Hyung Won; Sutton, Charles; Gehrmann, Sebastian; Schuh, Parker; Shi, Kensen; Tsvyashchenko, Sasha; Maynez, Joshua; Rao, Abhishek (2022-04-01). "PaLM: Scaling Language Modeling with

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ALiBi allows pretraining on short context windows, then finetuning on longer context windows. Since it is directly plugged into the attention mechanism, it can be combined with any positional encoder that is plugged into the "bottom" of the entire network (which is where the sinusoidal encoder on the

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A "decoder-only" Transformer is not literally decoder-only, since without an encoder, the cross-attention mechanism has nothing to attend to. Thus, the decoder layers in a decoder-only Transformer is composed of just two sublayers: the causally masked self-attention, and the feedforward network. This

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Transformer layers, which carry out repeated transformations on the vector representations, extracting more and more linguistic information. These consist of alternating attention and feedforward layers. There are two major types of transformer layers: encoder layers and decoder layers, with further

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controller (1992) learns to compute a weight matrix for further processing depending on the input. One of its two networks has "fast weights" or "dynamic links" (1981). A slow neural network learns by gradient descent to generate keys and values for computing the weight changes of the fast neural

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Transformers are used in large language models for autoregressive sequence generation: generating a stream of text, one token at a time. However, in most settings, decoding from language models is memory-bound, meaning that we have spare compute power available. Speculative decoding uses this spare

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As the Transformer architecture natively processes numerical data, not text, there must be a translation between text and tokens. A token is an integer that represents a character, or a short segment of characters. On the input side, the input text is parsed into a token sequence. Similarly, on the

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In a prefixLM task, the sequence is divided into two parts. The first part is presented as context, and the model predicts the first token of the second part. Then that would be revealed, and the model predicts the second token, and so on. The loss function for the task is still typically the same.

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The plain transformer architecture had difficulty converging. In the original paper the authors recommended using learning rate warmup. That is, the learning rate should linearly scale up from 0 to maximal value for the first part of the training (usually recommended to be 2% of the total number of

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Wolf, Thomas; Debut, Lysandre; Sanh, Victor; Chaumond, Julien; Delangue, Clement; Moi, Anthony; Cistac, Pierric; Rault, Tim; Louf, Remi; Funtowicz, Morgan; Davison, Joe; Shleifer, Sam; von Platen, Patrick; Ma, Clara; Jernite, Yacine; Plu, Julien; Xu, Canwen; Le Scao, Teven; Gugger, Sylvain; Drame,

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to an image. Parti is an encoder-decoder Transformer, where the encoder processes a text prompt, and the decoder generates a token representation of an image. Muse is an encoder-only Transformer that is trained to predict masked image tokens from unmasked image tokens. During generation, all input

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The original Transformer paper reported using a learned positional encoding, but finding it not superior to the sinusoidal one. Later, found that causal masking itself provides enough signal to a Transformer decoder that it can learn to implicitly perform absolute positional encoding without the

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Like the first encoder, the first decoder takes positional information and embeddings of the output sequence as its input, rather than encodings. The transformer must not use the current or future output to predict an output, so the output sequence must be partially masked to prevent this reverse

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The purpose of each encoder layer is to create contextualized representations of the tokens, where each representation corresponds to a token that "mixes" information from other input tokens via self-attention mechanism. Each decoder layer contains two attention sublayers: (1) cross-attention for

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where the first columns correspond to the "prefix", and the subsequent columns correspond to the autoregressively generated text based on the prefix. They resemble encoder-decoder models, but has less "sparsity". Such models are rarely used, though they are cited as theoretical possibilities and

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Key advancements in FlashAttention-2 include the reduction of non-matmul FLOPs, improved parallelism over the sequence length dimension, better work partitioning between GPU warps, and added support for head dimensions up to 256 and multi-query attention (MQA) and grouped-query attention (GQA).

1187:-size output vector, which was then processed by another recurrent network into an output. If the input is long, then the output vector would not be able to contain all relevant information, and the output quality degrades. As evidence, reversing the input sentence improved seq2seq translation. 6590:

Each decoder consists of three major components: a causally masked self-attention mechanism, a cross-attention mechanism, and a feed-forward neural network. The decoder functions in a similar fashion to the encoder, but an additional attention mechanism is inserted which instead draws relevant

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Each encoder layer consists of two major components: a self-attention mechanism and a feed-forward layer. It takes an input as a sequence of input vectors, applies the self-attention mechanism, to produce an intermediate sequence of vectors, then applies the feed-forward layer for each vector

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Dosovitskiy, Alexey; Beyer, Lucas; Kolesnikov, Alexander; Weissenborn, Dirk; Zhai, Xiaohua; Unterthiner, Thomas; Dehghani, Mostafa; Minderer, Matthias; Heigold, Georg; Gelly, Sylvain; Uszkoreit, Jakob (2021-06-03). "An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale".

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tokens are masked, and the highest-confidence predictions are included for the next iteration, until all tokens are predicted. Phenaki is a text-to-video model. It is a bidirectional masked transformer conditioned on pre-computed text tokens. The generated tokens are then decoded to a video.

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The original 2017 Transformer used the post-LN convention. It was difficult to train and required careful hyperparameter tuning and a "warm-up" in learning rate, where it starts small and gradually increases. The pre-LN convention was developed in 2020, which was found to be easier to train,

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The encoder layers are stacked. The first encoder layer takes the sequence of input vectors from the embedding layer, producing a sequence of vectors. This sequence of vectors is processed by the second encoder, and so on. The output from the final encoder layer is then used by the decoder.

11664: 8708: 9535: 9151: 6082:{\displaystyle M_{\text{causal}}={\begin{bmatrix}0&-\infty &-\infty &\dots &-\infty \\0&0&-\infty &\dots &-\infty \\0&0&0&\dots &-\infty \\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\dots &0\end{bmatrix}}} 6787:

The last decoder is followed by a final un-embedding layer. to produce the output probabilities over the vocabulary. Then, one of the tokens is sampled according to the probability, and the decoder can be run again to produce the next token, etc, autoregressively generating output text.

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Choromanski, Krzysztof; Likhosherstov, Valerii; Dohan, David; Song, Xingyou; Gane, Andreea; Sarlos, Tamas; Hawkins, Peter; Davis, Jared; Belanger, David; Colwell, Lucy; Weller, Adrian (2020-09-30). "Masked Language Modeling for Proteins via Linearly Scalable Long-Context Transformers".

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In an autoregressive task, the entire sequence is masked at first, and the model produces a probability distribution for the first token. Then the first token is revealed and the model predicts the second token, and so on. The loss function for the task is still typically the same. The

1216:. The new model was a seq2seq model where the encoder and the decoder were both 8 layers of bidirectional LSTM. It took nine months to develop, and it achieved a higher level of performance than the statistical approach, which took ten years to develop. In the same year, self-attention 11420:{\displaystyle {\text{Attention}}(q,K,V)={\text{softmax}}\left({\frac {qK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\approx {\frac {\varphi (q)^{T}\sum _{i}e^{\|k_{i}\|^{2}/2\sigma ^{2}}\varphi (k_{i})v_{i}^{T}}{\varphi (q)^{T}\sum _{i}e^{\|k_{i}\|^{2}/2\sigma ^{2}}\varphi (k_{i})}}} 11778:

Multimodal models can either be trained from scratch, or by finetuning. A 2022 study found that Transformers pretrained only on natural language can be finetuned on only 0.03% of parameters and become competitive with LSTMs on a variety of logical and visual tasks, demonstrating

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Jaegle, Andrew; Borgeaud, Sebastian; Alayrac, Jean-Baptiste; Doersch, Carl; Ionescu, Catalin; Ding, David; Koppula, Skanda; Zoran, Daniel; Brock, Andrew; Shelhamer, Evan; Hénaff, Olivier (2021-08-02). "Perceiver IO: A General Architecture for Structured Inputs & Outputs".

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There are also mixed seq2seq models. For example, in 2020, Google Translate replaced the previous RNN-encoder–RNN-decoder model by a Transformer-encoder–RNN-decoder model, on the argument that an RNN-decoder runs much faster than Transformer-decoder when run autoregressively.

4935: 1590: 6613: 11821:(2021), Parti (2022), Phenaki (2023), and Muse (2023). Unlike later models, DALL-E is not a diffusion model. Instead, it uses a decoder-only Transformer that autoregressively generates a text, followed by the token representation of an image, which is then converted by a 3133:. This allows the transformer to take any encoded position and find a linear sum of the encoded locations of its neighbors. This sum of encoded positions, when fed into the attention mechanism, would create attention weights on its neighbors, much like what happens in a 7484: 6861:(LayerNorm, or LN), which while conceptually unnecessary, are necessary for numerical stability and convergence. Similarly to how the feedforward network modules are applied individually to each vector, the LayerNorm is also applied individually to each vector. 1291:

Already in spring 2017, even before the "Attention is all you need" preprint was published, one of the co-authors applied the "decoder-only" variation of the architecture to generate fictitious Knowledge articles. Transformer architecture is now used in many

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If a transformer is used with a baked-in prompt, such as , then the key and value vectors can be computed for the prompt, and saved on disk. The saving in compute is significant when the model is used for many short interactions, such as in online chatbots.

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architecture. The encoder consists of encoding layers that process all the input tokens together one layer after another, while the decoder consists of decoding layers that iteratively process the encoder's output and the decoder's output tokens so far.

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word of the source text was processed. Although in theory such a vector retains the information about the whole original sentence, in practice the information is poorly preserved, since the input is processed sequentially by one recurrent network into a

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An improved version, FlashAttention-2, was developed to cater to the rising demand for language models capable of handling longer context lengths. It offers enhancements in work partitioning and parallelism, enabling it to achieve up to 230 TFLOPs/s on

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In general, there are 3 classes of language modelling tasks: "masked", "autoregressive", and "prefixLM". These classes are independent of a specific modeling architecture such as Transformer, but they are often discussed in the context of Transformer.

1283:, by removing its recurrence to process all tokens in parallel, but preserving its dot-product attention mechanism to keep its text processing performance. Its parallelizability was an important factor to its widespread use in large neural networks. 10816: 10405:

Ordinary transformers require a memory size that is quadratic in the size of the context window. Attention-free transformers reduce this to a linear dependence while still retaining the advantages of a transformer by linking the key to the value.

8935:{\displaystyle B={\begin{pmatrix}0&1&2&3&\cdots \\-1&0&1&2&\cdots \\-2&-1&0&1&\cdots \\-3&-2&-1&0&\cdots \\\vdots &\vdots &\vdots &\vdots &\ddots \\\end{pmatrix}}} 8405: 9895:

In speculative decoding, a smaller model or some other simple heuristic is used to generate a few speculative tokens that are subsequently verified by the larger model. For example, suppose a small model generated four speculative tokens:

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The idea of encoder-decoder sequence transduction had been developed in the early 2010s (see for previous papers). The papers most commonly cited as the originators that produced seq2seq are two concurrently published papers from 2014.

1323:(2018), an encoder-only Transformer model. In 2019 October, Google started using BERT to process search queries. In 2020, Google Translate replaced the previous RNN-encoder–RNN-decoder model by a Transformer-encoder–RNN-decoder model. 6540: 11530: 8599: 9372: 9045: 12275:

Parisotto, Emilio; Song, Francis; Rae, Jack; Pascanu, Razvan; Gulcehre, Caglar; Jayakumar, Siddhant; Jaderberg, Max; Kaufman, Raphaël Lopez; Clark, Aidan; Noury, Seb; Botvinick, Matthew; Heess, Nicolas; Hadsell, Raia (2020-11-21).

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Gulati, Anmol; Qin, James; Chiu, Chung-Cheng; Parmar, Niki; Zhang, Yu; Yu, Jiahui; Han, Wei; Wang, Shibo; Zhang, Zhengdong; Wu, Yonghui; Pang, Ruoming (2020). "Conformer: Convolution-augmented Transformer for Speech Recognition".

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incorporating the output of encoder (contextualized input token representations), and (2) self-attention for "mixing" information among the input tokens to the decoder (i.e. the tokens generated so far during inference time).

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For non-greedy decoding, similar ideas apply, except the speculative tokens are accepted or rejected stochastically, in a way that guarantees the final output distribution is the same as if speculative decoding was not used.

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Specifically, consider a transformer model like GPT-3 with a context window size of 512. To generate an entire context window autoregressively with greedy decoding, it must be run for 512 times, each time generating a token

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Raffel, Colin; Shazeer, Noam; Roberts, Adam; Lee, Katherine; Narang, Sharan; Matena, Michael; Zhou, Yanqi; Li, Wei; Liu, Peter J. (2019). "Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer".

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Chang, Huiwen; Zhang, Han; Barber, Jarred; Maschinot, A. J.; Lezama, Jose; Jiang, Lu; Yang, Ming-Hsuan; Murphy, Kevin; Freeman, William T. (2023-01-02). "Muse: Text-To-Image Generation via Masked Generative Transformers".

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judging the pragmatic acceptability of natural language. For example, the following sentence might be judged "not acceptable", because even though it is syntactically well-formed, it is improbable in ordinary human usage:

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In contrast, the cross-attention mechanism attends to the output vectors of the encoder, which is computed before the decoder starts decoding. Consequently, there is no need for masking in the cross-attention mechanism.

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Seq2seq models with attention (including self-attention) still suffered from the same issue with recurrent networks, which is that they are hard to parallelize, which prevented them to be accelerated on GPUs. In 2016,

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Tay, Yi; Dehghani, Mostafa; Abnar, Samira; Shen, Yikang; Bahri, Dara; Pham, Philip; Rao, Jinfeng; Yang, Liu; Ruder, Sebastian; Metzler, Donald (2020-11-08). "Long Range Arena: A Benchmark for Efficient Transformers".

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An "encoder-decoder" Transformer is generally the same as the original Transformer, with 2 sublayers per encoder layer and 3 sublayers per decoder layer, etc. They might have minor architectural improvements, such as

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Each encoder layer contains 2 sublayers: the self-attention and the feedforward network. Each decoder layer contains 3 sublayers: the causally masked self-attention, the cross-attention, and the feedforward network.

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Benchmarks revealed FlashAttention-2 to be up to 2x faster than FlashAttention and up to 9x faster than a standard attention implementation in PyTorch. Future developments include optimization for new hardware like

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Note that while each of these tasks is trivial or obvious for human native speakers of the language (or languages), they have typically proved challenging for previous generations of machine learning architecture.

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An un-embedding layer is almost the reverse of an embedding layer. Whereas an embedding layer converts a token into a vector, an un-embedding layer converts a vector into a probability distribution over tokens.

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within the scope of the context window with other (unmasked) tokens via a parallel multi-head attention mechanism allowing the signal for key tokens to be amplified and less important tokens to be diminished.

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Ainslie, Joshua; Lee-Thorp, James; de Jong, Michiel; Zemlyanskiy, Yury; Lebrón, Federico; Sanghai, Sumit (2023-12-23). "GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints".

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A standard Transformer architecture, showing on the left an encoder, and on the right a decoder. Note: it uses the pre-LN convention, which is different from the post-LN convention used in the original 2017

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Xiong, Ruibin; Yang, Yunchang; He, Di; Zheng, Kai; Zheng, Shuxin; Xing, Chen; Zhang, Huishuai; Lan, Yanyan; Wang, Liwei; Liu, Tie-Yan (2020-06-29). "On Layer Normalization in the Transformer Architecture".

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Nguyen, Toan Q.; Salazar, Julian (2019-11-02). Niehues, Jan; Cattoni, Rolando; Stüker, Sebastian; Negri, Matteo; Turchi, Marco; Ha, Thanh-Le; Salesky, Elizabeth; Sanabria, Ramon; Barrault, Loic (eds.).

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When an autoregressive transformer is used for inference, such as generating text, the query vector is different at each step, but the already-computed key and value vectors are always the same. The

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text generation. For decoding, all-to-all attention is inappropriate, because a token cannot attend to tokens not yet generated. Thus, the self-attention module in the decoder is causally masked.

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is the distance one wishes to shift. This allows the transformer to take any encoded position, and find the encoding of the position n-steps-ahead or n-steps-behind, by a matrix multiplication.

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for additional processing of their outputs and contain residual connections and layer normalization steps. These feed-forward layers contain most of the parameters in a Transformer model.

6750:{\displaystyle {\begin{aligned}H'&={\text{MaskedMultiheadedAttention}}(H,H,H)\\{\text{DecoderLayer}}(H)&={\text{FFN}}({\text{MultiheadedAttention}}(H',H^{E},H^{E}))\end{aligned}}} 9237: 3620: 11525: 6134: 2948: 9843: 3899: 3813: 1513:

In a masked task, one or more of the tokens is masked out, and the model would produce a probability distribution predicting what the masked-out tokens are based on the context. The

1115:(1995), a RNN which used various innovations to overcome the vanishing gradient problem, allowing efficient learning of long-sequence modelling. One key innovation was the use of an 12358:

Ruoss, Anian; Delétang, Grégoire; Medapati, Sourabh; Grau-Moya, Jordi; Wenliang, Li; Catt, Elliot; Reid, John; Genewein, Tim (2024-02-07). "Grandmaster-Level Chess Without Search".

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Villegas, Ruben; Babaeizadeh, Mohammad; Kindermans, Pieter-Jan; Moraldo, Hernan; Zhang, Han; Saffar, Mohammad Taghi; Castro, Santiago; Kunze, Julius; Erhan, Dumitru (2022-09-29).

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adapt the transformer to computer vision by breaking down input images as a series of patches, turning them into vectors, and treating them like tokens in a standard transformer.

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is encoder-only. They are less often used currently, as they were found to be not significantly better than training an encoder-decoder Transformer, then taking just the encoder.

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By convention, we write all vectors as row vectors. This, for example, means that pushing a vector through a linear layer means multiplying it by a weight matrix on the right, as

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An "encoder-only" Transformer applies the encoder to map an input text into a sequence of vectors that represent the input text. This is usually used for text embedding and

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A positional encoding is a fixed-size vector representation of the relative positions of tokens within a sequence: it provides the transformer model with information about

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A "prefixLM" (prefix language model) is a decoder-only architecture, but with prefix masking, which is different from causal masking. Specifically, it has mask of the form

6562: 6469: 3426:(BERT). It is typically larger than the embedding size. For example, in both GPT-2 series and BERT series, the intermediate size of a model is 4 times its embedding size: 9575: 8985: 16304: 9776:

in CPUs, future tokens are computed concurrently, by speculating on the value of previous tokens, and are later discarded if it turns out the speculation was incorrect.

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Jaegle, Andrew; Gimeno, Felix; Brock, Andrew; Zisserman, Andrew; Vinyals, Oriol; Carreira, Joao (2021-06-22). "Perceiver: General Perception with Iterative Attention".

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Devlin, Jacob; Chang, Ming-Wei; Lee, Kenton; Toutanova, Kristina (11 October 2018). "BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding".

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Choromanski, Krzysztof; Likhosherstov, Valerii; Dohan, David; Song, Xingyou; Gane, Andreea; Sarlos, Tamas; Hawkins, Peter; Davis, Jared; Mohiuddin, Afroz (2022-11-19),

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Devlin, Jacob; Chang, Ming-Wei; Lee, Kenton; Toutanova, Kristina (11 October 2018). "BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding".

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In words, it means that each token can pay attention to itself, and every token before it, but not any after it. As an example of an uncommon use of mask matrix, the

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Modern Transformers overcome this problem, but unlike RNNs, they require computation time that is quadratic in the size of the context window. The linearly scaling

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Radford, Alec; Kim, Jong Wook; Xu, Tao; Brockman, Greg; McLeavey, Christine; Sutskever, Ilya (2022). "Robust Speech Recognition via Large-Scale Weak Supervision".

11107:{\displaystyle e^{\langle x,y\rangle /\sigma ^{2}}=\mathbb {E} \approx \langle e^{\|x\|^{2}/2\sigma ^{2}}\varphi (x),e^{\|y\|^{2}/2\sigma ^{2}}\varphi (y)\rangle } 10400: 6571:

As the encoder processes the entire input all at once, every token can attend to every other token (all-to-all attention), so there is no need for causal masking.

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Radford, Alec; Jong Wook Kim; Xu, Tao; Brockman, Greg; McLeavey, Christine; Sutskever, Ilya (2022). "Robust Speech Recognition via Large-Scale Weak Supervision".

5715: 9845:. However, if we had some educated guess for the values of these tokens, we could verify all of them in parallel, in one run of the model, by checking that each 8333: 1677: 15057:

Ferrando, Javier; Sarti, Gabriele; Bisazza, Arianna; Costa-jussà, Marta R. (2024-05-01). "A Primer on the Inner Workings of Transformer-based Language Models".

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Zhai, Shuangfei; Talbott, Walter; Srivastava, Nitish; Huang, Chen; Goh, Hanlin; Zhang, Ruixiang; Susskind, Josh (2021-09-21). "An Attention Free Transformer".

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Contribution), Woosuk Kwon*, Zhuohan Li*, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Yu, Joey Gonzalez, Hao Zhang, and Ion Stoica (* Equal (2023-06-20).

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demonstrate the ability of transformers to perform a wide variety of NLP-related subtasks and their related real-world or practical applications, including:

8553:{\displaystyle {\text{RoPE}}{\big (}x,m{\big )}^{T}{\text{RoPE}}{\big (}y,n{\big )}={\text{RoPE}}{\big (}x,m+k{\big )}^{T}{\text{RoPE}}{\big (}y,n+k{\big )}} 8234: 14048:

Su, Jianlin; Lu, Yu; Pan, Shengfeng; Murtadha, Ahmed; Wen, Bo; Liu, Yunfeng (2021-04-01). "RoFormer: Enhanced Transformer with Rotary Position Embedding".

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Chung, Junyoung; Gulcehre, Caglar; Cho, KyungHyun; Bengio, Yoshua (2014). "Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling".

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Chen, Lili; Lu, Kevin; Rajeswaran, Aravind; Lee, Kimin; Grover, Aditya; Laskin, Michael; Abbeel, Pieter; Srinivas, Aravind; Mordatch, Igor (2021-06-24),

11808:, which is then treated like an image, i.e. broken down into a series of patches, turned into vectors and treated like tokens in a standard transformer. 10181:

Training transformer-based architectures can be expensive, especially for long inputs. Many methods have been developed to attempt to address the issue.

9899: 869: 12427: 5884:{\displaystyle {\begin{aligned}{\text{MaskedAttention}}(Q,K,V)={\text{softmax}}\left(M+{\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\end{aligned}}} 15552: 14750: 14136: 13336:

Esser, Patrick; Kulal, Sumith; Blattmann, Andreas; Entezari, Rahim; Müller, Jonas; Saini, Harry; Levi, Yam; Lorenz, Dominik; Sauer, Axel (2024-03-05),

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Array of probability distributions, with shape (decoder vocabulary size x length(decoder output sequence)) /* encoder */ z_e ← encoder.tokenizer(t_e)

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Kariampuzha, William; Alyea, Gioconda; Qu, Sue; Sanjak, Jaleal; Mathé, Ewy; Sid, Eric; Chatelaine, Haley; Yadaw, Arjun; Xu, Yanji; Zhu, Qian (2023).

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Peng, Bo; Alcaide, Eric; Anthony, Quentin; Albalak, Alon; Arcadinho, Samuel; Biderman, Stella; Cao, Huanqi; Cheng, Xin; Chung, Michael (2023-12-10),

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represents no attention paid, the linear bias matrix increases attention paid in one direction and decreases attention paid in the other direction.

7023: 6875: 2834: 2016: 16146: 14513: 14379: 12978:

Parikh, Ankur P.; Täckström, Oscar; Das, Dipanjan; Uszkoreit, Jakob (2016-09-25). "A Decomposable Attention Model for Natural Language Inference".

11659:{\displaystyle {\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\approx Q(K^{T}V/{\sqrt {d_{k}}})} 8703:{\displaystyle {\begin{aligned}{\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}+sB\right)V\end{aligned}}} 710: 14069:

Press, Ofir; Smith, Noah A.; Lewis, Mike (2021-08-01). "Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation".

13509:

Tay, Yi; Dehghani, Mostafa; Tran, Vinh Q.; Garcia, Xavier; Wei, Jason; Wang, Xuezhi; Chung, Hyung Won; Shakeri, Siamak; Bahri, Dara (2023-02-28),

9530:{\displaystyle {\text{MultiheadedAttention}}(Q,K,V)={\text{Concat}}_{i\in }\left({\text{Attention}}(XW_{i}^{Q},XW_{i}^{K},XW_{i}^{V})\right)W^{O}} 9146:{\displaystyle {\begin{aligned}{\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}+B\right)V\end{aligned}}} 2227: 1268:

you need". That hypothesis was against conventional wisdom of the time, and even his father, a well-known computational linguist, was skeptical.

13385:

Raffel, Colin; Shazeer, Noam; Roberts, Adam; Lee, Katherine; Narang, Sharan; Matena, Michael; Zhou, Yanqi; Li, Wei; Liu, Peter J. (2020-01-01).

12571: 12227:

Luong, Minh-Thang; Pham, Hieu; Manning, Christopher D. (August 17, 2015). "Effective Approaches to Attention-based Neural Machine Translation".

4711:{\displaystyle {\begin{aligned}{\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\end{aligned}}} 13809: 917: 17: 14948:

Yu, Jiahui; Xu, Yuanzhong; Koh, Jing Yu; Luong, Thang; Baid, Gunjan; Wang, Zirui; Vasudevan, Vijay; Ku, Alexander; Yang, Yinfei (2022-06-21),

14285:

Kwon, Woosuk; Li, Zhuohan; Zhuang, Siyuan; Sheng, Ying; Zheng, Lianmin; Yu, Cody Hao; Gonzalez, Joseph; Zhang, Hao; Stoica, Ion (2023-10-23).

11775:

Transformers can also be used/adapted for modalities (input or output) beyond just text, usually by finding a way to "tokenize" the modality.

12892:

Wu, Yonghui; et al. (2016-09-01). "Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation".

12700:

Cho, Kyunghyun; van Merriënboer, Bart; Gulcehre, Caglar; Bahdanau, Dzmitry; Bougares, Fethi; Schwenk, Holger; Bengio, Yoshua (October 2014).

6837: 1960:

The token embedding vectors are added to their respective positional encoding vectors (see below), producing the sequence of input vectors.

1137: 13065: 10421: 11855: 10699: 874: 725: 13760:

Raffel, Colin; Shazeer, Noam; Roberts, Adam; Lee, Katherine; Narang, Sharan; Matena, Michael; Zhou, Yanqi; Li, Wei; Liu, Peter J. (2020).

13170: 4996: 9730:{\displaystyle {\text{MultiQueryAttention}}(Q,K,V)={\text{Concat}}_{i\in }\left({\text{Attention}}(XW_{i}^{Q},XW^{K},XW^{V})\right)W^{O}} 456: 4454:, which is useful for training due to computational matrix operation optimizations that quickly compute matrix operations. The matrices 13320: 12206:

Bahdanau; Cho, Kyunghyun; Bengio, Yoshua (September 1, 2014). "Neural Machine Translation by Jointly Learning to Align and Translate".

