Attention (machine learning)

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problem. Networks that perform verbatim translation without regard to word order would show the highest scores along the (dominant) diagonal of the matrix. The off-diagonal dominance shows that the attention mechanism is more nuanced. On the first pass through the decoder, 94% of the attention weight

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model, as it was proposed in 2014, would encode an input text into a fixed-length vector, which would then be decoded into an output text. If the input text is long, the fixed-length vector would be unable to carry enough information for accurate decoding. An attention mechanism was proposed to solve

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In neural machine translation, the seq2seq method developed in the early 2010s uses two neural networks. An encoder network encodes an input sentence into numerical vectors, which a decoder network decodes into an output sentence in another language. During the evolution of seq2seq in the 2014-2017

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These variants recombine the encoder-side inputs to redistribute those effects to each target output. Often, a correlation-style matrix of dot products provides the re-weighting coefficients. In the figures below, W is the matrix of context attention weights, similar to the formula in Core

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Graves, Alex; Wayne, Greg; Reynolds, Malcolm; Harley, Tim; Danihelka, Ivo; Grabska-Barwińska, Agnieszka; Colmenarejo, Sergio Gómez; Grefenstette, Edward; Ramalho, Tiago; Agapiou, John; Badia, Adrià Puigdomènech; Hermann, Karl Moritz; Zwols, Yori; Ostrovski, Georg; Cain, Adam; King, Helen;

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Consider the seq2seq language English-to-French translation task. To be concrete, let us consider the translation of "the zone of international control <end>", which should translate to "la zone de contrôle international <end>". Here, we use the special <end> token as a

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This is the dot-attention mechanism. The particular version described in this section is "decoder cross-attention", as the output context vector is used by the decoder, and the input keys and values come from the encoder, but the query comes from the decoder, thus "cross-attention".

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An image captioning model was proposed in 2015, citing inspiration from the seq2seq model. that would encode an input image into a fixed-length vector. (Xu et al 2015), citing (Bahdanau et al 2014), applied the attention mechanism as used in the seq2seq model to image captioning.

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Georgescu, Mariana-Iuliana; Ionescu, Radu Tudor; Miron, Andreea-Iuliana; Savencu, Olivian; Ristea, Nicolae-Catalin; Verga, Nicolae; Khan, Fahad Shahbaz (2022-10-12). "Multimodal Multi-Head Convolutional Attention with Various Kernel Sizes for Medical Image Super-Resolution".

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Much effort has gone into understand Attention further by studying their roles in focused settings, such as in-context learning, masked language tasks, stripped down transformers, bigram statistics, N-gram statistics, pairwise convolutions, and arithmetic factoring.

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The diagram shows the Attention forward pass calculating correlations of the word "that" with other words in "See that girl run." Given the right weights from training, the network should be able to identify "girl" as a highly correlated word. Some things to note:

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This example focuses on the attention of a single word "that". In practice, the attention of each word is calculated in parallel to speed up calculations. Simply changing the lowercase "x" vector to the uppercase "X" matrix will yield the formula for

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2-layer decoder. The recurrent layer has 500 neurons and the fully-connected linear layer has 10k neurons (the size of the target vocabulary). The linear layer alone has 5 million (500 × 10k) weights – ~10 times more weights than the recurrent layer.

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used. T could be the embedding of the network's output word; i.e. embedding(argmax(FC output)). Alternatively with teacher forcing, T could be the embedding of the known correct word which can occur with a constant forcing probability, say 1/2.

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encoder. 500 outputs. Input count is 800–300 from source embedding + 500 from recurrent connections. The encoder feeds directly into the decoder only to initialize it, but not thereafter; hence, that direct connection is shown very faintly.

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For decoder self-attention, all-to-all attention is inappropriate, because during the autoregressive decoding process, the decoder cannot attend to future outputs that has yet to be decoded. This can be solved by forcing the attention weights

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Encoder-decoder with attention. Numerical subscripts (100, 300, 500, 9k, 10k) indicate vector sizes while lettered subscripts i and i − 1 indicate time steps. Grey regions in H matrix and w vector are zero values. See Legend for details.

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Unlike "hard" weights, which are computed during the backwards training pass, "soft" weights exist only in the forward pass and therefore change with every step of the input. Earlier designs implemented the attention mechanism in a serial

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is small, and the rest are very small. This can be interpreted as saying that the attention weight should be mostly applied to the 0th hidden vector of the encoder, a little to the 1st, and essentially none to the rest.

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Self-attention is essentially the same as cross-attention, except that query, key, and value vectors all come from the same model. Both encoder and decoder can use self-attention, but with subtle differences.

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formula above assumes that vectors are rows, which runs contrary to the standard math notation of column vectors. More correctly, we should take the transpose of the context vector and use the column-wise

4442: 4574:{\displaystyle {\text{Attention}}(\mathbf {Q} ,\mathbf {K} ,\mathbf {V} )={\text{softmax}}\left({\frac {\mathbf {Q} \mathbf {K} ^{T}}{\sqrt {d_{k}}}}\right)\mathbf {V} \in \mathbb {R} ^{m\times d_{v}}} 5555: 4984: 4937: 4894: 2628: 2107: 4996: 2536: 2186: 3851: 3136: 1077:. As the fovea of the eye is small, the eye cannot sharply resolve the entire visual field at once. The use of saccade control allows the eye to quickly scan important features of a scene. 1084:

and its variants. Meanwhile, developments in neural networks had inspired circuit models of biological visual attention. One well-cited network from 1998, for example, was inspired by the

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where the angled brackets denote dot product. This shows that it involves a multiplicative operation. Multiplicative operations within neural networks had been studied under the names of

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Lee, Juho; Lee, Yoonho; Kim, Jungtaek; Kosiorek, Adam R; Choi, Seungjin; Teh, Yee Whye (2018). "Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks".

1487:, autoregressively. That is, it always takes as input both the hidden vectors produced by the encoder, and what the decoder itself has produced before, to produce the next output word: 1013:

of recurrent neural networks. Recurrent neural networks favor more recent information contained in words at the end of a sentence, while information earlier in the sentence tends to be

6080: 5238: 4685: 6183:{\displaystyle {\text{MultiHead}}(\mathbf {A} \mathbf {Q} ,\mathbf {B} \mathbf {K} ,\mathbf {B} \mathbf {V} )=\mathbf {A} \,{\text{MultiHead}}(\mathbf {Q} ,\mathbf {K} ,\mathbf {V} )} 5617: 5170:{\displaystyle {\text{Attention}}(\mathbf {A} \mathbf {Q} ,\mathbf {B} \mathbf {K} ,\mathbf {B} \mathbf {V} )=\mathbf {A} \,{\text{Attention}}(\mathbf {Q} ,\mathbf {K} ,\mathbf {V} )} 1241:

One problem with seq2seq models was their use of recurrent neural networks, which are not parallelizable as both the encoder and the decoder must process the sequence token-by-token.

5507:{\displaystyle {\text{Attention}}(\mathbf {Q} ,\mathbf {K} ,\mathbf {V} )={\text{softmax}}\left({\frac {\mathbf {Q} \mathbf {K} ^{T}}{\sqrt {d_{k}}}}+\mathbf {M} \right)\mathbf {V} } 1853:, we make the model construct a triple of vectors: key, query, and value. The rough idea is that we have a "database" in the form of a list of key-value pairs. The decoder send in a 6448: 2315: 3078:

For encoder self-attention, we can start with a simple encoder without self-attention, such as an "embedding layer", which simply converts each input word into a vector by a fixed

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100-long vector attention weight. These are "soft" weights which changes during the forward pass, in contrast to "hard" neuronal weights that change during the learning phase.

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Decoder cross-attention, computing the context vector with alignment soft weights. Legend: c = Context, a = alignment soft weights, v = output vectors of the Value network.

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of images using handcrafted (not learned) features, which were then used to guide a second neural network in processing patches of the image in order of reducing saliency.

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500-long encoder hidden vector. At each point in time, this vector summarizes all the preceding words before it. The final h can be viewed as a "sentence" vector, or a

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The idea of using the attention mechanism for self-attention, instead of in an encoder-decoder (cross-attention), was also proposed during this period, such as in

904: 4279:( Qw * X ) in variant 4. Variant 5 uses a fully-connected layer to determine the coefficients. If the variant is QKV, then the dot products are normalized by the 6314: 5699: 5679: 5393: 5361: 4751: 4709: 4655: 2943: 1436: 4176:

Upper case variables represent the entire sentence, and not just the current word. For example, H is a matrix of the encoder hidden state—one word per column.

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As hand-crafting weights defeats the purpose of machine learning, the model must compute the attention weights on its own. Taking analogy from the language of

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of any of the three input matrices. The permutation invariance and equivariance properties of standard QKV attention do not hold for the masked variant.

851: 5939:{\displaystyle {\text{head}}_{i}={\text{Attention}}(\mathbf {Q} \mathbf {W} _{i}^{Q},\mathbf {K} \mathbf {W} _{i}^{K},\mathbf {V} \mathbf {W} _{i}^{V})} 3846: 8129: 2687:, the model would be forced to use the same hidden vector for both key and value, which might not be appropriate, as these two tasks are not the same. 3765:

Attention module – this can be a dot product of recurrent states, or the query-key-value fully-connected layers. The output is a 100-long vector w.

6326: 5949: 8723: 5824:{\displaystyle {\text{MultiHead}}(\mathbf {Q} ,\mathbf {K} ,\mathbf {V} )={\text{Concat}}({\text{head}}_{1},...,{\text{head}}_{h})\mathbf {W} ^{O}} 4049:, attention mechanisms can be distinguished by the dimension on which they operate, namely: spatial attention, channel attention, or combinations. 692: 1703:

In translating between languages, alignment is the process of matching words from the source sentence to words of the translated sentence. In the

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vectors, linearly transformed by another matrix to provide the model with freedom to find the best way to represent values. Without the matrices

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In general, the attention unit consists of dot products, with 3 trained, fully-connected neural network layers called query, key, and value.

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is processed by a neural network (which can be an LSTM, a Transformer encoder, or some other network) into a sequence of real-valued vectors

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that would allow a single word to excessively dominate the softmax resulting in attention to only one word, as a discrete hard max would do.

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When QKV attention is used as a building block for an autoregressive decoder, and when at training time all input and output matrices have

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Bahdanau, Dzmitry; Cho, Kyunghyun; Bengio, Yoshua (19 May 2016). "Neural Machine Translation by Jointly Learning to Align and Translate".

5240:. These properties are inherited when applying linear transforms to the inputs and outputs of QKV attention blocks. For example, a simple 7488:

Britz, Denny; Goldie, Anna; Luong, Minh-Thanh; Le, Quoc (2017-03-21). "Massive Exploration of Neural Machine Translation Architectures".

438: 6755: 3050:. In fact, it is theoretically possible for query, key, and value vectors to all be different, though that is rarely done in practice. 939: 742: 7272:

Xu, Kelvin; Ba, Jimmy; Kiros, Ryan; Cho, Kyunghyun; Courville, Aaron; Salakhudinov, Ruslan; Zemel, Rich; Bengio, Yoshua (2015-06-01).

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method that determines the relative importance of each component in a sequence relative to the other components in that sequence. In

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

6640: 3384: 2918:{\displaystyle c_{0}=\mathrm {Attention} (h_{0}^{d}W^{Q},HW^{K},HW^{V})=\mathrm {softmax} ((h_{0}^{d}W^{Q})\;(HW^{K})^{T})(HW^{V})} 1058: 4397: 8239: 818: 1728: 8122: 5059:{\displaystyle {\text{softmax}}(\mathbf {A} \mathbf {D} \mathbf {B} )=\mathbf {A} \,{\text{softmax}}(\mathbf {D} )\mathbf {B} } 1695:

to delimit the start of input for the decoder. The decoding terminates as soon as "<end>" appears in the decoder output.

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After the encoder has finished processing, the decoder starts operating over the hidden vectors, to produce an output sequence

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in a non-trivial way, because every row of the output is a function of all the rows of the input. Similar properties hold for

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In order to make a properly weighted sum, we need to transform this list of dot products into a probability distribution over

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attempted to solve this problem by processing the input sequence in parallel, before computing a "soft alignment matrix" (

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Woo, Sanghyun; Park, Jongchan; Lee, Joon-Young; Kweon, In So (2018-07-18). "CBAM: Convolutional Block Attention Module".

1805: 1017:. Attention allows a token equal access to any part of a sentence directly, rather than only through the previous state. 894: 1302: 727: 702: 651: 8825: 8452: 8259: 8115: 2109:. The linear maps are useful for providing the model with enough freedom to find the best way to represent the data. 1066: 775: 770: 423: 8780: 8089: 433: 71: 6961:

Ba, Jimmy; Mnih, Volodymyr; Kavukcuoglu, Koray (2015-04-23). "Multiple Object Recognition with Visual Attention".

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Cheng, Jianpeng; Dong, Li; Lapata, Mirella (2016-09-20). "Long Short-Term Memory-Networks for Machine Reading".

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Kramer, Arthur F.; Wiegmann, Douglas A.; Kirlik, Alex (2006-12-28). "1 Attention: From History to Application".

