50:(LTD) induction, and states that synaptic plasticity is stabilized by a dynamic adaptation of the time-averaged postsynaptic activity. According to the BCM model, when a pre-synaptic neuron fires, the post-synaptic neurons will tend to undergo LTP if it is in a high-activity state (e.g., is firing at high frequency, and/or has high internal calcium concentrations), or LTD if it is in a lower-activity state (e.g., firing in low frequency, low internal calcium concentrations). This theory is often used to explain how cortical neurons can undergo both LTP or LTD depending on different conditioning stimulus protocols applied to pre-synaptic neurons (usually high-frequency stimulation, or HFS, for LTP, or low-frequency stimulation, LFS, for LTD).
74:
allowing for decay of synapses, where no activity or unsynchronized activity between neurons results in a loss of connection strength. New biological evidence brought this activity to a peak in the 1970s, where theorists formalized various approximations in the theory, such as the use of firing frequency instead of potential in determining neuron excitation, and the assumption of ideal and, more importantly, linear synaptic integration of signals. That is, there is no unexpected behavior in the adding of input currents to determine whether or not a cell will fire.
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However, Hebb's rule has problems, namely that it has no mechanism for connections to get weaker and no upper bound for how strong they can get. In other words, the model is unstable, both theoretically and computationally. Later modifications gradually improved Hebb's rule, normalizing it and
89:, the latter of which plays an important role in the formation and storage of memories. Both of these areas are well-studied experimentally, but both theory and experiment have yet to establish conclusive synaptic behavior in other areas of the brain. It has been proposed that in the
1544:
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These approximations resulted in the basic form of BCM below in 1979, but the final step came in the form of mathematical analysis to prove stability and computational analysis to prove applicability, culminating in
Bienenstock, Cooper, and Munro's 1982 paper.
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3448:
101:
synapse follows an "inverse BCM rule", meaning that at the time of parallel fiber activation, a high calcium concentration in the
Purkinje cell results in LTD, while a lower concentration results in LTP. Furthermore, the biological implementation for
303:
1818:, or increases and decreases in synaptic strength, something which has not been observed in all cortical systems. Further, it requires a variable activation threshold and depends strongly on stability of the selected fixed points
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1777:{\displaystyle \,\phi (c,{\bar {c}})=c(c-\theta _{M})~~~{\textrm {and}}~~~\theta _{M}={\bar {c}}^{2}={\frac {1}{\tau }}\int _{-\infty }^{t}c^{2}(t^{\prime })e^{-(t-t^{\prime })/\tau }dt^{\prime },}
2239:
2110:
70:. This notion is foundational in the modern understanding of the brain as a neural network, and though not universally true, remains a good first approximation supported by decades of evidence.
3300:, which BCM was originally designed to model. This work provided further evidence of the necessity for a variable threshold function for stability in Hebbian-type learning (BCM or others).
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3134:
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1285:{\displaystyle \,\operatorname {sgn} \phi (c,{\bar {c}})=\operatorname {sgn} \left(c-\left({\frac {\bar {c}}{c_{0}}}\right)^{p}{\bar {c}}\right)~~{\textrm {for}}~c>0,~{\textrm {and}}}
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3523:, it has been put to use in lateral networks with some success. Furthermore, some existing computational network learning algorithms have been made to correspond to BCM learning.
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Rittenhouse, Cynthia D.; Harel Z. Shouval; Michael A. Paradiso; Mark F. Bear (1999). "Monocular deprivation induces homosynaptic long-term depression in visual cortex".
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is time since closure. Experiment agreed with the general shape of this prediction and provided an explanation for the dynamics of monocular eye closure (
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3511:) versus binocular eye closure. The experimental results are far from conclusive, but so far have favored BCM over competing theories of plasticity.
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3296:'s experimental work showed qualitative agreement with the final form of the BCM activation function. This experiment was later replicated in the
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1865:. However, the model's strength is that it incorporates all these requirements from independently derived rules of stability, such as
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confirmed BCM's prediction of synapse modification in the visual cortex when one eye is selectively closed. Specifically,
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2043:
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3820:"Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex"
1877:
This example is a particular case of the one at chapter "Mathematical results" of
Bienenstock at al. work, assuming
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3911:"Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade"
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3443:{\displaystyle \log \left({\frac {m_{\rm {closed}}(t)}{m_{\rm {closed}}(0)}}\right)\sim -{\overline {n^{2}}}t,}
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Repeating previous cycle we obtain, after several hundred of iterations, that stability is reached with
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878:. With this modification and discarding the uniform decay the rule takes the vectorial form:
298:{\displaystyle \,{\frac {dm_{j}(t)}{dt}}=\phi ({\textbf {c}}(t))d_{j}(t)-\epsilon m_{j}(t),}
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proposed a working mechanism for memory and computational adaption in the brain now called
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8:
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3988:(1996). "Experience-dependent modification of synaptic plasticity in rat visual cortex".