5671:

It may be necessary to cut out attention links between some word-pairs. For example, the decoder, when decoding for the token position

5325:{\displaystyle {\text{MultiheadedAttention}}(Q,K,V)={\text{Concat}}_{i\in }({\text{Attention}}(XW_{i}^{Q},XW_{i}^{K},XW_{i}^{V}))W^{O}} 957: 760: 4943: 4930:{\displaystyle \ell _{\text{seq, key}}=\ell _{\text{seq, value}},\;d_{\text{query}}=d_{\text{key}},\;d_{\text{value}}=d_{\text{head}}} 14641:

Peng, Hao; Pappas, Nikolaos; Yogatama, Dani; Schwartz, Roy; Smith, Noah A.; Kong, Lingpeng (2021-03-19). "Random Feature Attention".

12871:

Luong, Minh-Thang; Pham, Hieu; Manning, Christopher D. (2015). "Effective Approaches to Attention-based Neural Machine Translation".

5606: 3595:

The module takes three sequences, a query sequence, a key sequence, and a value sequence. The query sequence is a sequence of length

2213:

the words are in the input sequence. Without positional encoding, the model would be unable to process input sequence as more than a

15031: 14924:

Ramesh, Aditya; Pavlov, Mikhail; Goh, Gabriel; Gray, Scott; Voss, Chelsea; Radford, Alec; Chen, Mark; Sutskever, Ilya (2021-02-26),

1585:{\displaystyle {\text{Loss}}=-\sum _{t\in {\text{masked tokens}}}\ln({\text{probability of }}t{\text{ conditional on its context}})} 1171:

is another LSTM that converts the vector into a sequence of tokens. Similarly, (Cho et al, 2014) was 130M-parameter model that used

10415: 1649:

The following description follows exactly the Transformer as described in the original paper. There are variants, described in the

15662: 13602: 836: 14535: 13873: 13699: 12839: 12784:

Gruber, N.; Jockisch, A. (2020), "Are GRU cells more specific and LSTM cells more sensitive in motive classification of text?",

1190:(Bahdanau et al, 2014) introduced an attention mechanism to seq2seq for machine translation to solve the bottleneck problem (of 15545: 13202: 7479:{\displaystyle M_{\text{prefixLM}}={\begin{bmatrix}\mathbf {0} &-\infty \\\mathbf {0} &M_{\text{causal}}\end{bmatrix}}} 6805:(a) One encoder layer and one decoder layer. (b) Two encoder layers and two decoder layers. The sublayers are labelled as well. 1698:

output side, the output tokens are parsed back to text. The module doing the conversion between token sequences and texts is a

385: 16469: 14316: 12611:

Christoph von der Malsburg: The correlation theory of brain function. Internal Report 81-2, MPI Biophysical Chemistry, 1981.

12501: 12182: 3775: 13003: 12088: 9751:

method saves the computed key and value vectors at each attention block, so that they are not recomputed at each new token.

3960: 2109: 16335: 14218:"Introducing Together AI Chief Scientist Tri Dao, as he releases FlashAttention-2 to speed up model training and inference" 9331:

of a GPU, and by careful management of the blocks it minimizes data copying between GPU caches (as data movement is slow).

1869: 1008: 894: 657: 192: 12624:

Jerome A. Feldman, "Dynamic connections in neural networks," Biological Cybernetics, vol. 46, no. 1, pp. 27-39, Dec. 1982.

2628: 2489: 16436: 15987: 15724: 15330: 15094: 14435:

Chen, Charlie; Borgeaud, Sebastian; Irving, Geoffrey; Lespiau, Jean-Baptiste; Sifre, Laurent; Jumper, John (2023-02-02),

11797: 1393:(instead of after) multiheaded attention and feedforward layers stabilizes training, not requiring learning rate warmup. 1141:

network which computes answers to queries. This was later shown to be equivalent to the unnormalized linear Transformer.

912: 13677: 8596:

positional encoder that is directly plugged into the attention mechanism. Specifically, the ALiBi attention mechanism is

3144: 1108:

leaves the model's state at the end of a long sentence without precise, extractable information about preceding tokens.

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Un-embedding layer, which converts the final vector representations back to a probability distribution over the tokens.

1601: 1327: 1293: 1104:(1990). In theory, the information from one token can propagate arbitrarily far down the sequence, but in practice the 1070: 745: 720: 669: 5500:

As an example, in the smallest GPT-2 model, there are only self-attention mechanisms. It has the following dimensions:

1000: 16248: 15875: 15682: 15538: 13121: 9323:

FlashAttention is an algorithm that implements the transformer attention mechanism efficiently on a GPU. It performs

8338: 8156: 3717: 1260:

with an order of magnitude less parameters than LSTMs. One of its authors, Jakob Uszkoreit, suspected that attention

1209: 793: 788: 441: 12742:

Sutskever, Ilya; Vinyals, Oriol; Le, Quoc Viet (14 Dec 2014). "Sequence to sequence learning with neural networks".

5073: 3429: 3140:. In the author's words, "we hypothesized it would allow the model to easily learn to attend by relative position." 1015:

Transformers have the advantage of having no recurrent units, and therefore require less training time than earlier

16203: 13559: 9287:. This is contrasted with the original sinusoidal positional encoding, which is an "absolute positional encoding". 5355: 1238: 451: 89: 12490:

Parallel Distributed Processing, Volume 1: Explorations in the Microstructure of Cognition: Foundations, Chapter 2

6587:

A decoder consists of an embedding layer, followed by multiple decoder layers, followed by an un-embedding layer.

5891:

A non-masked attention module can be thought of as a masked attention module where the mask has all entries zero.

3099:{\displaystyle \sum _{j}c_{j}f(t+\Delta t_{j})=\left(\sum _{j}c_{j}\,\mathrm {diag} (f(\Delta t_{j}))\right)f(t)} 1735:. When faced with tokens outside the vocabulary, typically a special token is used, written as "" for "unknown". 1213: 14090:

Shaw, Peter; Uszkoreit, Jakob; Vaswani, Ashish (2018). "Self-Attention with Relative Position Representations".

12383:

Mariama; Lhoest, Quentin; Rush, Alexander (2020). "Transformers: State-of-the-Art Natural Language Processing".

10169:

is completely discarded. The process then repeats (starting from the 4th token) until all tokens are generated.

2831:

The main reason for using this positional encoding function is that using it, shifts are linear transformations:

16390: 16330: 15928: 3598: 1433: 950: 846: 610: 431: 14591: 11479: 7396: 7368: 7348:

The Transformer architecture, being modular, allows variations. Several common variations are described here.

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For example, the following matrix is commonly used in decoder self-attention modules, called "causal masking":

3143:

In typical implementations, all operations are done over the real numbers, not the complex numbers, but since

2922: 1194:

output vector), allowing the model to process long-distance dependencies more easily. They called their model

15923: 15612: 12385:

Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations

9783: 3861: 2479:{\displaystyle (f(t)_{2k},f(t)_{2k+1})=(\sin(\theta ),\cos(\theta ))\quad \forall k\in \{0,1,\ldots ,d/2-1\}} 821: 523: 299: 12419: 6968: 1175:(GRU) instead of LSTM. Later research showed that GRUs are neither better nor worse than LSTMs for seq2seq. 16365: 15762: 15719: 15672: 15667: 11935: 9296: 3818: 3625: 3508: 3134: 1711: 1354: 1086: 992: 778: 715: 625: 603: 446: 436: 31: 13451: 12930: 5141:, which allows for fast processing. The outputs for the attention layer are concatenated to pass into the 5062: 3655: 16416: 15712: 15638: 15408: 11898: 11835: 11430: 10185:(2020) is a standard benchmark for comparing the behavior of transformer architectures over long inputs. 7392: 7376: 7364: 6846: 3408: 1409: 1331: 1178:

These early seq2seq models had no attention mechanism, and the state vector is accessible only after the

1046: 929: 841: 826: 287: 109: 13319:

Liu, Zhuang; Mao, Hanzi; Wu, Chao-Yuan; Feichtenhofer, Christoph; Darrell, Trevor; Xie, Saining (2022).

11527:

first, then multiply it with the query. In essence, we have managed to obtain a more precise version of

8402:

The benefit of RoPE is that the dot-product between two vectors depends on their relative location only:

16040: 15975: 15576: 14505: 11721: 10654: 10327: 9180: 5142: 5046:. It is theoretically possible for all three to be different, but that is rarely the case in practice. 3907: 3262: 3188: 1412:

on a small task-specific dataset. The pretrain dataset is typically an unlabeled large corpus, such as

1366: 1249: 1105: 889: 816: 566: 461: 249: 182: 142: 12449: 11783:. The LLaVA was a vision-language model composed of a language model (Vicuna-13B) and a vision model ( 10136: 10100: 10037: 10001: 4789: 4729: 4340: 4260: 1504: 16441: 16299: 15938: 15769: 15592: 15519: 15465: 13698:

Yang, Zhilin; Dai, Zihang; Yang, Yiming; Carbonell, Jaime; Salakhutdinov, Russ R; Le, Quoc V (2019).

11921:

Beyond traditional NLP, the transformer architecture has had success in other applications, such as:

11871: 11669: 10602: 7551:

RoPE (rotary positional embedding), is best explained by considering a list of 2-dimensional vectors

6821: 6813: 5574: 5473: 4819: 4131: 1272: 996: 943: 549: 317: 187: 14885: 13801: 13654:

Proceedings of the 2019 ACL Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP

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z_d ← layer.layer_norm(z_d) z_d ← layer.masked_multiheaded_attention(z_d, z_d, z_d)

4759: 4450:

The attention calculation for all tokens can be expressed as one large matrix calculation using the

3233: 3206: 1974: 16464: 16340: 15597: 15509: 15201: 13478: 11903: 11764: 9324: 3496: 2171: 1402: 1097: 1016: 571: 491: 414: 332: 162: 124: 119: 79: 74: 6545: 6452: 16385: 16370: 16023: 16018: 15918: 15786: 15567: 15420: 15087: 11893: 11822: 9540: 8945: 6854: 518: 367: 267: 94: 14462:

Kitaev, Nikita; Kaiser, Łukasz; Levskaya, Anselm (2020). "Reformer: The Efficient Transformer".

7122:

The following is the pseudocode for a standard pre-LN encoder-decoder Transformer, adapted from

6591:

information from the encodings generated by the encoders. This mechanism can also be called the

16345: 16105: 15824: 15819: 15340: 15195: 12702:"Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation" 10291: 9242: 7528: 7512: 2790: 1638:

Embedding layer, which converts tokens and positions of the tokens into vector representations.

1160: 1112: 1058: 1020: 698: 674: 576: 337: 312: 272: 84: 14005:

Gehring, Jonas; Auli, Michael; Grangier, David; Yarats, Denis; Dauphin, Yann N. (2017-07-17).

12706:

Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP)

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This has a neutral effect on model quality and training speed, but increases inference speed.

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z_d ← layer.layer_norm(z_d) z_d ← layer.multiheaded_attention(z_d, z_e, z_e)

5740: 16375: 16360: 16325: 16013: 15913: 15781: 15396: 15207: 14872: 12615:

See Reprint in Models of Neural Networks II, chapter 2, pages 95-119. Springer, Berlin, 1994.

12026: 11994: 11863: 9773: 7748: 7356: 3478: 2599: 1593: 1320: 1074: 652: 474: 426: 282: 197: 69: 16243: 13624: 12567: 12117: 4400: 4128:. The attention weights are divided by the square root of the dimension of the key vectors, 4003: 3511:

units. For each unit, the transformer model learns three weight matrices: the query weights

3163: 16395: 16350: 15796: 15741: 15587: 15582: 15261: 14026:

Transformer Language Models without Positional Encodings Still Learn Positional Information

12658: 11988: 11909: 11839: 10073: 9848: 6760: 6600: 6535:{\displaystyle {\text{EncoderLayer}}(H)={\text{FFN}}({\text{MultiheadedAttention}}(H,H,H))} 5443: 4591: 4564: 4537: 4193: 4166: 4104: 4077: 3690: 3568: 3541: 3514: 3390: 3109: 1339: 1172: 1024: 581: 531: 10376: 7523:

The normalization used in the Transformer can be different from LayerNorm. One example is

2953:

By taking a linear sum, any convolution can also be implemented as linear transformations:

1271:

In 2017, the original (100M-sized) encoder-decoder transformer model was proposed in the "

8: 15970: 15948: 15697: 15692: 15650: 15602: 15471: 15028: 14685: 12677: 12288: 12006: 11957: 11945: 11882: 10370: 7508: 7400: 7252:

layer ← decoder.layers /* first sublayer */ z_d_copy ← copy(z_d)

6858: 5694: 3155: 1609: 1480: 1450: 1406: 1387: 1350: 1280: 1116: 1042: 684: 620: 591: 496: 322: 255: 241: 227: 202: 152: 104: 64: 12518: 8315: 7276:

z_d ← z_d + z_d_copy /* second sublayer */ z_d_copy ← copy(z_d)

5470:

It is theoretically possible for each attention head to have a different head dimension

3199: 1659: 16355: 15933: 15080: 15058: 15043: 15000: 14973: 14953: 14929: 14904: 14816: 14794: 14773: 14726:"Vicuna: An Open-Source Chatbot Impressing GPT-4 with 90%* ChatGPT Quality | LMSYS Org" 14664: 14642: 14621: 14572: 14547: 14485: 14463: 14440: 14401: 14294: 14265: 14243: 14148: 14116: 14091: 14070: 14049: 14029: 13987: 13959: 13918: 13885: 13852: 13831: 13773: 13736: 13711: 13657: 13539: 13514: 13428: 13398: 13365: 13341: 13300: 13275: 13250: 13101: 13045: 12979: 12893: 12872: 12851: 12821: 12808: 12764: 12743: 12709: 12594: 12396: 12359: 12296: 12277: 12256: 12228: 12207: 12153: 11982: 11801: 11790: 11784: 10232: 9875: 9156: 8990: 8733: 8713: 8563: 7300:

z_d ← z_d + z_d_copy /* third sublayer */ z_d_copy ← copy(z_d)

6157: 6139: 5763: 5720: 5674: 5423: 5335: 5151: 5138: 5054: 4517: 4497: 4477: 4457: 4430: 4380: 4320: 4300: 4240: 4220: 4053: 4033: 4000:

Attention weights are calculated using the query and key vectors: the attention weight

3488: 2579: 2559: 2296: 2214: 1787: 1767: 1739: 1438: 1428: 1413: 1346: 1312: 1257: 1054: 662: 586: 372: 167: 14293:. SOSP '23. New York, NY, USA: Association for Computing Machinery. pp. 611–626. 14192: 13648:

Clark, Kevin; Khandelwal, Urvashi; Levy, Omer; Manning, Christopher D. (August 2019).

12957:

Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing

12488: 12465: 7554: 1807: 1198:, as it "emulates searching through a source sentence during decoding a translation". 1159:(Sutskever et al, 2014) was a 380M-parameter model for machine translation using two 16421: 16409: 16213: 15865: 15736: 15729: 15160: 15005: 14707: 14373: 14312: 13991: 13979: 13783: 13594: 13408: 13386: 13073: 13011: 12922: 12825: 12813: 12546: 12538: 12497: 12469: 12400: 12392: 12337: 12145: 12137: 11953: 11925: 11780: 10193:

The standard attention graph is either all-to-all or causal, both of which scales as

9367:

Multi-Query Attention changes the multiheaded attention mechanism. Whereas normally,

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z_e ← layer.layer_norm(z_e) z_e ← layer.multiheaded_attention(z_e, z_e, z_e)

1420: 1066: 755: 598: 511: 307: 277: 222: 217: 172: 114: 14006: 13223: 13194: 12598: 1345:

Since 2020, Transformers have been applied in modalities beyond text, including the

1041:

Transformers were first developed as an improvement over previous architectures for

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Hendrycks, Dan; Gimpel, Kevin (2016-06-27). "Gaussian Error Linear Units (GELUs)".

13762:"Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer" 13667: 13387:"Exploring the limits of transfer learning with a unified text-to-text transformer" 12960: 12803: 12793: 12719: 12586: 12530: 12461: 12420:"Open Sourcing BERT: State-of-the-Art Pre-training for Natural Language Processing" 12388: 12329: 12157: 12129: 9991:{\displaystyle {\tilde {x}}_{1},{\tilde {x}}_{2},{\tilde {x}}_{3},{\tilde {x}}_{4}} 7352: 6842: 6801: 4451: 4160: 2596:

that would be input into the positional encoding function. The original paper uses

2010: 1699: 1692: 1454: 1362: 1253: 1205: 783: 536: 486: 396: 380: 350: 212: 207: 157: 147: 45: 14287:"Efficient Memory Management for Large Language Model Serving with PagedAttention" 14193:"FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning" 12657:

Katharopoulos, Angelos; Vyas, Apoorv; Pappas, Nikolaos; Fleuret, François (2020).

12612: 12174: 16279: 16223: 16045: 15687: 15607: 15313: 15124: 15035: 14865:"Phenaki: Variable Length Video Generation from Open Domain Textual Descriptions" 14286: 12113: 11930: 9174: 7324:

z_d ← z_d + z_d_copy z_d ← decoder.final_layer_norm(z_d) output_distributions ←

6829: 6579: 6168: 1217: 1050: 970: 811: 615: 481: 421: 11476:

This approximation can be computed in linear time, as we can compute the matrix

6176:

An encoder consists of an embedding layer, followed by multiple encoder layers.

1264:

recurrence is sufficient for language translation, thus the title "attention is

16253: 16218: 16208: 16033: 15791: 15617: 15225: 14990: 13915:

Proceedings of the 16th International Conference on Spoken Language Translation

12659:"Transformers are RNNs: Fast autoregressive Transformers with linear attention" 12317: 12133: 12080: 11915: 7222:

z_e ← encoder.final_layer_norm(z_e) /* decoder */ z_d ← decoder.tokenizer(t_d)

3137: 2780:{\displaystyle f(t)=\left(e^{it/r^{k}}\right)_{k=0,1,\ldots ,{\frac {d}{2}}-1}} 1751: 1443: 1308: 1062: 1004: 831: 362: 99: 14592:"Constructing Transformers For Longer Sequences with Sparse Attention Methods" 14536:"The Reversible Residual Network: Backpropagation Without Storing Activations" 14135:

Dao, Tri; Fu, Dan; Ermon, Stefano; Rudra, Atri; Ré, Christopher (2022-12-06).

13325:. Conference on Computer Vision and Pattern Recognition. pp. 11976–11986. 12959:. Austin, Texas: Association for Computational Linguistics. pp. 551–561. 12708:. Doha, Qatar: Association for Computational Linguistics. pp. 1724–1734. 12590: 3145:

complex multiplication can be implemented as real 2-by-2 matrix multiplication

1705:

The set of all tokens is the vocabulary of the tokenizer, and its size is the

1167:

is an LSTM that takes in a sequence of tokens and turns it into a vector. The

16458: 16198: 16178: 16095: 15774: 15373: 15273: 14864: 14711: 14702: 14137:"FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness" 13983: 13787: 13412: 13077: 13015: 12926: 12542: 12487:

Rumelhart, David E.; McClelland, James L.; Hinton, Geoffrey E. (1987-07-29).

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layer ← encoder.layers /* first sublayer */ z_e_copy ← copy(z_e)

5467:

is a final projection matrix owned by the whole multi-headed attention head.

2625:

The function is in a simpler form when written as a complex function of type

2218: 1514: 1461:

restoring or repairing incomplete or corrupted text. For example, the input,

1101: 984: 750: 679: 561: 292: 177: 14355: 14308: 13649: 12798: 12635: 12572:"Learning to control fast-weight memories: an alternative to recurrent nets" 11859: 10070:

are accepted. The same run of the large model already generated a new token

7186:

z_e ← z_e + z_e_copy /* second sublayer */ z_e_copy ← copy(z_e)

5717:. This may be accomplished before the softmax stage by adding a mask matrix 1615:

Note that "masked" as in "masked language modelling" is not "masked" as in "

1045:, but have found many applications since then. They are used in large-scale 16284: 16115: 15530: 15486: 15166: 15119: 15042:

Phuong, Mary; Hutter, Marcus (2022). "Formal Algorithms for Transformers".

15009: 14725: 13932: 13911:"Transformers without Tears: Improving the Normalization of Self-Attention" 13910: 13672: 12964: 12817: 12550: 9312: 4993:. If the attention head is used in a cross-attention fashion, then usually 2286:{\displaystyle f:\mathbb {R} \to \mathbb {R} ^{d};d\in \mathbb {Z} ,d>0} 1757: 1688: 1035: 14024:

Haviv, Adi; Ram, Ori; Press, Ofir; Izsak, Peter; Levy, Omer (2022-12-05),

13700:"XLNet: Generalized Autoregressive Pretraining for Language Understanding" 12723: 12149: 11114:

Consequently, the one-headed attention, with one query, can be written as

8592:

for the positional encoder on the original transformer. Instead, it is an

4843:. The attention mechanism requires the following three equalities to hold: 1096:

For many years, sequence modelling and generation was done by using plain

16380: 16151: 16060: 16055: 15677: 15655: 15481: 15443: 14974:"Precision information extraction for rare disease epidemiology at scale" 13974: 13947: 13761: 12534: 12318:"Learning to Throw With a Handful of Samples Using Decision Transformers" 12084: 11887: 11805: 11787:-L/14), connected by a linear layer. Only the linear layer is finetuned. 9356: 9336: 8987:. The idea being that the linear bias matrix is a softened mask. Just as 7539:

Transformers may use other positional encoding methods than sinusoidal.

7312:

z_d ← layer.layer_norm(z_d) z_d ← layer.feedforward(z_d)

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is a free parameter that should be significantly larger than the biggest

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which used neurons that multiply the outputs of other neurons, so-called

1031: 556: 50: 14684:

Lu, Kevin; Grover, Aditya; Abbeel, Pieter; Mordatch, Igor (2022-06-28).

14567:

Child, Rewon; Gray, Scott; Radford, Alec; Sutskever, Ilya (2019-04-23),

12519:"Learning, invariance, and generalization in high-order neural networks" 12038:

Some architectures, such as RWKV or state space models, avoid the issue.

8335:-dimensional vectors, a RoPE encoder is defined by a sequence of angles 5564:{\displaystyle d_{\text{emb}}=768,n_{\text{head}}=12,d_{\text{head}}=64} 3504:

The attention mechanism used in the Transformer architecture are scaled

3380:{\displaystyle \mathrm {FFN} (x)=\phi (xW^{(1)}+b^{(1)})W^{(2)}+b^{(2)}} 16274: 16233: 16228: 16141: 16050: 15958: 15870: 15850: 15335: 15233: 14950:

Scaling Autoregressive Models for Content-Rich Text-to-Image Generation

14836: 14332: 13656:. Florence, Italy: Association for Computational Linguistics: 276–286. 13338:

Scaling Rectified Flow Transformers for High-Resolution Image Synthesis

13171:"The inside story of how ChatGPT was built from the people who made it" 11948:

chess board positions. Using static evaluation alone (that is, with no

9300: 8305:{\displaystyle {\text{RoPE}}{\big (}z_{m},m{\big )}=e^{im\theta }z_{m}} 8153:

Equivalently, if we write the 2-dimensional vectors as complex numbers

3167:

A Transformer is composed of stacked encoder layers and decoder layers.

1518: 705: 401: 327: 14749:

Liu, Haotian; Li, Chunyuan; Wu, Qingyang; Lee, Yong Jae (2023-12-15).

14534:

Gomez, Aidan N; Ren, Mengye; Urtasun, Raquel; Grosse, Roger B (2017).

6872:

convention. In the post-LN convention, the output of each sublayer is

4217:

are different matrices allows attention to be non-symmetric: if token

3203:

The feedforward network module. It is a two-layered network that maps

2160: 16269: 16238: 16136: 15980: 15943: 15880: 15834: 15829: 15814: 15426: 15255: 15172: 15103: 14422:"Towards 100x Speedup: Full Stack Transformer Inference Optimization" 13857: 13544: 13247: 13106: 12952: 12364: 11976: 11939: 11811: 10806:{\displaystyle \mathbb {E} =e^{-{\frac {\|x-y\|^{2}}{2\sigma ^{2}}}}} 9315:

that supplies transformer-based architectures and pretrained models.

9295:

The transformer model has been implemented in standard deep learning

9034:

original transformer, as well as RoPE and many others, are located).

6471:

stands for "feed-forward network". We can more succinctly write it as

3261:

The feedforward network (FFN) modules in a Transformer are 2-layered

2165: 1028: 864: 645: 14862: 14437:

Accelerating Large Language Model Decoding with Speculative Sampling

14011:

Proceedings of the 34th International Conference on Machine Learning

12701: 12680:(2021). "Linear Transformers Are Secretly Fast Weight Programmers". 12316:

Monastirsky, Maxim; Azulay, Osher; Sintov, Avishai (February 2023).

12282:

Proceedings of the 37th International Conference on Machine Learning

9772:

compute power by computing several tokens in parallel. Similarly to

5039:{\displaystyle X_{\text{query}}\neq X_{\text{key}}=X_{\text{value}}} 4397:

is the weighted sum of the value vectors of all tokens, weighted by

16171: 16003: 15267: 15063: 15048: 14958: 14934: 14909: 14821: 14799: 14778: 14669: 14647: 14626: 14577: 14552: 14490: 14468: 14445: 14406: 14299: 14270: 14248: 14153: 14121: 14096: 14075: 14054: 14034: 13964: 13923: 13890: 13836: 13778: 13741: 13716: 13662: 13560:"Sequence Modeling with Neural Networks (Part 2): Attention Models" 13519: 13433: 13403: 13370: 13346: 13305: 13280: 13255: 13050: 12984: 12898: 12877: 12301: 12261: 12233: 6784:

is the matrix with rows being the output vectors from the encoder.

4159:, which stabilizes gradients during training, and passed through a 1316: 14240: 12856: 12769: 12748: 12714: 12699: 12640:

Proceedings of the Annual Meeting of the Cognitive Science Society

12253:

Decision Transformer: Reinforcement Learning via Sequence Modeling

12212: 9042:

Relative Position Encodings is similar to ALiBi, but more generic:

4720:

where the softmax is applied over each of the rows of the matrix.

1353:. The vision transformer, in turn, stimulated new developments in 1003:, and each token is converted into a vector via looking up from a 16294: 16131: 16085: 16008: 15908: 15903: 15855: 15301: 15154: 14686:"Frozen Pretrained Transformers as Universal Computation Engines" 14661: 14291:

Proceedings of the 29th Symposium on Operating Systems Principles

13946:

Dufter, Philipp; Schmitt, Martin; Schütze, Hinrich (2022-06-06).

13294: 12075: 11970: 11949: 11875: 11473:. Similarly for multiple queries, and for multiheaded attention. 9304: 8399:. Then the RoPE encoding is applied to each pair of coordinates. 7524: 7198:

z_e ← layer.layer_norm(z_e) z_e ← layer.feedforward(z_e)

3172: 2314: 1761: 1335: 1297: 1276: 1275:" paper. At the time, the focus of the research was on improving 640: 13830:

Shazeer, Noam (2020-02-01). "GLU Variants Improve Transformer".