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During the deep learning era, attention mechanism was developed to solve similar problems in encoding-decoding.

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is the 1-hot maximizer of the linear Decoder layer D; that is, it takes the argmax of D's linear layer output.

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

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The permutation properties of (standard, unmasked) QKV attention apply here also. For permutation matrices,

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design removed the slower sequential RNN and relied more heavily on the faster parallel attention scheme.

8993: 8289: 8215: 7355: 4387:{\displaystyle \mathbf {Q} \in \mathbb {R^{m\times d_{k}}} ,\mathbf {K} \in \mathbb {R^{n\times d_{k}}} } 976: 911: 823: 808: 269: 91: 7533:; Irie, Kazuki; Schmidhuber, Jürgen (2021). "Linear Transformers Are Secretly Fast Weight Programmers". 5626: 3085: 2948: 1644: 1592: 1543: 1494: 1444: 1375: 1329: 8617: 8552: 8153: 7151:

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

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Charton, François (2023). "Learning the Greatest Common Divisor: Explaining Transformer Predictions".

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Luong, Minh-Thang (2015-09-20). "Effective Approaches to Attention-Based Neural Machine Translation".

7104: 6674: 6023: 1687:, "<start> la zone de contrôle international") → "la zone de contrôle international <end>" 9041: 9018: 8876: 8515: 8346: 8169: 8101: 4109:

used to calculate attention. With only 1 input into corr, W is an auto-correlation of dot products. w

1273: 1009:, the attention mechanism was developed to address the weaknesses of leveraging information from the 925: 531: 299: 169: 3691:

300-long word embedding vector. The vectors are usually pre-calculated from other projects such as

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Academic reviews of the history of the attention mechanism are provided in Niu et al. and Soydaner.

8917: 8174: 6916:"Neural network model for selective attention in visual pattern recognition and associative recall" 6630: 4002:. The slow network learns by gradient descent. It was later renamed as "linearized self-attention". 3728: 1268: 1073:

is modulated by cognitive processes, insofar as the eye moves preferentially towards areas of high

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The decoder first processes the "<start>" input partially, to obtain an intermediate vector

8962: 8947: 8600: 8595: 8495: 8363: 8144: 5207: 1900:, the 0th hidden vector of decoder. Then, the intermediate vector is transformed by a linear map 1285: 1074: 500: 349: 249: 76: 2279: 8922: 8682: 8401: 8396: 6650: 5709: 2994: 2448:{\displaystyle (w_{00},w_{01},\dots )=\mathrm {softmax} (q_{0}k_{0}^{T},q_{0}k_{1}^{T},\dots )} 1986:. Meanwhile, the hidden vectors outputted by the encoder are transformed by another linear map 1871: 680: 656: 558: 319: 294: 254: 66: 5564: 3509: 1817:. On the second pass of the decoder, 88% of the attention weight is on the third English word 8952: 8937: 8902: 8590: 8490: 8358: 4733:

are weighted using the weights resulting from the softmax operation, so that the rows of the

3568:, called "causal masking". This attention mechanism is the "causally masked self-attention". 1257: 1047: 634: 456: 408: 264: 179: 51: 8820: 7177: 4584: 3545: 8972: 8927: 8373: 8318: 8164: 8159: 8093: 7800: 7367: 7354:

Summerfield, Christopher; Blunsom, Phil; Kavukcuoglu, Koray; Hassabis, Demis (2016-10-12).

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By noting that the transpose of a permutation matrix is also its inverse, it follows that:

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Weight matrices for query, key, value respectively. FC is a fully-connected weight matrix.

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period, the attention mechanism was refined, until it appeared in the Transformer in 2017.

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Tutorial variant training phase, T alternates between 2 sources depending on the level of

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A fully-connected layer is used to calculate attention instead of dot product correlation.

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Rende, Riccardo (2024). "Mapping of attention mechanisms to a generalized Potts model".

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500-long context vector = H * w. c is a linear combination of h vectors weighted by w.

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

7180:(1992). "Learning to control fast-weight memories: an alternative to recurrent nets". 7143: 7120: 6868: 4233:

Column-wise softmax(matrix of all combinations of dot products). The dot products are

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is the terminology used by Bahdanau et al) in order to allow for parallel processing.

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is permutation equivariant with respect to re-ordering the rows of the input matrix

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in humans had been well studied in neuroscience and cognitive psychology. In 1953,

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Graves, Alex; Wayne, Greg; Danihelka, Ivo (2014-12-10). "Neural Turing Machines".

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Sometimes, alignment can be multiple-to-multiple. For example, the English phrase

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where an LSTM is augmented with a memory network as it encodes an input sequence.

8856: 8800: 8622: 8264: 8184: 8004:"NLP From Scratch: Translation With a Sequence To Sequence Network and Attention" 6690: 4189: 1062: 793: 597: 463: 403: 6995: 8830: 8795: 8785: 8610: 8368: 8194: 7648: 7593: 7273: 6984:"Shifts in Selective Visual Attention: Towards the Underlying Neural Circuitry" 6732: 3995: 3708: 3634: 987: 983: 952: 813: 344: 81: 7979: 7955: 7931: 7274:"Show, Attend and Tell: Neural Image Caption Generation with Visual Attention" 7193: 7026: 6983: 6013:{\displaystyle \mathbf {W} _{i}^{Q},\mathbf {W} _{i}^{K},\mathbf {W} _{i}^{V}} 1825:. On the last pass, 95% of the attention weight is on the second English word 9035: 8775: 8755: 8672: 8351: 7387: 7128: 7081: 6939: 6892: 6835: 6740: 6698: 3999: 1085: 980: 960: 732: 661: 543: 274: 159: 7847:

Nguyen, Timothy (2024). "Understanding Transformers via N-gram Statistics".

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Kowler, Eileen; Anderson, Eric; Dosher, Barbara; Blaser, Erik (1995-07-01).

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Zhu, Xizhou; Cheng, Dazhi; Zhang, Zheng; Lin, Stephen; Dai, Jifeng (2019).

7395: 7339: 7089: 6947: 6791:"Some Experiments on the Recognition of Speech, with One and with Two Ears" 5181: 3676: 3128:. These can then be applied to a dot-product attention mechanism, to obtain 3079: 1861:, where the weight is proportional to how closely the query resembles each 1089: 1081: 1043: 1010: 7317: 6900: 6717:"Attention mechanism in neural networks: where it comes and where it goes" 1841: 8957: 8728: 8637: 8632: 8254: 8232: 7316:

Parikh, Ankur; Täckström, Oscar; Das, Dipanjan; Uszkoreit, Jakob (2016).

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Vinyals, Oriol; Toshev, Alexander; Bengio, Samy; Erhan, Dumitru (2015).

7058:"Learning, invariance, and generalization in high-order neural networks" 6988:

Matters of Intelligence: Conceptual Structures in Cognitive Neuroscience

6587:{\displaystyle {\text{Attention}}(Q,K,V)={\text{softmax}}(QW_{a}K^{T})V} 4147: 1804:

This view of the attention weights addresses some of the neural network

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Rumelhart, David E.; Hinton, G. E.; Mcclelland, James L. (1987-07-29).

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is equivariant with respect to re-ordering of the rows of input matrix

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Decoder cross-attention, computing the attention weights by dot-product

687: 383: 309: 8086:, ch. 10.4 Attention and ch. 9.7 Self-Attention Networks: Transformers 7356:"Hybrid computing using a neural network with dynamic external memory" 7042: 6817: 1095:

A key aspect of attention mechanism can be written (schematically) as

8846: 8815: 8713: 8557: 8520: 8457: 8411: 8406: 8391: 7594:"An Empirical Study of Spatial Attention Mechanisms in Deep Networks" 7559: 7027:"A model of saliency-based visual attention for rapid scene analysis" 6645: 3994:

fast weight programmers, or fast weight controllers (1992). A "slow"

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studied selective attention in the context of audition, known as the

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Proceedings of the 32nd International Conference on Machine Learning

7149:. In Rumelhart, David E.; Hinton, G. E.; PDP Research Group (eds.). 1267:

These strands of development were brought together in 2017 with the

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2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition

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Ha, David; Dai, Andrew; Le, Quoc V. (2016-12-01). "HyperNetworks".

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is applied independently to every row of its argument. The matrix

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to delimit the end of input for both the encoder and the decoder.

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in every element above the diagonal. The softmax output, also in

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2019 IEEE/CVF International Conference on Computer Vision (ICCV)

3791: 8886: 8866: 8738: 8530: 7318:"A Decomposable Attention Model for Natural Language Inference" 373: 7031:

IEEE Transactions on Pattern Analysis and Machine Intelligence

6379:{\displaystyle {\text{Attention}}(Q,K,V)={\text{softmax}}(e)V} 4133: 4101: 4091: 4081: 3653:

Dictionary size of input & output languages respectively.

8687: 8667: 8657: 8652: 8647: 8642: 8605: 8437: 7575:"Learning Positional Attention for Sequential Recommendation" 4095:

Both encoder & decoder are needed to calculate attention.

4085:

Both encoder & decoder are needed to calculate attention.

3998:

outputs the "fast" weights of another neural network through

3692: 3668: 3482:{\displaystyle H'=\mathrm {Attention} (HW^{Q},HW^{K},HW^{V})} 2112:

Now, the query and keys are compared by taking dot products:

617: 612: 339: 7722: 4437:{\displaystyle \mathbf {V} \in \mathbb {R^{n\times d_{v}}} } 3501:

Decoder self-attention with causal masking, detailed diagram

1080:

These research developments inspired algorithms such as the

1061:. Selective attention of vision was studied in the 1960s by 8677: 7315: 3990:

Many variants of attention implement soft weights, such as

1289:

Comparison of the data flow in CNN, RNN, and self-attention

6866: 4184:

S, decoder hidden state; T, target word embedding. In the

1857:, and obtain a reply in the form of a weighted sum of the 7352: 7144:"A General Framework for Parallel Distributed Processing" 7141: 3773:

500×100. 100 hidden vectors h concatenated into a matrix

7256: 5550:{\displaystyle \mathbf {M} \in \mathbb {R} ^{n\times n}} 4979:{\displaystyle \mathbf {D} \in \mathbb {R} ^{m\times n}} 4932:{\displaystyle \mathbf {B} \in \mathbb {R} ^{n\times n}} 4889:{\displaystyle \mathbf {A} \in \mathbb {R} ^{m\times m}} 4303: 2623:{\displaystyle v_{0}=h_{0}W^{V},v_{1}=h_{1}W^{V},\dots } 2102:{\displaystyle k_{0}=h_{0}W^{K},k_{1}=h_{1}W^{K},\dots } 990:

that can range from tens to millions of tokens in size.

905:

List of datasets in computer vision and image processing

1237:

Transformer (deep learning architecture) § History

6869:"The role of attention in the programming of saccades" 6675:"A review on the attention mechanism of deep learning" 6673:

Niu, Zhaoyang; Zhong, Guoqiang; Yu, Hui (2021-09-10).

3023:, is not necessarily the same as the key-value vector 7826:

He, Bobby (2023). "Simplifying Transformers Blocks".

7747:"Trained Transformers Learn Linear Models In-Context" 7529: 6990:. Dordrecht: Springer Netherlands. pp. 115–141. 6600: 6517: 6483: 6456: 6392: 6329: 6302: 6206: 6091: 6058: 6026: 5952: 5837: 5723: 5687: 5667: 5629: 5590: 5567: 5520: 5405: 5381: 5349: 5253: 5216: 5190: 5078: 4999: 4949: 4902: 4859: 4826: 4790: 4759: 4739: 4717: 4697: 4663: 4643: 4621: 4587: 4454: 4400: 4314: 3849: 3548: 3512: 3387: 3134: 3088: 3029: 2997: 2951: 2931: 2700: 2640: 2544: 2531:{\displaystyle c_{0}=w_{00}v_{0}+w_{01}v_{1}+\cdots } 2465: 2318: 2282: 2236: 2194: 2118: 2023: 1992: 1937: 1906: 1874: 1647: 1595: 1546: 1497: 1447: 1424: 1378: 1332: 1314:

Animation of seq2seq with RNN and attention mechanism

1101: 7933:

CS 152 NN—27: Attention: Keys, Queries, & Values

7416: 6753: 2181:{\displaystyle q_{0}k_{0}^{T},q_{0}k_{1}^{T},\dots } 964:

Attention mechanism with attention weights, overview

8054:"Attention and Augmented Recurrent Neural Networks" 5831:where each head is computed with QKV attention as: 4225:⊕, vector concatenation; ⊗, matrix multiplication. 4201:H, encoder hidden state; X, input word embeddings. 7487: 7235: 6613: 6586: 6496: 6469: 6442: 6378: 6308: 6285: 6182: 6074: 6041: 6012: 5938: 5823: 5693: 5673: 5653: 5611: 5576: 5549: 5506: 5387: 5355: 5332: 5232: 5198: 5169: 5058: 4978: 4931: 4888: 4834: 4812: 4772: 4745: 4725: 4703: 4679: 4649: 4629: 4599: 4573: 4436: 4386: 3971: 3560: 3534: 3481: 3373: 3120: 3042: 3015: 2983: 2937: 2917: 2679: 2622: 2530: 2447: 2300: 2264: 2222: 2180: 2101: 2005: 1978: 1919: 1892: 1691:Here, we use the special <start> token as a 1679: 1627: 1578: 1529: 1479: 1430: 1410: 1364: 1177: 8026: 7466: 7293: 7259:"Show and Tell: A Neural Image Caption Generator" 6960: 5184:with respect to re-ordering the queries (rows of 3589:A step-by-step sequence of a language translation 9033: 7995: 7591: 7172: 7170: 7025:Itti, L.; Koch, C.; Niebur, E. (November 1998). 6798:The Journal of the Acoustical Society of America 6319: 8052:Olah, Chris; Carter, Shan (September 8, 2016). 7888:Transformer Neural Network Derived From Scratch 7701: 7440: 8020: 7102: 7024: 4298: 4005:Bahdanau-style attention, also referred to as 1297: 900:List of datasets for machine-learning research 8123: 7840: 7167: 7103:Feldman, J. A.; Ballard, D. H. (1982-07-01). 5681:of the attention ouput is independent of row 4986:an arbitrary matrix. The softmax function is 933: 8137: 7271: 7055: 6507: 1154: 1112: 7902: 7502: 7462: 7460: 7458: 7176: 7105:"Connectionist models and their properties" 5561:, with zeros on and below the diagonal and 998:language translation system, but the later 8130: 8116: 8051: 7978:Alfredo Canziani & Yann Lecun (2021). 7954:Alfredo Canziani & Yann Lecun (2021). 7879: 7716: 7695: 7523: 7481: 7346: 7056:Giles, C. Lee; Maxwell, Tom (1987-12-01). 6981: 6782: 6672: 3597: 3082:. This gives a sequence of hidden vectors 2866: 940: 926: 8032: 7914: 7861: 7852: 7831: 7794: 7774: 7765: 7754:Journal of Machine Learning Research 1-55 7738: 7729: 7707: 7660: 7646: 7605: 7558: 7548: 7546: 7544: 7493: 7472: 7446: 7436: 7434: 7422: 7329: 7299: 7241: 7220: 6966: 6913: 6848: 6825: 6766:10.1093/acprof:oso/9780195305722.003.0001 6147: 6075:{\displaystyle \mathbf {A} ,\mathbf {B} } 5593: 5531: 5233:{\displaystyle \mathbf {K} ,\mathbf {V} } 5210:to re-ordering of the key-value pairs in 5134: 5034: 4960: 4913: 4870: 4793: 4711:key-value pairs. Value vectors in matrix 4680:{\displaystyle \mathbf {K} ,\mathbf {V} } 4548: 4426: 4422: 4415: 4411: 4376: 4372: 4365: 4361: 4340: 4336: 4329: 4325: 4267:( Qw * S ) in variant 2, and column 4012:Luong-style attention, which is known as 1715:. Stacking soft row vectors together for 1635:, "<start> la zone") → "la zone de" 7455: 7229: 6842: 6714: 6641:Transformer (deep learning architecture) 5708: 5612:{\displaystyle \mathbb {R} ^{n\times n}} 4146: 4132: 4100: 4090: 4080: 3575: 3496: 3070:Encoder self-attention, detailed diagram 3065: 3057: 1840: 1309: 1301: 1284: 959: 951: 7908: 7819: 7309: 7214: 7153:. Cambridge, Massachusetts: MIT Press. 6982:Koch, Christof; Ullman, Shimon (1987). 5704: 2312:, thus giving us the attention weights: 9034: 7971: 7947: 7923: 7846: 7541: 7431: 6788: 6443:{\displaystyle e=\tanh(W_{Q}Q+W_{K}K)} 3719:500-long decoder hidden state vector. 1836: 1280: 1210: 8111: 8094:Attention and Memory in Deep Learning 8001: 7981:NYU Deep Learning course, Spring 2020 7957:NYU Deep Learning course, Spring 2020 7780: 7744: 7647:Hu, Jie; Shen, Li; Sun, Gang (2018). 7585: 7552: 7289: 7287: 4304:Standard Scaled Dot-Product Attention 3062:Encoder self-attention, block diagram 8968:Generative adversarial network (GAN) 7640: 6710: 6708: 6668: 6666: 4813:{\displaystyle \mathbb {R} ^{d_{v}}} 3841:, resulting in the more correct form 3679:rather than vector multiplication. 3571: 1979:{\displaystyle q_{0}=h_{0}^{d}W^{Q}} 1698: 7567: 7135: 5713:Decoder multiheaded cross-attention 5370: 4292:is the height of the QKV matrices. 2694:More succinctly, we can write it as 895:Glossary of artificial intelligence 13: 7825: 7284: 7018: 6914:Fukushima, Kunihiko (1987-12-01). 6757:Attention: From Theory to Practice 5654:{\displaystyle 1\leq i<j\leq n} 5571: 5180:which shows that QKV attention is 4780:output matrix are confined to the 3424: 3421: 3418: 3415: 3412: 3409: 3406: 3403: 3400: 3295: 3292: 3289: 3286: 3283: 3280: 3277: 3274: 3271: 3184: 3181: 3178: 3175: 3172: 3169: 3166: 3163: 3160: 3121:{\displaystyle h_{0},h_{1},\dots } 2984:{\displaystyle h_{0},h_{1},\dots } 2828: 2825: 2822: 2819: 2816: 2813: 2810: 2739: 2736: 2733: 2730: 2727: 2724: 2721: 2718: 2715: 2376: 2373: 2370: 2367: 2364: 2361: 2358: 2308:. This can be accomplished by the 1680:{\displaystyle h_{0},h_{1},\dots } 1628:{\displaystyle h_{0},h_{1},\dots } 1579:{\displaystyle h_{0},h_{1},\dots } 1530:{\displaystyle h_{0},h_{1},\dots } 1480:{\displaystyle y_{0},y_{1},\dots } 1411:{\displaystyle h_{0},h_{1},\dots } 1365:{\displaystyle x_{0},x_{1},\dots } 14: 9053: 8045: 7649:"Squeeze-and-Excitation Networks" 6721:Neural Computing and Applications 6705: 6663: 4853:properties of QKV attention, let 3053: 2991:. Note that the querying vector, 2680:{\displaystyle W^{Q},W^{K},W^{V}} 2455:This is then used to compute the 1813:, so the network offers the word 1586:, "<start> la") → "la zone" 9006: 9005: 8985: 7813:10.1103/PhysRevResearch.6.023057 6270: 6264: 6250: 6244: 6230: 6224: 6208: 6173: 6165: 6157: 6143: 6132: 6127: 6119: 6114: 6106: 6101: 6068: 6060: 6042:{\displaystyle \mathbf {W} ^{O}} 6029: 5995: 5975: 5955: 5918: 5912: 5893: 5887: 5868: 5862: 5811: 5749: 5741: 5733: 5522: 5500: 5490: 5461: 5455: 5431: 5423: 5415: 5317: 5311: 5297: 5291: 5277: 5271: 5255: 5226: 5218: 5192: 5160: 5152: 5144: 5130: 5119: 5114: 5106: 5101: 5093: 5088: 5052: 5044: 5030: 5019: 5014: 5009: 4951: 4904: 4861: 4828: 4719: 4673: 4665: 4623: 4539: 4509: 4503: 4480: 4472: 4464: 4402: 4352: 4316: 3832:: the commonly written row-wise 3790: 7537:. Springer. pp. 9355–9366. 7410: 7265: 7250: 7208: 7096: 7049: 6715:Soydaner, Derya (August 2022). 6504:are learnable weight matrices. 5559:stricly upper triangular matrix 4063:1. encoder-decoder dot product 4039:factorized positional attention 1711:is aligned with the third word 1707:example above, the second word 1254:differentiable neural computers 1086:low-level primate visual system 1034: 8918:Recurrent neural network (RNN) 8908:Differentiable neural computer 8082:Speech and Language Processing 7891:. 2023. Event occurs at 05:30 7510:"Pytorch.org seq2seq tutorial" 6975: 6954: 6907: 6860: 6827:11858/00-001M-0000-002A-F750-3 6747: 6621:is a learnable weight matrix. 6578: 6552: 6541: 6523: 6437: 6405: 6370: 6364: 6353: 6335: 6280: 6220: 6212: 6177: 6153: 6136: 6097: 5933: 5858: 5806: 5764: 5753: 5729: 5435: 5411: 5327: 5267: 5259: 5164: 5140: 5123: 5084: 5048: 5040: 5023: 5005: 4484: 4460: 4255:in variant 1, and column 3952: 3941: 3917: 3910: 3887: 3884: 3871: 3854: 3476: 3428: 3354: 3299: 3243: 3188: 2912: 2896: 2893: 2884: 2867: 2863: 2835: 2832: 2803: 2743: 2442: 2380: 2351: 2319: 2265:{\displaystyle q_{0}k_{1}^{T}} 2223:{\displaystyle q_{0}k_{0}^{T}} 1230: 1166: 1157: 1145: 1136: 1124: 1115: 315:Relevance vector machine (RVM) 1: 8963:Variational autoencoder (VAE) 8923:Long short-term memory (LSTM) 8190:Computational learning theory 8084:(3rd ed. draft, January 2022) 7121:10.1016/S0364-0213(82)80001-3 6656: 6320:Bahdanau (Additive) Attention 4444:, the scaled dot-product, or 4047:convolutional neural networks 2945:is the matrix whose rows are 1809:is on the first English word 956:Attention mechanism, overview 804:Computational learning theory 368:Expectation–maximization (EM) 8943:Convolutional neural network 8064:(9). Distill Working Group. 6986:. In Vaina, Lucia M. (ed.). 6885:10.1016/0042-6989(94)00279-U 6854:Perception and Communication 6691:10.1016/j.neucom.2021.03.091 6193:from which we also see that 5199:{\displaystyle \mathbf {Q} } 4835:{\displaystyle \mathbf {V} } 4726:{\displaystyle \mathbf {V} } 4630:{\displaystyle \mathbf {Q} } 4141:used to calculate attention. 4069:3. encoder-only dot product 4057:Calculations section above. 3819:prevents a high variance in 1438:stands for "hidden vector". 1218:In machine translation, the 1188:higher-order neural networks 1027:Timeline of machine learning 761:Coefficient of determination 608:Convolutional neural network 320:Support vector machine (SVM) 7: 8938:Multilayer perceptron (MLP) 8079:and James H. Martin (2022) 6996:10.1007/978-94-009-3833-5_5 6760:. Oxford University Press. 6624: 4299:Mathematical representation 3985: 1298:seq2seq machine translation 1069:. It was also noticed that 977:natural language processing 912:Outline of machine learning 809:Empirical risk minimization 10: 9058: 9014:Artificial neural networks 8928:Gated recurrent unit (GRU) 8154:Differentiable programming 6733:10.1007/s00521-022-07366-3 5367:, which is defined below. 