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3596:"Bidirectional Parallel Fiber Plasticity in the Cerebellum under Climbing Fiber Control"
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1378:{\displaystyle \,\phi (0,{\bar {c}})=0~~{\textrm {for}}~{\textrm {all}}~{\bar {c}},}
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The conditions for stable learning are derived rigorously in BCM noting that with
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Coesmans, Michiel; Weber, John T.; Zeeuw, Chris I. De; Hansel, Christian (2004).
976:{\displaystyle {\dot {\mathbf {m} }}(t)=\phi (c(t),{\bar {c}}(t))\mathbf {d} (t)}
142:
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The first major experimental confirmation of BCM came in 1992 in investigating
517:{\displaystyle c(t)={\textbf {w}}(t){\textbf {d}}(t)=\sum _{j}w_{j}(t)d_{j}(t)}
94:
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describes the variance in spontaneous activity or noise in the closed eye and
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has become orthogonal to one of the input patterns, being the final values of
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3561:
3540:
Izhikevich, Eugene M.; Desai, Niraj S. (2003-07-01). "Relating STDP to BCM".
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82:
39:
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is the inner product of weights and input currents (weighted sum of inputs),
4161:
4125:"Reinforcement Learning, Spike-Time-Dependent Plasticity, and the BCM Rule"
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2033:{\displaystyle \theta _{M}=({\bar {c}}/c_{0})^{p}{\bar {c}}={\bar {c}}^{3}}
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is a non-linear function. This function must change sign at some threshold
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1117:{\displaystyle {\bar {c}}(t)\approx {\textbf {m}}(t){\bar {\mathbf {d} }}}
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and a decay function with time proportional to the square of the output.
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is the (often negligible) time constant of uniform decay of all synapses.
86:
81:
Since then, experiments have shown evidence for BCM behavior in both the
59:
35:
1481:{\displaystyle \theta _{M}({\bar {c}})=({\bar {c}}/c_{0})^{p}{\bar {c}}}
3815:
90:
4011:
3303:
Experimental evidence has been non-specific to BCM until
Rittenhouse
2112:
that fulfills the stability conditions said in previous chapter.
42:
developed in 1981. The BCM model proposes a sliding threshold for
4064:
3976:
2892:. Adding 10% of the derivative to the weights we obtain new ones
2608:. Adding 10% of the derivative to the weights we obtain new ones
3806:
3519:
While the algorithm of BCM is too complicated for large-scale
3702:"Spike-Timing-Dependent Plasticity: A Comprehensive Overview"
2473:
is equal to 0.095 and we use same value as initial average
1046:{\displaystyle c(t)={\textbf {m}}(t)\cdot {\textbf {d}}(t)}
3764:"Memories and memory: A physicist's approach to the brain"
38:, and Paul Munro, is a physical theory of learning in the
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When implemented, the theory is often taken such that
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2234:{\displaystyle \mathbf {d} =(d_{1},d_{2})=(0.9,0.1)}
2169:, its activity a repetitive cycle with half of time
2115:
Assume two presynaptic neurons that provides inputs
2105:{\displaystyle \phi (c,{\bar {c}})=c(c-\theta _{M})}
3649:. Kandel, Eric R. (5th ed.). New York. 2013.
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4105:. School of Computer Science, Tel-Aviv University
3884:. School of Computer Science, Tel-Aviv University
1053:and with the approximation of the average output
4207:
3212:Note how, as predicted, the final weight vector
3539:
3901:
3086:{\displaystyle {\bar {c}}={\sqrt {8}}/2=1.414}
753:to avoid the Hebbian problems of instability.
4122:
4093:
3875:
3129:{\displaystyle \theta _{M}={\sqrt {8}}=2.828}
1810:The model has drawbacks, as it requires both
733:, and requires a suitable choice of function
2330:value in first and second half of a cycle.
141:. There might be a discussion about this on
2971:{\displaystyle \mathbf {m} =(3.246,-0.927)}
3677:: CS1 maint: location missing publisher (
2925:{\displaystyle \mathbf {m} =(0.110,0.055)}
2724:{\displaystyle \mathbf {m} =(0.101,0.051)}
2641:{\displaystyle \mathbf {m} =(0.101,0.051)}
4143:
3947:
3937:
3846:
3771:International Journal of Modern Physics A
3735:
3717:
3611:
1548:
1300:
1134:
183:
161:Learn how and when to remove this message
3252:in both intervals zeros of the function
3202:{\displaystyle {\dot {m}}=(0.000,0.000)}
2885:{\displaystyle {\dot {m}}=(0.001,0.002)}
2601:{\displaystyle {\dot {m}}=(0.008,0.001)}
3878:"The BCM theory of synaptic plasticity"
2446:{\displaystyle \mathbf {m} =(0.1,0.05)}
2366:{\displaystyle \mathbf {m} =(0.1,0.05)}
650:. See below for details and properties.