13004:"8 Google Employees Invented Modern AI. Here's the Inside Story" 12704:. In Moschitti, Alessandro; Pang, Bo; Daelemans, Walter (eds.). 12073: 12071: 12069: 12067: 12065: 12063: 12061: 12059: 12057: 12055: 4986:{\displaystyle X_{\text{query}}=X_{\text{key}}=X_{\text{value}}} 4940:

If the attention head is used in a self-attention fashion, then

2317:. The full positional encoding defined in the original paper is: 1463:"Thank you ~~ me to your party ~~ week", 16309: 16289: 16161: 15953: 15178: 15114: 15056: 12083:; Shazeer, Noam; Parmar, Niki; Uszkoreit, Jakob; Jones, Llion; 11818: 7237:

z_d ← decoder.embedding(z_d) + decoder.positional_embedding(t)

7147:

z_e ← encoder.embedding(z_e) + encoder.positional_embedding(t)

5656:{\displaystyle W^{O}\in \mathbb {R} ^{(64\times 12)\times 768}} 2221:" and "dog bites man" would be processed exactly the same way. 1358: 1123:. Neural networks using multiplicative units were later called 1023:(LSTM). Later variations have been widely adopted for training 988: 391: 27:

Machine learning algorithm used for natural-language processing

12656: 12357: 12294: 12009: – Series of large language models developed by Google AI 10333:

Sparse attention uses attention graphs that grows slower than

7106:{\displaystyle x+\mathrm {Sublayer} (\mathrm {LayerNorm} (x))} 6958:{\displaystyle \mathrm {LayerNorm} (x+\mathrm {Sublayer} (x))} 2912:{\displaystyle f(t+\Delta t)=\mathrm {diag} (f(\Delta t))f(t)} 2099:{\displaystyle \mathrm {UnEmbed} (x)=\mathrm {softmax} (xW+b)} 1307:(2018) was a bi-directional LSTM that produces contextualized 16110: 16090: 16080: 16075: 16070: 16065: 16028: 15860: 15402: 14690:

Proceedings of the AAAI Conference on Artificial Intelligence

14396:

Leviathan, Yaniv; Kalman, Matan; Matias, Yossi (2023-05-18),

14356:"vLLM: Easy, Fast, and Cheap LLM Serving with PagedAttention" 13195:"Improving language understanding with unsupervised learning" 12756: 12079: 12052: 11985: – Variant of Transformer designed for vision processing 11867: 11851: 11847: 11843: 11718:

are first independently sampled from the normal distribution

11666:

Performer (2022) uses the same Random Feature Attention, but

6090: 5420:

are "projection matrices" owned by individual attention head

5066:

Exact dimension counts within a multiheaded attention module.

1592:

and the model is trained to minimize this loss function. The

635: 630: 357: 15072: 14813: 12951:

Cheng, Jianpeng; Dong, Li; Lapata, Mirella (November 2016).

4377:

could be small). The output of the attention unit for token

1061:, audio, multi-modal processing, robotics, and even playing 16100: 15414: 13335: 12977: 11979: – Variant of Transformer designed for multimodal data 9872:

is indeed the token with the largest log-likelihood in the

9344: 9340: 7505: 5148:

Concretely, let the multiple attention heads be indexed by

1304: 14792: 14765: 14640: 14619: 14262: 13647: 11814:

are a variant of Transformers designed for multimodality.

9998:. These tokens are run through the larger model, and only 5352:

is the concatenation of word embeddings, and the matrices

3407:

is its activation function. The original Transformer used

1963:

The number of dimensions in an embedding vector is called

1596:

are trained for masked token prediction and another task.

1416:. Tasks for pretraining and fine-tuning commonly include: 1077:(bidirectional encoder representations from transformers). 14901: 14566: 14434: 14398:

Fast Inference from Transformers via Speculative Decoding

14004: 13650:"What Does BERT Look at? An Analysis of BERT's Attention" 13039: 12486: 9347:), a 2x speed increase over the original FlashAttention. 2224:

The positional encoding is defined as a function of type

999:". Text is converted to numerical representations called 14971: 13917:. Hong Kong: Association for Computational Linguistics. 11997: – Series of language models developed by Google AI 8231:, then RoPE encoding is just multiplication by an angle: 7020:

In the pre-LN convention, the output of each sublayer is

3500:

Exact dimension counts within an attention head module.

1338:, became unexpectedly popular, triggering a boom around 1330:

of decoder-only Transformers became state of the art in

923:

List of datasets in computer vision and image processing

14113:

Rethinking Positional Encoding in Language Pre-training

13759: 13537: 13425: 13384: 13099: 12315: 12274: 1756:

Each token is converted into an embedding vector via a

14683: 12762: 10592:{\displaystyle \varphi (x)={\frac {1}{\sqrt {D}}}^{T}} 8772: 7990: 7925: 7850: 7431: 6323: 6251: 5919: 3990:{\displaystyle d_{\text{emb, query}}=d_{\text{query}}} 3772:. The matrix of all query vectors is the query matrix: 2145:{\displaystyle (d_{\text{emb}},n_{\text{vocabulary}})} 14533: 14395: 13508: 13318: 13122:"Google: BERT now used on almost every English query" 12953:"Long Short-Term Memory-Networks for Machine Reading" 12675: 12381: 12278:"Stabilizing Transformers for Reinforcement Learning" 12112: 11724: 11672: 11533: 11482: 11433: 11120: 10819: 10702: 10657: 10651:

are independent samples from the normal distribution

10605: 10424: 10379: 10339: 10294: 10258: 10235: 10199: 10139: 10103: 10076: 10040: 10004: 9902: 9878: 9851: 9786: 9585: 9543: 9375: 9245: 9183: 9159: 9048: 9013: 8993: 8948: 8760: 8736: 8716: 8602: 8566: 8408: 8341: 8318: 8237: 8159: 7771: 7751: 7557: 7412: 7384: 7114:

requiring no warm-up, leading to faster convergence.

7026: 6971: 6878: 6763: 6616: 6548: 6477: 6455: 6186: 6142: 6099: 5900: 5786: 5766: 5760:

at entries where the attention link must be cut, and

5743: 5723: 5697: 5677: 5609: 5577: 5506: 5476: 5446: 5426: 5358: 5338: 5174: 5154: 5076: 4999: 4946: 4849: 4822: 4792: 4762: 4732: 4621: 4594: 4567: 4540: 4520: 4500: 4480: 4460: 4433: 4403: 4383: 4343: 4323: 4303: 4297:

is large), this does not necessarily mean that token

4263: 4243: 4223: 4196: 4169: 4134: 4107: 4080: 4056: 4036: 4006: 3963: 3910: 3864: 3821: 3778: 3720: 3693: 3658: 3628: 3601: 3571: 3544: 3517: 3432: 3393: 3271: 3236: 3209: 3112: 2959: 2925: 2837: 2793: 2681: 2631: 2602: 2582: 2562: 2492: 2323: 2299: 2230: 2174: 2112: 2019: 1977: 1872: 1810: 1790: 1770: 1714: 1662: 1527: 14837:"Parti: Pathways Autoregressive Text-to-Image Model" 14771: 14482: 14461: 14089: 13945: 13697: 12955:. In Su, Jian; Duh, Kevin; Carreras, Xavier (eds.). 12840:"Sequence to Sequence Learning with Neural Networks" 12838:

Sutskever, Ilya; Vinyals, Oriol; Le, Quoc V (2014).

11912:

based on requirements expressed in natural language.

10252:

Reformer (2020) reduces the computational load from

7017:

is the function implemented by the sublayer itself.

6833:

Block diagram for the full Transformer architecture.

4615:

respectively. Then we can represent the attention as

3687:

in the query sequence, it is multiplied by a matrix

3414:

The number of neurons in the middle layer is called

2669:{\displaystyle f:\mathbb {R} \to \mathbb {C} ^{d/2}} 2546:{\displaystyle \theta ={\frac {t}{r^{k}}},r=N^{2/d}} 1619:", and "prefixLM" (prefix language modeling) is not 1163:(LSTM). The architecture consists of two parts. The 14923: 13948:"Position Information in Transformers: An Overview" 13272: 12250: 7534: 7499: 6564:is applied to each row of the matrix individually. 4813:. The output dimension of an attention head is its 1764:representation of the token by an embedding matrix 1631:All transformers have the same primary components: 1377: 1369:(2024), are based on the Transformer architecture. 14569:Generating Long Sequences with Sparse Transformers 14023: 12837: 12741: 11755: 11710: 11658: 11519: 11465: 11419: 11106: 10805: 10688: 10643: 10591: 10394: 10361: 10318: 10280: 10241: 10221: 10161: 10125: 10089: 10062: 10026: 9990: 9884: 9864: 9837: 9729: 9569: 9529: 9279: 9231: 9165: 9145: 9022: 8999: 8979: 8934: 8742: 8722: 8702: 8572: 8552: 8391: 8327: 8304: 8223: 8145: 7757: 7737: 7478: 7336:output_distributions.append(decoder.unembed(z_d)) 7105: 7009: 6957: 6825:Transformer decoder with norm-first and norm-last. 6817:Transformer encoder with norm-first and norm-last. 6776: 6749: 6556: 6534: 6463: 6439: 6148: 6128: 6081: 5883: 5772: 5752: 5729: 5709: 5691:, should not have access to the token at position 5683: 5655: 5595: 5563: 5489: 5459: 5432: 5412: 5344: 5324: 5160: 5125: 5038: 4985: 4929: 4835: 4805: 4775: 4745: 4710: 4607: 4580: 4553: 4526: 4506: 4486: 4466: 4439: 4419: 4389: 4369: 4329: 4309: 4289: 4249: 4229: 4209: 4182: 4151: 4120: 4093: 4062: 4042: 4022: 3989: 3949: 3893: 3850: 3807: 3764: 3706: 3679: 3641: 3614: 3584: 3557: 3530: 3461: 3399: 3379: 3249: 3222: 3125: 3098: 2942: 2911: 2820: 2779: 2668: 2614: 2588: 2568: 2545: 2478: 2305: 2285: 2198: 2144: 2098: 1990: 1952: 1858: 1796: 1776: 1727: 1671: 1584: 14755:Advances in Neural Information Processing Systems 14540:Advances in Neural Information Processing Systems 14284: 14141:Advances in Neural Information Processing Systems 13878:Advances in Neural Information Processing Systems 13704:Advances in Neural Information Processing Systems 12844:Advances in Neural Information Processing Systems 12562: 12560: 12205: 12096:Advances in Neural Information Processing Systems 7511:. Other activation functions were developed. The 16456: 13362: 12891: 12870: 12226: 11817:For image generation, notable architectures are 7531:. Other examples include ScaleNorm, or FixNorm. 6791: 1027:(LLM) on large (language) datasets, such as the 14134: 14111:Ke, Guolin; He, Di; Liu, Tie-Yan (2021-03-15), 14068: 14047: 13850: 13288: 12950: 12777: 12650: 12613:http://cogprints.org/1380/1/vdM_correlation.pdf 12175:"Better Language Models and Their Implications" 10188: 8392:{\displaystyle \theta ^{(1)},...,\theta ^{(n)}} 8224:{\displaystyle z_{m}:=x_{m}^{(1)}+ix_{m}^{(2)}} 3765:{\displaystyle q_{i}=x_{i,{\text{query}}}W^{Q}} 3472: 3175:models, the original transformer model used an 1401:Transformers typically are first pretrained by 13042:RWKV: Reinventing RNNs for the Transformer Era 12783: 12557: 12447: 12353: 12351: 9537:with Multi-Query Attention, there is just one 9037: 8588:ALiBi (Attention with Linear Biases) is not a 5126:{\displaystyle \left(W^{Q},W^{K},W^{V}\right)} 4723:The number of dimensions in a query vector is 3462:{\displaystyle d_{\text{ffn}}=4d_{\text{emb}}} 1252:, which are easy to parallelize, and achieved 918:List of datasets for machine-learning research 15546: 15088: 14786: 14353: 14007:"Convolutional Sequence to Sequence Learning" 13907: 13871: 13268: 13266: 12634:Hinton, Geoffrey E.; Plaut, David C. (1987). 12448:Feldman, J. A.; Ballard, D. H. (1982-07-01). 12120:(1 November 1997). "Long Short-Term Memory". 11973: – Family of machine learning approaches 10176: 8545: 8523: 8505: 8482: 8467: 8451: 8433: 8416: 8268: 8245: 7837: 7779: 7518: 6864:There are two common conventions in use: the 5413:{\displaystyle W_{i}^{Q},W_{i}^{K},W_{i}^{V}} 3649:. Similarly for the key and value sequences. 3150: 1212:, which replaced the previous model based on 951: 15560: 15041: 14947: 14807: 14378:: CS1 maint: multiple names: authors list ( 13730: 12605: 12516: 12220: 12087:; Kaiser, Łukasz; Polosukhin, Illia (2017). 11366: 11352: 11253: 11239: 11101: 11060: 11053: 11004: 10997: 10989: 10980: 10939: 10932: 10883: 10876: 10868: 10837: 10825: 10774: 10761: 10741: 10711: 10576: 10557: 10545: 10526: 10511: 10492: 10480: 10461: 7515:used SwiGLU; both GPT-1 and BERT used GELU. 4163:which normalizes the weights. The fact that 3492:Scaled dot-product attention, block diagram. 2473: 2435: 14457: 14455: 13731:Phuong, Mary; Hutter, Marcus (2022-07-19), 12912: 12737: 12735: 12733: 12669: 12636:"Using Fast Weights to Deblur Old Memories" 12633: 12618: 12566: 12450:"Connectionist models and their properties" 12377: 12375: 12348: 12201: 12199: 10409: 9290: 7128:Encoder input t_e Decoder input t_d 5497:, but that is rarely the case in practice. 3187:Both the encoder and decoder layers have a 1635:Tokenizers, which convert text into tokens. 1311:, improving upon the line of research from 1239:Attention (machine learning) § History 1100:(RNNs). A well-cited early example was the 15553: 15539: 15095: 15081: 14748: 13263: 13066:"Was Linguistic A.I. Created by Accident?" 12517:Giles, C. Lee; Maxwell, Tom (1987-12-01). 10369:. For example, BigBird (2020) uses random 6845:for the full Transformer architecture, in 4903: 4876: 3622:, and each entry is a vector of dimension 1232: 958: 944: 15062: 15047: 14999: 14989: 14957: 14933: 14908: 14820: 14798: 14777: 14701: 14668: 14646: 14625: 14576: 14551: 14489: 14467: 14444: 14405: 14298: 14269: 14247: 14152: 14120: 14095: 14074: 14053: 14033: 13973: 13963: 13922: 13889: 13856: 13835: 13777: 13740: 13715: 13671: 13661: 13625:"Keras documentation: GPT2Backbone model" 13543: 13518: 13511:UL2: Unifying Language Learning Paradigms 13432: 13402: 13369: 13345: 13304: 13279: 13254: 13105: 13049: 12983: 12897: 12876: 12855: 12807: 12797: 12768: 12747: 12713: 12363: 12300: 12260: 12232: 12211: 11991: – Type of artificial neural network 11834:The transformer has had great success in 11804:, first turning the speech signal into a 10861: 10704: 5625: 3615:{\displaystyle \ell _{\text{seq, query}}} 3036: 2936: 2648: 2639: 2267: 2247: 2238: 1144: 1007:table. At each layer, each token is then 987:architecture developed by researchers at 14452: 13391:The Journal of Machine Learning Research 13358: 13356: 13243: 13241: 12730: 12372: 12196: 11520:{\displaystyle \varphi (k_{i})v_{i}^{T}} 9362: 6836: 6828: 6820: 6812: 6800: 6578: 6167: 6129:{\displaystyle PM_{\text{causal}}P^{-1}} 5061: 5053: 5049: 3495: 3487: 3198: 3162: 3154: 3147:, this is a mere notational difference. 2943:{\displaystyle \Delta t\in \mathbb {R} } 2159: 1405:on a large generic dataset, followed by 1383:training steps), before decaying again. 1065:. It has also led to the development of 969: 14897: 14895: 14858: 14856: 14110: 13829: 12106: 10249:is the number of tokens in a sequence. 9838:{\displaystyle x_{1},x_{2},...,x_{512}} 9766: 9327:, such that each block fits within the 3894:{\displaystyle V=X_{\text{value}}W^{V}} 3815:Similarly, we construct the key matrix 3808:{\displaystyle Q=X_{\text{query}}W^{Q}} 1760:. Equivalently stated, it multiplies a 1479:translation between natural languages ( 14: 16457: 13874:"Root Mean Square Layer Normalization" 13533: 13531: 13529: 13095: 13093: 13063: 12997: 12995: 12695: 12693: 12691: 12029:(2014) further reduced its complexity. 7389:changing the location of normalization 7010:{\displaystyle \mathrm {Sublayer} (x)} 6542:with the implicit convention that the 4514:are defined as the matrices where the 3194: 2155: 1505:Large language model § Evaluation 1457:pretraining tasks. Some examples are: 1248:applied a self-attention mechanism to 15534: 15076: 14506:"Reformer: The Efficient Transformer" 14391: 14389: 13903: 13901: 13802:"Recent Advances in Google Translate" 13755: 13753: 13751: 13588: 13586: 13584: 13504: 13502: 13500: 13498: 13473: 13471: 13446: 13444: 13353: 13238: 13216: 13187: 13147:"Recent Advances in Google Translate" 12906: 12885: 12414: 12412: 12410: 12246: 12244: 10414:Random Feature Attention (2021) uses 7391:, etc. This is also usually used for 6180:individually. Schematically, we have: 5058:Multiheaded attention, block diagram. 3851:{\displaystyle K=X_{\text{key}}W^{K}} 3642:{\displaystyle d_{\text{emb, query}}} 1953:{\displaystyle \mathrm {Embed} (3)=M} 1804:, then the one-hot representation is 1784:. For example, if the input token is 1728:{\displaystyle n_{\text{vocabulary}}} 1616: 1604:are trained by autoregressive tasks. 1334:. In 2022, a chatbot based on GPT-3, 995:mechanism, proposed in a 2017 paper " 16391:Generative adversarial network (GAN) 15515: 14892: 14853: 13872:Zhang, Biao; Sennrich, Rico (2019). 13766:Journal of Machine Learning Research 13297:Rethinking Attention with Performers 12786:Frontiers in Artificial Intelligence 12322:IEEE Robotics and Automation Letters 12169: 12167: 12003: – Type of large language model 10696:. This choice of parameters satisfy 3680:{\displaystyle x_{i,{\text{query}}}} 2168:positional encoding with parameters 1650: 1396: 1349:, speech recognition, robotics, and 15331:Quantum Artificial Intelligence Lab 13592: 13526: 13329: 13090: 12992: 12688: 12496:. Cambridge, Mass: Bradford Books. 12480: 11466:{\displaystyle \sigma =d_{K}^{1/4}} 9007:represent full attention paid, and 6853:The final points of detail are the 5666: 2009:The un-embedding layer is a linear- 1453:report documents a large number of 1071:generative pre-trained transformers 913:Glossary of artificial intelligence 24: 15477:Generative pre-trained transformer 15020: 14926:Zero-Shot Text-to-Image Generation 14419: 14386: 13898: 13748: 13733:Formal Algorithms for Transformers 13581: 13495: 13468: 13441: 13378: 12913:Lewis-Kraus, Gideon (2016-12-14). 12407: 12241: 12001:Generative pre-trained transformer 11584: 11171: 9359:GPUs and new data types like FP8. 9104: 9017: 8658: 7494: 7444: 7087: 7084: 7081: 7078: 7075: 7072: 7069: 7066: 7063: 7055: 7052: 7049: 7046: 7043: 7040: 7037: 7034: 6994: 6991: 6988: 6985: 6982: 6979: 6976: 6973: 6939: 6936: 6933: 6930: 6927: 6924: 6921: 6918: 6904: 6901: 6898: 6895: 6892: 6889: 6886: 6883: 6880: 6599:information flow. This allows for 6014: 5984: 5971: 5951: 5938: 5930: 5848: 5747: 4676: 3279: 3276: 3273: 3060: 3047: 3044: 3041: 3038: 2992: 2926: 2885: 2872: 2869: 2866: 2863: 2850: 2426: 2074: 2071: 2068: 2065: 2062: 2059: 2056: 2039: 2036: 2033: 2030: 2027: 2024: 2021: 1886: 1883: 1880: 1877: 1874: 1738:Some commonly used tokenizers are 1621:"prefixLM" (prefix language model) 1357:. Image and video generators like 25: 16481: 15038:, Harvard NLP group, 3 April 2018 14978:Journal of Translational Medicine 12164: 11756:{\displaystyle N(0,\sigma ^{2}I)} 10689:{\displaystyle N(0,\sigma ^{2}I)} 9318: 9232:{\displaystyle B_{i,j}=B_{i',j'}} 8730:is a real number ("scalar"), and 3950:{\displaystyle W^{Q},W^{K},W^{V}} 3483: 1517:for the task is typically sum of 1210:Google Neural Machine Translation 16429: 16428: 16408: 15514: 15505: 15504: 14965: 14941: 14917: 14829: 13622: 13022:from the original on 20 Mar 2024 13001: 11952:search) transformer achieved an 11770: 10162:{\displaystyle {\tilde {x}}_{4}} 10126:{\displaystyle {\tilde {x}}_{3}} 10063:{\displaystyle {\tilde {x}}_{2}} 10027:{\displaystyle {\tilde {x}}_{1}} 9325:matrix multiplications in blocks 7535:Alternative positional encodings 7500:Alternative activation functions 7452: 7435: 7385:alternative activation functions 6233:combine them into a matrix 6093:considers all masks of the form 4937:but is otherwise unconstrained. 4806:{\displaystyle d_{\text{value}}} 4746:{\displaystyle d_{\text{query}}} 4370:{\displaystyle q_{j}\cdot k_{i}} 4290:{\displaystyle q_{i}\cdot k_{j}} 3904:It is usually the case that all 1742:, WordPiece, and SentencePiece. 1576: conditional on its context 1378:Methods for stabilizing training 14742: 14718: 14677: 14655: 14634: 14613: 14602:from the original on 2021-09-18 14584: 14560: 14527: 14516:from the original on 2020-10-22 14498: 14476: 14428: 14413: 14347: 14325: 14278: 14256: 14234: 14210: 14185: 14161: 14128: 14104: 14083: 14062: 14041: 14017: 13998: 13939: 13865: 13844: 13823: 13812:from the original on 4 Jul 2024 13794: 13724: 13691: 13680:from the original on 2020-10-21 13641: 13616: 13605:from the original on 2020-10-18 13570:from the original on 2020-10-21 13552: 13419: 13312: 13205:from the original on 2023-03-18 13163: 13139: 13114: 13057: 13033: 12971: 12944: 12864: 12831: 12684:. Springer. pp. 9355–9366. 12627: 12510: 12441: 12430:from the original on 2021-01-13 12185:from the original on 2020-12-19 12032: 12020: 11829: 11711:{\displaystyle w_{1},...,w_{D}} 10644:{\displaystyle w_{1},...,w_{D}} 5596:{\displaystyle 12\times 64=768} 5490:{\displaystyle d_{\text{head}}} 4836:{\displaystyle d_{\text{head}}} 4152:{\displaystyle {\sqrt {d_{k}}}} 2425: 2000: 1682: 1626: 1612:are trained by prefixLM tasks. 1296:that contribute to the ongoing 1214:statistical machine translation 1091: 16341:Recurrent neural network (RNN) 16331:Differentiable neural computer 13064:Marche, Stephen (2024-08-23). 12676:Schlag, Imanol; Irie, Kazuki; 12393:10.18653/v1/2020.emnlp-demos.6 12309: 12268: 11750: 11728: 11653: 11618: 11557: 11539: 11499: 11486: 11411: 11398: 11328: 11321: 11298: 11285: 11215: 11208: 11144: 11126: 11098: 11092: 11042: 11036: 10983: 10977: 10971: 10921: 10915: 10865: 10744: 10738: 10732: 10723: 10717: 10708: 10683: 10661: 10580: 10452: 10434: 10428: 10389: 10383: 10356: 10343: 10313: 10298: 10275: 10262: 10216: 10203: 10147: 10111: 10048: 10012: 9976: 9954: 9932: 9910: 9709: 9656: 9641: 9628: 9609: 9591: 9509: 9446: 9431: 9418: 9399: 9381: 9076: 9058: 8630: 8612: 8384: 8378: 8353: 8347: 8216: 8210: 8189: 8183: 8118: 8112: 8082: 8076: 8045: 8039: 8009: 8003: 7969: 7963: 7944: 7938: 7824: 7818: 7800: 7794: 7732: 7717: 7712: 7706: 7688: 7682: 7669: 7663: 7658: 7652: 7634: 7628: 7615: 7609: 7604: 7598: 7580: 7574: 7561: 7558: 7504:The original transformer uses 7343: 7100: 7097: 7091: 7059: 7004: 6998: 6952: 6949: 6943: 6908: 6740: 6737: 6700: 6692: 6677: 6671: 6659: 6641: 6529: 6526: 6508: 6500: 6489: 6483: 6415: 6406: 6387: 6379: 6367: 6358: 6339: 6331: 6308: 6302: 5814: 5796: 5642: 5630: 5309: 5306: 5243: 5235: 5230: 5217: 5198: 5180: 4776:{\displaystyle d_{\text{key}}} 4649: 4631: 3372: 3366: 3353: 3347: 3339: 3334: 3328: 3315: 3309: 3298: 3289: 3283: 3250:{\displaystyle d_{\text{emb}}} 3223:{\displaystyle d_{\text{emb}}} 3093: 3087: 3076: 3073: 3057: 3051: 3005: 2983: 2906: 2900: 2894: 2891: 2882: 2876: 2856: 2841: 2691: 2685: 2643: 2422: 2419: 2413: 2401: 2395: 2386: 2380: 2362: 2355: 2337: 2330: 2324: 2242: 2139: 2113: 2093: 2078: 2049: 2043: 1991:{\displaystyle d_{\text{emb}}} 1944: 1902: 1896: 1890: 1853: 1811: 1579: 1563: 1386:A 2020 paper found that using 1286: 1017:recurrent neural architectures 333:Relevance vector machine (RVM) 18:Transformer (machine learning) 13: 1: 16386:Variational autoencoder (VAE) 16346:Long short-term memory (LSTM) 15613:Computational learning theory 15102: 13595:"The Illustrated Transformer" 12466:10.1016/S0364-0213(82)80001-3 12045: 7355:for downstream applications. 7117: 6792:Full transformer architecture 3957:are square matrices, meaning 2199:{\displaystyle N=10000,d=100} 1866:, and its embedding vector is 1620: 1355:convolutional neural networks 1326:Starting in 2018, the OpenAI 822:Computational learning theory 386:Expectation–maximization (EM) 16470:Neural network architectures 16366:Convolutional neural network 11926:biological sequence analysis 11800:follow the same pattern for 10189:Alternative attention graphs 7543:positional encoding module. 6796: 6557:{\displaystyle {\text{FFN}}} 6464:{\displaystyle {\text{FFN}}} 3473:Scaled dot-product attention 3135:convolutional neural network 1745: 1087:Timeline of machine learning 991:and based on the multi-head 779:Coefficient of determination 626:Convolutional neural network 338:Support vector machine (SVM) 32:Transformer (disambiguation) 7: 16361:Multilayer perceptron (MLP) 14751:"Visual Instruction Tuning" 12665:. PMLR. pp. 5156–5165. 12089:"Attention is All you Need" 11964: 11836:natural language processing 9570:{\displaystyle W^{K},W^{V}} 9038:Relative Position Encodings 8980:{\displaystyle B_{i,j}=j-i} 7388: 6847:object-oriented programming 5143:feed-forward neural network 4427:, the attention from token 3189:feed-forward neural network 1521:for the masked-out tokens: 1489:The course is jumping well. 1465:might generate the output, 1372: 1332:natural language generation 1047:natural language processing 930:Outline of machine learning 827:Empirical risk minimization 10: 16486: 16437:Artificial neural networks 16351:Gated recurrent unit (GRU) 15577:Differentiable programming 14991:10.1186/s12967-023-04011-y 14546:. Curran Associates, Inc. 13884:. Curran Associates, Inc. 13710:. Curran Associates, Inc. 13479:"Causal language modeling" 13452:"Masked language modeling" 12915:"The Great A.I. Awakening" 12850:. Curran Associates, Inc. 12134:10.1162/neco.1997.9.8.1735 10328:locality-sensitive hashing 10177:Sub-quadratic transformers 9742: 7519:Alternative normalizations 6638:MaskedMultiheadedAttention 6574: 6163: 3714:to produce a query vector 3476: 3230:-dimensional vectors into 3159:One encoder-decoder block. 3151:Encoder-decoder (overview) 1749: 1686: 1502: 1236: 1229:, was proposed for LSTMs. 1148: 1106:vanishing-gradient problem 1084: 1080: 567:Feedforward neural network 318:Artificial neural networks 29: 16404: 16318: 16262: 16191: 16124: 15996: 15896: 15889: 15843: 15807: 15770:Artificial neural network 15750: 15626: 15593:Automatic differentiation 15566: 15500: 15466:Attention Is All You Need 15457: 15436: 15389: 15360: 15353: 15323: 15294: 15287: 15248: 15217: 15188: 15147: 15140: 15133: 15110: 15029:The Annotated transformer 13952:Computational Linguistics 12591:10.1162/neco.1992.4.1.131 12102:. Curran Associates, Inc. 10319:{\displaystyle O(N\ln N)} 9311:is a library produced by 9280:{\displaystyle i-j=i'-j'} 7487:benchmarked comparisons. 7248:1:length(decoder.layers) 7158:1:length(encoder.layers) 6593:encoder-decoder attention 6193:given input vectors 2821:{\displaystyle r=N^{2/d}} 1273:Attention is all you need 1098:recurrent neural networks 997:Attention Is All You Need 550:Artificial neural network 15598:Neuromorphic engineering 15561:Differentiable computing 14703:10.1609/aaai.v36i7.20729 13397:(1): 140:5485–140:5551. 12334:10.1109/LRA.2022.3229266 12013: 11904:named entity recognition 10410:Random Feature Attention 10362:{\displaystyle O(N^{2})} 10330:and reversible layers. 10281:{\displaystyle O(N^{2})} 10222:{\displaystyle O(N^{2})} 9291:Efficient implementation 9023:{\displaystyle -\infty } 8583: 5753:{\displaystyle -\infty } 5603:, its projection matrix 3565:, and the value weights 2217:, as for example, both " 1498: 1425:next-sentence prediction 1403:self-supervised learning 1227:intra-sentence attention 859:Journals and conferences 806:Mathematical foundations 716:Temporal difference (TD) 572:Recurrent neural network 492:Conditional random field 415:Dimensionality reduction 163:Dimensionality reduction 125:Quantum machine learning 120:Neuromorphic engineering 80:Self-supervised learning 75:Semi-supervised learning 16371:Residual neural network 15787:Artificial Intelligence 14309:10.1145/3600006.3613165 13322:A ConvNet for the 2020s 13228:, OpenAI, June 11, 2018 13225:finetune-transformer-lm 12799:10.3389/frai.2020.00040 11956:of 2895, putting it at 11823:variational autoencoder 10416:Fourier random features 7765:. Then RoPE encoding is 7758:{\displaystyle \theta } 7546: 7353:representation learning 6610:Schematically, we have: 2615:{\displaystyle N=10000} 1303:In language modelling, 1233:Parallelizing attention 1111:A key breakthrough was 268:Apprenticeship learning 15341:Tensor Processing Unit 14880:Cite journal requires 14420:Fu, Yao (2023-12-13). 13933:10.5281/zenodo.3525484 11894:document summarization 11765:Gram-Schmidt processed 11757: 11712: 11660: 11521: 11467: 11421: 11108: 10807: 10690: 10645: 10593: 10396: 10363: 10320: 10282: 10243: 10223: 10163: 10127: 10091: 10064: 10028: 9992: 9886: 9866: 9839: 9731: 9571: 9531: 9281: 9233: 9167: 9147: 9024: 9001: 8981: 8936: 8744: 8724: 8704: 8574: 8554: 8393: 8329: 8306: 8225: 8147: 7759: 7745:. Now pick some angle 7739: 7480: 7107: 7011: 6959: 6850: 6834: 6826: 6818: 6806: 6778: 6751: 6584: 6558: 6536: 6465: 6441: 6173: 6150: 6130: 6083: 5885: 5774: 5754: 5731: 5711: 5685: 5657: 5597: 5565: 5491: 5461: 5434: 5414: 5346: 5326: 5162: 5133:matrices is called an 5127: 5067: 5059: 5040: 4987: 4931: 4837: 4807: 4777: 4753:and similarly for the 4747: 4712: 4609: 4582: 4555: 4528: 4508: 4488: 4468: 4441: 4421: 4420:{\displaystyle a_{ij}} 4391: 4371: 4331: 4311: 4291: 4251: 4231: 4211: 4184: 4153: 4122: 4095: 4064: 4044: 4024: 4023:{\displaystyle a_{ij}} 3991: 3951: 3895: 3852: 3809: 3766: 3708: 3681: 3643: 3616: 3586: 3559: 3532: 3501: 3493: 3463: 3401: 3381: 3263:multilayer perceptrons 3258: 3251: 3224: 3168: 3160: 3127: 3100: 2944: 2913: 2822: 2781: 2670: 2616: 2590: 2570: 2547: 2480: 2307: 2287: 2206: 2200: 2146: 2100: 1992: 1954: 1860: 1798: 1778: 1729: 1673: 1586: 1246:decomposable attention 1161:long short-term memory 1151:Seq2seq § History 1145:Attention with seq2seq 1059:reinforcement learning 1021:long short-term memory 976: 817:Bias–variance tradeoff 699:Reinforcement learning 675:Spiking neural network 85:Reinforcement learning 16326:Neural Turing machine 15914:Human image synthesis 14841:sites.research.google 13175:MIT Technology Review 12027:Gated recurrent units 11995:BERT (language model) 11910:writing computer code 11840:large language models 11758: 11713: 11661: 11522: 11468: 11422: 11109: 10808: 10691: 10646: 10594: 10397: 10364: 10321: 10283: 10244: 10224: 10164: 10128: 10092: 10090:{\displaystyle x_{3}} 10065: 10029: 9993: 9887: 9867: 9865:{\displaystyle x_{t}} 9840: 9774:speculative execution 9732: 9572: 9532: 9363:Multi-Query Attention 9282: 9234: 9168: 9148: 9025: 9002: 8982: 8937: 8745: 8725: 8705: 8575: 8555: 8394: 8330: 8307: 8226: 8148: 7760: 7740: 7527:which is used in the 7481: 7403:are encoder-decoder. 