3492: 2301:{\displaystyle 0,1,\dots } 1326:An input sequence of text 1234: 1024: 1020: 549:Feedforward neural network 300:Artificial neural networks 16:Machine learning technique 8981: 8895: 8839: 8768: 8701: 8573: 8473: 8466: 8420: 8384: 8347:Artificial neural network 8327: 8203: 8170:Automatic differentiation 8143: 7194:10.1162/neco.1992.4.1.131 6856:. London: Pergamon Press. 6508:Luong Attention (General) 6195:multi-head self-attention 4273:( Kw * X ) * column 4261:( Kw * H ) * column 4027:and successfully used in 3749:100-long alignment score 3016:{\displaystyle h_{0}^{d}} 1893:{\displaystyle h_{0}^{d}} 1537:, "<start>") → "la" 1274:Attention Is All You Need 1059:filter model of attention 532:Artificial neural network 8175:Neuromorphic engineering 8138:Differentiable computing 7984:. Event occurs at 20:15 7960:. Event occurs at 05:30 7936:. Event occurs at 06:30 7873:transformer-circuits.pub 7783:Physical Review Research 6631:Recurrent neural network 6049:are parameter matrices. 5577:{\displaystyle -\infty } 4851:permutation equivariance 4657:queries, while matrices 4014:multiplicative attention 3729:recurrent neural network 3645:Length of hidden vector 3535:{\displaystyle w_{ij}=0} 1269:Transformer architecture 1005:Inspired by ideas about 996:recurrent neural network 841:Journals and conferences 788:Mathematical foundations 698:Temporal difference (TD) 554:Recurrent neural network 474:Conditional random field 397:Dimensionality reduction 145:Dimensionality reduction 107:Quantum machine learning 102:Neuromorphic engineering 62:Self-supervised learning 57:Semi-supervised learning 8948:Residual neural network 8364:Artificial Intelligence 7671:10.1109/CVPR.2018.00745 7616:10.1109/ICCV.2019.00679 4988:permutation equivariant 4209:Attention coefficients 4066:2. encoder-decoder QKV 1201:fast weight controllers 1067:partial report paradigm 250:Apprenticeship learning 8070:10.23915/distill.00001 7869:"Transformer Circuits" 7655:. pp. 7132–7141. 7600:. pp. 6687–6696. 7306:(orig-date 1 Sep 2014) 6651:Dynamic neural network 6615: 6588: 6498: 6471: 6444: 6380: 6310: 6287: 6184: 6076: 6043: 6014: 5940: 5825: 5714: 5695: 5675: 5655: 5613: 5578: 5551: 5508: 5389: 5357: 5334: 5234: 5200: 5171: 5060: 4980: 4933: 4890: 4847:permutation invariance 4836: 4814: 4774: 4747: 4727: 4705: 4681: 4651: 4631: 4601: 4600:{\displaystyle {}^{T}} 4575: 4438: 4388: 4152: 4142: 4128: 4096: 4086: 4025:decomposable attention 4023:introduced in 2016 as 4019:highly parallelizable 3973: 3637:size (word dimension) 3590: 3562: 3561:{\displaystyle i<j} 3536: 3502: 3483: 3375: 3122: 3071: 3063: 3044: 3017: 2985: 2939: 2919: 2681: 2624: 2532: 2449: 2302: 2266: 2224: 2182: 2103: 2007: 1980: 1921: 1894: 1846: 1681: 1629: 1580: 1531: 1481: 1432: 1412: 1366: 1315: 1307: 1290: 1258:neural Turing machines 1243:Decomposable attention 1179: 965: 957: 799:Bias–variance tradeoff 681:Reinforcement learning 657:Spiking neural network 67:Reinforcement learning 8903:Neural Turing machine 8491:Human image synthesis 7745:Zhang, Ruiqi (2024). 7261:. pp. 3156–3164. 6616: 6614:{\displaystyle W_{a}} 6589: 6499: 6497:{\displaystyle W_{K}} 6472: 6470:{\displaystyle W_{Q}} 6445: 6381: 6311: 6288: 6185: 6077: 6044: 6015: 5941: 5826: 5717:Multi-head attention 5712: 5696: 5676: 5656: 5614: 5579: 5552: 5509: 5390: 5358: 5335: 5244:function defined as: 5235: 5201: 5172: 5061: 4981: 4934: 4891: 4837: 4820:given by the rows of 4815: 4775: 4773:{\displaystyle d_{v}} 4748: 4728: 4706: 4682: 4652: 4632: 4602: 4576: 4439: 4389: 4150: 4136: 4104: 4094: 4084: 3974: 3675:→ x implemented as a 3671:dictionary vectors. 3626:Max. sentence length 3588: 3563: 3537: 3500: 3484: 3376: 3123: 3069: 3061: 3045: 3043:{\displaystyle h_{0}} 3018: 2986: 2940: 2920: 2682: 2625: 2533: 2450: 2303: 2267: 2225: 2183: 2104: 2008: 2006:{\displaystyle W^{K}} 1981: 1922: 1920:{\displaystyle W^{Q}} 1895: 1844: 1682: 1630: 1581: 1532: 1482: 1433: 1413: 1367: 1313: 1305: 1288: 1180: 1048:cocktail party effect 986:across a fixed-width 963: 955: 635:Neural radiance field 457:Structured prediction 180:Structured prediction 52:Unsupervised learning 8994:Computer programming 8973:Graph neural network 8548:Text-to-video models 8526:Text-to-image models 8374:Large language model 8359:Scientific computing 8165:Statistical manifold 8160:Information geometry 7930:Neil Rhodes (2021). 7340:10.18653/v1/d16-1244 7074:10.1364/AO.26.004972 6932:10.1364/AO.26.004985 6598: 6515: 6481: 6454: 6390: 6327: 6300: 6204: 6089: 6056: 6024: 5950: 5835: 5721: 5705:Multi-Head Attention 5685: 5665: 5627: 5588: 5565: 5518: 5403: 5379: 5365:multi-head attention 5347: 5251: 5214: 5188: 5076: 4997: 4947: 4941:permutation matrices 4900: 4857: 4824: 4788: 4757: 4737: 4715: 4695: 4661: 4641: 4619: 4585: 4452: 4398: 4312: 4173:Variables X, H, S, T 4075:5. Pytorch tutorial 4072:4. encoder-only QKV 4035:positional attention 3847: 3711:as Hinton calls it. 3546: 3510: 3385: 3381:or more succinctly, 3132: 3086: 3027: 2995: 2949: 2929: 2698: 2638: 2542: 2463: 2316: 2280: 2234: 2192: 2116: 2021: 1990: 1935: 1904: 1872: 1645: 1593: 1544: 1495: 1445: 1422: 1376: 1330: 1193:multiplication units 1099: 824:Statistical learning 722:Learning with humans 514:Local outlier factor 8340:In-context learning 8180:Pattern recognition 7805:2024PhRvR...6b3057R 7380:10.1038/nature20101 7372:2016Natur.538..471G 7178:Schmidhuber, Jürgen 6810:1953ASAJ...25..975C 6727:(16): 13371–13385. 6009: 5989: 5969: 5932: 5907: 5882: 4990:in the sense that: 4687:jointly contain an 4161: 3611: 3262: 3151: 3012: 2852: 2760: 2435: 2407: 2261: 2219: 2171: 2143: 1965: 1889: 1281:Machine translation 1271:, published in the 1211:Recurrent attention 1040:Selective attention 1007:attention in humans 667:Electrochemical RAM 574:reservoir computing 305:Logistic regression 224:Supervised learning 210:Multimodal learning 185:Feature engineering 130:Generative modeling 92:Rule-based learning 87:Curriculum learning 47:Supervised learning 22:Part of a series on 8933:Echo state network 8821:Jürgen Schmidhuber 8516:Facial recognition 8511:Speech recognition 8421:Software libraries 7280:. PMLR: 2048–2057. 7182:Neural Computation 6789:Cherry EC (1953). 6611: 6584: 6494: 6467: 6440: 6376: 6306: 6283: 6180: 6072: 6039: 6010: 5993: 5973: 5953: 5936: 5916: 5891: 5866: 5821: 5715: 5691: 5671: 5651: 5609: 5574: 5547: 5504: 5385: 5353: 5330: 5230: 5196: 5167: 5056: 4976: 4929: 4886: 4845:To understand the 4832: 4810: 4770: 4743: 4723: 4701: 4677: 4647: 4627: 4597: 4571: 4434: 4384: 4159: 4153: 4143: 4129: 4097: 4087: 4007:additive attention 3969: 3967: 3928: 3609: 3591: 3558: 3532: 3503: 3479: 3371: 3369: 3250: 3139: 3118: 3072: 3064: 3040: 3013: 2998: 2981: 2935: 2915: 2838: 2746: 2677: 2620: 2528: 2445: 2421: 2393: 2298: 2262: 2247: 2220: 2205: 2178: 2157: 2129: 2099: 2003: 1976: 1951: 1917: 1890: 1875: 1847: 1677: 1625: 1576: 1527: 1477: 1428: 1408: 1362: 1316: 1308: 1291: 1175: 1111: 966: 958: 235: • 150:Density estimation 9029: 9028: 8791:Stephen Grossberg 8764: 8763: 8096:(video lecture), 8002:Robertson, Sean. 7680:978-1-5386-6420-9 7625:978-1-7281-4803-8 7366:(7626): 471–476. 7160:978-0-262-68053-0 7109:Cognitive Science 7068:(23): 4972–4978. 7043:10.1109/34.730558 7037:(11): 1254–1259. 7005:978-94-009-3833-5 6926:(23): 4985–4992. 6879:(13): 1897–1916. 6818:10.1121/1.1907229 6775:978-0-19-530572-2 6550: 6521: 6362: 6333: 6309:{\displaystyle X} 6218: 6151: 6095: 5856: 5842: 5798: 5771: 5762: 5727: 5694:{\displaystyle j} 5674:{\displaystyle i} 5484: 5483: 5444: 5409: 5399:variant is used: 5388:{\displaystyle n} 5356:{\displaystyle X} 5265: 5138: 5082: 5038: 5003: 4784:of the points in 4746:{\displaystyle m} 4704:{\displaystyle n} 4650:{\displaystyle m} 4532: 4531: 4493: 4458: 4296: 4295: 4157: 4156: 3921: 3785: 3784: 3586: 3572:General attention 2938:{\displaystyle H} 2925:where the matrix 1837:Attention weights 1791: 1790: 1699:Attention weights 1693:control character 1431:{\displaystyle h} 1321:control character 1163: 1142: 1121: 1102: 950: 949: 755:Model diagnostics 738:Human-in-the-loop 581:Boltzmann machine 494:Anomaly detection 290:Linear regression 205:Ontology learning 200:Grammar induction 175:Semantic analysis 170:Association rules 155:Anomaly detection 97:Neuro-symbolic AI 9049: 9042:Machine learning 9019:Machine learning 9009: 9008: 8989: 8744:Action selection 8734:Self-driving car 8541:Stable Diffusion 8506:Speech synthesis 8471: 8470: 8335:Machine learning 8211:Gradient descent 8132: 8125: 8118: 8109: 8108: 8073: 8039: 8038: 8036: 8024: 8018: 8017: 8015: 8014: 7999: 7993: 7992: 7990: 7989: 7975: 7969: 7968: 7966: 7965: 7951: 7945: 7944: 7942: 7941: 7927: 7921: 7920: 7918: 7906: 7900: 7899: 7897: 7896: 7883: 7877: 