68:cells that fire together, wire together
4208:
3758:
2684:{\displaystyle \mathbf {d} =(0.2,0.7)}
2406:{\displaystyle \mathbf {d} =(0.9,0.1)}
2274:{\displaystyle \mathbf {d} =(0.2,0.7)}
726:{\displaystyle {\dot {m_{j}}}=cd_{j}}
677:This model is a modified form of the
3802:
3800:
3798:
3641:
3639:
3589:
3587:
2310:time average will be the average of
1388:or equivalently, that the threshold
113:
3480:{\displaystyle {\overline {n^{2}}}}
3007:{\displaystyle c={\sqrt {8}}=2.828}
1807:is a time constant of selectivity.
1086:
1029:
1010:
822:{\displaystyle \phi (c,{\bar {c}})}
449:
433:
231:
13:
3839:10.1523/JNEUROSCI.02-01-00032.1982
3706:Frontiers in Synaptic Neuroscience
3389:
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3374:
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173:The basic BCM rule takes the form
106:in BCM has yet to be established.
14:
4237:
4194:
3795:
3636:
3584:
2812:{\displaystyle \theta _{M}=0.000}
2651:In next half of time, inputs are
2528:{\displaystyle \theta _{M}=0.001}
4096:"BCM Learning Rule, Comp Issues"
2943:
2900:
2699:
2659:
2616:
2421:
2381:
2341:
2249:
2177:
1104:
960:
892:
643:{\displaystyle c<\theta _{M}}
118:
4123:Baras, Dorit; Ron Meir (2007).
4116:
4087:
4034:
3700:; Sjöström, Per Jesper (2012).
3521:parallel distributed processing
3514:
4094:Intrator, Nathan (2006–2007).
3970:
3895:
3876:Intrator, Nathan (2006–2007).
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2018:
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1965:
1956:
1745:
1726:
1715:
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1601:
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1535:are fixed positive constants.
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1304:
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338:is the synaptic weight of the
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200:
53:
16:Neuroscience model of learning
1:
3526:
3275:
2333:Let initial value of weights
610:{\displaystyle \phi (c)<0}
3647:Principles of neural science
3613:10.1016/j.neuron.2004.10.031
3472:
3429:
2373:. In the first half of time
756:Bienenstock at al. rewrite
7:
4154:10.1162/neco.2007.19.8.2245
3827:The Journal of Neuroscience
3155:{\displaystyle \phi =0.000}
2838:{\displaystyle \phi =0.003}
2554:{\displaystyle \phi =0.009}
575:{\displaystyle \theta _{M}}
407:th synapse's input current,
10:
4242:
4221:Computational neuroscience
3554:10.1162/089976603321891783
2779:{\displaystyle {\bar {c}}}
2495:{\displaystyle {\bar {c}}}
2303:{\displaystyle {\bar {c}}}
1872:
851:{\displaystyle {\bar {c}}}
3783:10.1142/s0217751x0000272x
666:{\displaystyle \epsilon }
109:
24:BCM synaptic modification
3719:10.3389/fnsyn.2012.00002
2786:of full cycle is 0.075,
1124:, it is sufficient that
778:{\displaystyle \phi (c)}
548:{\displaystyle \phi (c)}
3939:10.1073/pnas.89.10.4363
3033:{\displaystyle c=0.000}
2750:{\displaystyle c=0.055}
1929:{\displaystyle c_{0}=1}
858:is the time average of
4172:. 2561. Archived from
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3130:
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2106:
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1930:
1897:
1859:
1839:
1812:long-term potentiation
1801:
1778:
1529:
1502:
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872:
852:
823:
779:
747:
727:
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611:
576:
549:
518:
401:
381:
352:
332:
299:
44:long-term potentiation
3918:Proc. Natl. Acad. Sci
3681:) CS1 maint: others (
3509:monocular deprivation
3502:
3482:
3445:
3267:
3265:{\displaystyle \phi }
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3204:
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2162:{\displaystyle d_{2}}
2137:
2135:{\displaystyle d_{1}}
2107:
2035:
1931:
1898:
1860:
1840:
1838:{\displaystyle c_{0}}
1802:
1800:{\displaystyle \tau }
1779:
1530:
1528:{\displaystyle c_{0}}
1503:
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1119:
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978:
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853:
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746:{\displaystyle \phi }
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612:
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519:
402:
382:
380:{\displaystyle d_{j}}
353:
333:
331:{\displaystyle m_{j}}
300:
4201:Scholarpedia article
3808:Bienenstock, Elie L.