7397:instruction following 7369:instruction following 7340:output_distributions 7210:z_e ← z_e + z_e_copy 7108: 7012: 6960: 6840: 6832: 6824: 6816: 6804: 6779: 6777:{\displaystyle H^{E}} 6752: 6582: 6559: 6537: 6466: 6442: 6171: 6151: 6131: 6084: 5886: 5775: 5755: 5732: 5712: 5686: 5658: 5598: 5566: 5492: 5462: 5460:{\displaystyle W^{O}} 5435: 5415: 5347: 5327: 5163: 5128: 5065: 5057: 5050:Multiheaded attention 5041: 4988: 4932: 4838: 4808: 4778: 4748: 4713: 4610: 4608:{\displaystyle v_{i}} 4583: 4581:{\displaystyle k_{i}} 4556: 4554:{\displaystyle q_{i}} 4529: 4509: 4489: 4469: 4442: 4422: 4392: 4372: 4332: 4317:will attend to token 4312: 4292: 4252: 4232: 4212: 4210:{\displaystyle W^{K}} 4185: 4183:{\displaystyle W^{Q}} 4154: 4123: 4121:{\displaystyle k_{j}} 4096: 4094:{\displaystyle q_{i}} 4065: 4045: 4025: 3992: 3952: 3896: 3858:and the value matrix 3853: 3810: 3767: 3709: 3707:{\displaystyle W^{Q}} 3682: 3644: 3617: 3587: 3585:{\displaystyle W^{V}} 3560: 3558:{\displaystyle W^{K}} 3533: 3531:{\displaystyle W^{Q}} 3499: 3491: 3479:Dot-product attention 3464: 3402: 3400:{\displaystyle \phi } 3382: 3257:-dimensional vectors. 3252: 3225: 3202: 3166: 3158: 3128: 3126:{\displaystyle c_{j}} 3101: 2945: 2914: 2823: 2782: 2671: 2617: 2591: 2571: 2548: 2481: 2308: 2288: 2201: 2163: 2147: 2106:The matrix has shape 2101: 1993: 1955: 1861: 1799: 1779: 1750:Further information: 1730: 1674: 1594:BERT series of models 1587: 1434:reading comprehension 1340:large language models 1319:. It was followed by 1173:gated recurrent units 1130:higher-order networks 1025:large language models 973: 653:Neural radiance field 475:Structured prediction 198:Structured prediction 70:Unsupervised learning 16417:Computer programming 16396:Graph neural network 15971:Text-to-video models 15949:Text-to-image models 15797:Large language model 15782:Scientific computing 15588:Statistical manifold 15583:Information geometry 13975:10.1162/coli_a_00445 13673:10.18653/v1/W19-4828 12965:10.18653/v1/D16-1053 12535:10.1364/AO.26.004972 11989:Large language model 11796:Conformer and later 11722: 11670: 11531: 11480: 11431: 11118: 10817: 10700: 10655: 10603: 10422: 10395:{\displaystyle O(N)} 10377: 10371:small-world networks 10337: 10292: 10256: 10233: 10197: 10137: 10101: 10074: 10038: 10002: 9900: 9876: 9849: 9784: 9767:Speculative decoding 9583: 9541: 9378:MultiheadedAttention 9373: 9243: 9181: 9157: 9046: 9011: 8991: 8946: 8758: 8734: 8714: 8600: 8564: 8406: 8339: 8316: 8235: 8157: 7769: 7749: 7555: 7410: 7399:. The models in the 7371:. The models in the 7363:is usually used for 7024: 6969: 6876: 6855:residual connections 6761: 6697:MultiheadedAttention 6614: 6546: 6505:MultiheadedAttention 6475: 6453: 6384:MultiheadedAttention 6336:MultiheadedAttention 6184: 6140: 6097: 5898: 5784: 5764: 5741: 5721: 5695: 5675: 5663:is a square matrix. 5607: 5575: 5504: 5474: 5444: 5424: 5356: 5336: 5177:MultiheadedAttention 5172: 5152: 5074: 4997: 4944: 4847: 4820: 4790: 4760: 4730: 4619: 4592: 4565: 4538: 4534:th rows are vectors 4518: 4498: 4478: 4458: 4431: 4401: 4381: 4341: 4321: 4301: 4261: 4241: 4221: 4194: 4167: 4132: 4105: 4078: 4054: 4034: 4004: 3961: 3908: 3862: 3819: 3776: 3718: 3691: 3656: 3626: 3599: 3569: 3542: 3515: 3430: 3391: 3269: 3234: 3207: 3110: 2957: 2923: 2835: 2791: 2679: 2629: 2600: 2580: 2560: 2490: 2321: 2297: 2228: 2172: 2110: 2017: 1975: 1870: 1808: 1788: 1768: 1712: 1660: 1602:GPT series of models 1568:probability of 1525: 1250:feedforward networks 1222:, originally called 1121:multiplicative units 842:Statistical learning 740:Learning with humans 532:Local outlier factor 30:For other uses, see 15763:In-context learning 15603:Pattern recognition 15472:Future of Go Summit 14512:. 16 January 2020. 12724:10.3115/v1/D14-1179 12678:Schmidhuber, Jürgen 12568:Schmidhuber, Jürgen 12426:. 2 November 2018. 12118:Schmidhuber, Jürgen 12007:T5 (language model) 11931:video understanding 11899:document generation 11883:machine translation 11791:Vision transformers 11516: 11462: 11315: 9676: 9588:MultiQueryAttention 9508: 9487: 9466: 8220: 8193: 8122: 8086: 8049: 8013: 7973: 7948: 7828: 7804: 7716: 7692: 7662: 7638: 7608: 7584: 7509:activation function 6859:layer normalization 5710:{\displaystyle t+1} 5409: 5391: 5373: 5305: 5284: 5263: 3195:Feedforward network 2313:is a positive even 2156:Positional encoding 1610:T5 series of models 1481:machine translation 1388:layer normalization 1281:machine translation 1117:attention mechanism 1067:pre-trained systems 1055:vision transformers 1043:machine translation 685:Electrochemical RAM 592:reservoir computing 323:Logistic regression 242:Supervised learning 228:Multimodal learning 203:Feature engineering 148:Generative modeling 110:Rule-based learning 105:Curriculum learning 65:Supervised learning 40:Part of a series on 16356:Echo state network 16244:Jürgen Schmidhuber 15939:Facial recognition 15934:Speech recognition 15844:Software libraries 15218:In popular culture 15034:2021-09-22 at the 14337:, vLLM, 2024-06-20 14013:. PMLR: 1243–1252. 13599:jalammar.github.io 13126:Search Engine Land 12919:The New York Times 12579:Neural Computation 12387:. pp. 38–45. 12284:. PMLR: 7487–7498. 12122:Neural Computation 11983:Vision transformer 11802:speech recognition 11753: 11708: 11656: 11517: 11502: 11463: 11440: 11417: 11346: 11301: 11233: 11104: 10803: 10686: 10641: 10589: 10392: 10359: 10316: 10278: 10239: 10219: 10159: 10123: 10087: 10060: 10024: 9988: 9882: 9862: 9835: 9727: 9662: 9567: 9527: 9494: 9473: 9452: 9277: 9229: 9163: 9143: 9141: 9020: 8997: 8977: 8932: 8926: 8740: 8720: 8700: 8698: 8570: 8550: 8389: 8328:{\displaystyle 2n} 8325: 8302: 8221: 8200: 8173: 8143: 8137: 8102: 8066: 8029: 7993: 7976: 7953: 7928: 7914: 7808: 7784: 7755: 7735: 7696: 7672: 7642: 7618: 7588: 7564: 7476: 7470: 7379:are decoder-only. 7103: 7007: 6955: 6851: 6835: 6827: 6819: 6807: 6774: 6747: 6745: 6585: 6583:One decoder layer. 6554: 6532: 6461: 6437: 6435: 6427: 6287: 6174: 6172:One encoder layer. 6158:permutation matrix 6146: 6126: 6079: 6073: 5881: 5879: 5770: 5750: 5727: 5707: 5681: 5653: 5593: 5561: 5487: 5457: 5430: 5410: 5395: 5377: 5359: 5342: 5322: 5291: 5270: 5249: 5158: 5123: 5068: 5060: 5036: 4983: 4927: 4833: 4803: 4773: 4743: 4708: 4706: 4605: 4578: 4551: 4524: 4504: 4484: 4464: 4437: 4417: 4387: 4367: 4327: 4307: 4287: 4247: 4227: 4207: 4180: 4149: 4118: 4091: 4060: 4040: 4020: 3987: 3947: 3891: 3848: 3805: 3762: 3704: 3677: 3639: 3612: 3582: 3555: 3538:, the key weights 3528: 3502: 3494: 3459: 3397: 3377: 3259: 3247: 3220: 3169: 3161: 3123: 3106:for any constants 3096: 3025: 2969: 2940: 2909: 2818: 2777: 2666: 2612: 2586: 2566: 2543: 2476: 2303: 2283: 2207: 2196: 2142: 2096: 1988: 1950: 1856: 1794: 1774: 1740:byte pair encoding 1725: 1672:{\displaystyle xW} 1669: 1582: 1556: 1439:sentiment analysis 1429:question answering 1363:Stable Diffusion 3 1347:vision transformer 1258:textual entailment 1224:intra-attention or 977: 253: • 168:Density estimation 16452: 16451: 16214:Stephen Grossberg 16187: 16186: 15528: 15527: 15453: 15452: 15349: 15348: 15283: 15282: 15244: 15243: 15134:Computer programs 14598:. 25 March 2021. 14334:vllm-project/vllm 14318:979-8-4007-0229-7 14173:crfm.stanford.edu 13201:. June 11, 2018. 12529:(23): 4972–4978. 12503:978-0-262-68053-0 12454:Cognitive Science 11781:transfer learning 11651: 11603: 11602: 11566: 11537: 11415: 11337: 11224: 11190: 11189: 11153: 11124: 10799: 10450: 10449: 10242:{\displaystyle N} 10150: 10114: 10051: 10015: 9979: 9957: 9935: 9913: 9885:{\displaystyle t} 9654: 9638: 9619: 9589: 9444: 9428: 9409: 9379: 9166:{\displaystyle B} 9123: 9122: 9085: 9056: 9000:{\displaystyle 0} 8754:matrix defined by 8743:{\displaystyle B} 8723:{\displaystyle s} 8677: 8676: 8639: 8610: 8573:{\displaystyle k} 8519: 8478: 8447: 8412: 8241: 7775: 7465: 7420: 7377:Chinchilla series 6698: 6690: 6669: 6639: 6552: 6506: 6498: 6481: 6459: 6385: 6377: 6337: 6329: 6300: 6234: 6194: 6149:{\displaystyle P} 6110: 5908: 5867: 5866: 5823: 5794: 5773:{\displaystyle 0} 5730:{\displaystyle M} 5684:{\displaystyle t} 5552: 5533: 5514: 5484: 5433:{\displaystyle i} 5345:{\displaystyle X} 5332:where the matrix 5241: 5227: 5208: 5178: 5161:{\displaystyle i} 5033: 5020: 5007: 4980: 4967: 4954: 4924: 4911: 4897: 4884: 4870: 4857: 4830: 4800: 4770: 4740: 4695: 4694: 4658: 4629: 4527:{\displaystyle i} 4507:{\displaystyle V} 4487:{\displaystyle K} 4467:{\displaystyle Q} 4440:{\displaystyle i} 4390:{\displaystyle i} 4330:{\displaystyle i} 4310:{\displaystyle j} 4250:{\displaystyle j} 4237:attends to token 4230:{\displaystyle i} 4147: 4063:{\displaystyle j} 4043:{\displaystyle i} 3984: 3971: 3878: 3835: 3792: 3748: 3673: 3636: 3609: 3456: 3440: 3416:intermediate size 3244: 3217: 3016: 2960: 2767: 2589:{\displaystyle k} 2569:{\displaystyle N} 2514: 2306:{\displaystyle d} 2136: 2123: 1985: 1797:{\displaystyle 3} 1777:{\displaystyle M} 1722: 1651:following section 1577: 1569: 1553: 1539: 1531: 1471:me to your party 1421:language modeling 1397:Pretrain-finetune 1294:generative models 1125:sigma-pi networks 968: 967: 773:Model diagnostics 756:Human-in-the-loop 599:Boltzmann machine 512:Anomaly detection 308:Linear regression 223:Ontology learning 218:Grammar induction 193:Semantic analysis 188:Association rules 173:Anomaly detection 115:Neuro-symbolic AI 16:(Redirected from 16477: 16442:Machine learning 16432: 16431: 16412: 16167:Action selection 16157:Self-driving car 15964:Stable Diffusion 15929:Speech synthesis 15894: 15893: 15758:Machine learning 15634:Gradient descent 15555: 15548: 15541: 15532: 15531: 15518: 15517: 15508: 15507: 15492:Google Workspace 15358: 15357: 15292: 15291: 15288:Machine learning 15145: 15144: 15138: 15137: 15097: 15090: 15083: 15074: 15073: 15068: 15066: 15053: 15051: 15027:Alexander Rush, 15014: 15013: 15003: 14993: 14969: 14963: 14962: 14961: 14945: 14939: 14938: 14937: 14921: 14915: 14914: 14912: 14899: 14890: 14889: 14883: 14878: 14876: 14868: 14860: 14851: 14850: 14848: 14847: 14833: 14827: 14826: 14824: 14811: 14805: 14804: 14802: 14790: 14784: 14783: 14781: 14769: 14763: 14762: 14746: 14740: 14739: 14737: 14736: 14722: 14716: 14715: 14705: 14696:(7): 7628–7636. 14681: 14675: 14674: 14672: 14659: 14653: 14652: 14650: 14638: 14632: 14631: 14629: 14617: 14611: 14610: 14608: 14607: 14588: 14582: 14581: 14580: 14564: 14558: 14557: 14555: 14531: 14525: 14524: 14522: 14521: 14502: 14496: 14495: 14493: 14480: 14474: 14473: 14471: 14459: 14450: 14449: 14448: 14432: 14426: 14425: 14417: 14411: 14410: 14409: 14393: 14384: 14383: 14377: 14369: 14367: 14366: 14351: 14345: 14344: 14343: 14342: 14329: 14323: 14322: 14302: 14282: 14276: 14275: 14273: 14260: 14254: 14253: 14251: 14238: 14232: 14231: 14229: 14228: 14214: 14208: 14207: 14205: 14204: 14189: 14183: 14182: 14180: 14179: 14165: 14159: 14158: 14156: 14132: 14126: 14125: 14124: 14108: 14102: 14101: 14099: 14087: 14081: 14080: 14078: 14066: 14060: 14059: 14057: 14045: 14039: 14038: 14037: 14021: 14015: 14014: 14002: 13996: 13995: 13977: 13967: 13943: 13937: 13936: 13926: 13905: 13896: 13895: 13893: 13869: 13863: 13862: 13860: 13848: 13842: 13841: 13839: 13827: 13821: 13820: 13818: 13817: 13808:. June 8, 2020. 13798: 13792: 13791: 13781: 13757: 13746: 13745: 13744: 13728: 13722: 13721: 13719: 13695: 13689: 13688: 13686: 13685: 13675: 13665: 13645: 13639: 13638: 13636: 13635: 13620: 13614: 13613: 13611: 13610: 13590: 13579: 13578: 13576: 13575: 13556: 13550: 13549: 13547: 13535: 13524: 13523: 13522: 13506: 13493: 13492: 13490: 13489: 13475: 13466: 13465: 13463: 13462: 13448: 13439: 13438: 13436: 13423: 13417: 13416: 13406: 13382: 13376: 13375: 13373: 13360: 13351: 13350: 13349: 13333: 13327: 13326: 13316: 13310: 13309: 13308: 13292: 13286: 13285: 13283: 13270: 13261: 13260: 13258: 13245: 13236: 13235: 13234: 13233: 13220: 13214: 13213: 13211: 13210: 13191: 13185: 13184: 13182: 13181: 13167: 13161: 13160: 13158: 13157: 13143: 13137: 13136: 13134: 13133: 13118: 13112: 13111: 13109: 13097: 13088: 13087: 13085: 13084: 13061: 13055: 13054: 13053: 13037: 13031: 13030: 13028: 13027: 12999: 12990: 12989: 12987: 12975: 12969: 12968: 12948: 12942: 12941: 12939: 12938: 12929:. Archived from 12910: 12904: 12903: 12901: 12889: 12883: 12882: 12880: 12868: 12862: 12861: 12859: 12835: 12829: 12828: 12811: 12801: 12781: 12775: 12774: 12772: 12760: 12754: 12753: 12751: 12739: 12728: 12727: 12717: 12697: 12686: 12685: 12673: 12667: 12666: 12654: 12648: 12647: 12631: 12625: 12622: 12616: 12609: 12603: 12602: 12576: 12564: 12555: 12554: 12514: 12508: 12507: 12495: 12484: 12478: 12477: 12445: 12439: 12438: 12436: 12435: 12416: 12405: 12404: 12379: 12370: 12369: 12367: 12355: 12346: 12345: 12313: 12307: 12306: 12304: 12292: 12286: 12285: 12272: 12266: 12265: 12264: 12248: 12239: 12238: 12236: 12224: 12218: 12217: 12215: 12203: 12194: 12193: 12191: 12190: 12171: 12162: 12161: 12128:(8): 1735–1780. 12114:Hochreiter, Sepp 12110: 12104: 12103: 12093: 12077: 12039: 12036: 12030: 12024: 11763:, then they are 11762: 11760: 11759: 11754: 11746: 11745: 11717: 11715: 11714: 11709: 11707: 11706: 11682: 11681: 11665: 11663: 11662: 11657: 11652: 11650: 11649: 11640: 11638: 11630: 11629: 11608: 11604: 11601: 11600: 11591: 11590: 11589: 11588: 11587: 11573: 11567: 11564: 11538: 11535: 11526: 11524: 11523: 11518: 11515: 11510: 11498: 11497: 11472: 11470: 11469: 11464: 11461: 11457: 11448: 11426: 11424: 11423: 11418: 11416: 11414: 11410: 11409: 11394: 11393: 11392: 11391: 11379: 11374: 11373: 11364: 11363: 11345: 11336: 11335: 11316: 11314: 11309: 11297: 11296: 11281: 11280: 11279: 11278: 11266: 11261: 11260: 11251: 11250: 11232: 11223: 11222: 11203: 11195: 11191: 11188: 11187: 11178: 11177: 11176: 11175: 11174: 11160: 11154: 11151: 11125: 11122: 11113: 11111: 11110: 11105: 11088: 11087: 11086: 11085: 11073: 11068: 11067: 11032: 11031: 11030: 11029: 11017: 11012: 11011: 10967: 10966: 10965: 10964: 10952: 10947: 10946: 10911: 10910: 10909: 10908: 10896: 10891: 10890: 10864: 10856: 10855: 10854: 10853: 10844: 10812: 10810: 10809: 10804: 10802: 10801: 10800: 10798: 10797: 10796: 10783: 10782: 10781: 10759: 10707: 10695: 10693: 10692: 10687: 10679: 10678: 10650: 10648: 10647: 10642: 10640: 10639: 10615: 10614: 10598: 10596: 10595: 10590: 10588: 10587: 10569: 10568: 10538: 10537: 10504: 10503: 10473: 10472: 10451: 10445: 10441: 10401: 10399: 10398: 10393: 10368: 10366: 10365: 10360: 10355: 10354: 10325: 10323: 10322: 10317: 10287: 10285: 10284: 10279: 10274: 10273: 10248: 10246: 10245: 10240: 10228: 10226: 10225: 10220: 10215: 10214: 10183:Long Range Arena 10168: 10166: 10165: 10160: 10158: 10157: 10152: 10151: 10143: 10132: 10130: 10129: 10124: 10122: 10121: 10116: 10115: 10107: 10096: 10094: 10093: 10088: 10086: 10085: 10069: 10067: 10066: 10061: 10059: 10058: 10053: 10052: 10044: 10033: 10031: 10030: 10025: 10023: 10022: 10017: 10016: 10008: 9997: 9995: 9994: 9989: 9987: 9986: 9981: 9980: 9972: 9965: 9964: 9959: 9958: 9950: 9943: 9942: 9937: 9936: 9928: 9921: 9920: 9915: 9914: 9906: 9891: 9889: 9888: 9883: 9871: 9869: 9868: 9863: 9861: 9860: 9844: 9842: 9841: 9836: 9834: 9833: 9809: 9808: 9796: 9795: 9736: 9734: 9733: 9728: 9726: 9725: 9716: 9712: 9708: 9707: 9692: 9691: 9675: 9670: 9655: 9652: 9645: 9644: 9640: 9639: 9636: 9620: 9617: 9590: 9587: 9576: 9574: 9573: 9568: 9566: 9565: 9553: 9552: 9536: 9534: 9533: 9528: 9526: 9525: 9516: 9512: 9507: 9502: 9486: 9481: 9465: 9460: 9445: 9442: 9435: 9434: 9430: 9429: 9426: 9410: 9407: 9380: 9377: 9286: 9284: 9283: 9278: 9276: 9265: 9238: 9236: 9235: 9230: 9228: 9227: 9226: 9215: 9199: 9198: 9172: 9170: 9169: 9164: 9152: 9150: 9149: 9144: 9142: 9135: 9131: 9124: 9121: 9120: 9111: 9110: 9109: 9108: 9107: 9093: 9086: 9083: 9057: 9054: 9029: 9027: 9026: 9021: 9006: 9004: 9003: 8998: 8986: 8984: 8983: 8978: 8964: 8963: 8942:in other words, 8941: 8939: 8938: 8933: 8931: 8930: 8749: 8747: 8746: 8741: 8729: 8727: 8726: 8721: 8709: 8707: 8706: 8701: 8699: 8692: 8688: 8678: 8675: 8674: 8665: 8664: 8663: 8662: 8661: 8647: 8640: 8637: 8611: 8608: 8579: 8577: 8576: 8571: 8560:for any integer 8559: 8557: 8556: 8551: 8549: 8548: 8527: 8526: 8520: 8517: 8515: 8514: 8509: 8508: 8486: 8485: 8479: 8476: 8471: 8470: 8455: 8454: 8448: 8445: 8443: 8442: 8437: 8436: 8420: 8419: 8413: 8410: 8398: 8396: 8395: 8390: 8388: 8387: 8357: 8356: 8334: 8332: 8331: 8326: 8311: 8309: 8308: 8303: 8301: 8300: 8291: 8290: 8272: 8271: 8259: 8258: 8249: 8248: 8242: 8239: 8230: 8228: 8227: 8222: 8219: 8208: 8192: 8181: 8169: 8168: 8152: 8150: 8149: 8144: 8142: 8141: 8121: 8110: 8085: 8074: 8048: 8037: 8012: 8001: 7981: 7980: 7972: 7961: 7947: 7936: 7919: 7918: 7841: 7840: 7827: 7816: 7803: 7792: 7783: 7782: 7776: 7773: 7764: 7762: 7761: 7756: 7744: 7742: 7741: 7738:{\displaystyle } 7736: 7715: 7704: 7691: 7680: 7661: 7650: 7637: 7626: 7607: 7596: 7583: 7572: 7485: 7483: 7482: 7477: 7475: 7474: 7467: 7466: 7463: 7455: 7438: 7422: 7421: 7418: 7112: 7110: 7109: 7104: 7090: 7058: 7016: 7014: 7013: 7008: 6997: 6964: 6962: 6961: 6956: 6942: 6907: 6843:object hierarchy 6783: 6781: 6780: 6775: 6773: 6772: 6756: 6754: 6753: 6748: 6746: 6736: 6735: 6723: 6722: 6710: 6699: 6696: 6691: 6688: 6670: 6667: 6640: 6637: 6628: 6563: 6561: 6560: 6555: 6553: 6550: 6541: 6539: 6538: 6533: 6507: 6504: 6499: 6496: 6482: 6479: 6470: 6468: 6467: 6462: 6460: 6457: 6446: 6444: 6443: 6438: 6436: 6432: 6431: 6414: 6413: 6386: 6383: 6378: 6375: 6366: 6365: 6338: 6335: 6330: 6327: 6301: 6298: 6292: 6291: 6277: 6276: 6263: 6262: 6235: 6232: 6220: 6219: 6207: 6206: 6195: 6192: 6155: 6153: 6152: 6147: 6135: 6133: 6132: 6127: 6125: 6124: 6112: 6111: 6108: 6088: 6086: 6085: 6080: 6078: 6077: 5910: 5909: 5906: 5890: 5888: 5887: 5882: 5880: 5873: 5869: 5868: 5865: 5864: 5855: 5854: 5853: 5852: 5851: 5837: 5824: 5821: 5795: 5792: 5780:at other places: 5779: 5777: 5776: 5771: 5759: 5757: 5756: 5751: 5736: 5734: 5733: 5728: 5716: 5714: 5713: 5708: 5690: 5688: 5687: 5682: 5667:Masked attention 5662: 5660: 5659: 5654: 5652: 5651: 5628: 5619: 5618: 5602: 5600: 5599: 5594: 5570: 5568: 5567: 5562: 5554: 5553: 5550: 5535: 5534: 5531: 5516: 5515: 5512: 5496: 5494: 5493: 5488: 5486: 5485: 5482: 5466: 5464: 5463: 5458: 5456: 5455: 5439: 5437: 5436: 5431: 5419: 5417: 5416: 5411: 5408: 5403: 5390: 5385: 5372: 5367: 5351: 5349: 5348: 5343: 5331: 5329: 5328: 5323: 5321: 5320: 5304: 5299: 5283: 5278: 5262: 5257: 5242: 5239: 5234: 5233: 5229: 5228: 5225: 5209: 5206: 5179: 5176: 5167: 5165: 5164: 5159: 5132: 5130: 5129: 5124: 5122: 5118: 5117: 5116: 5104: 5103: 5091: 5090: 5045: 5043: 5042: 5037: 5035: 5034: 5031: 5022: 5021: 5018: 5009: 5008: 5005: 4992: 4990: 4989: 4984: 4982: 4981: 4978: 4969: 4968: 4965: 4956: 4955: 4952: 4936: 4934: 4933: 4928: 4926: 4925: 4922: 4913: 4912: 4909: 4899: 4898: 4895: 4886: 4885: 4882: 4872: 4871: 4868: 4859: 4858: 4855: 4842: 4840: 4839: 4834: 4832: 4831: 4828: 4812: 4810: 4809: 4804: 4802: 4801: 4798: 4782: 4780: 4779: 4774: 4772: 4771: 4768: 4752: 4750: 4749: 4744: 4742: 4741: 4738: 4717: 4715: 4714: 4709: 4707: 4700: 4696: 4693: 4692: 4683: 4682: 4681: 4680: 4679: 4665: 4659: 4656: 4630: 4627: 4614: 4612: 4611: 4606: 4604: 4603: 4587: 4585: 4584: 4579: 4577: 4576: 4560: 4558: 4557: 4552: 4550: 4549: 4533: 4531: 4530: 4525: 4513: 4511: 4510: 4505: 4493: 4491: 4490: 4485: 4473: 4471: 4470: 4465: 4452:softmax function 4446: 4444: 4443: 4438: 4426: 4424: 4423: 4418: 4416: 4415: 4396: 4394: 4393: 4388: 4376: 4374: 4373: 4368: 4366: 4365: 4353: 4352: 4336: 4334: 4333: 4328: 4316: 4314: 4313: 4308: 4296: 4294: 4293: 4288: 4286: 4285: 4273: 4272: 4256: 4254: 4253: 4248: 4236: 4234: 4233: 4228: 4216: 4214: 4213: 4208: 4206: 4205: 4189: 4187: 4186: 4181: 4179: 4178: 4158: 4156: 4155: 4150: 4148: 4146: 4145: 4136: 4127: 4125: 4124: 4119: 4117: 4116: 4100: 4098: 4097: 4092: 4090: 4089: 4069: 4067: 4066: 4061: 4049: 4047: 4046: 4041: 4029: 4027: 4026: 4021: 4019: 4018: 3996: 3994: 3993: 3988: 3986: 3985: 3982: 3973: 3972: 3969: 3956: 3954: 3953: 3948: 3946: 3945: 3933: 3932: 3920: 3919: 3900: 3898: 3897: 3892: 3890: 3889: 3880: 3879: 3876: 3857: 3855: 3854: 3849: 3847: 3846: 3837: 3836: 3833: 3814: 3812: 3811: 3806: 3804: 3803: 3794: 3793: 3790: 3771: 3769: 3768: 3763: 3761: 3760: 3751: 3750: 3749: 3746: 3730: 3729: 3713: 3711: 3710: 3705: 3703: 3702: 3686: 3684: 3683: 3678: 3676: 3675: 3674: 3671: 3652:For each vector 3648: 3646: 3645: 3640: 3638: 3637: 3634: 3621: 3619: 3618: 3613: 3611: 3610: 3607: 3591: 3589: 3588: 3583: 3581: 3580: 3564: 3562: 3561: 3556: 3554: 3553: 3537: 3535: 3534: 3529: 3527: 3526: 3468: 3466: 3465: 3460: 3458: 3457: 3454: 3442: 3441: 3438: 3424:feedforward size 3406: 3404: 3403: 3398: 3386: 3384: 3383: 3378: 3376: 3375: 3357: 3356: 3338: 3337: 3319: 3318: 3282: 3256: 3254: 3253: 3248: 3246: 3245: 3242: 3229: 3227: 3226: 3221: 3219: 3218: 3215: 3132: 3130: 3129: 3124: 3122: 3121: 3105: 3103: 3102: 3097: 3083: 3079: 3072: 3071: 3050: 3035: 3034: 3024: 3004: 3003: 2979: 2978: 2968: 2949: 2947: 2946: 2941: 2939: 2918: 2916: 2915: 2910: 2875: 2827: 2825: 2824: 2819: 2817: 2816: 2812: 2786: 2784: 2783: 2778: 2776: 2775: 2768: 2760: 2733: 2729: 2728: 2727: 2726: 2717: 2675: 2673: 2672: 2667: 2665: 2664: 2660: 2651: 2642: 2621: 2619: 2618: 2613: 2595: 2593: 2592: 2587: 2575: 2573: 2572: 2567: 2552: 2550: 2549: 2544: 2542: 2541: 2537: 2515: 2513: 2512: 2500: 2485: 2483: 2482: 2477: 2463: 2379: 2378: 2348: 2347: 2312: 2310: 2309: 2304: 2292: 2290: 2289: 2284: 2270: 2256: 2255: 2250: 2241: 2205: 2203: 2202: 2197: 2151: 2149: 2148: 2143: 2138: 2137: 2134: 2125: 2124: 2121: 2105: 2103: 2102: 2097: 2077: 2042: 1997: 1995: 1994: 1989: 1987: 1986: 1983: 1959: 1957: 1956: 1951: 1889: 1865: 1863: 1862: 1859:{\displaystyle } 1857: 1803: 1801: 1800: 1795: 1783: 1781: 1780: 1775: 1734: 1732: 1731: 1726: 1724: 1723: 1720: 1693:Lexical analysis 1678: 1676: 1675: 1670: 1617:masked attention 1591: 1589: 1588: 1583: 1578: 1575: 1570: 1567: 1555: 1554: 1551: 1532: 1529: 1519:log-perplexities 1455:natural language 1208:was revamped to 1206:Google Translate 960: 953: 946: 907:Related articles 784:Confusion matrix 537:Isolation forest 482:Graphical models 261: 260: 213:Learning to rank 208:Feature learning 46:Machine learning 37: 36: 21: 16485: 16484: 16480: 16479: 16478: 16476: 16475: 16474: 16465:Google software 16455: 16454: 16453: 16448: 16400: 16314: 16280:Google DeepMind 16258: 16224:Geoffrey Hinton 16183: 16120: 16046:Project Debater 15992: 15890:Implementations 15885: 15839: 15803: 15746: 15688:Backpropagation 15622: 15608:Tensor calculus 15562: 15559: 15529: 15524: 15496: 15449: 15432: 15390:Language models 15385: 15345: 15319: 15295:Neural networks 15279: 15240: 15213: 15184: 15129: 15125:Google DeepMind 15106: 15101: 15071: 15036:Wayback Machine 15023: 15021:Further reading 15018: 15017: 14970: 14966: 14946: 14942: 14922: 14918: 14900: 14893: 14881: 14879: 14870: 14869: 14861: 14854: 14845: 14843: 14835: 14834: 14830: 14812: 14808: 14791: 14787: 14770: 14766: 14747: 14743: 14734: 14732: 14724: 14723: 14719: 14682: 14678: 14660: 14656: 14639: 14635: 14618: 14614: 14605: 14603: 14590: 14589: 14585: 14565: 14561: 14532: 14528: 14519: 14517: 14504: 14503: 14499: 14481: 14477: 14460: 14453: 14433: 14429: 14418: 14414: 14394: 14387: 14371: 14370: 14364: 14362: 14352: 14348: 14340: 14338: 14331: 14330: 14326: 14319: 14283: 14279: 14261: 14257: 14239: 14235: 14226: 14224: 14216: 14215: 14211: 14202: 14200: 14191: 14190: 14186: 14177: 14175: 14169:"Stanford CRFM" 14167: 14166: 14162: 14147:: 16344–16359. 