7876: 7865: 7859: 7858: 7856: 7844: 7838: 7837: 7835: 7823: 7817: 7816: 7798: 7778: 7772: 7771: 7769: 7751: 7742: 7736: 7735: 7733: 7720: 7714: 7713: 7711: 7699: 7693: 7692: 7664: 7644: 7638: 7637: 7609: 7589: 7583: 7582: 7571: 7565: 7564: 7562: 7550: 7539: 7538: 7527: 7521: 7520: 7518: 7516: 7506: 7500: 7499: 7497: 7485: 7479: 7478: 7476: 7464: 7453: 7452: 7450: 7438: 7429: 7428: 7426: 7414: 7408: 7407: 7350: 7344: 7343: 7333: 7313: 7307: 7305: 7303: 7291: 7282: 7281: 7269: 7263: 7262: 7254: 7248: 7247: 7245: 7233: 7227: 7226: 7224: 7212: 7206: 7205: 7174: 7165: 7164: 7148: 7139: 7133: 7132: 7100: 7094: 7093: 7053: 7047: 7046: 7022: 7016: 7015: 7013: 7012: 6979: 6973: 6972: 6970: 6958: 6952: 6951: 6911: 6905: 6904: 6864: 6858: 6857: 6846: 6840: 6839: 6829: 6795: 6786: 6780: 6779: 6751: 6745: 6744: 6712: 6703: 6702: 6670: 6620: 6618: 6617: 6612: 6610: 6609: 6593: 6591: 6590: 6585: 6577: 6576: 6567: 6566: 6551: 6548: 6522: 6519: 6503: 6501: 6500: 6495: 6493: 6492: 6476: 6474: 6473: 6468: 6466: 6465: 6449: 6447: 6446: 6441: 6433: 6432: 6417: 6416: 6385: 6383: 6382: 6377: 6363: 6360: 6334: 6331: 6315: 6313: 6312: 6307: 6292: 6290: 6289: 6284: 6279: 6278: 6273: 6267: 6259: 6258: 6253: 6247: 6239: 6238: 6233: 6227: 6219: 6216: 6211: 6189: 6187: 6186: 6181: 6176: 6168: 6160: 6152: 6149: 6146: 6135: 6130: 6122: 6117: 6109: 6104: 6096: 6093: 6081: 6079: 6078: 6073: 6071: 6063: 6048: 6046: 6045: 6040: 6038: 6037: 6032: 6019: 6017: 6016: 6011: 6008: 6003: 5998: 5988: 5983: 5978: 5968: 5963: 5958: 5945: 5943: 5942: 5937: 5931: 5926: 5921: 5915: 5906: 5901: 5896: 5890: 5881: 5876: 5871: 5865: 5857: 5854: 5849: 5848: 5843: 5840: 5830: 5828: 5827: 5822: 5820: 5819: 5814: 5805: 5804: 5799: 5796: 5778: 5777: 5772: 5769: 5763: 5760: 5752: 5744: 5736: 5728: 5725: 5700: 5698: 5697: 5692: 5680: 5678: 5677: 5672: 5660: 5658: 5657: 5652: 5621:lower triangular 5618: 5616: 5615: 5610: 5608: 5607: 5596: 5583: 5581: 5580: 5575: 5556: 5554: 5553: 5548: 5546: 5545: 5534: 5525: 5514:where the mask, 5513: 5511: 5510: 5505: 5503: 5498: 5494: 5493: 5485: 5482: 5481: 5472: 5471: 5470: 5469: 5464: 5458: 5452: 5445: 5442: 5434: 5426: 5418: 5410: 5407: 5397:masked attention 5394: 5392: 5391: 5386: 5371:Masked Attention 5362: 5360: 5359: 5354: 5339: 5337: 5336: 5331: 5326: 5325: 5320: 5314: 5306: 5305: 5300: 5294: 5286: 5285: 5280: 5274: 5266: 5263: 5258: 5239: 5237: 5236: 5231: 5229: 5221: 5205: 5203: 5202: 5197: 5195: 5176: 5174: 5173: 5168: 5163: 5155: 5147: 5139: 5136: 5133: 5122: 5117: 5109: 5104: 5096: 5091: 5083: 5080: 5065: 5063: 5062: 5057: 5055: 5047: 5039: 5036: 5033: 5022: 5017: 5012: 5004: 5001: 4985: 4983: 4982: 4977: 4975: 4974: 4963: 4954: 4938: 4936: 4935: 4930: 4928: 4927: 4916: 4907: 4895: 4893: 4892: 4887: 4885: 4884: 4873: 4864: 4841: 4839: 4838: 4833: 4831: 4819: 4817: 4816: 4811: 4809: 4808: 4807: 4806: 4796: 4779: 4777: 4776: 4771: 4769: 4768: 4752: 4750: 4749: 4744: 4732: 4730: 4729: 4724: 4722: 4710: 4708: 4707: 4702: 4686: 4684: 4683: 4678: 4676: 4668: 4656: 4654: 4653: 4648: 4636: 4634: 4633: 4628: 4626: 4613:softmax function 4606: 4604: 4603: 4598: 4596: 4595: 4590: 4580: 4578: 4577: 4572: 4570: 4569: 4568: 4567: 4551: 4542: 4537: 4533: 4530: 4529: 4520: 4519: 4518: 4517: 4512: 4506: 4500: 4494: 4491: 4483: 4475: 4467: 4459: 4456: 4443: 4441: 4440: 4435: 4433: 4432: 4431: 4430: 4429: 4405: 4393: 4391: 4390: 4385: 4383: 4382: 4381: 4380: 4379: 4355: 4347: 4346: 4345: 4344: 4343: 4319: 4291: 4287: 4286: 4285: 4162: 4158: 4060: 4059: 3978: 3976: 3975: 3970: 3968: 3964: 3963: 3962: 3950: 3949: 3948: 3939: 3938: 3929: 3909: 3908: 3899: 3898: 3879: 3878: 3869: 3868: 3840: 3835: 3825: 3818: 3817: 3811: 3805:Softmax scaling 3794: 3612: 3608: 3601: 3587: 3567: 3565: 3564: 3559: 3541: 3539: 3538: 3533: 3525: 3524: 3488: 3486: 3485: 3480: 3475: 3474: 3459: 3458: 3443: 3442: 3427: 3395: 3380: 3378: 3377: 3372: 3370: 3360: 3353: 3352: 3337: 3336: 3321: 3320: 3311: 3310: 3298: 3258: 3242: 3241: 3226: 3225: 3210: 3209: 3200: 3199: 3187: 3147: 3127: 3125: 3124: 3119: 3111: 3110: 3098: 3097: 3049: 3047: 3046: 3041: 3039: 3038: 3022: 3020: 3019: 3014: 3011: 3006: 2990: 2988: 2987: 2982: 2974: 2973: 2961: 2960: 2944: 2942: 2941: 2936: 2924: 2922: 2921: 2916: 2911: 2910: 2892: 2891: 2882: 2881: 2862: 2861: 2851: 2846: 2831: 2802: 2801: 2786: 2785: 2770: 2769: 2759: 2754: 2742: 2710: 2709: 2686: 2684: 2683: 2678: 2676: 2675: 2663: 2662: 2650: 2649: 2629: 2627: 2626: 2621: 2613: 2612: 2603: 2602: 2590: 2589: 2577: 2576: 2567: 2566: 2554: 2553: 2537: 2535: 2534: 2529: 2521: 2520: 2511: 2510: 2498: 2497: 2488: 2487: 2475: 2474: 2454: 2452: 2451: 2446: 2434: 2429: 2420: 2419: 2406: 2401: 2392: 2391: 2379: 2344: 2343: 2331: 2330: 2310:softmax function 2307: 2305: 2304: 2299: 2271: 2269: 2268: 2263: 2260: 2255: 2246: 2245: 2229: 2227: 2226: 2221: 2218: 2213: 2204: 2203: 2187: 2185: 2184: 2179: 2170: 2165: 2156: 2155: 2142: 2137: 2128: 2127: 2108: 2106: 2105: 2100: 2092: 2091: 2082: 2081: 2069: 2068: 2056: 2055: 2046: 2045: 2033: 2032: 2012: 2010: 2009: 2004: 2002: 2001: 1985: 1983: 1982: 1977: 1975: 1974: 1964: 1959: 1947: 1946: 1926: 1924: 1923: 1918: 1916: 1915: 1899: 1897: 1896: 1891: 1888: 1883: 1851:database queries 1734: 1733: 1729:alignment matrix 1686: 1684: 1683: 1678: 1670: 1669: 1657: 1656: 1634: 1632: 1631: 1626: 1618: 1617: 1605: 1604: 1585: 1583: 1582: 1577: 1569: 1568: 1556: 1555: 1536: 1534: 1533: 1528: 1520: 1519: 1507: 1506: 1486: 1484: 1483: 1478: 1470: 1469: 1457: 1456: 1437: 1435: 1434: 1429: 1417: 1415: 1414: 1409: 1401: 1400: 1388: 1387: 1371: 1369: 1368: 1363: 1355: 1354: 1342: 1341: 1260:. It was termed 1184: 1182: 1181: 1176: 1174: 1173: 1164: 1161: 1153: 1152: 1143: 1140: 1132: 1131: 1122: 1119: 1110: 1055:Donald Broadbent 973:machine learning 942: 935: 928: 889:Related articles 766:Confusion matrix 519:Isolation forest 464:Graphical models 243: 242: 195:Learning to rank 190:Feature learning 28:Machine learning 19: 18: 9057: 9056: 9052: 9051: 9050: 9048: 9047: 9046: 9032: 9031: 9030: 9025: 8977: 8891: 8857:Google DeepMind 8835: 8801:Geoffrey Hinton 8760: 8697: 8623:Project Debater 8569: 8467:Implementations 8462: 8416: 8380: 8323: 8265:Backpropagation 8199: 8185:Tensor calculus 8139: 8136: 8048: 8043: 8042: 8025: 8021: 8012: 8010: 8000: 7996: 7987: 7985: 7977: 7976: 7972: 7963: 7961: 7953: 7952: 7948: 7939: 7937: 7929: 7928: 7924: 7907: 7903: 7894: 7892: 7885: 7884: 7880: 7867: 7866: 7862: 7845: 7841: 7824: 7820: 7779: 7775: 7749: 7743: 7739: 7721: 7717: 7700: 7696: 7681: 7645: 7641: 7626: 7590: 7586: 7573: 7572: 7568: 7551: 7542: 7528: 7524: 7514: 7512: 7508: 7507: 7503: 7486: 7482: 7465: 7456: 7439: 7432: 7415: 7411: 7351: 7347: 7314: 7310: 7292: 7285: 7270: 7266: 7255: 7251: 7234: 7230: 7213: 7209: 7175: 7168: 7161: 7146: 7140: 7136: 7101: 7097: 7054: 7050: 7023: 7019: 7010: 7008: 7006: 6980: 6976: 6959: 6955: 6912: 6908: 6873:Vision Research 6865: 6861: 6847: 6843: 6793: 6787: 6783: 6776: 6752: 6748: 6713: 6706: 6671: 6664: 6659: 6627: 6605: 6601: 6599: 6596: 6595: 6572: 6568: 6562: 6558: 6547: 6518: 6516: 6513: 6512: 6510: 6488: 6484: 6482: 6479: 6478: 6461: 6457: 6455: 6452: 6451: 6428: 6424: 6412: 6408: 6391: 6388: 6387: 6359: 6330: 6328: 6325: 6324: 6322: 6301: 6298: 6297: 6274: 6269: 6268: 6263: 6254: 6249: 6248: 6243: 6234: 6229: 6228: 6223: 6215: 6207: 6205: 6202: 6201: 6172: 6164: 6156: 6148: 6142: 6131: 6126: 6118: 6113: 6105: 6100: 6092: 6090: 6087: 6086: 6067: 6059: 6057: 6054: 6053: 6033: 6028: 6027: 6025: 6022: 6021: 6004: 5999: 5994: 5984: 5979: 5974: 5964: 5959: 5954: 5951: 5948: 5947: 5927: 5922: 5917: 5911: 5902: 5897: 5892: 5886: 5877: 5872: 5867: 5861: 5853: 5844: 5839: 5838: 5836: 5833: 5832: 5815: 5810: 5809: 5800: 5795: 5794: 5773: 5768: 5767: 5759: 5748: 5740: 5732: 5724: 5722: 5719: 5718: 5707: 5686: 5683: 5682: 5666: 5663: 5662: 5628: 5625: 5624: 5597: 5592: 5591: 5589: 5586: 5585: 5566: 5563: 5562: 5535: 5530: 5529: 5521: 5519: 5516: 5515: 5499: 5489: 5477: 5473: 5465: 5460: 5459: 5454: 5453: 5451: 5450: 5446: 5441: 5430: 5422: 5414: 5406: 5404: 5401: 5400: 5380: 5377: 5376: 5373: 5348: 5345: 5344: 5321: 5316: 5315: 5310: 5301: 5296: 5295: 5290: 5281: 5276: 5275: 5270: 5262: 5254: 5252: 5249: 5248: 5225: 5217: 5215: 5212: 5211: 5191: 5189: 5186: 5185: 5159: 5151: 5143: 5135: 5129: 5118: 5113: 5105: 5100: 5092: 5087: 5079: 5077: 5074: 5073: 5051: 5043: 5035: 5029: 5018: 5013: 5008: 5000: 4998: 4995: 4994: 4964: 4959: 4958: 4950: 4948: 4945: 4944: 4917: 4912: 4911: 4903: 4901: 4898: 4897: 4874: 4869: 4868: 4860: 4858: 4855: 4854: 4827: 4825: 4822: 4821: 4802: 4798: 4797: 4792: 4791: 4789: 4786: 4785: 4764: 4760: 4758: 4755: 4754: 4738: 4735: 4734: 4718: 4716: 4713: 4712: 4696: 4693: 4692: 4672: 4664: 4662: 4659: 4658: 4642: 4639: 4638: 4622: 4620: 4617: 4616: 4591: 4589: 4588: 4586: 4583: 4582: 4563: 4559: 4552: 4547: 4546: 4538: 4525: 4521: 4513: 4508: 4507: 4502: 4501: 4499: 