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2417:
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2337:
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2285:
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2173:
2146:
2119:
2044:
1940:
1936:. With these values
1907:
1881:
1849:
1822:
1816:long-term depression
1791:
1545:
1512:
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1392:
1297:
1131:
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833:
789:
760:
737:
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657:
621:
586:
559:
530:
413:
391:
364:
342:
315:
180:
131:confusing or unclear
66:, or the maxim that
48:long-term depression
4057:1999Natur.397..347R
4004:1996Natur.381..526K
3930:1992PNAS...89.4363D
3040:(remainder time),
2453:, the weighted sum
2241:and remainder time
1896:{\displaystyle p=2}
1691:
139:clarify the article
104:synaptic plasticity
4132:Neural Computation
4103:Neural Computation
3882:Neural Computation
3542:Neural Computation
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514:
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377:
348:
328:
295:
3998:(6582): 526–528.
3978:Kirkwood, Alfredo
3924:(10): 4363–4367.
3777:(26): 4069–4082.
3698:Gerstner, Wulfram
3656:978-0-07-139011-8
3500:{\displaystyle t}
3475:
3432:
3405:
3245:{\displaystyle c}
3225:{\displaystyle m}
3178:
3118:
3067:
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3014:(first half) and
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2861:
2773:
2577:
2489:
2466:{\displaystyle c}
2323:{\displaystyle c}
2297:
2068:
2021:
2005:
1968:
1858:{\displaystyle p}
1672:
1652:
1628:
1625:
1622:
1617:
1612:
1609:
1606:
1570:
1501:{\displaystyle p}
1475:
1438:
1417:
1369:
1359:
1354:
1349:
1344:
1339:
1336:
1322:
1279:
1274:
1259:
1254:
1249:
1246:
1236:
1215:
1203:
1162:
1111:
1088:
1069:
1031:
1012:
944:
899:
871:{\displaystyle c}
845:
813:
704:
466:
451:
435:
400:{\displaystyle j}
351:{\displaystyle j}
233:
218:
171:
170:
163:
4233:
4188:
4187:
4185:
4184:
4178:
4147:
4138:(8): 2245–2279.
4129:
4120:
4114:
4113:
4111:
4110:
4100:
4091:
4085:
4084:
4051:(6717): 347–50.
4038:
4032:
4031:
4012:10.1038/381526a0
3974:
3968:
3967:
3965:
3964:
3951:
3941:
3915:
3903:Dudek, Serena M.
3899:
3893:
3892:
3890:
3889:
3873:
3867:
3866:
3864:
3863:
3850:
3824:
3818:(January 1982).
3804:
3793:
3792:
3790:
3789:
3768:
3756:
3750:
3749:
3739:
3721:
3696:Markram, Henry;
3693:
3687:
3686:
3676:
3668:
3643:
3634:
3633:
3615:
3591:
3582:
3581:
3548:(7): 1511–1523.
3537:
3506:
3504:
3503:
3498:
3486:
3484:
3483:
3478:
3476:
3471:
3470:
3461:
3449:
3447:
3446:
3441:
3433:
3428:
3427:
3418:
3410:
3406:
3404:
3394:
3393:
3392:
3366:
3356:
3355:
3354:
3328:
3271:
3269:
3268:
3263:
3251:
3249:
3248:
3243:
3231:
3229:
3228:
3223:
3208:
3206:
3205:
3200:
3180:
3179:
3171:
3161:
3159:
3158:
3153:
3135:
3133:
3132:
3127:
3119:
3114:
3109:
3108:
3092:
3090:
3089:
3084:
3073:
3068:
3063:
3058:
3057:
3049:
3039:
3037:
3036:
3031:
3013:
3011:
3010:
3005:
2997:
2992:
2977:
2975:
2974:
2969:
2946:
2931:
2929:
2928:
2923:
2903:
2891:
2889:
2888:
2883:
2863:
2862:
2854:
2844:
2842:
2841:
2836:
2818:
2816:
2815:
2810:
2802:
2801:
2785:
2783:
2782:
2777:
2775:
2774:
2766:
2756:
2754:
2753:
2748:
2730:
2728:
2727:
2722:
2702:
2690:
2688:
2687:
2682:
2662:
2647:
2645:
2644:
2639:
2619:
2607:
2605:
2604:
2599:
2579:
2578:
2570:
2560:
2558:
2557:
2552:
2534:
2532:
2531:
2526:
2518:
2517:
2501:
2499:
2498:
2493:
2491:
2490:
2482:
2472:
2470:
2469:
2464:
2452:
2450:
2449:
2444:
2424:
2412:
2410:
2409:
2404:
2384:
2372:
2370:
2369:
2364:
2344:
2329:
2327:
2326:
2321:
2309:
2307:
2306:
2301:
2299:
2298:
2290:
2280:
2278:
2277:
2272:
2252:
2240:
2238:
2237:
2232:
2209:
2208:
2196:
2195:
2180:
2168:
2166:
2165:
2160:
2158:
2157:
2141:
2139:
2138:
2133:
2131:
2130:
2111:
2109:
2108:
2103:
2098:
2097:
2070:
2069:
2061:
2039:
2037:
2036:
2031:
2029:
2028:
2023:
2022:
2014:
2007:
2006:
1998:
1995:
1994:
1985:
1984:
1975:
1970:
1969:
1961:
1952:
1951:
1935:
1933:
1932:
1927:
1919:
1918:
1902:
1900:
1899:
1894:
1864:
1862:
1861:
1856:
1844:
1842:
1841:
1836:
1834:
1833:
1806:
1804:
1803:
1798:
1783:
1781:
1780:
1775:
1770:
1769:
1757:
1756:
1752:
1744:
1743:
1714:
1713:
1701:
1700:
1690:
1685:
1673:
1665:
1660:
1659:
1654:
1653:
1645:
1638:
1637:
1626:
1623:
1620:
1619:
1618:
1615:
1610:
1607:
1604:
1600:
1599:
1572:
1571:
1563:
1534:
1532:
1531:
1526:
1524:
1523:
1507:
1505:
1504:
1499:
1487:
1485:
1484:
1479:
1477:
1476:
1468:
1465:
1464:
1455:
1454:
1445:
1440:
1439:
1431:
1419:
1418:
1410:
1404:
1403:
1384:
1382:
1381:
1376:
1371:
1370:
1362:
1357:
1356:
1355:
1352:
1347:
1346:
1345:
1342:
1337:
1334:
1324:
1323:
1315:
1291:
1289:
1288:
1283:
1281:
1280:
1277:
1272:
1257:
1256:
1255:
1252:
1247:
1244:
1243:
1239:
1238:
1237:
1229:
1226:
1225:
1220:
1216:
1214:
1213:
1204:
1196:
1194:
1164:
1163:
1155:
1123:
1121:
1120:
1115:
1113:
1112:
1107:
1102:
1090:
1089:
1071:
1070:
1062:
1052:
1050:
1049:
1044:
1033:
1032:
1014:
1013:
982:
980:
979:
974:
963:
946:
945:
937:
901:
900:
895:
890:
877:
875:
874:
869:
857:
855:
854:
849:
847:
846:
838:
828:
826:
825:
820:
815:
814:
806:
784:
782:
781:
776:
752:
750:
749:
744:
732:
730:
729:
724:
722:
721:
706:
705:
700:
699:
690:
679:Hebbian learning
672:
670:
669:
664:
649:
647:
646:
641:
639:
638:
616:
614:
613:
608:
581:
579:
578:
573:
571:
570:
554:
552:
551:
546:
523:
521:
520:
515:
504:
503:
485:
484:
474:
453:
452:
437:
436:
406:
404:
403:
398:
386:
384:
383:
378:
376:
375:
357:
355:
354:
349:
337:
335:
334:
329:
327:
326:
304:
302:
301:
296:
282:
281:
257:
256:
235:
234:
219:
217:
209:
199:
198:
185:
166:
159:
155:
152:
146:
122:
121:
114:
64:Hebbian learning
32:Elie Bienenstock
4241:
4240:
4236:
4235:
4234:
4232:
4231:
4230:
4226:Neuroplasticity
4206:
4205:
4197:
4192:
4191:
4182:
4180:
4176:
4127:
4121:
4117:
4108:
4106:
4098:
4092:
4088:
4039:
4035:
3975:
3971:
3962:
3960:
3913:
3900:
3896:
3887:
3885:
3874:
3870:
3861:
3859:
3822:
3805:
3796:
3787:
3785:
3766:
3757:
3753:
3694:
3690:
3670:
3669:
3657:
3645:
3644:
3637:
3592:
3585:
3538:
3534:
3529:
3517:
3492:
3489:
3488:
3466:
3462:
3460:
3458:
3455:
3454:
3423:
3419:
3417:
3373:
3372:
3368:
3367:
3335:
3334:
3330:
3329:
3327:
3323:
3315:
3312:
3311:
3278:
3257:
3254:
3253:
3237:
3234:
3233:
3217:
3214:
3213:
3170:
3169:
3167:
3164:
3163:
3141:
3138:
3137:
3113:
3104:
3100:
3098:
3095:
3094:
3069:
3062:
3048:
3047:
3045:
3042:
3041:
3019:
3016:
3015:
2991:
2983:
2980:
2979:
2942:
2940:
2937:
2936:
2899:
2897:
2894:
2893:
2853:
2852:
2850:
2847:
2846:
2824:
2821:
2820:
2797:
2793:
2791:
2788:
2787:
2765:
2764:
2762:
2759:
2758:
2736:
2733:
2732:
2698:
2696:
2693:
2692:
2658:
2656:
2653:
2652:
2615:
2613:
2610:
2609:
2569:
2568:
2566:
2563:
2562:
2540:
2537:
2536:
2513:
2509:
2507:
2504:
2503:
2481:
2480:
2478:
2475:
2474:
2458:
2455:
2454:
2420:
2418:
2415:
2414:
2380:
2378:
2375:
2374:
2340:
2338:
2335:
2334:
2315:
2312:
2311:
2289:
2288:
2286:
2283:
2282:
2248:
2246:
2243:
2242:
2204:
2200:
2191:
2187:
2176:
2174:
2171:
2170:
2153:
2149:
2147:
2144:
2143:
2126:
2122:
2120:
2117:
2116:
2093:
2089:
2060:
2059:
2045:
2042:
2041:
2024:
2013:
2012:
2011:
1997:
1996:
1990:
1986:
1980:
1976:
1971:
1960:
1959:
1947:
1943:
1941:
1938:
1937:
1914:
1910:
1908:
1905:
1904:
1882:
1879:
1878:
1875:
1867:normalizability
1850:
1847:
1846:
1829:
1825:
1823:
1820:
1819:
1792:
1789:
1788:
1765:
1761:
1748:
1739:
1735:
1722:
1718:
1709:
1705:
1696:
1692:
1686:
1678:
1664:
1655:
1644:
1643:
1642:
1633:
1629:
1614:
1613:
1595:
1591:
1562:
1561:
1546:
1543:
1542:
1519:
1515:
1513:
1510:
1509:
1493:
1490:
1489:
1467:
1466:
1460:
1456:
1450:
1446:
1441:
1430:
1429:
1409:
1408:
1399:
1395:
1393:
1390:
1389:
1361:
1360:
1351:
1350:
1341:
1340:
1314:
1313:
1298:
1295:
1294:
1276:
1275:
1251:
1250:
1228:
1227:
1221:
1209:
1205:
1195:
1193:
1189:
1188:
1181:
1177:
1154:
1153:
1132:
1129:
1128:
1103:
1101:
1100:
1085:
1084:
1061:
1060:
1058:
1055:
1054:
1028:
1027:
1009:
1008:
991:
988:
987:
959:
936:
935:
891:
889:
888:
886:
883:
882:
863:
860:
859:
837:
836:
834:
831:
830:
805:
804:
790:
787:
786:
761:
758:
757:
738:
735:
734:
717:
713:
695:
691:
689:
688:
686:
683:
682:
658:
655:
654:
634:
630:
622:
619:
618:
617:if and only if
587:
584:
583:
566:
562:
560:
557:
556:
531:
528:
527:
499:
495:
480:
476:
470:
448:
447:
432:
431:
414:
411:
410:
392:
389:
388:
371:
367:
365:
362:
361:
343:
340:
339:
322:
318:
316:
313:
312:
277:
273:
252:
248:
230:
229:
210:
194:
190:
186:
184:
181:
178:
177:
167:
156:
150:
147:
136:
123:
119:
112:
56:
17:
12:
11:
5:
4239:
4229:
4228:
4223:
4218:
4204:
4203:
4196:
4195:External links
4193:
4190:
4189:
4145:10.1.1.119.395
4115:
4086:
4033:
3982:Marc G. Rioult
3969:
3894:
3868:
3794:
3751:
3688:
3655:
3635:
3606:(4): 691–700.