14133: 14129: 14109: 14105: 14088: 14084: 14067: 14063: 14046: 14042: 14022: 14018: 14003: 13999: 13944: 13940: 13906: 13899: 13870: 13866: 13849: 13845: 13828: 13824: 13815: 13813: 13806:Google Research 13800: 13799: 13795: 13758: 13749: 13729: 13725: 13696: 13692: 13683: 13681: 13646: 13642: 13633: 13631: 13621: 13617: 13608: 13606: 13591: 13582: 13573: 13571: 13558: 13557: 13553: 13536: 13527: 13507: 13496: 13487: 13485: 13477: 13476: 13469: 13460: 13458: 13450: 13449: 13442: 13424: 13420: 13383: 13379: 13361: 13354: 13334: 13330: 13317: 13313: 13293: 13289: 13271: 13264: 13246: 13239: 13231: 13229: 13222: 13221: 13217: 13208: 13206: 13193: 13192: 13188: 13179: 13177: 13169: 13168: 13164: 13155: 13153: 13151:research.google 13145: 13144: 13140: 13131: 13129: 13120: 13119: 13115: 13098: 13091: 13082: 13080: 13062: 13058: 13038: 13034: 13025: 13023: 13000: 12993: 12976: 12972: 12949: 12945: 12936: 12934: 12911: 12907: 12890: 12886: 12869: 12865: 12836: 12832: 12782: 12778: 12761: 12757: 12740: 12731: 12698: 12689: 12674: 12670: 12655: 12651: 12632: 12628: 12623: 12619: 12610: 12606: 12574: 12565: 12558: 12515: 12511: 12504: 12493: 12485: 12481: 12446: 12442: 12433: 12431: 12418: 12417: 12408: 12380: 12373: 12356: 12349: 12314: 12310: 12293: 12289: 12273: 12269: 12249: 12242: 12225: 12221: 12204: 12197: 12188: 12186: 12173: 12172: 12165: 12111: 12107: 12091: 12081:Vaswani, Ashish 12078: 12053: 12048: 12043: 12042: 12037: 12033: 12025: 12021: 12016: 11967: 11936:protein folding 11832: 11773: 11741: 11737: 11723: 11720: 11719: 11702: 11698: 11677: 11673: 11671: 11668: 11667: 11645: 11641: 11639: 11634: 11625: 11621: 11596: 11592: 11583: 11582: 11578: 11574: 11572: 11568: 11563: 11534: 11532: 11529: 11528: 11511: 11506: 11493: 11489: 11481: 11478: 11477: 11453: 11449: 11444: 11432: 11429: 11428: 11405: 11401: 11387: 11383: 11375: 11369: 11365: 11359: 11355: 11351: 11347: 11341: 11331: 11327: 11317: 11310: 11305: 11292: 11288: 11274: 11270: 11262: 11256: 11252: 11246: 11242: 11238: 11234: 11228: 11218: 11214: 11204: 11202: 11183: 11179: 11170: 11169: 11165: 11161: 11159: 11155: 11150: 11121: 11119: 11116: 11115: 11081: 11077: 11069: 11063: 11059: 11052: 11048: 11025: 11021: 11013: 11007: 11003: 10996: 10992: 10960: 10956: 10948: 10942: 10938: 10931: 10927: 10904: 10900: 10892: 10886: 10882: 10875: 10871: 10860: 10849: 10845: 10840: 10824: 10820: 10818: 10815: 10814: 10792: 10788: 10784: 10777: 10773: 10760: 10758: 10754: 10750: 10703: 10701: 10698: 10697: 10674: 10670: 10656: 10653: 10652: 10635: 10631: 10610: 10606: 10604: 10601: 10600: 10583: 10579: 10564: 10560: 10533: 10529: 10499: 10495: 10468: 10464: 10440: 10423: 10420: 10419: 10412: 10378: 10375: 10374: 10373:which grows as 10350: 10346: 10338: 10335: 10334: 10293: 10290: 10289: 10269: 10265: 10257: 10254: 10253: 10234: 10231: 10230: 10210: 10206: 10198: 10195: 10194: 10191: 10179: 10153: 10142: 10141: 10140: 10138: 10135: 10134: 10117: 10106: 10105: 10104: 10102: 10099: 10098: 10081: 10077: 10075: 10072: 10071: 10054: 10043: 10042: 10041: 10039: 10036: 10035: 10018: 10007: 10006: 10005: 10003: 10000: 9999: 9982: 9971: 9970: 9969: 9960: 9949: 9948: 9947: 9938: 9927: 9926: 9925: 9916: 9905: 9904: 9903: 9901: 9898: 9897: 9877: 9874: 9873: 9856: 9852: 9850: 9847: 9846: 9829: 9825: 9804: 9800: 9791: 9787: 9785: 9782: 9781: 9769: 9759:to KV caching. 9745: 9721: 9717: 9703: 9699: 9687: 9683: 9671: 9666: 9651: 9650: 9646: 9635: 9631: 9621: 9616: 9615: 9586: 9584: 9581: 9580: 9561: 9557: 9548: 9544: 9542: 9539: 9538: 9521: 9517: 9503: 9498: 9482: 9477: 9461: 9456: 9441: 9440: 9436: 9425: 9421: 9411: 9406: 9405: 9376: 9374: 9371: 9370: 9365: 9321: 9293: 9269: 9258: 9244: 9241: 9240: 9219: 9208: 9207: 9203: 9188: 9184: 9182: 9179: 9178: 9175:Toeplitz matrix 9158: 9155: 9154: 9140: 9139: 9116: 9112: 9103: 9102: 9098: 9094: 9092: 9091: 9087: 9082: 9053: 9049: 9047: 9044: 9043: 9040: 9012: 9009: 9008: 8992: 8989: 8988: 8953: 8949: 8947: 8944: 8943: 8925: 8924: 8919: 8914: 8909: 8904: 8898: 8897: 8892: 8887: 8879: 8871: 8862: 8861: 8856: 8851: 8846: 8838: 8829: 8828: 8823: 8818: 8813: 8808: 8799: 8798: 8793: 8788: 8783: 8778: 8768: 8767: 8759: 8756: 8755: 8735: 8732: 8731: 8715: 8712: 8711: 8697: 8696: 8670: 8666: 8657: 8656: 8652: 8648: 8646: 8645: 8641: 8636: 8607: 8603: 8601: 8598: 8597: 8586: 8565: 8562: 8561: 8544: 8543: 8522: 8521: 8516: 8510: 8504: 8503: 8502: 8481: 8480: 8475: 8466: 8465: 8450: 8449: 8444: 8438: 8432: 8431: 8430: 8415: 8414: 8409: 8407: 8404: 8403: 8377: 8373: 8346: 8342: 8340: 8337: 8336: 8317: 8314: 8313: 8296: 8292: 8280: 8276: 8267: 8266: 8254: 8250: 8244: 8243: 8238: 8236: 8233: 8232: 8209: 8204: 8182: 8177: 8164: 8160: 8158: 8155: 8154: 8136: 8135: 8111: 8106: 8075: 8070: 8063: 8062: 8038: 8033: 8002: 7997: 7986: 7985: 7975: 7974: 7962: 7957: 7950: 7949: 7937: 7932: 7921: 7920: 7913: 7912: 7898: 7883: 7882: 7865: 7846: 7845: 7836: 7835: 7817: 7812: 7793: 7788: 7778: 7777: 7772: 7770: 7767: 7766: 7750: 7747: 7746: 7705: 7700: 7681: 7676: 7651: 7646: 7627: 7622: 7597: 7592: 7573: 7568: 7556: 7553: 7552: 7549: 7537: 7521: 7502: 7497: 7495:Subsequent work 7469: 7468: 7462: 7458: 7456: 7451: 7448: 7447: 7439: 7434: 7427: 7426: 7417: 7413: 7411: 7408: 7407: 7393:text generation 7365:text generation 7346: 7341: 7120: 7062: 7033: 7025: 7022: 7021: 6972: 6970: 6967: 6966: 6917: 6879: 6877: 6874: 6873: 6799: 6794: 6768: 6764: 6762: 6759: 6758: 6744: 6743: 6731: 6727: 6718: 6714: 6703: 6695: 6687: 6680: 6666: 6663: 6662: 6636: 6629: 6621: 6617: 6615: 6612: 6611: 6577: 6549: 6547: 6544: 6543: 6503: 6495: 6478: 6476: 6473: 6472: 6456: 6454: 6451: 6450: 6434: 6433: 6426: 6425: 6419: 6418: 6409: 6405: 6382: 6374: 6371: 6370: 6361: 6357: 6334: 6326: 6319: 6318: 6311: 6297: 6294: 6293: 6286: 6285: 6279: 6278: 6272: 6268: 6265: 6264: 6258: 6254: 6247: 6246: 6239: 6231: 6228: 6227: 6215: 6211: 6202: 6198: 6196: 6191: 6187: 6185: 6182: 6181: 6166: 6141: 6138: 6137: 6117: 6113: 6107: 6103: 6098: 6095: 6094: 6072: 6071: 6066: 6061: 6056: 6051: 6045: 6044: 6039: 6034: 6029: 6024: 6018: 6017: 6009: 6004: 5999: 5994: 5988: 5987: 5979: 5974: 5966: 5961: 5955: 5954: 5946: 5941: 5933: 5925: 5915: 5914: 5905: 5901: 5899: 5896: 5895: 5878: 5877: 5860: 5856: 5847: 5846: 5842: 5838: 5836: 5829: 5825: 5820: 5793:MaskedAttention 5791: 5787: 5785: 5782: 5781: 5765: 5762: 5761: 5742: 5739: 5738: 5722: 5719: 5718: 5696: 5693: 5692: 5676: 5673: 5672: 5669: 5629: 5624: 5623: 5614: 5610: 5608: 5605: 5604: 5576: 5573: 5572: 5549: 5545: 5530: 5526: 5511: 5507: 5505: 5502: 5501: 5481: 5477: 5475: 5472: 5471: 5451: 5447: 5445: 5442: 5441: 5425: 5422: 5421: 5404: 5399: 5386: 5381: 5368: 5363: 5357: 5354: 5353: 5337: 5334: 5333: 5316: 5312: 5300: 5295: 5279: 5274: 5258: 5253: 5238: 5224: 5220: 5210: 5205: 5204: 5175: 5173: 5170: 5169: 5153: 5150: 5149: 5112: 5108: 5099: 5095: 5086: 5082: 5081: 5077: 5075: 5072: 5071: 5052: 5030: 5026: 5017: 5013: 5004: 5000: 4998: 4995: 4994: 4977: 4973: 4964: 4960: 4951: 4947: 4945: 4942: 4941: 4921: 4917: 4908: 4904: 4894: 4890: 4881: 4877: 4867: 4863: 4854: 4850: 4848: 4845: 4844: 4827: 4823: 4821: 4818: 4817: 4797: 4793: 4791: 4788: 4787: 4767: 4763: 4761: 4758: 4757: 4737: 4733: 4731: 4728: 4727: 4705: 4704: 4688: 4684: 4675: 4674: 4670: 4666: 4664: 4660: 4655: 4626: 4622: 4620: 4617: 4616: 4599: 4595: 4593: 4590: 4589: 4572: 4568: 4566: 4563: 4562: 4545: 4541: 4539: 4536: 4535: 4519: 4516: 4515: 4499: 4496: 4495: 4479: 4476: 4475: 4459: 4456: 4455: 4447:to each token. 4432: 4429: 4428: 4408: 4404: 4402: 4399: 4398: 4382: 4379: 4378: 4361: 4357: 4348: 4344: 4342: 4339: 4338: 4322: 4319: 4318: 4302: 4299: 4298: 4281: 4277: 4268: 4264: 4262: 4259: 4258: 4242: 4239: 4238: 4222: 4219: 4218: 4201: 4197: 4195: 4192: 4191: 4174: 4170: 4168: 4165: 4164: 4141: 4137: 4135: 4133: 4130: 4129: 4112: 4108: 4106: 4103: 4102: 4085: 4081: 4079: 4076: 4075: 4055: 4052: 4051: 4035: 4032: 4031: 4011: 4007: 4005: 4002: 4001: 3981: 3977: 3968: 3964: 3962: 3959: 3958: 3941: 3937: 3928: 3924: 3915: 3911: 3909: 3906: 3905: 3885: 3881: 3875: 3871: 3863: 3860: 3859: 3842: 3838: 3832: 3828: 3820: 3817: 3816: 3799: 3795: 3789: 3785: 3777: 3774: 3773: 3756: 3752: 3745: 3738: 3734: 3725: 3721: 3719: 3716: 3715: 3698: 3694: 3692: 3689: 3688: 3670: 3663: 3659: 3657: 3654: 3653: 3633: 3629: 3627: 3624: 3623: 3606: 3602: 3600: 3597: 3596: 3576: 3572: 3570: 3567: 3566: 3549: 3545: 3543: 3540: 3539: 3522: 3518: 3516: 3513: 3512: 3486: 3481: 3475: 3453: 3449: 3437: 3433: 3431: 3428: 3427: 3392: 3389: 3388: 3365: 3361: 3346: 3342: 3327: 3323: 3308: 3304: 3272: 3270: 3267: 3266: 3241: 3237: 3235: 3232: 3231: 3214: 3210: 3208: 3205: 3204: 3197: 3177:encoder-decoder 3153: 3117: 3113: 3111: 3108: 3107: 3067: 3063: 3037: 3030: 3026: 3020: 3015: 3011: 2999: 2995: 2974: 2970: 2964: 2958: 2955: 2954: 2935: 2924: 2921: 2920: 2862: 2836: 2833: 2832: 2808: 2804: 2800: 2792: 2789: 2788: 2759: 2734: 2722: 2718: 2713: 2706: 2702: 2698: 2697: 2680: 2677: 2676: 2656: 2652: 2647: 2646: 2638: 2630: 2627: 2626: 2601: 2598: 2597: 2581: 2578: 2577: 2561: 2558: 2557: 2533: 2529: 2525: 2508: 2504: 2499: 2491: 2488: 2487: 2459: 2365: 2361: 2340: 2336: 2322: 2319: 2318: 2298: 2295: 2294: 2266: 2251: 2246: 2245: 2237: 2229: 2226: 2225: 2173: 2170: 2169: 2164:A diagram of a 2158: 2133: 2129: 2120: 2116: 2111: 2108: 2107: 2055: 2020: 2018: 2015: 2014: 2003: 1982: 1978: 1976: 1973: 1972: 1971:and written as 1873: 1871: 1868: 1867: 1809: 1806: 1805: 1789: 1786: 1785: 1769: 1766: 1765: 1754: 1748: 1719: 1715: 1713: 1710: 1709: 1707:vocabulary size 1695: 1687:Main articles: 1685: 1661: 1658: 1657: 1629: 1574: 1566: 1550: 1543: 1528: 1526: 1523: 1522: 1507: 1501: 1399: 1380: 1375: 1309:word embeddings 1289: 1241: 1235: 1219:avant la lettre 1153: 1147: 1094: 1089: 1083: 1051:computer vision 1019:(RNNs) such as 964: 935: 934: 908: 900: 899: 860: 852: 851: 812:Kernel machines 807: 799: 798: 774: 766: 765: 746:Active learning 741: 733: 732: 701: 691: 690: 616:Diffusion model 552: 542: 541: 514: 504: 503: 477: 467: 466: 422:Factor analysis 417: 407: 406: 390: 353: 343: 342: 263: 262: 246: 245: 244: 233: 232: 138: 130: 129: 95:Online learning 60: 48: 35: 28: 23: 22: 15: 12: 11: 5: 16483: 16473: 16472: 16467: 16450: 16449: 16447: 16446: 16445: 16444: 16439: 16426: 16425: 16424: 16419: 16405: 16402: 16401: 16399: 16398: 16393: 16388: 16383: 16378: 16373: 16368: 16363: 16358: 16353: 16348: 16343: 16338: 16333: 16328: 16322: 16320: 16316: 16315: 16313: 16312: 16307: 16302: 16297: 16292: 16287: 16282: 16277: 16272: 16266: 16264: 16260: 16259: 16257: 16256: 16254:Ilya Sutskever 16251: 16246: 16241: 16236: 16231: 16226: 16221: 16219:Demis Hassabis 16216: 16211: 16209:Ian Goodfellow 16206: 16201: 16195: 16193: 16189: 16188: 16185: 16184: 16182: 16181: 16176: 16175: 16174: 16164: 16159: 16154: 16149: 16144: 16139: 16134: 16128: 16126: 16122: 16121: 16119: 16118: 16113: 16108: 16103: 16098: 16093: 16088: 16083: 16078: 16073: 16068: 16063: 16058: 16053: 16048: 16043: 16038: 16037: 16036: 16026: 16021: 16016: 16011: 16006: 16000: 15998: 15994: 15993: 15991: 15990: 15985: 15984: 15983: 15978: 15968: 15967: 15966: 15961: 15956: 15946: 15941: 15936: 15931: 15926: 15921: 15916: 15911: 15906: 15900: 15898: 15891: 15887: 15886: 15884: 15883: 15878: 15873: 15868: 15863: 15858: 15853: 15847: 15845: 15841: 15840: 15838: 15837: 15832: 15827: 15822: 15817: 15811: 15809: 15805: 15804: 15802: 15801: 15800: 15799: 15792:Language model 15789: 15784: 15779: 15778: 15777: 15767: 15766: 15765: 15754: 15752: 15748: 15747: 15745: 15744: 15742:Autoregression 15739: 15734: 15733: 15732: 15722: 15720:Regularization 15717: 15716: 15715: 15710: 15705: 15695: 15690: 15685: 15683:Loss functions 15680: 15675: 15670: 15665: 15660: 15659: 15658: 15648: 15643: 15642: 15641: 15630: 15628: 15624: 15623: 15621: 15620: 15618:Inductive bias 15615: 15610: 15605: 15600: 15595: 15590: 15585: 15580: 15572: 15570: 15564: 15563: 15558: 15557: 15550: 15543: 15535: 15526: 15525: 15523: 15522: 15512: 15501: 15498: 15497: 15495: 15494: 15489: 15484: 15479: 15474: 15469: 15461: 15459: 15455: 15454: 15451: 15450: 15448: 15447: 15440: 15438: 15434: 15433: 15431: 15430: 15424: 15418: 15412: 15406: 15400: 15393: 15391: 15387: 15386: 15384: 15383: 15377: 15371: 15364: 15362: 15355: 15351: 15350: 15347: 15346: 15344: 15343: 15338: 15333: 15327: 15325: 15321: 15320: 15318: 15317: 15311: 15305: 15298: 15296: 15289: 15285: 15284: 15281: 15280: 15278: 15277: 15271: 15265: 15259: 15252: 15250: 15246: 15245: 15242: 15241: 15239: 15238: 15230: 15221: 15219: 15215: 15214: 15212: 15211: 15205: 15199: 15192: 15190: 15186: 15185: 15183: 15182: 15176: 15170: 15164: 15158: 15151: 15149: 15142: 15135: 15131: 15130: 15128: 15127: 15122: 15117: 15111: 15108: 15107: 15100: 15099: 15092: 15085: 15077: 15070: 15069: 15054: 15039: 15024: 15022: 15019: 15016: 15015: 14964: 14940: 14916: 14891: 14882:|journal= 14852: 14828: 14806: 14785: 14764: 14761:: 34892–34916. 14741: 14717: 14676: 14654: 14633: 14612: 14596:Google AI Blog 14583: 14559: 14526: 14510:Google AI Blog 14497: 14475: 14451: 14427: 14412: 14385: 14346: 14324: 14317: 14277: 14255: 14233: 14209: 14184: 14160: 14127: 14103: 14082: 14061: 14040: 14016: 13997: 13958:(3): 733–763. 13938: 13897: 13864: 13843: 13822: 13793: 13747: 13723: 13690: 13640: 13615: 13593:Alammar, Jay. 13580: 13566:. 2016-04-18. 13551: 13525: 13494: 13483:huggingface.co 13467: 13456:huggingface.co 13440: 13418: 13377: 13352: 13328: 13311: 13287: 13262: 13237: 13215: 13186: 13162: 13138: 13113: 13089: 13070:The New Yorker 13056: 13032: 13002:Levy, Steven. 12991: 12970: 12943: 12933:on 24 May 2023 12905: 12884: 12863: 12830: 12776: 12755: 12729: 12687: 12668: 12649: 12626: 12617: 12604: 12585:(1): 131–139. 12556: 12523:Applied Optics 12509: 12502: 12479: 12460:(3): 205–254. 12440: 12424:Google AI Blog 12406: 12371: 12347: 12328:(2): 576–583. 12308: 12287: 12267: 12240: 12219: 12195: 12181:. 2019-02-14. 12163: 12105: 12085:Gomez, Aidan N 12050: 12049: 12047: 12044: 12041: 12040: 12031: 12018: 12017: 12015: 12012: 12011: 12010: 12004: 11998: 11992: 11986: 11980: 11974: 11966: 11963: 11962: 11961: 11943: 11933: 11928: 11919: 11918: 11916:speech-to-text 11913: 11907: 11901: 11896: 11891: 11885: 11831: 11828: 11772: 11769: 11752: 11749: 11744: 11740: 11736: 11733: 11730: 11727: 11705: 11701: 11697: 11694: 11691: 11688: 11685: 11680: 11676: 11655: 11648: 11644: 11637: 11633: 11628: 11624: 11620: 11617: 11614: 11611: 11607: 11599: 11595: 11586: 11581: 11577: 11571: 11562: 11559: 11556: 11553: 11550: 11547: 11544: 11541: 11514: 11509: 11505: 11501: 11496: 11492: 11488: 11485: 11460: 11456: 11452: 11447: 11443: 11439: 11436: 11413: 11408: 11404: 11400: 11397: 11390: 11386: 11382: 11378: 11372: 11368: 11362: 11358: 11354: 11350: 11344: 11340: 11334: 11330: 11326: 11323: 11320: 11313: 11308: 11304: 11300: 11295: 11291: 11287: 11284: 11277: 11273: 11269: 11265: 11259: 11255: 11249: 11245: 11241: 11237: 11231: 11227: 11221: 11217: 11213: 11210: 11207: 11201: 11198: 11194: 11186: 11182: 11173: 11168: 11164: 11158: 11149: 11146: 11143: 11140: 11137: 11134: 11131: 11128: 11103: 11100: 11097: 11094: 11091: 11084: 11080: 11076: 11072: 11066: 11062: 11058: 11055: 11051: 11047: 11044: 11041: 11038: 11035: 11028: 11024: 11020: 11016: 11010: 11006: 11002: 10999: 10995: 10991: 10988: 10985: 10982: 10979: 10976: 10973: 10970: 10963: 10959: 10955: 10951: 10945: 10941: 10937: 10934: 10930: 10926: 10923: 10920: 10917: 10914: 10907: 10903: 10899: 10895: 10889: 10885: 10881: 10878: 10874: 10870: 10867: 10863: 10859: 10852: 10848: 10843: 10839: 10836: 10833: 10830: 10827: 10823: 10795: 10791: 10787: 10780: 10776: 10772: 10769: 10766: 10763: 10757: 10753: 10749: 10746: 10743: 10740: 10737: 10734: 10731: 10728: 10725: 10722: 10719: 10716: 10713: 10710: 10706: 10685: 10682: 10677: 10673: 10669: 10666: 10663: 10660: 10638: 10634: 10630: 10627: 10624: 10621: 10618: 10613: 10609: 10586: 10582: 10578: 10575: 10572: 10567: 10563: 10559: 10556: 10553: 10550: 10547: 10544: 10541: 10536: 10532: 10528: 10525: 10522: 10519: 10516: 10513: 10510: 10507: 10502: 10498: 10494: 10491: 10488: 10485: 10482: 10479: 10476: 10471: 10467: 10463: 10460: 10457: 10454: 10448: 10444: 10439: 10436: 10433: 10430: 10427: 10411: 10408: 10391: 10388: 10385: 10382: 10358: 10353: 10349: 10345: 10342: 10315: 10312: 10309: 10306: 10303: 10300: 10297: 10277: 10272: 10268: 10264: 10261: 10238: 10218: 10213: 10209: 10205: 10202: 10190: 10187: 10178: 10175: 10156: 10149: 10146: 10120: 10113: 10110: 10084: 10080: 10057: 10050: 10047: 10021: 10014: 10011: 9985: 9978: 9975: 9968: 9963: 9956: 9953: 9946: 9941: 9934: 9931: 9924: 9919: 9912: 9909: 9881: 9859: 9855: 9832: 9828: 9824: 9821: 9818: 9815: 9812: 9807: 9803: 9799: 9794: 9790: 9768: 9765: 9753:PagedAttention 9744: 9741: 9724: 9720: 9715: 9711: 9706: 9702: 9698: 9695: 9690: 9686: 9682: 9679: 9674: 9669: 9665: 9661: 9658: 9649: 9643: 9634: 9630: 9627: 9624: 9614: 9611: 9608: 9605: 9602: 9599: 9596: 9593: 9564: 9560: 9556: 9551: 9547: 9524: 9520: 9515: 9511: 9506: 9501: 9497: 9493: 9490: 9485: 9480: 9476: 9472: 9469: 9464: 9459: 9455: 9451: 9448: 9439: 9433: 9424: 9420: 9417: 9414: 9404: 9401: 9398: 9395: 9392: 9389: 9386: 9383: 9364: 9361: 9320: 9319:FlashAttention 9317: 9292: 9289: 9275: 9272: 9268: 9264: 9261: 9257: 9254: 9251: 9248: 9225: 9222: 9218: 9214: 9211: 9206: 9202: 9197: 9194: 9191: 9187: 9162: 9138: 9134: 9130: 9127: 9119: 9115: 9106: 9101: 9097: 9090: 9081: 9078: 9075: 9072: 9069: 9066: 9063: 9060: 9052: 9051: 9039: 9036: 9019: 9016: 8996: 8976: 8973: 8970: 8967: 8962: 8959: 8956: 8952: 8929: 8923: 8920: 8918: 8915: 8913: 8910: 8908: 8905: 8903: 8900: 8899: 8896: 8893: 8891: 8888: 8886: 8883: 8880: 8878: 8875: 8872: 8870: 8867: 8864: 8863: 8860: 8857: 8855: 8852: 8850: 8847: 8845: 8842: 8839: 8837: 8834: 8831: 8830: 8827: 8824: 8822: 8819: 8817: 8814: 8812: 8809: 8807: 8804: 8801: 8800: 8797: 8794: 8792: 8789: 8787: 8784: 8782: 8779: 8777: 8774: 8773: 8771: 8766: 8763: 8739: 8719: 8695: 8691: 8687: 8684: 8681: 8673: 8669: 8660: 8655: 8651: 8644: 8635: 8632: 8629: 8626: 8623: 8620: 8617: 8614: 8606: 8605: 8585: 8582: 8569: 8547: 8542: 8539: 8536: 8533: 8530: 8525: 8513: 8507: 8501: 8498: 8495: 8492: 8489: 8484: 8474: 8469: 8464: 8461: 8458: 8453: 8441: 8435: 8429: 8426: 8423: 8418: 8386: 8383: 8380: 8376: 8372: 8369: 8366: 8363: 8360: 8355: 8352: 8349: 8345: 8324: 8321: 8312:For a list of 8299: 8295: 8289: 8286: 8283: 8279: 8275: 8270: 8265: 8262: 8257: 8253: 8247: 8218: 8215: 8212: 8207: 8203: 8199: 8196: 8191: 8188: 8185: 8180: 8176: 8172: 8167: 8163: 8140: 8134: 8131: 8128: 8125: 8120: 8117: 8114: 8109: 8105: 8101: 8098: 8095: 8092: 8089: 8084: 8081: 8078: 8073: 8069: 8065: 8064: 8061: 8058: 8055: 8052: 8047: 8044: 8041: 8036: 8032: 8028: 8025: 8022: 8019: 8016: 8011: 8008: 8005: 8000: 7996: 7992: 7991: 7989: 7984: 7979: 7971: 7968: 7965: 7960: 7956: 7952: 7951: 7946: 7943: 7940: 7935: 7931: 7927: 7926: 7924: 7917: 7911: 7908: 7905: 7902: 7899: 7897: 7894: 7891: 