4495: 4490: 4479: 4471: 4463: 4455: 4453: 4450: 4449: 4448:is defined as: 4425: 4421: 4414: 4410: 4409: 4401: 4399: 4396: 4395: 4375: 4371: 4364: 4360: 4359: 4351: 4339: 4335: 4328: 4324: 4323: 4315: 4313: 4310: 4309: 4306: 4301: 4289: 4283: 4281: 4280: 4278: 4272: 4266: 4260: 4254: 4249: 4244:in variant #3, 4242: 4238: 4190:teacher forcing 4126: 4120: 4114: 3988: 3983: 3982: 3981: 3980: 3966: 3965: 3955: 3951: 3944: 3940: 3934: 3930: 3920: 3916: 3904: 3900: 3894: 3890: 3883: 3874: 3870: 3864: 3860: 3850: 3848: 3845: 3844: 3838: 3833: 3824: 3820: 3815: 3813: 3810: 3806: 3795: 3607: 3606: 3605: 3576: 3574: 3547: 3544: 3543: 3517: 3513: 3511: 3508: 3507: 3495: 3470: 3466: 3454: 3450: 3438: 3434: 3399: 3388: 3386: 3383: 3382: 3368: 3367: 3358: 3357: 3348: 3344: 3332: 3328: 3316: 3312: 3306: 3302: 3270: 3263: 3254: 3247: 3246: 3237: 3233: 3221: 3217: 3205: 3201: 3195: 3191: 3159: 3152: 3143: 3135: 3133: 3130: 3129: 3106: 3102: 3093: 3089: 3087: 3084: 3083: 3056: 3034: 3030: 3028: 3025: 3024: 3007: 3002: 2996: 2993: 2992: 2969: 2965: 2956: 2952: 2950: 2947: 2946: 2930: 2927: 2926: 2906: 2902: 2887: 2883: 2877: 2873: 2857: 2853: 2847: 2842: 2809: 2797: 2793: 2781: 2777: 2765: 2761: 2755: 2750: 2714: 2705: 2701: 2699: 2696: 2695: 2671: 2667: 2658: 2654: 2645: 2641: 2639: 2636: 2635: 2608: 2604: 2598: 2594: 2585: 2581: 2572: 2568: 2562: 2558: 2549: 2545: 2543: 2540: 2539: 2516: 2512: 2506: 2502: 2493: 2489: 2483: 2479: 2470: 2466: 2464: 2461: 2460: 2430: 2425: 2415: 2411: 2402: 2397: 2387: 2383: 2357: 2339: 2335: 2326: 2322: 2317: 2314: 2313: 2281: 2278: 2277: 2256: 2251: 2241: 2237: 2235: 2232: 2231: 2214: 2209: 2199: 2195: 2193: 2190: 2189: 2166: 2161: 2151: 2147: 2138: 2133: 2123: 2119: 2117: 2114: 2113: 2087: 2083: 2077: 2073: 2064: 2060: 2051: 2047: 2041: 2037: 2028: 2024: 2022: 2019: 2018: 1997: 1993: 1991: 1988: 1987: 1970: 1966: 1960: 1955: 1942: 1938: 1936: 1933: 1932: 1911: 1907: 1905: 1902: 1901: 1884: 1879: 1873: 1870: 1869: 1839: 1829:, so it offers 1821:, so it offers 1797:corresponds to 1701: 1665: 1661: 1652: 1648: 1646: 1643: 1642: 1613: 1609: 1600: 1596: 1594: 1591: 1590: 1564: 1560: 1551: 1547: 1545: 1542: 1541: 1515: 1511: 1502: 1498: 1496: 1493: 1492: 1465: 1461: 1452: 1448: 1446: 1443: 1442: 1423: 1420: 1419: 1396: 1392: 1383: 1379: 1377: 1374: 1373: 1350: 1346: 1337: 1333: 1331: 1328: 1327: 1300: 1283: 1262:intra-attention 1239: 1233: 1213: 1169: 1165: 1160: 1148: 1144: 1139: 1127: 1123: 1118: 1106: 1100: 1097: 1096: 1071:saccade control 1063:George Sperling 1037: 1029: 1023: 946: 917: 916: 890: 882: 881: 842: 834: 833: 794:Kernel machines 789: 781: 780: 756: 748: 747: 728:Active learning 723: 715: 714: 683: 673: 672: 598:Diffusion model 534: 524: 523: 496: 486: 485: 459: 449: 448: 404:Factor analysis 399: 389: 388: 372: 335: 325: 324: 245: 244: 228: 227: 226: 215: 214: 120: 112: 111: 77:Online learning 42: 30: 17: 12: 11: 5: 9055: 9045: 9044: 9027: 9026: 9024: 9023: 9022: 9021: 9016: 9003: 9002: 9001: 8996: 8982: 8979: 8978: 8976: 8975: 8970: 8965: 8960: 8955: 8950: 8945: 8940: 8935: 8930: 8925: 8920: 8915: 8910: 8905: 8899: 8897: 8893: 8892: 8890: 8889: 8884: 8879: 8874: 8869: 8864: 8859: 8854: 8849: 8843: 8841: 8837: 8836: 8834: 8833: 8831:Ilya Sutskever 8828: 8823: 8818: 8813: 8808: 8803: 8798: 8796:Demis Hassabis 8793: 8788: 8786:Ian Goodfellow 8783: 8778: 8772: 8770: 8766: 8765: 8762: 8761: 8759: 8758: 8753: 8752: 8751: 8741: 8736: 8731: 8726: 8721: 8716: 8711: 8705: 8703: 8699: 8698: 8696: 8695: 8690: 8685: 8680: 8675: 8670: 8665: 8660: 8655: 8650: 8645: 8640: 8635: 8630: 8625: 8620: 8615: 8614: 8613: 8603: 8598: 8593: 8588: 8583: 8577: 8575: 8571: 8570: 8568: 8567: 8562: 8561: 8560: 8555: 8545: 8544: 8543: 8538: 8533: 8523: 8518: 8513: 8508: 8503: 8498: 8493: 8488: 8483: 8477: 8475: 8468: 8464: 8463: 8461: 8460: 8455: 8450: 8445: 8440: 8435: 8430: 8424: 8422: 8418: 8417: 8415: 8414: 8409: 8404: 8399: 8394: 8388: 8386: 8382: 8381: 8379: 8378: 8377: 8376: 8369:Language model 8366: 8361: 8356: 8355: 8354: 8344: 8343: 8342: 8331: 8329: 8325: 8324: 8322: 8321: 8319:Autoregression 8316: 8311: 8310: 8309: 8299: 8297:Regularization 8294: 8293: 8292: 8287: 8282: 8272: 8267: 8262: 8260:Loss functions 8257: 8252: 8247: 8242: 8237: 8236: 8235: 8225: 8220: 8219: 8218: 8207: 8205: 8201: 8200: 8198: 8197: 8195:Inductive bias 8192: 8187: 8182: 8177: 8172: 8167: 8162: 8157: 8149: 8147: 8141: 8140: 8135: 8134: 8127: 8120: 8112: 8106: 8105: 8092:(4 May 2020), 8087: 8074: 8047: 8046:External links 8044: 8041: 8040: 8019: 7994: 7970: 7946: 7922: 7901: 7878: 7860: 7839: 7818: 7773: 7737: 7715: 7694: 7679: 7639: 7624: 7584: 7566: 7540: 7531:Schlag, Imanol 7522: 7501: 7480: 7454: 7430: 7409: 7345: 7308: 7283: 7264: 7249: 7228: 7207: 7188:(1): 131–139. 7166: 7159: 7134: 7115:(3): 205–254. 7095: 7062:Applied Optics 7048: 7017: 7004: 6974: 6953: 6920:Applied Optics 6906: 6859: 6841: 6781: 6774: 6746: 6704: 6679:Neurocomputing 6661: 6660: 6658: 6655: 6654: 6653: 6648: 6643: 6638: 6633: 6626: 6623: 6608: 6604: 6583: 6580: 6575: 6571: 6565: 6561: 6557: 6554: 6546: 6543: 6540: 6537: 6534: 6531: 6528: 6525: 6509: 6506: 6491: 6487: 6464: 6460: 6439: 6436: 6431: 6427: 6423: 6420: 6415: 6411: 6407: 6404: 6401: 6398: 6395: 6375: 6372: 6369: 6366: 6358: 6355: 6352: 6349: 6346: 6343: 6340: 6337: 6321: 6318: 6305: 6294: 6293: 6282: 6277: 6272: 6266: 6262: 6257: 6252: 6246: 6242: 6237: 6232: 6226: 6222: 6214: 6210: 6191: 6190: 6179: 6175: 6171: 6167: 6163: 6159: 6155: 6145: 6141: 6138: 6134: 6129: 6125: 6121: 6116: 6112: 6108: 6103: 6099: 6070: 6066: 6062: 6036: 6031: 6007: 6002: 5997: 5992: 5987: 5982: 5977: 5972: 5967: 5962: 5957: 5935: 5930: 5925: 5920: 5914: 5910: 5905: 5900: 5895: 5889: 5885: 5880: 5875: 5870: 5864: 5860: 5852: 5847: 5818: 5813: 5808: 5803: 5793: 5790: 5787: 5784: 5781: 5776: 5766: 5758: 5755: 5751: 5747: 5743: 5739: 5735: 5731: 5706: 5703: 5690: 5670: 5650: 5647: 5644: 5641: 5638: 5635: 5632: 5606: 5603: 5600: 5595: 5573: 5570: 5544: 5541: 5538: 5533: 5528: 5524: 5502: 5497: 5492: 5488: 5480: 5476: 5468: 5463: 5457: 5449: 5440: 5437: 5433: 5429: 5425: 5421: 5417: 5413: 5384: 5372: 5369: 5352: 5341: 5340: 5329: 5324: 5319: 5313: 5309: 5304: 5299: 5293: 5289: 5284: 5279: 5273: 5269: 5261: 5257: 5242:self-attention 5228: 5224: 5220: 5194: 5178: 5177: 5166: 5162: 5158: 5154: 5150: 5146: 5142: 5132: 5128: 5125: 5121: 5116: 5112: 5108: 5103: 5099: 5095: 5090: 5086: 5067: 5066: 5054: 5050: 5046: 5042: 5032: 5028: 5025: 5021: 5016: 5011: 5007: 4973: 4970: 4967: 4962: 4957: 4953: 4926: 4923: 4920: 4915: 4910: 4906: 4883: 4880: 4877: 4872: 4867: 4863: 4830: 4805: 4801: 4795: 4767: 4763: 4742: 4721: 4700: 4675: 4671: 4667: 4646: 4625: 4594: 4566: 4562: 4558: 4555: 4550: 4545: 4541: 4536: 4528: 4524: 4516: 4511: 4505: 4498: 4489: 4486: 4482: 4478: 4474: 4470: 4466: 4462: 4428: 4424: 4420: 4417: 4413: 4408: 4404: 4378: 4374: 4370: 4367: 4363: 4358: 4354: 4350: 4342: 4338: 4334: 4331: 4327: 4322: 4318: 4308:For matrices: 4305: 4302: 4300: 4297: 4294: 4293: 4274: 4268: 4262: 4256: 4252: 4247: 4240: 4236: 4231: 4227: 4226: 4223: 4219: 4218: 4215: 4214:Qw, Kw, Vw, FC 4211: 4210: 4207: 4203: 4202: 4199: 4195: 4194: 4182: 4178: 4177: 4174: 4170: 4169: 4166: 4155: 4154: 4144: 4130: 4122: 4116: 4110: 4098: 4088: 4077: 4076: 4073: 4070: 4067: 4064: 4043: 4042: 4032: 4021:self-attention 4017: 4010: 4003: 4000:outer products 3996:neural network 3987: 3984: 3961: 3958: 3954: 3947: 3943: 3937: 3933: 3927: 3924: 3919: 3915: 3912: 3907: 3903: 3897: 3893: 3889: 3886: 3882: 3877: 3873: 3867: 3863: 3859: 3856: 3853: 3852: 3843: 3842: 3827: 3822: 3808: 3803: 3796: 3789: 3788: 3787: 3786: 3783: 3782: 3779: 3775: 3774: 3771: 3767: 3766: 3763: 3759: 3758: 3755: 3751: 3750: 3747: 3743: 3742: 3738: 3734: 3733: 3725: 3721: 3720: 3717: 3713: 3712: 3709:thought vector 3705: 3701: 3700: 3689: 3685: 3684: 3665: 3655: 3654: 3651: 3647: 3646: 3643: 3639: 3638: 3632: 3628: 3627: 3624: 3620: 3619: 3616: 3602: 3596: 3595: 3573: 3570: 3557: 3554: 3551: 3531: 3528: 3523: 3520: 3516: 3494: 3491: 3478: 3473: 3469: 3465: 3462: 3457: 3453: 3449: 3446: 3441: 3437: 3433: 3430: 3426: 3423: 3420: 3417: 3414: 3411: 3408: 3405: 3402: 3398: 3394: 3391: 3366: 3363: 3361: 3359: 3356: 3351: 3347: 3343: 3340: 3335: 3331: 3327: 3324: 3319: 3315: 3309: 3305: 3301: 3297: 3294: 3291: 3288: 3285: 3282: 3279: 3276: 3273: 3269: 3266: 3264: 3261: 3257: 3253: 3249: 3248: 3245: 3240: 3236: 3232: 3229: 3224: 3220: 3216: 3213: 3208: 3204: 3198: 3194: 3190: 3186: 3183: 3180: 3177: 3174: 3171: 3168: 3165: 3162: 3158: 3155: 3153: 3150: 3146: 3142: 3138: 3137: 3117: 3114: 3109: 3105: 3101: 3096: 3092: 3055: 3054:Self-attention 3052: 3037: 3033: 3010: 3005: 3001: 2980: 2977: 2972: 2968: 2964: 2959: 2955: 2934: 2914: 2909: 2905: 2901: 2898: 2895: 2890: 2886: 2880: 2876: 2872: 2869: 2865: 2860: 2856: 2850: 2845: 2841: 2837: 2834: 2830: 2827: 2824: 2821: 2818: 2815: 2812: 