Synaptic plasticity in neuromorphic hardware. Stefano Fusi Columbia University
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1 Synaptic plasticity in neuromorphic hardware Stefano Fusi Columbia University
2 The memory problem Several efficient memory models assume that the synaptic dynamic variables are unbounded, or can be modified with arbitrary precision Neuromorphic hardware implementations impose constraints on the dynamics of the synaptic variables Formalize the problem and analyze different strategies
3 Formalizing the memory problem time (for example )
4 time w ij 1 w ij Memory strength
5 Example: the Hopfield model
6 w ij =0 p time w ij 1
7 w ij =0 p time w ij 1
8 w ij =0 w ij p
9 w ij =0 w ij p Memories are random and uncorrelated
10 w ij =0 w ij p Memories are random and uncorrelated
11 w ij =0 w ij p Memories are random and uncorrelated 1
12 w ij =0 w ij p Memories are random and uncorrelated 1 0
13 Memory noise
14 Memory noise
15 Memory noise Noise increases with the number of memories
16 Number of memories (or time) Hopfield 1982, Amit Gutfreund Sompolinsky, 1985
17 Blackout Catastrophe Hopfield 1982, Amit Gutfreund Sompolinsky 1985
18 toward more realistic synapses Unbounded
19 toward more realistic synapses Unbounded Bounded (binary), offline learning Sompolinsky 1986
20 toward more realistic synapses Unbounded Bounded (binary), offline learning Sompolinsky 1986 Bounded (binary), online learning
21 w time time time
22 A learning rule for binary synapses pre post w= w=-1 with probability q w= w=+1
23 Initial signal
24 Signal after p memories
25 Signal after p memories Noise (at equilibrium) Amit Fusi 1992, Amit Fusi 1994
26
27
28 Learning rate SNR(0) Number of memories FAST ~ 1 SLOW 0
29 Sparse representations =1 with probability f =0 with probability 1-f Learning rule pre post w=1 with probability q + q + = w=-1 with probability q - q - = f Tsodyks Feigelman 1989, Amit Fusi 1994
30 Learning rate SPARSE SNR(0) Number of memories SLOW Amit Fusi, Neural Computation, 1994
31 A significant improvement, but 1) Not robust to noise ( must be exactly 0). In the presence of noise: p ~ N syn 2) The amount of information per memory is significantly smaller (it scales like f) 3) Not scalable (for large N syn it is very difficult to readout the relevant info) Ben Dayan Rubin, Fusi, Frontiers in Comp. Neuroscience 2007
32 Learning systems with multiple timescales Fast SNR Slow p
33 FAST SLOW N syn /m N syn /m N syn /m N syn /m q 1 q 2 q m-1 m groups q m =q s q k =(q s ) (k-1)/(m-1)
34
35 SNR Learning rate SNR(0) Number of memories FAST SLOW HETEROGENEOUS Fusi, Abbott, Neuron 2005; Roxin Fusi, PLoS Comp Biol. 2013
36 SNR Learning rate SNR(0) Number of memories FAST SLOW HETEROGENEOUS Fusi, Abbott, Neuron 2005; Roxin Fusi, PLoS Comp Biol. 2013
37 SNR
38 N log(1/q s ) q s N q s N m e-q st q s N e -q st
39 Heterogeneous systems with memory transfer A. Roxin, S. Fusi, PLoS Comp. Biology 2013
40 FAST SLOW N/m N/m N/m N/m q 1 q 2 q m-1 m groups q m =q s q k =(q s ) k/m
41 FAST INPUT SLOW Memory transfer q 1 q 2 q m-1 q m =q s
42 FAST SLOW q 1 q 2 q m-1 q m =q s S 1 S 2 S m-1 S m Readout: S = max {S 1,,S m }
43 N log(1/q s ) N m q s N ~m 1/4 ~1/q s ~m/q s
44 Learning rate SNR(0) Number of memories FAST SLOW HETEROGENEOUS HETEROGENEOUS with MEMORY TRANSFER
45 Fusi, Annunziato, Badoni, Salamon, Amit, Neural Computation (2000)
46 Giacomo Indiveri+ Fabio Stefanini
47 Autonomous real-time associative learning of visual stimuli on chip Poster M. Giulioni M. Giulioni, F. Corradi, V. Dante, P. Del Giudice, in preparation Two simple visual stimuli are acquired by a silicon retina (INI-Zurich) Input to a recurrent network of spiking IF neurons and plastic Hebbian, stochastic synapses on two chips Mean-field theory (effective response function) to navigate the parameter space Autonomous Hebbian learning generates stimulus-selective attractor states with error correction properties
48 Conclusions Neuromorphic synapses that are bistable require special machinery for preventing catastrophic forgetting Two important principles to improve performance: 1) Heterogeneity (multiple timescales) 2) Efficient memory transfer
49 People Theory of memory Daniel Amit Nicolas Brunel Francesco Battaglia Francesco Carusi Walter Senn Larry Abbott Daniel Ben Dayan Rubin Alex Roxin Srdjan Ostojic Marcus Benna Synaptic dynamics Hardware implementation Roberto Riccardi Gaetano Salina Mario Annunziato Paolo Del Giudice Maurizio Mattia Davide Badoni Stefano Buglioni Vittorio Dante Giacomo Indiveri Srinjoy Mitra Elisabetta Chicca Fabio Stefanini Mario Annunziato Joseph Brader Walter Senn Mattia Rigotti Dani Marti Kyo Iigaya
50 Teacher Teacher LTP Long-Term Potentiation Teacher Teacher LTD Long-Term Depression
51 Fusi, Annunziato, Badoni, Salamon, Amit, Neural Computation (2000)
52 No modification Long term modification Teacher Teacher
53 Brader, Senn, Fusi, Neural Computation (2007)
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