7888: 7885: 7884: 7881: 7878: 7875: 7872: 7869: 7866: 7864: 7861: 7858: 7855: 7852: 7851: 7849: 7844: 7839: 7834: 7831: 7826: 7823: 7820: 7815: 7811: 7807: 7802: 7799: 7796: 7791: 7787: 7781: 7754: 7734: 7731: 7728: 7725: 7722: 7719: 7714: 7711: 7708: 7703: 7699: 7695: 7690: 7687: 7684: 7679: 7675: 7671: 7668: 7665: 7660: 7657: 7654: 7649: 7645: 7641: 7636: 7633: 7630: 7625: 7621: 7617: 7614: 7611: 7606: 7603: 7600: 7595: 7591: 7587: 7582: 7579: 7576: 7571: 7567: 7563: 7560: 7548: 7545: 7536: 7533: 7520: 7517: 7501: 7498: 7496: 7493: 7473: 7461: 7457: 7454: 7450: 7449: 7446: 7443: 7440: 7437: 7433: 7432: 7430: 7425: 7416: 7345: 7342: 7332:1:length(z_d) 7320:1:length(z_d) 7308:1:length(z_d) 7296:1:length(z_d) 7284:1:length(z_d) 7272:1:length(z_d) 7260:1:length(z_d) 7233:1:length(z_d) 7218:1:length(z_e) 7206:1:length(z_e) 7194:1:length(z_e) 7182:1:length(z_e) 7170:1:length(z_e) 7143:1:length(z_e) 7124: 7119: 7116: 7102: 7099: 7096: 7093: 7089: 7086: 7083: 7080: 7077: 7074: 7071: 7068: 7065: 7061: 7057: 7054: 7051: 7048: 7045: 7042: 7039: 7036: 7032: 7029: 7006: 7003: 7000: 6996: 6993: 6990: 6987: 6984: 6981: 6978: 6975: 6954: 6951: 6948: 6945: 6941: 6938: 6935: 6932: 6929: 6926: 6923: 6920: 6916: 6913: 6910: 6906: 6903: 6900: 6897: 6894: 6891: 6888: 6885: 6882: 6798: 6795: 6793: 6790: 6771: 6767: 6742: 6739: 6734: 6730: 6726: 6721: 6717: 6713: 6709: 6706: 6702: 6694: 6686: 6683: 6681: 6679: 6676: 6673: 6665: 6664: 6661: 6658: 6655: 6652: 6649: 6646: 6643: 6635: 6632: 6630: 6627: 6624: 6620: 6619: 6601:autoregressive 6576: 6573: 6531: 6528: 6525: 6522: 6519: 6516: 6513: 6510: 6502: 6494: 6491: 6488: 6485: 6430: 6424: 6421: 6420: 6417: 6412: 6408: 6404: 6401: 6398: 6395: 6392: 6389: 6381: 6373: 6372: 6369: 6364: 6360: 6356: 6353: 6350: 6347: 6344: 6341: 6333: 6325: 6324: 6322: 6317: 6314: 6312: 6310: 6307: 6304: 6296: 6295: 6290: 6284: 6281: 6280: 6275: 6271: 6267: 6266: 6261: 6257: 6253: 6252: 6250: 6245: 6242: 6240: 6238: 6230: 6229: 6226: 6223: 6218: 6214: 6210: 6205: 6201: 6197: 6190: 6189: 6165: 6162: 6145: 6123: 6120: 6116: 6106: 6102: 6076: 6070: 6067: 6065: 6062: 6060: 6057: 6055: 6052: 6050: 6047: 6046: 6043: 6040: 6038: 6035: 6033: 6030: 6028: 6025: 6023: 6020: 6019: 6016: 6013: 6010: 6008: 6005: 6003: 6000: 5998: 5995: 5993: 5990: 5989: 5986: 5983: 5980: 5978: 5975: 5973: 5970: 5967: 5965: 5962: 5960: 5957: 5956: 5953: 5950: 5947: 5945: 5942: 5940: 5937: 5934: 5932: 5929: 5926: 5924: 5921: 5920: 5918: 5913: 5904: 5876: 5872: 5863: 5859: 5850: 5845: 5841: 5835: 5832: 5828: 5819: 5816: 5813: 5810: 5807: 5804: 5801: 5798: 5790: 5789: 5769: 5749: 5746: 5726: 5706: 5703: 5700: 5680: 5668: 5665: 5650: 5647: 5644: 5641: 5638: 5635: 5632: 5627: 5622: 5617: 5613: 5592: 5589: 5586: 5583: 5580: 5560: 5557: 5548: 5544: 5541: 5538: 5529: 5525: 5522: 5519: 5510: 5480: 5454: 5450: 5429: 5407: 5402: 5398: 5394: 5389: 5384: 5380: 5376: 5371: 5366: 5362: 5341: 5319: 5315: 5311: 5308: 5303: 5298: 5294: 5290: 5287: 5282: 5277: 5273: 5269: 5266: 5261: 5256: 5252: 5248: 5245: 5237: 5232: 5223: 5219: 5216: 5213: 5203: 5200: 5197: 5194: 5191: 5188: 5185: 5182: 5168:, then we have 5157: 5135:attention head 5121: 5115: 5111: 5107: 5102: 5098: 5094: 5089: 5085: 5080: 5051: 5048: 5029: 5025: 5016: 5012: 5003: 4976: 4972: 4963: 4959: 4950: 4920: 4916: 4907: 4902: 4893: 4889: 4880: 4875: 4866: 4862: 4853: 4826: 4815:head dimension 4796: 4766: 4736: 4703: 4699: 4691: 4687: 4678: 4673: 4669: 4663: 4654: 4651: 4648: 4645: 4642: 4639: 4636: 4633: 4625: 4624: 4602: 4598: 4575: 4571: 4548: 4544: 4523: 4503: 4483: 4463: 4436: 4414: 4411: 4407: 4386: 4364: 4360: 4356: 4351: 4347: 4326: 4306: 4284: 4280: 4276: 4271: 4267: 4246: 4226: 4204: 4200: 4177: 4173: 4144: 4140: 4115: 4111: 4088: 4084: 4059: 4039: 4017: 4014: 4010: 3980: 3976: 3967: 3944: 3940: 3936: 3931: 3927: 3923: 3918: 3914: 3888: 3884: 3874: 3870: 3867: 3845: 3841: 3831: 3827: 3824: 3802: 3798: 3788: 3784: 3781: 3759: 3755: 3744: 3741: 3737: 3733: 3728: 3724: 3701: 3697: 3669: 3666: 3662: 3632: 3605: 3579: 3575: 3552: 3548: 3525: 3521: 3485: 3484:Attention head 3482: 3477:Main article: 3474: 3471: 3452: 3448: 3445: 3436: 3396: 3374: 3371: 3368: 3364: 3360: 3355: 3352: 3349: 3345: 3341: 3336: 3333: 3330: 3326: 3322: 3317: 3314: 3311: 3307: 3303: 3300: 3297: 3294: 3291: 3288: 3285: 3281: 3278: 3275: 3240: 3213: 3196: 3193: 3152: 3149: 3138:language model 3120: 3116: 3095: 3092: 3089: 3086: 3082: 3078: 3075: 3070: 3066: 3062: 3059: 3056: 3053: 3049: 3046: 3043: 3040: 3033: 3029: 3023: 3019: 3014: 3010: 3007: 3002: 2998: 2994: 2991: 2988: 2985: 2982: 2977: 2973: 2967: 2963: 2938: 2934: 2931: 2928: 2908: 2905: 2902: 2899: 2896: 2893: 2890: 2887: 2884: 2881: 2878: 2874: 2871: 2868: 2865: 2861: 2858: 2855: 2852: 2849: 2846: 2843: 2840: 2815: 2811: 2807: 2803: 2799: 2796: 2774: 2771: 2766: 2763: 2758: 2755: 2752: 2749: 2746: 2743: 2740: 2737: 2732: 2725: 2721: 2716: 2712: 2709: 2705: 2701: 2696: 2693: 2690: 2687: 2684: 2663: 2659: 2655: 2650: 2645: 2641: 2637: 2634: 2611: 2608: 2605: 2585: 2565: 2540: 2536: 2532: 2528: 2524: 2521: 2518: 2511: 2507: 2503: 2498: 2495: 2475: 2472: 2469: 2466: 2462: 2458: 2455: 2452: 2449: 2446: 2443: 2440: 2437: 2434: 2431: 2428: 2424: 2421: 2418: 2415: 2412: 2409: 2406: 2403: 2400: 2397: 2394: 2391: 2388: 2385: 2382: 2377: 2374: 2371: 2368: 2364: 2360: 2357: 2354: 2351: 2346: 2343: 2339: 2335: 2332: 2329: 2326: 2302: 2282: 2279: 2276: 2273: 2269: 2265: 2262: 2259: 2254: 2249: 2244: 2240: 2236: 2233: 2195: 2192: 2189: 2186: 2183: 2180: 2177: 2157: 2154: 2141: 2132: 2128: 2119: 2115: 2095: 2092: 2089: 2086: 2083: 2080: 2076: 2073: 2070: 2067: 2064: 2061: 2058: 2054: 2051: 2048: 2045: 2041: 2038: 2035: 2032: 2029: 2026: 2023: 2002: 1999: 1981: 1969:embedding size 1949: 1946: 1943: 1940: 1937: 1934: 1931: 1928: 1925: 1922: 1919: 1916: 1913: 1910: 1907: 1904: 1901: 1898: 1895: 1892: 1888: 1885: 1882: 1879: 1876: 1855: 1852: 1849: 1846: 1843: 1840: 1837: 1834: 1831: 1828: 1825: 1822: 1819: 1816: 1813: 1793: 1773: 1752:Word embedding 1747: 1744: 1718: 1684: 1681: 1668: 1665: 1647: 1646: 1643: 1639: 1636: 1628: 1625: 1581: 1573: 1565: 1562: 1559: 1549: 1546: 1542: 1538: 1535: 1500: 1497: 1492: 1491: 1484: 1477: 1451:T5 transformer 1447: 1446: 1441: 1436: 1431: 1426: 1423: 1398: 1395: 1379: 1376: 1374: 1371: 1288: 1285: 1237:Main article: 1234: 1231: 1149:Main article: 1146: 1143: 1093: 1090: 1082: 1079: 1009:contextualized 1005:word embedding 966: 965: 963: 962: 955: 948: 940: 937: 936: 933: 932: 927: 926: 925: 915: 909: 906: 905: 902: 901: 898: 897: 892: 887: 882: 877: 872: 867: 861: 858: 857: 854: 853: 850: 849: 844: 839: 834: 832:Occam learning 829: 824: 819: 814: 808: 805: 804: 801: 800: 797: 796: 791: 789:Learning curve 786: 781: 775: 772: 771: 768: 767: 764: 763: 758: 753: 748: 742: 739: 738: 735: 734: 731: 730: 729: 728: 718: 713: 708: 702: 697: 696: 693: 692: 689: 688: 682: 677: 672: 667: 666: 665: 655: 650: 649: 648: 643: 638: 633: 623: 618: 613: 608: 607: 606: 596: 595: 594: 589: 584: 579: 569: 564: 559: 553: 548: 547: 544: 543: 540: 539: 534: 529: 521: 515: 510: 509: 506: 505: 502: 501: 500: 499: 494: 489: 478: 473: 472: 469: 468: 465: 464: 459: 454: 449: 444: 439: 434: 429: 424: 418: 413: 412: 409: 408: 405: 404: 399: 394: 388: 383: 378: 370: 365: 360: 354: 349: 348: 345: 344: 341: 340: 335: 330: 325: 320: 315: 310: 305: 297: 296: 295: 290: 285: 275: 273:Decision trees 270: 264: 250:classification 240: 239: 238: 235: 234: 231: 230: 225: 220: 215: 210: 205: 200: 195: 190: 185: 180: 175: 170: 165: 160: 155: 150: 145: 143:Classification 139: 136: 135: 132: 131: 128: 127: 122: 117: 112: 107: 102: 100:Batch learning 97: 92: 87: 82: 77: 72: 67: 61: 58: 57: 54: 53: 42: 41: 26: 9: 6: 4: 3: 2: 16482: 16471: 16468: 16466: 16463: 16462: 16460: 16443: 16440: 16438: 16435: 16434: 16427: 16423: 16420: 16418: 16415: 16414: 16411: 16407: 16406: 16403: 16397: 16394: 16392: 16389: 16387: 16384: 16382: 16379: 16377: 16374: 16372: 16369: 16367: 16364: 16362: 16359: 16357: 16354: 16352: 16349: 16347: 16344: 16342: 16339: 16337: 16334: 16332: 16329: 16327: 16324: 16323: 16321: 16319:Architectures 16317: 16311: 16308: 16306: 16303: 16301: 16298: 16296: 16293: 16291: 16288: 16286: 16283: 16281: 16278: 16276: 16273: 16271: 16268: 16267: 16265: 16263:Organizations 16261: 16255: 16252: 16250: 16247: 16245: 16242: 16240: 16237: 16235: 16232: 16230: 16227: 16225: 16222: 16220: 16217: 16215: 16212: 16210: 16207: 16205: 16202: 16200: 16199:Yoshua Bengio 16197: 16196: 16194: 16190: 16180: 16179:Robot control 16177: 16173: 16170: 16169: 16168: 16165: 16163: 16160: 16158: 16155: 16153: 16150: 16148: 16145: 16143: 16140: 16138: 16135: 16133: 16130: 16129: 16127: 16123: 16117: 16114: 16112: 16109: 16107: 16104: 16102: 16099: 16097: 16096:Chinchilla AI 16094: 16092: 16089: 16087: 16084: 16082: 16079: 16077: 16074: 16072: 16069: 16067: 16064: 16062: 16059: 16057: 16054: 16052: 16049: 16047: 16044: 16042: 16039: 16035: 16032: 16031: 16030: 16027: 16025: 16022: 16020: 16017: 16015: 16012: 16010: 16007: 16005: 16002: 16001: 15999: 15995: 15989: 15986: 15982: 15979: 15977: 15974: 15973: 15972: 15969: 15965: 15962: 15960: 15957: 15955: 15952: 15951: 15950: 15947: 15945: 15942: 15940: 15937: 15935: 15932: 15930: 15927: 15925: 15922: 15920: 15917: 15915: 15912: 15910: 15907: 15905: 15902: 15901: 15899: 15895: 15892: 15888: 15882: 15879: 15877: 15874: 15872: 15869: 15867: 15864: 15862: 15859: 15857: 15854: 15852: 15849: 15848: 15846: 15842: 15836: 15833: 15831: 15828: 15826: 15823: 15821: 15818: 15816: 15813: 15812: 15810: 15806: 15798: 15795: 15794: 15793: 15790: 15788: 15785: 15783: 15780: 15776: 15775:Deep learning 15773: 15772: 15771: 15768: 15764: 15761: 15760: 15759: 15756: 15755: 15753: 15749: 15743: 15740: 15738: 15735: 15731: 15728: 15727: 15726: 15723: 15721: 15718: 15714: 15711: 15709: 15706: 15704: 15701: 15700: 15699: 15696: 15694: 15691: 15689: 15686: 15684: 15681: 15679: 15676: 15674: 15671: 15669: 15666: 15664: 15663:Hallucination 15661: 15657: 15654: 15653: 15652: 15649: 15647: 15644: 15640: 15637: 15636: 15635: 15632: 15631: 15629: 15625: 15619: 15616: 15614: 15611: 15609: 15606: 15604: 15601: 15599: 15596: 15594: 15591: 15589: 15586: 15584: 15581: 15579: 15578: 15574: 15573: 15571: 15569: 15565: 15556: 15551: 15549: 15544: 15542: 15537: 15536: 15533: 15521: 15513: 15511: 15503: 15502: 15499: 15493: 15490: 15488: 15485: 15483: 15480: 15478: 15475: 15473: 15470: 15467: 15463: 15462: 15460: 15456: 15445: 15442: 15441: 15439: 15435: 15428: 15425: 15422: 15419: 15416: 15413: 15410: 15407: 15404: 15401: 15398: 15395: 15394: 15392: 15388: 15381: 15378: 15375: 15372: 15369: 15366: 15365: 15363: 15359: 15356: 15354:Generative AI 15352: 15342: 15339: 15337: 15334: 15332: 15329: 15328: 15326: 15322: 15315: 15312: 15309: 15306: 15303: 15300: 15299: 15297: 15293: 15290: 15286: 15275: 15274:AlphaGeometry 15272: 15269: 15266: 15263: 15260: 15257: 15254: 15253: 15251: 15247: 15236: 15235: 15231: 15228: 15227: 15223: 15222: 15220: 15216: 15209: 15206: 15203: 15200: 15197: 15194: 15193: 15191: 15187: 15180: 15177: 15174: 15171: 15168: 15165: 15162: 15159: 15156: 15153: 15152: 15150: 15146: 15143: 15139: 15136: 15132: 15126: 15123: 15121: 15118: 15116: 15113: 15112: 15109: 15105: 15098: 15093: 15091: 15086: 15084: 15079: 15078: 15075: 15065: 15060: 15055: 15050: 15045: 15040: 15037: 15033: 15030: 15026: 15025: 15011: 15007: 15002: 14997: 14992: 14987: 14983: 14979: 14975: 14968: 14960: 14955: 14951: 14944: 14936: 14931: 14927: 14920: 14911: 14906: 14898: 14896: 14887: 14874: 14866: 14859: 14857: 14842: 14838: 14832: 14823: 14818: 14810: 14801: 14796: 14789: 14780: 14775: 14768: 14760: 14756: 14752: 14745: 14731: 14727: 14721: 14713: 14709: 14704: 14699: 14695: 14691: 14687: 14680: 14671: 14666: 14658: 14649: 14644: 14637: 14628: 14623: 14616: 14601: 14597: 14593: 14587: 14579: 14574: 14570: 14563: 14554: 14549: 14545: 14541: 14537: 14530: 14515: 14511: 14507: 14501: 14492: 14487: 14479: 14470: 14465: 14458: 14456: 14447: 14442: 14438: 14431: 14423: 14416: 14408: 14403: 14399: 14392: 14390: 14381: 14375: 14361: 14357: 14350: 14336: 14335: 14328: 14320: 14314: 14310: 14306: 14301: 14296: 14292: 14288: 14281: 14272: 14267: 14259: 14250: 14245: 14237: 14223: 14219: 14213: 14198: 14197:Princeton NLP 14194: 14188: 14174: 14170: 14164: 14155: 14150: 14146: 14142: 14138: 14131: 14123: 14118: 14114: 14107: 14098: 14093: 14086: 14077: 14072: 14065: 14056: 14051: 14044: 14036: 14031: 14027: 14020: 14012: 14008: 14001: 13993: 13989: 13985: 13981: 13976: 13971: 13966: 13961: 13957: 13953: 13949: 13942: 13934: 13930: 13925: 13920: 13916: 13912: 13904: 13902: 13892: 13887: 13883: 13879: 13875: 13868: 13859: 13854: 13847: 13838: 13833: 13826: 13811: 13807: 13803: 13797: 13789: 13785: 13780: 13775: 13772:(140): 1–67. 13771: 13767: 13763: 13756: 13754: 13752: 13743: 13738: 13734: 13727: 13718: 13713: 13709: 13705: 13701: 13694: 13679: 13674: 13669: 13664: 13659: 13655: 13651: 13644: 13630: 13626: 13623:Team, Keras. 13619: 13604: 13600: 13596: 13589: 13587: 13585: 13569: 13565: 13561: 13555: 13546: 13541: 13534: 13532: 13530: 13521: 13516: 13512: 13505: 13503: 13501: 13499: 13484: 13480: 13474: 13472: 13457: 13453: 13447: 13445: 13435: 13430: 13422: 13414: 13410: 13405: 13400: 13396: 13392: 13388: 13381: 13372: 13367: 13359: 13357: 13348: 13343: 13339: 13332: 13324: 13323: 13315: 13307: 13302: 13298: 13291: 13282: 13277: 13269: 13267: 13257: 13252: 13244: 13242: 13227: 13226: 13219: 13204: 13200: 13196: 13190: 13176: 13172: 13166: 13152: 13148: 13142: 13127: 13123: 13117: 13108: 13103: 13096: 13094: 13079: 13075: 13071: 13067: 13060: 13052: 13047: 13043: 13036: 13021: 13017: 13013: 13009: 13005: 12998: 12996: 12986: 12981: 12974: 12966: 12962: 12958: 12954: 12947: 12932: 12928: 12924: 12920: 12916: 12909: 12900: 12895: 12888: 12879: 12874: 12867: 12858: 12853: 12849: 12845: 12841: 12834: 12827: 12823: 12819: 12815: 12810: 12805: 12800: 12795: 12791: 12787: 12780: 12771: 12766: 12759: 12750: 12745: 12738: 12736: 12734: 12725: 12721: 12716: 12711: 12707: 12703: 12696: 12694: 12692: 12683: 12679: 12672: 12664: 12660: 12653: 12645: 12641: 12637: 12630: 12621: 12614: 12608: 12600: 12596: 12592: 12588: 12584: 12580: 12573: 12569: 12563: 12561: 12552: 12548: 12544: 12540: 12536: 12532: 12528: 12524: 12520: 12513: 12505: 12499: 12492: 12491: 12483: 12475: 12471: 12467: 12463: 12459: 12455: 12451: 12444: 12429: 12425: 12421: 12415: 12413: 12411: 12402: 12398: 12394: 12390: 12386: 12378: 12376: 12366: 12361: 12354: 12352: 12343: 12339: 12335: 12331: 12327: 12323: 12319: 12312: 12303: 12298: 12291: 12283: 12279: 12271: 12263: 12258: 12254: 12247: 12245: 12235: 12230: 12223: 12214: 12209: 12202: 12200: 12184: 12180: 12176: 12170: 12168: 12159: 12155: 12151: 12147: 12143: 12139: 12135: 12131: 12127: 12123: 12119: 12115: 12109: 12101: 12097: 12090: 12086: 12082: 12076: 12074: 12072: 12070: 12068: 12066: 12064: 12062: 12060: 12058: 12056: 12051: 12035: 12028: 12023: 12019: 12008: 12005: 12002: 11999: 11996: 11993: 11990: 11987: 11984: 11981: 11978: 11975: 11972: 11969: 11968: 11959: 11955: 11951: 11947: 11944: 11941: 11937: 11934: 11932: 11929: 11927: 11924: 11923: 11922: 11917: 11914: 11911: 11908: 11905: 11902: 11900: 11897: 11895: 11892: 11889: 11886: 11884: 11881: 11880: 11879: 11877: 11873: 11869: 11865: 11861: 11857: 11853: 11849: 11845: 11841: 11837: 11827: 11824: 11820: 11815: 11813: 11809: 11807: 11803: 11799: 11794: 11792: 11788: 11786: 11782: 11776: 11771:Multimodality 11768: 11766: 11747: 11742: 11738: 11734: 11731: 11725: 11703: 11699: 11695: 11692: 11689: 11686: 11683: 11678: 11674: 11646: 11642: 11635: 11631: 11626: 11622: 11615: 11612: 11609: 11605: 11597: 11593: 11579: 11575: 11569: 11560: 11554: 11551: 11548: 11545: 11542: 11512: 11507: 11503: 11494: 11490: 11483: 11474: 11458: 11454: 11450: 11445: 11441: 11437: 11434: 11406: 11402: 11395: 11388: 11384: 11380: 11376: 11370: 11360: 11356: 11348: 11342: 11338: 11332: 11324: 11318: 11311: 11306: 11302: 11293: 11289: 11282: 11275: 11271: 11267: 11263: 11257: 11247: 11243: 11235: 11229: 11225: 11219: 11211: 11205: 11199: 11196: 11192: 11184: 11180: 11166: 11162: 11156: 11147: 11141: 11138: 11135: 11132: 11129: 11095: 11089: 11082: 11078: 11074: 11070: 11064: 11056: 11049: 11045: 11039: 11033: 11026: 11022: 11018: 11014: 11008: 11000: 10993: 10986: 10974: 10968: 10961: 10957: 10953: 10949: 10943: 10935: 10928: 10924: 10918: 10912: 10905: 10901: 10897: 10893: 10887: 10879: 10872: 10857: 10850: 10846: 10841: 10834: 10831: 10828: 10821: 10793: 10789: 10785: 10778: 10770: 10767: 10764: 10755: 10751: 10747: 10735: 10729: 10726: 10720: 10714: 10680: 10675: 10671: 10667: 10664: 10658: 10636: 10632: 10628: 10625: 10622: 10619: 10616: 10611: 10607: 10584: 10573: 10570: 10565: 10561: 10554: 10551: 10548: 10542: 10539: 10534: 10530: 10523: 10520: 10517: 10514: 10508: 10505: 10500: 10496: 10489: 10486: 10483: 10477: 10474: 10469: 10465: 10458: 10455: 10446: 10442: 10437: 10431: 10425: 10417: 10407: 10403: 10386: 10380: 10372: 10351: 10347: 10340: 10331: 10329: 10310: 10307: 10304: 10301: 10295: 10270: 10266: 10259: 10250: 10236: 10211: 10207: 10200: 10186: 10184: 10174: 10170: 10154: 10144: 10118: 10108: 10082: 10078: 10055: 10045: 10019: 10009: 9983: 9973: 9966: 9961: 9951: 9944: 9939: 9929: 9922: 9917: 9907: 9893: 9879: 9857: 9853: 9830: 9826: 9822: 9819: 9816: 9813: 9810: 9805: 9801: 9797: 9792: 9788: 9777: 9775: 9764: 9760: 9758: 9757:memory paging 9754: 9750: 9740: 9737: 9722: 9718: 9713: 9704: 9700: 9696: 9693: 9688: 9684: 9680: 9677: 9672: 9667: 9663: 9659: 9647: 9632: 9625: 9622: 9612: 9606: 9603: 9600: 9597: 9594: 9578: 9562: 9558: 9554: 9549: 9545: 9522: 9518: 9513: 9504: 9499: 9495: 9491: 9488: 9483: 9478: 9474: 9470: 9467: 9462: 9457: 9453: 9449: 9437: 9422: 9415: 9412: 9402: 9396: 9393: 9390: 9387: 9384: 9368: 9360: 9358: 9352: 9348: 9346: 9342: 9338: 9332: 9330: 9326: 9316: 9314: 9310: 9306: 9302: 9298: 9288: 9273: 9270: 9266: 9262: 9259: 9255: 9252: 9249: 9246: 9223: 9220: 9216: 9212: 9209: 9204: 9200: 9195: 9192: 9189: 9185: 9176: 9160: 9136: 9132: 9128: 9125: 9117: 9113: 9099: 9095: 9088: 9079: 9073: 9070: 9067: 9064: 9061: 9035: 9031: 9014: 8994: 8974: 8971: 8968: 8965: 8960: 8957: 8954: 8950: 8927: 8921: 8916: 8911: 8906: 8901: 8894: 8889: 8884: 8881: 8876: 8873: 8868: 8865: 8858: 8853: 8848: 8843: 8840: 8835: 8832: 8825: 8820: 8815: 8810: 8805: 8802: 8795: 8790: 8785: 8780: 8775: 8769: 8764: 8761: 8753: 8737: 8717: 8693: 8689: 8685: 8682: 8679: 8671: 8667: 8653: 8649: 8642: 8633: 8627: 8624: 8621: 8618: 8615: 8595: 8591: 8581: 8567: 8540: 8537: 8534: 8531: 8528: 8511: 8499: 8496: 8493: 8490: 8487: 8472: 8462: 8459: 8456: 8439: 8427: 8424: 8421: 8400: 8381: 8374: 8370: 8367: 8364: 8361: 8358: 8350: 8343: 8322: 8319: 8297: 8293: 8287: 8284: 8281: 8277: 8273: 8263: 8260: 8255: 8251: 8213: 8205: 8201: 8197: 8194: 8186: 8178: 8174: 8170: 8165: 8161: 8138: 8132: 8129: 8126: 8123: 8115: 8107: 8103: 8099: 8096: 8093: 8090: 8087: 8079: 8071: 8067: 8059: 8056: 8053: 8050: 8042: 8034: 8030: 8026: 8023: 8020: 8017: 8014: 8006: 7998: 7994: 7987: 7982: 7977: 7966: 7958: 7954: 7941: 7933: 7929: 7922: 7915: 7909: 7906: 7903: 7900: 7895: 7892: 7889: 7886: 7879: 7876: 7873: 7870: 7867: 7862: 7859: 7856: 7853: 7847: 7842: 7832: 7829: 7821: 7813: 7809: 7805: 7797: 7789: 7785: 7752: 7729: 7726: 7723: 7720: 7709: 7701: 7697: 7693: 7685: 7677: 7673: 7666: 7655: 7647: 7643: 7639: 7631: 7623: 7619: 7612: 7601: 7593: 7589: 7585: 7577: 7569: 7565: 7544: 7540: 7532: 7530: 7526: 7516: 7514: 7510: 7507: 7492: 7488: 7471: 7459: 7441: 7428: 7423: 7414: 7404: 7402: 7398: 7394: 7390: 7386: 7380: 7378: 7374: 7370: 7366: 7360: 7358: 7354: 7349: 7339: 7335: 7331: 7327: 7323: 7319: 7315: 7311: 7307: 7303: 7299: 7295: 7291: 7287: 7283: 7279: 7275: 7271: 7267: 7263: 7259: 7255: 7251: 7247: 7243: 7240: 7236: 7232: 7228: 7225: 7221: 7217: 7213: 7209: 7205: 7201: 7197: 7193: 7189: 7185: 7181: 7177: 7173: 7169: 7165: 7161: 7157: 7153: 7150: 7146: 7142: 7138: 7135: 7131: 7127: 7123: 7115: 7094: 7030: 7027: 7018: 7001: 6946: 6914: 6911: 6871: 6867: 6862: 6860: 6856: 6848: 6844: 6839: 6831: 6823: 6815: 6811: 6803: 6789: 6785: 6769: 6765: 6732: 6728: 6724: 6719: 6715: 6711: 6707: 6704: 6684: 6682: 6674: 6656: 6653: 6650: 6647: 6644: 6633: 6631: 6625: 6622: 6608: 6604: 6602: 6596: 6594: 6588: 6581: 6572: 6569: 6565: 6523: 6520: 6517: 6514: 6511: 6492: 6486: 6447: 6428: 6422: 6410: 6402: 6399: 6396: 6393: 6390: 6362: 6354: 6351: 6348: 6345: 6342: 6320: 6315: 6313: 6305: 6288: 6282: 6273: 6269: 6259: 6255: 6248: 6243: 6241: 6236: 6224: 6221: 6216: 6212: 6208: 6203: 6199: 6177: 6170: 6161: 6159: 6143: 6121: 6118: 6114: 6104: 6100: 6092: 6074: 6068: 6063: 6058: 6053: 6048: 6041: 6036: 6031: 6026: 6021: 6011: 6006: 6001: 5996: 5991: 5981: 5976: 5968: 5963: 5958: 5948: 5943: 5935: 5927: 5922: 5916: 5911: 5902: 5892: 5874: 5870: 5861: 5857: 5843: 5839: 5833: 5830: 5826: 5817: 5811: 5808: 5805: 5802: 5799: 5767: 5744: 5724: 5704: 5701: 5698: 5678: 5664: 5648: 5645: 5639: 5636: 5633: 5620: 5615: 5611: 5590: 5587: 5584: 5581: 5578: 5558: 5555: 5546: 5542: 5539: 5536: 5527: 5523: 5520: 5517: 5508: 5498: 5478: 5468: 5452: 5448: 5427: 5405: 5400: 5396: 5392: 5387: 5382: 5378: 5374: 5369: 5364: 5360: 5339: 5317: 5313: 5301: 5296: 5292: 5288: 5285: 5280: 5275: 5271: 5267: 5264: 5259: 5254: 5250: 5246: 5221: 5214: 5211: 5201: 5195: 5192: 5189: 5186: 5183: 5155: 5146: 5144: 5140: 5136: 5119: 5113: 5109: 5105: 5100: 5096: 5092: 5087: 5083: 5078: 5064: 5056: 5047: 5027: 5023: 5014: 5010: 5001: 4974: 4970: 4961: 4957: 4948: 4938: 4918: 4914: 4905: 4900: 4891: 4887: 4878: 4873: 4864: 