3583:
3531:
3530:
3528:
3525:
3516:
3513:
3496:
3474:
3469:
3465:
3451:
3450:
3439:
3436:
3431:
3426:
3422:
3416:
3413:
3409:
3403:
3400:
3397:
3391:
3388:
3385:
3382:
3379:
3376:
3371:
3365:
3362:
3359:
3353:
3350:
3347:
3344:
3341:
3338:
3333:
3326:
3322:
3319:
3277:
3274:
3261:
3241:
3221:
3198:
3195:
3192:
3189:
3186:
3183:
3177:
3174:
3151:
3148:
3145:
3125:
3122:
3117:
3112:
3107:
3103:
3082:
3079:
3076:
3072:
3066:
3061:
3055:
3052:
3029:
3026:
3023:
3003:
3000:
2995:
2990:
2987:
2967:
2964:
2961:
2958:
2955:
2952:
2949:
2945:
2921:
2918:
2915:
2912:
2909:
2906:
2902:
2881:
2878:
2875:
2872:
2869:
2866:
2860:
2857:
2834:
2831:
2828:
2808:
2805:
2800:
2796:
2772:
2769:
2746:
2743:
2740:
2731:. That means
2720:
2717:
2714:
2711:
2708:
2705:
2701:
2680:
2677:
2674:
2671:
2668:
2665:
2661:
2637:
2634:
2631:
2628:
2625:
2622:
2618:
2597:
2594:
2591:
2588:
2585:
2582:
2576:
2573:
2550:
2547:
2544:
2524:
2521:
2516:
2512:
2488:
2485:
2462:
2442:
2439:
2436:
2433:
2430:
2427:
2423:
2402:
2399:
2396:
2393:
2390:
2387:
2383:
2362:
2359:
2356:
2353:
2350:
2347:
2343:
2319:
2296:
2293:
2270:
2267:
2264:
2261:
2258:
2255:
2251:
2230:
2227:
2224:
2221:
2218:
2215:
2212:
2207:
2203:
2199:
2194:
2190:
2186:
2183:
2179:
2156:
2152:
2129:
2125:
2101:
2096:
2092:
2088:
2085:
2082:
2079:
2076:
2073:
2067:
2064:
2058:
2055:
2052:
2049:
2040:and we decide
2027:
2020:
2017:
2010:
2004:
2001:
1993:
1989:
1983:
1979:
1974:
1967:
1964:
1958:
1955:
1950:
1946:
1925:
1922:
1917:
1913:
1892:
1889:
1886:
1874:
1871:
1854:
1832:
1828:
1796:
1785:
1784:
1773:
1768:
1764:
1760:
1755:
1751:
1747:
1742:
1738:
1734:
1731:
1728:
1725:
1721:
1717:
1712:
1708:
1704:
1699:
1695:
1689:
1684:
1681:
1677:
1671:
1668:
1663:
1658:
1651:
1648:
1641:
1636:
1632:
1603:
1598:
1594:
1590:
1587:
1584:
1581:
1578:
1575:
1569:
1566:
1560:
1557:
1554:
1551:
1522:
1518:
1497:
1474:
1471:
1463:
1459:
1453:
1449:
1444:
1437:
1434:
1428:
1425:
1422:
1416:
1413:
1407:
1402:
1398:
1386:
1385:
1374:
1368:
1365:
1333:
1330:
1327:
1321:
1318:
1312:
1309:
1306:
1303:
1292:
1271:
1268:
1265:
1262:
1242:
1235:
1232:
1224:
1219:
1212:
1208:
1202:
1199:
1192:
1187:
1184:
1180:
1176:
1173:
1170:
1167:
1161:
1158:
1152:
1149:
1146:
1143:
1140:
1137:
1110:
1106:
1099:
1096:
1093:
1083:
1080:
1077:
1074:
1068:
1065:
1042:
1039:
1036:
1026:
1023:
1020:
1017:
1007:
1004:
1001:
998:
995:
984:
983:
972:
969:
966:
962:
958:
955:
952:
949:
943:
940:
934:
931:
928:
925:
922:
919:
916:
913:
910:
907:
904:
898:
894:
867:
844:
841:
818:
812:
809:
803:
800:
797:
794:
785:as a function
774:
771:
768:
765:
742:
720:
716:
712:
709:
703:
698:
694:
675:
674:
662:
651:
637:
633:
629:
626:
606:
603:
600:
597:
594:
591:
569:
565:
544:
541:
538:
535:
525:
513:
510:
507:
502:
498:
494:
491:
488:
483:
479:
473:
469:
465:
462:
459:
456:
446:
443:
440:
430:
427:
424:
421:
418:
408:
396:
374:
370:
359:
347:
325:
321:
306:
305:
294:
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263:
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189:
169:
168:
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95:parallel-fiber
55:
52:
15:
9:
6:
4:
3:
2:
4238:
4227:
4224:
4222:
4219:
4217:
4214:
4213:
4211:
4202:
4199:
4198:
4179:on 2011-07-21
4175:
4171:
4167:
4163:
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4126:
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4090:
4082:
4078:
4074:
4070:
4066:
4065:10.1038/16922
4062:
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3298:visual cortex
3295:
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2502:. That means
2483:
2460:
2437:
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2025:
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2008:
1999:
1991:
1981:
1977:
1972:
1962:
1953:
1948:
1944:
1923:
1920:
1915:
1911:
1890:
1887:
1884:
1870:
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1826:
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1293:
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1190:
1185:
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1135:
1127:
1126:
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1037:
1024:
1018:
1005:
999:
993:
967:
950:
938:
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920:
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911:
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896:
881:
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879:
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801:
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792:
769:
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710:
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481:
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311:
310:
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292:
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274:
270:
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261:
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249:
239:
223:
220:
214:
211:
203:
195:
191:
187:
176:
175:
174:
165:
162:
154:
144:
143:the talk page
140:
134:
132:
127:This article
125:
116:
115:
107:
105:
100:
99:Purkinje cell
96:
92:
88:
84:
83:visual cortex
79:
75:
71:
69:
65:
61:
51:
49:
45:
41:
40:visual cortex
37:
33:
29:
25:
21:
4181:. Retrieved
4174:the original
4135:
4131:
4118:
4107:. Retrieved
4102:
4089:
4048:
4042:
4036:
3995:
3989:
3986:Mark F. Bear
3972:
3961:. Retrieved
3921:
3917:
3897:
3886:. Retrieved
3881:
3871:
3860:. Retrieved
3833:(1): 32–48.