2808: 2805: 2800: 2796: 2792: 2789: 2784: 2780: 2776: 2773: 2768: 2764: 2758: 2753: 2749: 2745: 2741: 2738: 2735: 2732: 2729: 2726: 2723: 2720: 2717: 2713: 2708: 2704: 2674: 2670: 2666: 2661: 2657: 2653: 2648: 2644: 2619: 2616: 2611: 2607: 2601: 2597: 2593: 2588: 2584: 2580: 2575: 2571: 2565: 2561: 2557: 2552: 2548: 2527: 2524: 2519: 2515: 2509: 2505: 2501: 2496: 2492: 2486: 2482: 2478: 2473: 2469: 2457:context vector 2444: 2441: 2438: 2433: 2428: 2424: 2418: 2414: 2410: 2405: 2400: 2396: 2390: 2386: 2382: 2378: 2375: 2372: 2369: 2366: 2363: 2360: 2356: 2353: 2350: 2347: 2342: 2338: 2334: 2329: 2325: 2321: 2297: 2294: 2291: 2288: 2285: 2259: 2254: 2250: 2244: 2240: 2217: 2212: 2208: 2202: 2198: 2177: 2174: 2169: 2164: 2160: 2154: 2150: 2146: 2141: 2136: 2132: 2126: 2122: 2098: 2095: 2090: 2086: 2080: 2076: 2072: 2067: 2063: 2059: 2054: 2050: 2044: 2040: 2036: 2031: 2027: 2000: 1996: 1973: 1969: 1963: 1958: 1954: 1950: 1945: 1941: 1914: 1910: 1887: 1882: 1878: 1838: 1835: 1806:explainability 1789: 1788: 1785: 1782: 1779: 1775: 1774: 1771: 1768: 1765: 1761: 1760: 1757: 1754: 1751: 1747: 1746: 1743: 1740: 1737: 1700: 1697: 1689: 1688: 1676: 1673: 1668: 1664: 1660: 1655: 1651: 1639: 1636: 1624: 1621: 1616: 1612: 1608: 1603: 1599: 1587: 1575: 1572: 1567: 1563: 1559: 1554: 1550: 1538: 1526: 1523: 1518: 1514: 1510: 1505: 1501: 1476: 1473: 1468: 1464: 1460: 1455: 1451: 1427: 1407: 1404: 1399: 1395: 1391: 1386: 1382: 1361: 1358: 1353: 1349: 1345: 1340: 1336: 1299: 1296: 1282: 1279: 1232: 1229: 1223:this problem. 1212: 1209: 1205:hyper-networks 1197:sigma-pi units 1172: 1168: 1159: 1156: 1151: 1147: 1138: 1135: 1130: 1126: 1117: 1114: 1109: 1105: 1088:. It produced 1036: 1033: 1022: 1019: 948: 947: 945: 944: 937: 930: 922: 919: 918: 915: 914: 909: 908: 907: 897: 891: 888: 887: 884: 883: 880: 879: 874: 869: 864: 859: 854: 849: 843: 840: 839: 836: 835: 832: 831: 826: 821: 816: 814:Occam learning 811: 806: 801: 796: 790: 787: 786: 783: 782: 779: 778: 773: 771:Learning curve 768: 763: 757: 754: 753: 750: 749: 746: 745: 740: 735: 730: 724: 721: 720: 717: 716: 713: 712: 711: 710: 700: 695: 690: 684: 679: 678: 675: 674: 671: 670: 664: 659: 654: 649: 648: 647: 637: 632: 631: 630: 625: 620: 615: 605: 600: 595: 590: 589: 588: 578: 577: 576: 571: 566: 561: 551: 546: 541: 535: 530: 529: 526: 525: 522: 521: 516: 511: 503: 497: 492: 491: 488: 487: 484: 483: 482: 481: 476: 471: 460: 455: 454: 451: 450: 447: 446: 441: 436: 431: 426: 421: 416: 411: 406: 400: 395: 394: 391: 390: 387: 386: 381: 376: 370: 365: 360: 352: 347: 342: 336: 331: 330: 327: 326: 323: 322: 317: 312: 307: 302: 297: 292: 287: 279: 278: 277: 272: 267: 257: 255:Decision trees 252: 246: 232:classification 222: 221: 220: 217: 216: 213: 212: 207: 202: 197: 192: 187: 182: 177: 172: 167: 162: 157: 152: 147: 142: 137: 132: 127: 125:Classification 121: 118: 117: 114: 113: 110: 109: 104: 99: 94: 89: 84: 82:Batch learning 79: 74: 69: 64: 59: 54: 49: 43: 40: 39: 36: 35: 24: 23: 15: 9: 6: 4: 3: 2: 9054: 9043: 9040: 9039: 9037: 9020: 9017: 9015: 9012: 9011: 9004: 9000: 8997: 8995: 8992: 8991: 8988: 8984: 8983: 8980: 8974: 8971: 8969: 8966: 8964: 8961: 8959: 8956: 8954: 8951: 8949: 8946: 8944: 8941: 8939: 8936: 8934: 8931: 8929: 8926: 8924: 8921: 8919: 8916: 8914: 8911: 8909: 8906: 8904: 8901: 8900: 8898: 8896:Architectures 8894: 8888: 8885: 8883: 8880: 8878: 8875: 8873: 8870: 8868: 8865: 8863: 8860: 8858: 8855: 8853: 8850: 8848: 8845: 8844: 8842: 8840:Organizations 8838: 8832: 8829: 8827: 8824: 8822: 8819: 8817: 8814: 8812: 8809: 8807: 8804: 8802: 8799: 8797: 8794: 8792: 8789: 8787: 8784: 8782: 8779: 8777: 8776:Yoshua Bengio 8774: 8773: 8771: 8767: 8757: 8756:Robot control 8754: 8750: 8747: 8746: 8745: 8742: 8740: 8737: 8735: 8732: 8730: 8727: 8725: 8722: 8720: 8717: 8715: 8712: 8710: 8707: 8706: 8704: 8700: 8694: 8691: 8689: 8686: 8684: 8681: 8679: 8676: 8674: 8673:Chinchilla AI 8671: 8669: 8666: 8664: 8661: 8659: 8656: 8654: 8651: 8649: 8646: 8644: 8641: 8639: 8636: 8634: 8631: 8629: 8626: 8624: 8621: 8619: 8616: 8612: 8609: 8608: 8607: 8604: 8602: 8599: 8597: 8594: 8592: 8589: 8587: 8584: 8582: 8579: 8578: 8576: 8572: 8566: 8563: 8559: 8556: 8554: 8551: 8550: 8549: 8546: 8542: 8539: 8537: 8534: 8532: 8529: 8528: 8527: 8524: 8522: 8519: 8517: 8514: 8512: 8509: 8507: 8504: 8502: 8499: 8497: 8494: 8492: 8489: 8487: 8484: 8482: 8479: 8478: 8476: 8472: 8469: 8465: 8459: 8456: 8454: 8451: 8449: 8446: 8444: 8441: 8439: 8436: 8434: 8431: 8429: 8426: 8425: 8423: 8419: 8413: 8410: 8408: 8405: 8403: 8400: 8398: 8395: 8393: 8390: 8389: 8387: 8383: 8375: 8372: 8371: 8370: 8367: 8365: 8362: 8360: 8357: 8353: 8352:Deep learning 8350: 8349: 8348: 8345: 8341: 8338: 8337: 8336: 8333: 8332: 8330: 8326: 8320: 8317: 8315: 8312: 8308: 8305: 8304: 8303: 8300: 8298: 8295: 8291: 8288: 8286: 8283: 8281: 8278: 8277: 8276: 8273: 8271: 8268: 8266: 8263: 8261: 8258: 8256: 8253: 8251: 8248: 8246: 8243: 8241: 8240:Hallucination 8238: 8234: 8231: 8230: 8229: 8226: 8224: 8221: 8217: 8214: 8213: 8212: 8209: 8208: 8206: 8202: 8196: 8193: 8191: 8188: 8186: 8183: 8181: 8178: 8176: 8173: 8171: 8168: 8166: 8163: 8161: 8158: 8156: 8155: 8151: 8150: 8148: 8146: 8142: 8133: 8128: 8126: 8121: 8119: 8114: 8113: 8110: 8104:, via YouTube 8103: 8099: 8095: 8091: 8088: 8085: 8083: 8078: 8075: 8071: 8067: 8063: 8059: 8055: 8050: 8049: 8035: 8030: 8023: 8009: 8005: 7998: 7983: 7982: 7974: 7959: 7958: 7950: 7935: 7934: 7926: 7917: 7912: 7905: 7890: 7889: 7882: 7874: 7870: 7864: 7855: 7850: 7843: 7834: 7829: 7822: 7814: 7810: 7806: 7802: 7797: 7792: 7789:(2): 023057. 7788: 7784: 7777: 7768: 7763: 7759: 7755: 7748: 7741: 7732: 7727: 7719: 7710: 7705: 7698: 7690: 7686: 7682: 7676: 7672: 7668: 7663: 7658: 7654: 7650: 7643: 7635: 7631: 7627: 7621: 7617: 7613: 7608: 7603: 7599: 7595: 7588: 7580: 7579:catalyzex.com 7576: 7570: 7561: 7556: 7549: 7547: 7545: 7536: 7532: 7526: 7511: 7505: 7496: 7491: 7484: 7475: 7470: 7463: 7461: 7459: 7449: 7444: 7437: 7435: 7425: 7420: 7413: 7405: 7401: 7397: 7393: 7389: 7385: 7381: 7377: 7373: 7369: 7365: 7361: 7357: 7349: 7341: 7337: 7332: 7327: 7323: 7319: 7312: 7302: 7297: 7290: 7288: 7279: 7275: 7268: 7260: 7253: 7244: 7239: 7232: 7223: 7218: 7211: 7203: 7199: 7195: 7191: 7187: 7183: 7179: 7173: 7171: 7162: 7156: 7152: 7145: 7138: 7130: 7126: 7122: 7118: 7114: 7110: 7106: 7099: 7091: 7087: 7083: 7079: 7075: 7071: 7067: 7063: 7059: 7052: 7044: 7040: 7036: 7032: 7028: 7021: 7007: 7001: 6997: 6993: 6989: 6985: 6978: 6969: 6964: 6957: 6949: 6945: 6941: 6937: 6933: 6929: 6925: 6921: 6917: 6910: 6902: 6898: 6894: 6890: 6886: 6882: 6878: 6874: 6870: 6863: 6855: 6851: 6845: 6837: 6833: 6828: 6823: 6819: 6815: 6811: 6807: 6804:(5): 975–79. 6803: 6799: 6792: 6785: 6777: 6771: 6767: 6763: 6759: 6758: 6750: 6742: 6738: 6734: 6730: 6726: 6722: 6718: 6711: 6709: 6700: 6696: 6692: 6688: 6684: 6680: 6676: 6669: 6667: 6662: 6652: 6649: 6647: 6644: 6642: 6639: 6637: 6634: 6632: 6629: 6628: 6622: 6606: 6602: 6581: 6573: 6569: 6563: 6559: 6555: 6544: 6538: 6535: 6532: 6529: 6526: 6505: 6489: 6485: 6462: 6458: 6434: 6429: 6425: 6421: 6418: 6413: 6409: 6402: 6399: 6396: 6393: 6373: 6367: 6356: 6350: 6347: 6344: 6341: 6338: 6317: 6303: 6275: 6260: 6255: 6240: 6235: 6200: 6199: 6198: 6196: 6169: 6161: 6139: 6123: 6110: 6085: 6084: 6083: 6064: 6050: 6034: 6005: 6000: 5990: 5985: 5980: 5970: 5965: 5960: 5928: 5923: 5908: 5903: 5898: 5883: 5878: 5873: 5850: 5845: 5816: 5801: 5791: 5788: 5785: 5782: 5779: 5774: 5756: 5745: 5737: 5711: 5702: 5688: 5668: 5648: 5645: 5642: 5639: 5636: 5633: 5630: 5622: 5604: 5601: 5598: 5568: 5560: 5542: 5539: 5536: 5526: 5495: 5486: 5478: 5474: 5466: 5447: 5438: 5427: 5419: 5398: 5382: 5368: 5366: 5350: 5322: 5307: 5302: 5287: 5282: 5247: 5246: 5245: 5243: 5222: 5209: 5183: 5156: 5148: 5126: 5110: 5097: 5072: 5071: 5070: 5026: 4993: 4992: 4991: 4989: 4971: 4968: 4965: 4955: 4942: 4924: 4921: 4918: 4908: 4881: 4878: 4875: 4865: 4852: 4848: 4843: 4803: 4799: 4783: 4765: 4761: 4740: 4698: 4690: 4669: 4644: 4614: 4610: 4592: 4564: 4560: 4556: 4553: 4543: 4534: 4526: 4522: 4514: 4496: 4487: 4476: 4468: 4447: 4446:QKV attention 4418: 4406: 4368: 4356: 4348: 4332: 4320: 4277: 4271: 4265: 4259: 4251: 4243: 4232: 4229: 4228: 4224: 4221: 4220: 4216: 4213: 4212: 4208: 4205: 4204: 4200: 4197: 4196: 4191: 4187: 4183: 4180: 4179: 4175: 4172: 4171: 4167: 4164: 4163: 4149: 4145: 4140: 4135: 4131: 4125: 4119: 4113: 4108: 4103: 4099: 4093: 4089: 4083: 4079: 4078: 4074: 4071: 4068: 4065: 4062: 4061: 4058: 4054: 4050: 4048: 4040: 4036: 4033: 4031:a year later, 4030: 4026: 4022: 4018: 4015: 4011: 4008: 4004: 4001: 3997: 3993: 3992: 3991: 3959: 3956: 3945: 3935: 3931: 3925: 3922: 3913: 3905: 3901: 3895: 3891: 3880: 3875: 3865: 3861: 3857: 3831: 3828: 3804: 3800: 3799: 3793: 3780: 3777: 3776: 3772: 3769: 3768: 3764: 3761: 3760: 3756: 3753: 3752: 3748: 3745: 3744: 3739: 3736: 3735: 3730: 3726: 3723: 3722: 