Similarity alignment a new theory of neural computation. Dmitri Mitya Chklovskii
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1 Similarity alignment a new theory of neural computation Dmitri Mitya Chklovskii Flatiron Institute Neuroscience Institute Simons Foundation NYU Medical Center
2 Imaging neural population activity 50μm Raw data: Yuste lab CaImAn software: Pnevmatikakis & Giovannucci (Chklovskii group, Flatiron Institute) Stimulus vector : xt Neural activity vector : yt
3 What does neural activity represent? What is neural computation?
4 The linear reconstruction view =. y t,1 +.. y t,2 +. y t,3 + stimulus features neural activities x t T = W y t Bialek, Atick, Abbott, Olshausen & Field, Problems with linear reconstruction Lack of invariance among different brains Leads to neural networks with nonbiological synaptic learning rules Unclear how to generate higher order features
5 Similarity of neural activity patterns in IT Human Cortex Similarity Kriegeskorte et. al., 2008 Kiani et. al., 2007
6 Similarity of neural activity patterns in IT Monkey Cortex Human Cortex Similarity Kriegeskorte et. al., 2008 Kiani et. al., 2007
7 [Neural] representation is representation of similarities S. Edelman, 1998 stimulus space, x t,2 x t,3 R nn activity space, R kk y t,2 x t,1 y t,1 Similar stimuli evoke similar activity patterns What metric should be used for stimulus similarity?
8 Similarity of neural activity patterns in V1 Kriegeskorte et. al., 2008 Similarity Kiani lab
9 Object classification as manifold learning DiCarlo & Cox, 2007 pixel intensity space V1 neural activity space IT neural activity space
10 Biologically plausible manifold learning LLE ISOMAP MVU KernelPCA t-sne BP Autoencoders Biologically implausible Input : Output : x x y y 1 T 1 min yt 0 T T T T T ( x ) 2 t xτ yt yτ t= 1 τ= 1 1 T yy T tt yy ττ xx T tt xx ττ
11 Optimization problem Deriving a neural network 1 min yt 0 T T T T T ( x ) 2 t xτ yt yτ 1 T T T T T T min 2 yt yτxτ xt + yt yτyτ yt yt 0 t= 1 τ= 1 T t= 1 τ= 1 T T T T 1 T T 1 T min 2 yt τ τ t t τ τ t t 0 y x x y y y y y = 1 τ= 1 τ= 1 + t T T T YX T YY min 2 y tw xt + ytw yt y 0 t Online algorithm ( y YX η ( W YY W ) ), ( yti, xt j- ), ( yti, yt j- ) y max + x y,0 t t t t W W +η W YX YX YX i, j i j, i, j W W +η W YY YY YY i, j i j, i, j Local learning rules! x t,1 x t,2 x t,3 x t,4 W YX Hebbian Neural network y t,1 y t,2 -W YY anti-hebbian Pehlevan & Chklovskii (2014) Pehlevan, Sengupta & Chklovskii (2017)
12 Experimental confirmation of the learning rule +η ( - ) YX YX YX i, j i, j t, i t, j i, j W W y x W Stationary point: synaptic weight ~ activity correlation WW YYYY 1 TT TT ττ=1 yy ττ xx ττ TT
13 Similarity matching network can cluster x 2 x t,1 x t,2 W YX x 1 -W YY y t,1 y t,2 y t,3 Pehlevan & Chklovskii (2014)
14 Clustering by similarity alignment 1 min yt 0 T T T T T ( x ) 2 t xτ yt yτ t= 1 τ= 1 1 animate inanimate neural activity patterns animate inanimate similarity
15 Similarity alignment network learns V1 features from natural images natural images W W Pehlevan & Chklovskii (2014)
16 Manifold learning and segregation by stacking similarity alignment layers Input Layer 1 (k=64) Layer 2 (k=32) Layer 3 (k=16) Layer 4 (k=8) Layer 5 (k=4) Layer 6 (k=2) Similarity matrices: 2-dimensional embeddings: Tepper, Sengupta & Chklovskii (2017)
17 Stacking similarity networks (in progress) Hebbian anti-hebbian DiCarlo & Cox, 2007
18 Family of similarity alignment networks COMPUTATIONAL OBJECTIVE Similarity alignment Nonnegativity constraint Rank and sparsity regularizers Constrained output correlation Constrained spectral norm of the output similarity matrix Copositive output similarity matrix Constrained L1-norm of activity BIOLOGICAL FEATURE Hebbian plasticity Neural rectification Adaptive neural thresholds Adaptive lateral weights Anti-Hebbian interneurons Anti-Hebbian inhibitory interneurons Giant interneuron Hu,Pehlevan & Chklovskii (2014), Pehlevan & Chklovskii (2014), Pehlevan, Hu, Chklovskii (2015), Pehlevan & Chklovskii (2015), Pehlevan & Chklovskii (2016), Pehlevan, Mohan & Chklovskii (2017), Pehlevan, Sengupta & Chklovskii (2017), Tepper, Sengupta & Chklovskii (2017), Pehlevan, Genkin & Chklovskii (2017)
19 Summary Similar stimuli evoke similar activity patterns Neural computation is local similarity alignment Machine Learning Algorithms Experimental Neuroscience Data
20 Acknowledgements Cengiz Pehlevan Mariano Tepper Alex Genkin Anirvan Sengupta Tao Hu Sreyas Mohan
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