3830:
3826:
3786:. Retrieved
3774:
3770:
3760:Cooper, L.N.
3754:
3709:
3705:
3691:
3646:
3603:
3599:
3545:
3541:
3535:
3518:
3515:Applications
3452:
3304:
3302:
3294:Serena Dudek
3279:
3211:
2934:
2691:and weights
2650:
2332:
2114:
1876:
1809:
1786:
1537:
1387:
985:
755:
676:
307:
172:
157:
151:January 2012
148:
137:Please help
128:
80:
76:
72:
67:
57:
30:, named for
27:
23:
19:
18:
3812:Leon Cooper
3290:hippocampus
582:, that is,
358:th synapse,
87:hippocampus
60:Donald Hebb
54:Development
36:Leon Cooper
4216:Biophysics
4210:Categories
4183:2007-11-11
4109:2007-11-11
3963:2007-11-11
3888:2007-11-11
3862:2007-11-11
3816:Paul Munro
3788:2007-11-11
3527:References
3276:Experiment
133:to readers
91:cerebellum
20:BCM theory
4140:CiteSeerX
3907:Mark Bear
3728:1663-3563
3673:cite book
3665:795553723
3562:0899-7667
3473:¯
3430:¯
3415:−
3412:∼
3321:
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702:˙
661:ϵ
632:θ
590:ϕ
564:θ
534:ϕ
468:∑
271:ϵ
268:−
224:ϕ
58:In 1949,
46:(LTP) or
26:, or the
4170:40872097
4162:17571943
3909:(1992).
3762:(2000).
3746:22807913
3622:15541316
3570:12816564
1488:, where
85:and the
28:BCM rule
4081:4302032
4073:9950426
4053:Bibcode
4028:2705694
4020:8632826
4000:Bibcode
3958:1350090
3926:Bibcode
3857:7054394
3848:6564292
3737:3395004
3630:9061314
3578:1919612
3288:in the
1873:Example
308:where:
129:may be
4168:
4160:
4142:
4079:
4071:
4044:Nature
4026:
4018:
3991:Nature
3956:
3946:
3855:
3845:
3744:
3734:
3726:
3663:
3653:
3628:
3620:
3600:Neuron
3576:
3568:
3560:
3453:where
3305:et al.
1787:where
1627:
1624:
1621:
1611:
1608:
1605:
1358:
1348:
1338:
1335:
1273:
1258:
1248:
1245:
829:where
681:rule,
110:Theory
93:, the
4177:(PDF)
4166:S2CID
4128:(PDF)
4099:(PDF)
4077:S2CID
4024:S2CID
3949:49082
3914:(PDF)
3823:(PDF)
3767:(PDF)
3712:: 2.
3626:S2CID
3574:S2CID
3194:0.000
3188:0.000
3150:0.000
3124:2.828
3081:1.414
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3002:2.828
2963:0.927
2954:3.246
2917:0.055
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2877:0.002
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2523:0.001
4158:PMID
4069:PMID
4016:PMID
3954:PMID
3853:PMID
3742:PMID
3724:ISSN
3683:link
3679:link
3661:OCLC
3651:ISBN
3618:PMID
3566:PMID
3558:ISSN
3284:and
3162:and
2438:0.05
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2142:and
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1845:and
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1508:and
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653:and
628:<
602:<
4150:doi
4061:doi
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4008:doi
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3934:doi
3843:PMC
3835:doi
3779:doi
3732:PMC
3714:doi
3608:doi
3550:doi
3318:log
3286:LTD
3282:LTP
2978:,
2757:,
2676:0.7
2670:0.2
2432:0.1
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1616:and
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4212::
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3797:^
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