3718: 3715: 3714: 3710: 3706: 3703: 3702: 3698: 3694: 3690: 3687: 3686: 3682: 3678: 3674: 3670: 3666: 3664: 3660: 3657: 3656: 3652: 3649: 3648: 3644: 3641: 3640: 3636: 3633: 3630: 3629: 3625: 3622: 3621: 3617: 3614: 3613: 3600: 3594: 3569: 3555: 3552: 3549: 3529: 3526: 3521: 3518: 3514: 3499: 3490: 3471: 3467: 3463: 3460: 3455: 3451: 3447: 3444: 3439: 3435: 3431: 3396: 3392: 3389: 3364: 3362: 3349: 3345: 3341: 3338: 3333: 3329: 3325: 3322: 3317: 3313: 3307: 3303: 3267: 3265: 3259: 3255: 3251: 3238: 3234: 3230: 3227: 3222: 3218: 3214: 3211: 3206: 3202: 3196: 3192: 3156: 3154: 3148: 3144: 3140: 3115: 3112: 3107: 3103: 3099: 3094: 3090: 3081: 3076: 3068: 3060: 3051: 3035: 3031: 3008: 3003: 2999: 2978: 2975: 2970: 2966: 2962: 2957: 2953: 2932: 2907: 2903: 2899: 2888: 2878: 2874: 2870: 2858: 2854: 2848: 2843: 2839: 2806: 2798: 2794: 2790: 2787: 2782: 2778: 2774: 2771: 2766: 2762: 2756: 2751: 2747: 2711: 2706: 2702: 2692: 2688: 2672: 2668: 2664: 2659: 2655: 2651: 2646: 2642: 2633: 2617: 2614: 2609: 2605: 2599: 2595: 2591: 2586: 2582: 2578: 2573: 2569: 2563: 2559: 2555: 2550: 2546: 2525: 2522: 2517: 2513: 2507: 2503: 2499: 2494: 2490: 2484: 2480: 2476: 2471: 2467: 2458: 2439: 2436: 2431: 2426: 2422: 2416: 2412: 2408: 2403: 2398: 2394: 2388: 2384: 2354: 2348: 2345: 2340: 2336: 2332: 2327: 2323: 2311: 2295: 2292: 2289: 2286: 2283: 2274: 2257: 2252: 2248: 2242: 2238: 2215: 2210: 2206: 2200: 2196: 2175: 2172: 2167: 2162: 2158: 2152: 2148: 2144: 2139: 2134: 2130: 2124: 2120: 2110: 2096: 2093: 2088: 2084: 2078: 2074: 2070: 2065: 2061: 2057: 2052: 2048: 2042: 2038: 2034: 2029: 2025: 2016: 1998: 1994: 1971: 1967: 1961: 1956: 1952: 1948: 1943: 1939: 1930: 1912: 1908: 1885: 1880: 1876: 1866: 1864: 1860: 1856: 1852: 1843: 1834: 1832: 1828: 1824: 1820: 1816: 1812: 1807: 1802: 1800: 1796: 1786: 1783: 1780: 1777: 1776: 1772: 1769: 1766: 1763: 1762: 1758: 1755: 1752: 1749: 1748: 1744: 1741: 1738: 1736: 1735: 1732: 1730: 1726: 1722: 1718: 1714: 1710: 1706: 1696: 1694: 1674: 1671: 1666: 1662: 1658: 1653: 1649: 1640: 1637: 1622: 1619: 1614: 1610: 1606: 1601: 1597: 1588: 1573: 1570: 1565: 1561: 1557: 1552: 1548: 1539: 1524: 1521: 1516: 1512: 1508: 1503: 1499: 1490: 1489: 1488: 1474: 1471: 1466: 1462: 1458: 1453: 1449: 1439: 1425: 1405: 1402: 1397: 1393: 1389: 1384: 1380: 1359: 1356: 1351: 1347: 1343: 1338: 1334: 1324: 1322: 1312: 1304: 1295: 1287: 1278: 1276: 1275: 1270: 1265: 1263: 1259: 1255: 1250: 1248: 1244: 1238: 1228: 1224: 1221: 1216: 1208: 1206: 1202: 1198: 1194: 1190: 1189: 1170: 1149: 1133: 1128: 1107: 1103: 1093: 1091: 1090:saliency maps 1087: 1083: 1078: 1076: 1072: 1068: 1064: 1060: 1057:proposed the 1056: 1051: 1049: 1045: 1041: 1032: 1028: 1018: 1016: 1012: 1011:hidden layers 1008: 1003: 1001: 997: 991: 989: 985: 982: 978: 974: 970: 962: 954: 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282: 236: 230: 9010:Categories 8958:Autoencoder 8913:Transformer 8781:Alex Graves 8729:OpenAI Five 8633:IBM Watsonx 8255:Convolution 8233:Overfitting 8090:Alex Graves 8008:pytorch.org 7515:December 2, 5182:equivariant 4782:convex hull 4137:Decoder is 4105:Decoder is 3727:500 neuron 3667:9k and 10k 1799:cherchez-le 1231:Transformer 1000:transformer 703:Multi-agent 640:Transformer 539:Autoencoder 295:Naive Bayes 33:data mining 8999:Technology 8852:EleutherAI 8811:Fei-Fei Li 8806:Yann LeCun 8719:Q-learning 8702:Decisional 8628:IBM Watson 8536:Midjourney 8428:TensorFlow 8275:Activation 8228:Regression 8223:Clustering 8034:1810.00825 8013:2021-12-22 7988:2021-12-22 7964:2021-12-22 7940:2021-12-22 7916:2308.15594 7895:2024-04-07 7854:2407.12034 7833:2311.01906 7796:2304.07235 7767:2306.09927 7731:2204.04218 7709:1807.06521 7662:1709.01507 7607:1904.05873 7495:1703.03906 7448:1601.06733 7331:1606.01933 7222:1609.09106 7011:2024-08-06 6657:References 2230:is large, 1795:look it up 1727:yields an 1705:I love you 1235:See also: 1025:See also: 1015:attenuated 984:embeddings 688:Q-learning 586:Restricted 384:Mean shift 333:Clustering 310:Perceptron 238:regression 140:Clustering 135:Regression 8882:MIT CSAIL 8847:Anthropic 8816:Andrew Ng 8714:AlphaZero 8558:VideoPoet 8521:AlphaFold 8458:MindSpore 8412:SpiNNaker 8407:Memristor 8314:Diffusion 8290:Rectifier 8270:Batchnorm 8250:Attention 8245:Adversary 7689:206597034 7634:118673006 7535:ICML 2021 7474:1409.0473 7424:1410.5401 7404:205251479 7388:1476-4687 7301:1409.0473 7243:1409.3215 7129:0364-0213 7082:0003-6935 6968:1412.7755 6940:0003-6935 6893:0042-6989 6836:0001-4966 6741:0941-0643 6699:0925-2312 6685:: 48–62. 6646:Attention 6520:Attention 6403:⁡ 6332:Attention 6217:MultiHead 6213:↦ 6150:MultiHead 6094:MultiHead 5855:Attention 5726:MultiHead 5646:≤ 5634:≤ 5602:× 5572:∞ 5569:− 5540:× 5527:∈ 5408:Attention 5264:Attention 5260:↦ 5208:invariant 5137:Attention 5081:Attention 4969:× 4956:∈ 4922:× 4909:∈ 4879:× 4866:∈ 4689:unordered 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8280:Softmax 8145:General 8058:Distill 7801:Bibcode 7368:Bibcode 6901:7660596 6806:Bibcode 6636:seq2seq 6549:softmax 6361:softmax 5443:softmax 5206:); and 5037:softmax 5002:softmax 4691:set of 4492:softmax 4282:√ 4186:Pytorch 4160:Legend 3839:softmax 3834:softmax 3814:√ 3650:9k, 10k 3610:Legend 3493:Masking 1931:vector 1927:into a 1277:paper. 1220:seq2seq 1021:History 852:NeurIPS 669:(ECRAM) 623:AlexNet 265:Bagging 8887:Huawei 8867:OpenAI 8769:People 8739:MuZero 8601:Gemini 8596:Claude 8531:DALL-E 8443:Theano 7687: 7677: 7632: 7622: 7402: 7394: 7386: 7360:Nature 7200: 7157: 7127: 7088: 7080: 7002: 6946: 6938: 6899: 6891: 6834: 6772: 6739: 6697: 6594:where 6386:where 6020:, and 5761:Concat 5661:, row 4943:; and 4581:where 4288:where 2538:where 1859:values 1723:, and 1203:, and 645:Vision 501:RANSAC 379:OPTICS 374:DBSCAN 358:-means 165:AutoML 8953:Mamba 8724:SARSA 8688:LLaMA 8683:BLOOM 8668:GPT-J 8658:GPT-4 8653:GPT-3 8648:GPT-2 8643:GPT-1 8606:LaMDA 8438:Keras 8029:arXiv 7911:arXiv 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4326:R 4317:Q 4290:d 4284:d 4276:j 4270:i 4264:j 4258:i 4253:j 4248:i 4246:h 4241:j 4237:i 4235:x 4206:W 4127:. 4124:j 4121:x 4118:i 4041:. 4016:, 4009:, 3979:. 3960:m 3957:s 3953:] 3946:T 3942:) 3936:q 3932:W 3923:x 3918:( 3911:) 3906:T 3902:X 3896:k 3892:W 3888:( 3885:[ 3876:T 3872:) 3866:v 3862:W 3858:X 3855:( 3823:k 3809:k 3778:c 3770:H 3762:A 3754:w 3737:D 3724:E 3716:s 3704:h 3688:x 3681:Y 3673:x 3663:Y 3659:x 3556:j 3550:i 3530:0 3527:= 3522:j 3519:i 3515:w 3477:) 3472:V 3468:W 3464:H 3461:, 3456:K 3452:W 3448:H 3445:, 3440:Q 3436:W 3432:H 3429:( 3425:n 3422:o 3419:i 3416:t 3413:n 3410:e 3407:t 3404:t 3401:A 3397:= 3390:H 3355:) 3350:V 3346:W 3342:H 3339:, 3334:K 3330:W 3326:H 3323:, 3318:Q 3314:W 3308:1 3304:h 3300:( 3296:n 3293:o 3290:i 3287:t 3284:n 3281:e 3278:t 3275:t 3272:A 3268:= 3256:1 3252:h 3244:) 3239:V 3235:W 3231:H 3228:, 3223:K 3219:W 3215:H 3212:, 3207:Q 3203:W 3197:0 3193:h 3189:( 3185:n 3182:o 3179:i 3176:t 3173:n 3170:e 3167:t 3164:t 3161:A 3157:= 3145:0 3141:h 3113:, 3108:1 3104:h 3100:, 3095:0 3091:h 3036:0 3032:h 3009:d 3004:0 3000:h 2976:, 2971:1 2967:h 2963:, 2958:0 2954:h 2933:H 2913:) 2908:V 2904:W 2900:H 2897:( 2894:) 2889:T 2885:) 2879:K 2875:W 2871:H 2868:( 2864:) 2859:Q 2855:W 2849:d 2844:0 2840:h 2836:( 2833:( 2829:x 2826:a 2823:m 2820:t 2817:f 2814:o 2811:s 2807:= 2804:) 2799:V 2795:W 2791:H 2788:, 2783:K 2779:W 2775:H 2772:, 2767:Q 2763:W 2757:d 2752:0 2748:h 2744:( 2740:n 2737:o 2734:i 2731:t 2728:n 2725:e 2722:t 2719:t 2716:A 2712:= 2707:0 2703:c 2673:V 2669:W 2665:, 2660:K 2656:W 2652:, 2647:Q 2643:W 2615:, 2610:V 2606:W 2600:1 2596:h 2592:= 2587:1 2583:v 2579:, 2574:V 2570:W 2564:0 2560:h 2556:= 2551:0 2547:v 2523:+ 2518:1 2514:v 2504:w 2500:+ 2495:0 2491:v 2481:w 2477:= 2472:0 2468:c 2459:: 2443:) 2437:, 2432:T 2427:1 2423:k 2417:0 2413:q 2409:, 2404:T 2399:0 2395:k 2389:0 2385:q 2381:( 2377:x 2374:a 2371:m 2368:t 2365:f 2362:o 2359:s 2355:= 2352:) 2346:, 2337:w 2333:, 2324:w 2320:( 2293:, 2290:1 2287:, 2284:0 2258:T 2253:1 2249:k 2243:0 2239:q 2216:T 2211:0 2207:k 2201:0 2197:q 2173:, 2168:T 2163:1 2159:k 2153:0 2149:q 2145:, 2140:T 2135:0 2131:k 2125:0 2121:q 2094:, 2089:K 2085:W 2079:1 2075:h 2071:= 2066:1 2062:k 2058:, 2053:K 2049:W 2043:0 2039:h 2035:= 2030:0 2026:k 1999:K 1995:W 1972:Q 1968:W 1962:d 1957:0 1953:h 1949:= 1944:0 1940:q 1913:Q 1909:W 1886:d 1881:0 1877:h 1811:I 1739:I 1672:, 1667:1 1663:h 1659:, 1654:0 1650:h 1641:( 1620:, 1615:1 1611:h 1607:, 1602:0 1598:h 1589:( 1571:, 1566:1 1562:h 1558:, 1553:0 1549:h 1540:( 1522:, 1517:1 1513:h 1509:, 1504:0 1500:h 1491:( 1472:, 1467:1 1463:y 1459:, 1454:0 1450:y 1426:h 1403:, 1398:1 1394:h 1390:, 1385:0 1381:h 1357:, 1352:1 1348:x 1344:, 1339:0 1335:x 1171:i 1167:) 1158:( 1150:i 1146:) 1137:( 1134:, 1129:i 1125:) 1116:( 1108:i 941:e 934:t 927:v 507:k 356:k 283:k 241:) 229:(

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Knowledge

Attention (machine learning)

Index