4860: 4851: 4824: 4816: 4794: 4786: 4764: 4756: 4734: 4726: 4721: 4718: 4701: 4697: 4689: 4685: 4671: 4667: 4661: 4652: 4646: 4643: 4640: 4637: 4634: 4600: 4596: 4573: 4569: 4546: 4542: 4521: 4501: 4481: 4461: 4453: 4448: 4434: 4412: 4409: 4405: 4384: 4362: 4358: 4354: 4349: 4345: 4324: 4304: 4282: 4278: 4274: 4269: 4265: 4244: 4224: 4202: 4198: 4175: 4171: 4162: 4142: 4138: 4113: 4109: 4086: 4082: 4073: 4057: 4037: 4015: 4012: 4008: 3998: 3978: 3974: 3965: 3942: 3938: 3934: 3929: 3925: 3921: 3916: 3912: 3902: 3886: 3882: 3872: 3868: 3865: 3843: 3839: 3829: 3825: 3822: 3800: 3796: 3786: 3782: 3779: 3757: 3753: 3742: 3739: 3735: 3731: 3726: 3722: 3699: 3695: 3667: 3664: 3660: 3650: 3630: 3603: 3593: 3577: 3573: 3550: 3546: 3523: 3519: 3510: 3507: 3498: 3490: 3480: 3470: 3450: 3446: 3443: 3434: 3425: 3421: 3417: 3412: 3410: 3394: 3369: 3362: 3358: 3350: 3343: 3331: 3324: 3320: 3312: 3305: 3301: 3295: 3292: 3286: 3264: 3238: 3211: 3201: 3192: 3190: 3185: 3181: 3178: 3174: 3171:Like earlier 3165: 3157: 3148: 3146: 3141: 3139: 3136: 3118: 3114: 3090: 3084: 3080: 3068: 3064: 3054: 3031: 3027: 3021: 3017: 3012: 3008: 3000: 2996: 2989: 2986: 2980: 2975: 2971: 2965: 2961: 2951: 2932: 2929: 2903: 2897: 2888: 2879: 2859: 2853: 2847: 2844: 2838: 2829: 2813: 2809: 2805: 2801: 2797: 2794: 2772: 2769: 2764: 2761: 2756: 2753: 2750: 2747: 2744: 2741: 2738: 2735: 2730: 2723: 2719: 2714: 2710: 2707: 2703: 2699: 2694: 2688: 2682: 2661: 2657: 2653: 2635: 2632: 2623: 2609: 2606: 2603: 2583: 2563: 2554: 2538: 2534: 2530: 2526: 2522: 2519: 2516: 2509: 2505: 2501: 2496: 2493: 2470: 2467: 2464: 2460: 2456: 2453: 2450: 2447: 2444: 2441: 2438: 2432: 2429: 2416: 2410: 2407: 2404: 2398: 2392: 2389: 2383: 2375: 2372: 2369: 2366: 2358: 2352: 2349: 2344: 2341: 2333: 2327: 2316: 2300: 2280: 2277: 2274: 2271: 2263: 2260: 2257: 2252: 2234: 2231: 2222: 2220: 2219:man bites dog 2216: 2212: 2193: 2190: 2187: 2184: 2181: 2178: 2175: 2167: 2162: 2153: 2130: 2126: 2117: 2090: 2087: 2084: 2081: 2052: 2046: 2012: 2007: 1998: 1979: 1970: 1966: 1961: 1947: 1941: 1938: 1935: 1932: 1929: 1926: 1923: 1920: 1917: 1914: 1911: 1908: 1905: 1899: 1893: 1850: 1847: 1844: 1841: 1838: 1835: 1832: 1829: 1826: 1823: 1820: 1817: 1814: 1791: 1771: 1763: 1759: 1753: 1743: 1741: 1736: 1716: 1708: 1703: 1701: 1694: 1690: 1680: 1666: 1663: 1654: 1652: 1644: 1640: 1637: 1634: 1633: 1632: 1624: 1622: 1618: 1613: 1611: 1605: 1603: 1597: 1595: 1571: 1560: 1557: 1552:masked tokens 1547: 1544: 1540: 1536: 1533: 1520: 1516: 1515:loss function 1511: 1506: 1496: 1490: 1485: 1482: 1478: 1476: 1474: 1470: 1464: 1460: 1459: 1458: 1456: 1452: 1445: 1442: 1440: 1437: 1435: 1432: 1430: 1427: 1424: 1422: 1419: 1418: 1417: 1415: 1411: 1408: 1404: 1394: 1392: 1389: 1384: 1370: 1368: 1364: 1360: 1356: 1352: 1348: 1343: 1341: 1337: 1333: 1329: 1324: 1322: 1318: 1314: 1310: 1306: 1301: 1299: 1295: 1284: 1282: 1278: 1274: 1269: 1267: 1263: 1259: 1255: 1251: 1247: 1240: 1230: 1228: 1225: 1221: 1220: 1215: 1211: 1207: 1202: 1199: 1197: 1193: 1188: 1186: 1181: 1176: 1174: 1170: 1166: 1162: 1157: 1152: 1142: 1139: 1134: 1132: 1131: 1126: 1122: 1118: 1114: 1109: 1107: 1103: 1102:Elman network 1099: 1088: 1078: 1076: 1072: 1068: 1064: 1060: 1056: 1052: 1048: 1044: 1039: 1037: 1033: 1030: 1026: 1022: 1018: 1013: 1010: 1006: 1002: 998: 994: 990: 986: 985:deep learning 982: 972: 961: 956: 954: 949: 947: 942: 941: 939: 938: 931: 928: 924: 921: 920: 919: 916: 914: 911: 910: 904: 903: 896: 893: 891: 888: 886: 883: 881: 878: 876: 873: 871: 868: 866: 863: 862: 856: 855: 848: 845: 843: 840: 838: 835: 833: 830: 828: 825: 823: 820: 818: 815: 813: 810: 809: 803: 802: 795: 792: 790: 787: 785: 782: 780: 777: 776: 770: 769: 762: 759: 757: 754: 752: 751:Crowdsourcing 749: 747: 744: 743: 737: 736: 727: 724: 723: 722: 719: 717: 714: 712: 709: 707: 704: 703: 700: 695: 694: 686: 683: 681: 680:Memtransistor 678: 676: 673: 671: 668: 664: 661: 660: 659: 656: 654: 651: 647: 644: 642: 639: 637: 634: 632: 629: 628: 627: 624: 622: 619: 617: 614: 612: 609: 605: 602: 601: 600: 597: 593: 590: 588: 585: 583: 580: 578: 575: 574: 573: 570: 568: 565: 563: 562:Deep learning 560: 558: 555: 554: 551: 546: 545: 538: 535: 533: 530: 528: 526: 522: 520: 517: 516: 513: 508: 507: 498: 497:Hidden Markov 495: 493: 490: 488: 485: 484: 483: 480: 479: 476: 471: 470: 463: 460: 458: 455: 453: 450: 448: 445: 443: 440: 438: 435: 433: 430: 428: 425: 423: 420: 419: 416: 411: 410: 403: 400: 398: 395: 393: 389: 387: 384: 382: 379: 377: 375: 371: 369: 366: 364: 361: 359: 356: 355: 352: 347: 346: 339: 336: 334: 331: 329: 326: 324: 321: 319: 316: 314: 311: 309: 306: 304: 302: 298: 294: 293:Random forest 291: 289: 286: 284: 281: 280: 279: 276: 274: 271: 269: 266: 265: 258: 257: 252: 251: 243: 237: 236: 229: 226: 224: 221: 219: 216: 214: 211: 209: 206: 204: 201: 199: 196: 194: 191: 189: 186: 184: 181: 179: 178:Data cleaning 176: 174: 171: 169: 166: 164: 161: 159: 156: 154: 151: 149: 146: 144: 141: 140: 134: 133: 126: 123: 121: 118: 116: 113: 111: 108: 106: 103: 101: 98: 96: 93: 91: 90:Meta-learning 88: 86: 83: 81: 78: 76: 73: 71: 68: 66: 63: 62: 56: 55: 52: 47: 44: 43: 39: 38: 33: 19: 16285:Hugging Face 16249:David Silver 15897:Audio–visual 15751:Applications 15730:Augmentation 15575: 15487:Google Pixel 15307: 15232: 15224: 15189:Competitions 15167:AlphaGo Zero 15120:Google Brain 14981: 14977: 14967: 14949: 14943: 14925: 14919: 14873:cite journal 14844:. 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Many 11833: 11830:Applications 11816: 11810: 11795: 11789: 11777: 11774: 11475: 10413: 10404: 10332: 10251: 10192: 10182: 10180: 10171: 9894: 9892:-th output. 9778: 9770: 9761: 9752: 9748: 9746: 9738: 9579: 9369: 9366: 9353: 9349: 9333: 9322: 9313:Hugging Face 9309:Transformers 9308: 9294: 9041: 9032: 8751: 8593: 8589: 8587: 8401: 7550: 7541: 7538: 7529:Llama series 7522: 7513:Llama series 7503: 7489: 7405: 7381: 7361: 7350: 7347: 7337: 7333: 7329: 7325: 7321: 7317: 7313: 7309: 7305: 7301: 7297: 7293: 7289: 7285: 7281: 7277: 7273: 7269: 7265: 7261: 7257: 7253: 7249: 7245: 7241: 7238: 7234: 7230: 7226: 7223: 7219: 7215: 7211: 7207: 7203: 7199: 7195: 7191: 7187: 7183: 7179: 7175: 7171: 7167: 7163: 7159: 7155: 7151: 7148: 7144: 7140: 7136: 7133: 7129: 7125: 7121: 7019: 6869: 6865: 6863: 6852: 6808: 6786: 6668:DecoderLayer 6609: 6605: 6597: 6592: 6589: 6586: 6570: 6566: 6480:EncoderLayer 6448: 6299:EncoderLayer 6178: 6175: 6156:is a random 5893: 5670: 5499: 5469: 5147: 5134: 5069: 4939: 4814: 4784: 4754: 4724: 4722: 4719: 4449: 3999: 3903: 3651: 3594: 3503: 3423: 3419: 3415: 3413: 3411:activation. 3260: 3186: 3182: 3176: 3170: 3142: 2952: 2830: 2624: 2555: 2223: 2215:bag of words 2210: 2208: 2008: 2004: 2001:Un-embedding 1968: 1964: 1962: 1758:lookup table 1755: 1737: 1706: 1704: 1696: 1689:Tokenization 1683:Tokenization 1655: 1648: 1630: 1627:Architecture 1614: 1606: 1598: 1512: 1508: 1493: 1488: 1472: 1469:for inviting 1468: 1466: 1462: 1448: 1444:paraphrasing 1400: 1390: 1385: 1381: 1365:(2024), and 1344: 1325: 1313:bag of words 1302: 1290: 1270: 1265: 1261: 1245: 1242: 1226: 1223: 1218: 1203: 1200: 1195: 1191: 1189: 1184: 1179: 1177: 1168: 1164: 1158: 1154: 1135: 1128: 1124: 1120: 1110: 1095: 1092:Predecessors 1040: 1036:Common Crawl 1014: 980: 978: 975:Transformer. 837:PAC learning 524: 373: 368:Hierarchical 300: 254: 248: 16433:Categories 16381:Autoencoder 16336:Transformer 16204:Alex Graves 16152:OpenAI Five 16056:IBM Watsonx 15678:Convolution 15656:Overfitting 15482:Google Labs 15308:Transformer 14264:Pathways". 11958:grandmaster 11888:time series 11806:spectrogram 10097:to replace 9177:, that is, 8752:linear bias 8590:replacement 7344:Terminology 5070:One set of 4072:dot product 4030:from token 3506:dot-product 3422:(BERT), or 3420:filter size 1965:hidden size 1467:"Thank you 1410:fine-tuning 1287:AI boom era 1138:fast weight 1073:(GPTs) and 981:transformer 721:Multi-agent 658:Transformer 557:Autoencoder 313:Naive Bayes 51:data mining 16459:Categories 16422:Technology 16275:EleutherAI 16234:Fei-Fei Li 16229:Yann LeCun 16142:Q-learning 16125:Decisional 16051:IBM Watson 15959:Midjourney 15851:TensorFlow 15698:Activation 15651:Regression 15646:Clustering 15409:Chinchilla 15336:TensorFlow 15234:The MANIAC 15064:2405.00208 15049:2207.09238 14984:(1): 157. 14959:2206.10789 14935:2102.12092 14910:2301.00704 14846:2024-08-09 14822:2107.14795 14800:2103.03206 14779:2212.04356 14735:2024-08-11 14670:2006.03555 14648:2103.02143 14627:2105.14103 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12434:2019-08-25 12302:2212.04356 12262:2106.01345 12234:1508.04025 12189:2019-08-25 12046:References 11946:evaluating 11890:prediction 11856:AlbertAGPT 11812:Perceivers 9749:KV caching 9301:TensorFlow 9297:frameworks 8594:additional 7373:GPT series 7118:Pseudocode 6841:Schematic 4869:seq, value 4785:value size 4725:query size 3970:emb, query 3635:emb, query 3608:seq, query 2166:sinusoidal 2135:vocabulary 1721:vocabulary 1503:See also: 1407:supervised 1351:multimodal 1328:GPT series 1256:result in 1192:fixed-size 1085:See also: 1069:, such as 706:Q-learning 604:Restricted 402:Mean shift 351:Clustering 328:Perceptron 256:regression 158:Clustering 153:Regression 16305:MIT CSAIL 16270:Anthropic 16239:Andrew Ng 16137:AlphaZero 15981:VideoPoet 15944:AlphaFold 15881:MindSpore 15835:SpiNNaker 15830:Memristor 15737:Diffusion 15713:Rectifier 15693:Batchnorm 15673:Attention 15668:Adversary 15427:VideoPoet 15368:Assistant 15262:AlphaStar 15256:AlphaFold 15202:Lee Sedol 15173:AlphaZero 15104:Google AI 14730:lmsys.org 14712:2374-3468 14360:vLLM Blog 13992:231986066 13984:0891-2017 13788:1533-7928 13413:1532-4435 13078:0028-792X 13016:1059-1028 12927:0362-4331 12857:1409.3215 12826:220252321 12770:1412.3555 12749:1409.3215 12715:1406.1078 12682:ICML 2021 12663:ICML 2020 12543:0003-6935 12474:0364-0213 12401:208117506 12342:2377-3766 12213:1409.0473 12142:0899-7667 11977:Perceiver 11940:AlphaFold 11938:(such as 11739:σ 11613:≈ 11536:Attention 11484:φ 11435:σ 11396:φ 11385:σ 11367:‖ 11353:‖ 11339:∑ 11319:φ 11283:φ 11272:σ 11254:‖ 11240:‖ 11226:∑ 11206:φ 11200:≈ 11123:Attention 11102:⟩ 11090:φ 11079:σ 11061:‖ 11054:‖ 11034:φ 11023:σ 11005:‖ 10998:‖ 10990:⟨ 10987:≈ 10981:⟩ 10969:φ 10958:σ 10940:‖ 10933:‖ 10913:φ 10902:σ 10884:‖ 10877:‖ 10869:⟨ 10847:σ 10838:⟩ 10826:⟨ 10790:σ 10775:‖ 10768:− 10762:‖ 10756:− 10742:⟩ 10730:φ 10715:φ 10712:⟨ 10672:σ 10577:⟩ 10558:⟨ 10555:⁡ 10546:⟩ 10527:⟨ 10524:⁡ 10518:⋯ 10512:⟩ 10493:⟨ 10490:⁡ 10481:⟩ 10462:⟨ 10459:⁡ 10426:φ 10326:by using 10308:⁡ 10148:~ 10112:~ 10049:~ 10013:~ 9977:~ 9955:~ 9933:~ 9911:~ 9653:Attention 9626:∈ 9443:Attention 9416:∈ 9267:− 9250:− 9239:whenever 9055:Attention 9018:∞ 9015:− 8972:− 8922:⋱ 8917:⋮ 8912:⋮ 8907:⋮ 8902:⋮ 8895:⋯ 8882:− 8874:− 8866:− 8859:⋯ 8841:− 8833:− 8826:⋯ 8803:− 8796:⋯ 8609:Attention 8375:θ 8344:θ 8288:θ 8133:θ 8127:⁡ 8097:θ 8091:⁡ 8060:θ 8054:⁡ 8027:− 8024:θ 8018:⁡ 7910:θ 7904:⁡ 7896:θ 7890:⁡ 7880:θ 7874:⁡ 7868:− 7863:θ 7857:⁡ 7753:θ 7445:∞ 7442:− 7401:T5 series 6797:Sublayers 6423:⋮ 6283:⋮ 6225:… 6119:− 6064:… 6042:⋮ 6037:⋱ 6032:⋮ 6027:⋮ 6022:⋮ 6015:∞ 6012:− 6007:… 5985:∞ 5982:− 5977:… 5972:∞ 5969:− 5952:∞ 5949:− 5944:… 5939:∞ 5936:− 5931:∞ 5928:− 5748:∞ 5745:− 5646:× 5637:× 5621:∈ 5582:× 5240:Attention 5215:∈ 5011:≠ 4865:ℓ 4852:ℓ 4628:Attention 4355:⋅ 4275:⋅ 4050:to token 3604:ℓ 3509:attention 3395:ϕ 3296:ϕ 3061:Δ 3018:∑ 2993:Δ 2962:∑ 2933:∈ 2927:Δ 2886:Δ 2851:Δ 2770:− 2754:… 2644:→ 2494:θ 2468:− 2451:… 2433:∈ 2427:∀ 2417:θ 2411:⁡ 2399:θ 2393:⁡ 2264:∈ 2243:→ 1942:… 1851:… 1746:Embedding 1700:tokenizer 1642:variants. 1561:⁡ 1548:∈ 1541:∑ 1537:− 1204:In 2016, 1196:RNNsearch 1029:Knowledge 993:attention 865:ECML PKDD 847:VC theory 794:ROC curve 726:Self-play 646:DeepDream 487:Bayes net 278:Ensembles 59:Paradigms 16413:Portals 16172:Auto-GPT 16004:Word2vec 15808:Hardware 15725:Datasets 15627:Concepts 15510:Category 15458:See also 15361:Chatbots 15268:AlphaDev 15148:Versions 15032:Archived 15010:36855134 14600:Archived 14514:Archived 14374:cite web 14222:TOGETHER 13810:Archived 13678:Archived 13629:keras.io 13603:Archived 13568:Archived 13203:Archived 13020:Archived 12818:33733157 12599:16683347 12570:(1992). 12551:20523475 12428:Archived 12183:Archived 11965:See also 11842:such as 11819:DALL-E 1 9755:applies 9577:, thus: 9299:such as 9274:′ 9263:′ 9224:′ 9213:′ 7419:prefixLM 7326:for each 7314:for each 7302:for each 7290:for each 7278:for each 7266:for each 7254:for each 7212:for each 7200:for each 7188:for each 7176:for each 7164:for each 6868:and the 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870:NeurIPS 687:(ECRAM) 641:AlexNet 283:Bagging 16310:Huawei 16290:OpenAI 16192:People 16162:MuZero 16024:Gemini 16019:Claude 15954:DALL-E 15866:Theano 15446:(2024) 15429:(2024) 15423:(2023) 15421:Gemini 15417:(2022) 15411:(2022) 15405:(2021) 15399:(2018) 15382:(2023) 15380:Gemini 15376:(2022) 15370:(2016) 15316:(2022) 15310:(2017) 15304:(2016) 15276:(2024) 15270:(2023) 15264:(2019) 15258:(2018) 15237:(2023) 15229:(2017) 15210:(2017) 15208:Ke Jie 15204:(2016) 15198:(2015) 15181:(2019) 15179:MuZero 15175:(2017) 15169:(2017) 15163:(2016) 15161:Master 15157:(2015) 15115:Google 15008: 14998: 14710: 14315: 13990: 13982: 13786: 13564:Indico 13411: 13076: 13014: 12925: 12824: 12816: 12806: 12792:: 40, 12597: 12549: 12541: 12500: 12472: 12399: 12340: 12179:OpenAI 12156: 12148: 12140: 11960:level. 11860:Claude 11427:where 10599:where 10229:where 10133:, and 9618:Concat 9408:Concat 9339:GPUs ( 9153:where 8710:Here, 7464:causal 7338:return 7126:input: 6965:where 6870:pre-LN 6849:style. 6757:where 6449:where 6109:causal 5907:causal 5571:Since 5440:, and 5207:Concat 4588:, and 4337:(i.e. 4257:(i.e. 3387:where 2919:where 2787:where 2556:Here, 2486:where 2013:layer: 1475:week". 1391:before 1359:DALL-E 1032:corpus 1001:tokens 989:Google 663:Vision 519:RANSAC 397:OPTICS 392:DBSCAN 376:-means 183:AutoML 16376:Mamba 16147:SARSA 16111:LLaMA 16106:BLOOM 16091:GPT-J 16081:GPT-4 16076:GPT-3 16071:GPT-2 16066:GPT-1 16029:LaMDA 15861:Keras 15437:Other 15403:LaMDA 15324:Other 15249:Other 15059:arXiv 15044:arXiv 14954:arXiv 14930:arXiv 14905:arXiv 14817:arXiv 14795:arXiv 14774:arXiv 14665:arXiv 14643:arXiv 14622:arXiv 14573:arXiv 14548:arXiv 14486:arXiv 14464:arXiv 14441:arXiv 14402:arXiv 14295:arXiv 14266:arXiv 14244:arXiv 14149:arXiv 14117:arXiv 14092:arXiv 14071:arXiv 14050:arXiv 14030:arXiv 13988:S2CID 13960:arXiv 13919:arXiv 13886:arXiv 13853:arXiv 13832:arXiv 13774:arXiv 13737:arXiv 13712:arXiv 13658:arXiv 13540:arXiv 13515:arXiv 13429:arXiv 13399:arXiv 13366:arXiv 13342:arXiv 13301:arXiv 13276:arXiv 13251:arXiv 13102:arXiv 13046:arXiv 13008:Wired 12980:arXiv 12894:arXiv 12873:arXiv 12852:arXiv 12822:S2CID 12765:arXiv 12744:arXiv 12710:arXiv 12595:S2CID 12575:(PDF) 12494:(PDF) 12397:S2CID 12360:arXiv 12297:arXiv 12257:arXiv 12229:arXiv 12208:arXiv 12154:S2CID 12092:(PDF) 12014:Notes 11906:(NER) 11868:XLNet 11852:GPT-4 11848:GPT-3 11844:GPT-2 10813:, or 9637:heads 9427:heads 9329:cache 9173:is a 8584:ALiBi 6091:XLNet 5226:heads 5032:value 5006:query 4979:value 4953:query 4910:value 4883:query 4799:value 4739:query 3983:query 3877:value 3791:query 3747:query 3672:query 2610:10000 2211:where 2182:10000 1499:Tasks 1185:fixed 1063:chess 983:is a 885:IJCAI 711:SARSA 670:Mamba 636:LeNet 631:U-Net 457:t-SNE 381:Fuzzy 358:BIRCH 16300:Mila 16101:PaLM 16034:Bard 16014:BERT 15997:Text 15976:Sora 15444:Vids 15415:PaLM 15397:BERT 15314:Gato 15006:PMID 14886:help 14708:ISSN 14380:link 14313:ISBN 13980:ISSN 13784:ISSN 13409:ISSN 13074:ISSN 13012:ISSN 12923:ISSN 12814:PMID 12547:PMID 12539:ISSN 12498:ISBN 12470:ISSN 12338:ISSN 12146:PMID 12138:ISSN 11874:and 11864:BERT 10034:and 9357:H100 9345:BF16 9341:FP16 9337:A100 9303:and 8518:RoPE 8477:RoPE 8446:RoPE 8411:RoPE 8240:RoPE 7774:RoPE 7547:RoPE 7506:ReLU 7395:and 7375:and 7367:and 7357:BERT 7242:each 7227:each 7152:each 7137:each 6857:and 5551:head 5532:head 5483:head 4923:head 4829:head 4783:and 4494:and 4190:and 4101:and 3409:ReLU 2278:> 1691:and 1608:The 1530:Loss 1473:last 1449:The 1367:Sora 1321:BERT 1315:and 1305:ELMo 1279:for 1254:SOTA 1180:last 1113:LSTM 1075:BERT 1034:and 895:JMLR 880:ICLR 875:ICML 761:RLHF 577:LSTM 363:CURE 49:and 16041:NMT 15924:OCR 15919:HWR 15871:JAX 15825:VPU 15820:TPU 15815:IPU 15639:SGD 14996:PMC 14986:doi 14698:doi 14305:doi 13970:doi 13929:doi 13668:doi 12961:doi 12804:PMC 12794:doi 12720:doi 12587:doi 12531:doi 12462:doi 12389:doi 12330:doi 12130:doi 11954:Elo 11785:ViT 10552:sin 10521:cos 10487:sin 10456:cos 10288:to 9831:512 8124:sin 8088:cos 8051:sin 8015:cos 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8535:n 8532:, 8529:y 8524:( 8512:T 8506:) 8500:k 8497:+ 8494:m 8491:, 8488:x 8483:( 8473:= 8468:) 8463:n 8460:, 8457:y 8452:( 8440:T 8434:) 8428:m 8425:, 8422:x 8417:( 8385:) 8382:n 8379:( 8371:, 8368:. 8365:. 8362:. 8359:, 8354:) 8351:1 8348:( 8323:n 8320:2 8298:m 8294:z 8285:m 8282:i 8278:e 8274:= 8269:) 8264:m 8261:, 8256:m 8252:z 8246:( 8217:) 8214:2 8211:( 8206:m 8202:x 8198:i 8195:+ 8190:) 8187:1 8184:( 8179:m 8175:x 8166:m 8162:z 8139:) 8130:m 8119:) 8116:1 8113:( 8108:m 8104:x 8100:+ 8094:m 8083:) 8080:2 8077:( 8072:m 8068:x 8057:m 8046:) 8043:2 8040:( 8035:m 8031:x 8021:m 8010:) 8007:1 8004:( 7999:m 7995:x 7988:( 7983:= 7978:) 7970:) 7967:2 7964:( 7959:m 7955:x 7945:) 7942:1 7939:( 7934:m 7930:x 7923:( 7916:) 7907:m 7893:m 7877:m 7860:m 7848:( 7843:= 7838:) 7833:m 7830:, 7825:) 7822:2 7819:( 7814:m 7810:x 7806:, 7801:) 7798:1 7795:( 7790:m 7786:x 7780:( 7733:] 7730:. 7727:. 7724:. 7721:, 7718:) 7713:) 7710:2 7707:( 7702:3 7698:x 7694:, 7689:) 7686:1 7683:( 7678:3 7674:x 7670:( 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6388:( 6380:( 6368:) 6363:0 6359:) 6355:H 6352:, 6349:H 6346:, 6343:H 6340:( 6332:( 6321:[ 6316:= 6309:) 6306:H 6303:( 6289:] 6274:1 6270:h 6260:0 6256:h 6249:[ 6244:= 6237:H 6222:, 6217:1 6213:h 6209:, 6204:0 6200:h 6144:P 6122:1 6115:P 6105:M 6101:P 6075:] 6069:0 6059:0 6054:0 6049:0 6002:0 5997:0 5992:0 5964:0 5959:0 5923:0 5917:[ 5912:= 5903:M 5875:V 5871:) 5862:k 5858:d 5849:T 5844:K 5840:Q 5834:+ 5831:M 5827:( 5818:= 5815:) 5812:V 5809:, 5806:K 5803:, 5800:Q 5797:( 5768:0 5725:M 5705:1 5702:+ 5699:t 5679:t 5643:) 5631:( 5626:R 5616:O 5612:W 5588:= 5556:= 5547:d 5543:, 5537:= 5528:n 5524:, 5518:= 5509:d 5479:d 5453:O 5449:W 5428:i 5406:V 5401:i 5397:W 5393:, 5388:K 5383:i 5379:W 5375:, 5370:Q 5365:i 5361:W 5340:X 5318:O 5314:W 5310:) 5307:) 5302:V 5297:i 5293:W 5289:X 5286:, 5281:K 5276:i 5272:W 5268:X 5265:, 5260:Q 5255:i 5251:W 5247:X 5244:( 5236:( 5231:] 5222:n 5218:[ 5212:i 5202:= 5199:) 5196:V 5193:, 5190:K 5187:, 5184:Q 5181:( 5156:i 5120:) 5114:V 5110:W 5106:, 5101:K 5097:W 5093:, 5088:Q 5084:W 5079:( 5028:X 5024:= 5015:X 5002:X 4975:X 4971:= 4962:X 4958:= 4949:X 4919:d 4915:= 4906:d 4901:, 4892:d 4888:= 4879:d 4874:, 4861:= 4825:d 4795:d 4765:d 4735:d 4702:V 4698:) 4690:k 4686:d 4677:T 4672:K 4668:Q 4662:( 4653:= 4650:) 4647:V 4644:, 4641:K 4638:, 4635:Q 4632:( 4601:i 4597:v 4574:i 4570:k 4547:i 4543:q 4522:i 4502:V 4482:K 4462:Q 4435:i 4413:j 4410:i 4406:a 4385:i 4363:i 4359:k 4350:j 4346:q 4325:i 4305:j 4283:j 4279:k 4270:i 4266:q 4245:j 4225:i 4203:K 4199:W 4176:Q 4172:W 4143:k 4139:d 4114:j 4110:k 4087:i 4083:q 4058:j 4038:i 4016:j 4013:i 4009:a 3979:d 3975:= 3966:d 3943:V 3939:W 3935:, 3930:K 3926:W 3922:, 3917:Q 3913:W 3887:V 3883:W 3873:X 3869:= 3866:V 3844:K 3840:W 3830:X 3826:= 3823:K 3801:Q 3797:W 3787:X 3783:= 3780:Q 3758:Q 3754:W 3743:, 3740:i 3736:x 3732:= 3727:i 3723:q 3700:Q 3696:W 3668:, 3665:i 3661:x 3631:d 3578:V 3574:W 3551:K 3547:W 3524:Q 3520:W 3451:d 3447:4 3444:= 3435:d 3373:) 3370:2 3367:( 3363:b 3359:+ 3354:) 3351:2 3348:( 3344:W 3340:) 3335:) 3332:1 3329:( 3325:b 3321:+ 3316:) 3313:1 3310:( 3306:W 3302:x 3299:( 3293:= 3290:) 3287:x 3284:( 3280:N 3277:F 3274:F 3265:: 3239:d 3212:d 3119:j 3115:c 3094:) 3091:t 3088:( 3085:f 3081:) 3077:) 3074:) 3069:j 3065:t 3058:( 3055:f 3052:( 3048:g 3045:a 3042:i 3039:d 3032:j 3028:c 3022:j 3013:( 3009:= 3006:) 3001:j 2997:t 2990:+ 2987:t 2984:( 2981:f 2976:j 2972:c 2966:j 2937:R 2930:t 2907:) 2904:t 2901:( 2898:f 2895:) 2892:) 2889:t 2883:( 2880:f 2877:( 2873:g 2870:a 2867:i 2864:d 2860:= 2857:) 2854:t 2848:+ 2845:t 2842:( 2839:f 2814:d 2810:/ 2806:2 2802:N 2798:= 2795:r 2773:1 2765:2 2762:d 2757:, 2751:, 2748:1 2745:, 2742:0 2739:= 2736:k 2731:) 2724:k 2720:r 2715:/ 2711:t 2708:i 2704:e 2700:( 2695:= 2692:) 2689:t 2686:( 2683:f 2662:2 2658:/ 2654:d 2649:C 2640:R 2636:: 2633:f 2607:= 2604:N 2584:k 2564:N 2539:d 2535:/ 2531:2 2527:N 2523:= 2520:r 2517:, 2510:k 2506:r 2502:t 2497:= 2474:} 2471:1 2465:2 2461:/ 2457:d 2454:, 2448:, 2445:1 2442:, 2439:0 2436:{ 2430:k 2423:) 2420:) 2414:( 2405:, 2402:) 2396:( 2387:( 2384:= 2381:) 2376:1 2373:+ 2370:k 2367:2 2363:) 2359:t 2356:( 2353:f 2350:, 2345:k 2342:2 2338:) 2334:t 2331:( 2328:f 2325:( 2301:d 2281:0 2275:d 2272:, 2268:Z 2261:d 2258:; 2253:d 2248:R 2239:R 2235:: 2232:f 2191:= 2188:d 2185:, 2179:= 2176:N 2140:) 2131:n 2127:, 2118:d 2114:( 2094:) 2091:b 2088:+ 2085:W 2082:x 2079:( 2075:x 2072:a 2069:m 2066:t 2063:f 2060:o 2057:s 2053:= 2050:) 2047:x 2044:( 2040:d 2037:e 2034:b 2031:m 2028:E 2025:n 2022:U 1980:d 1948:M 1945:] 1939:, 1936:0 1933:, 1930:0 1927:, 1924:1 1921:, 1918:0 1915:, 1912:0 1909:, 1906:0 1903:[ 1900:= 1897:) 1894:3 1891:( 1887:d 1884:e 1881:b 1878:m 1875:E 1854:] 1848:, 1845:0 1842:, 1839:0 1836:, 1833:1 1830:, 1827:0 1824:, 1821:0 1818:, 1815:0 1812:[ 1792:3 1772:M 1717:n 1667:W 1664:x 1580:) 1572:t 1564:( 1545:t 1534:= 1483:) 1053:( 959:e 952:t 945:v 525:k 374:k 301:k 259:) 247:( 34:. 20:)

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