Artificial Spiking Neural Networks

Sander M. Bohte

CWI

Amsterdam

The Netherlands

Overview

• From neurones to neurons• Artificial Spiking Neural Networks

(ASNN)– Dynamic Feature Binding– Computing with spike-times– Neurons-to-neurones– Computing graphical models in ASNN

• Conclusion

Of neurones and neurons

• Artificial Neural Networks– (neuro)biology -> Artificial Intelligence (AI)

– Model of how we think the brain processes information

• New data on how the brain works!– Artificial Spiking Neural Networks

Real Neurons

• Real cortical neurons communicate with spikes or action potentials

current response'EPSC'

Real Neurons

• The artificial sigmoidal neuron models the rate at which spikes are generated

• artificial neuron computes function of weighted input:

x = f( )w x ij ijjx

w x ij i

Artificial Neural Networks

• Artificial Neural Networks can:– approximate any function

• (Multi-Layer Perceptrons)

– act as associative memory• (Hopfield networks, Sparse Distributed

Memory)

– learn temporal sequences• (Recurrent Neural Networks)

ANN’s

• BUT....– for AI neural networks are not competitive

• classification/clustering

– ... or not suitable• structured learning/representation (“binding”

problem, e.g. grammar)

– and scale poorly• networks of networks of networks...

– for understanding the brain the neuron model is wrong

• individual spikes are important, not just rate

Dynamic Feature Binding

• “bind” local features into coherent percepts:

Binding

• representing multiple objects?

• like language without grammar! (i.e. no predicates)

or

?

?

Binding

• Conjunction coding:

or

?

?

Binding

• Synchronizing spikes?

New Data!

• neurons belonging to same percept tend to synchronize (Gray & Singer, Nature 1987)

• timing of (single) spikes can be remarkably reproducible– fly: same stimulus (movie)

• same spike ± < 1ms

• Spikes are rare: average brain activity < 1Hz– “rates” are not energy efficient

Computing with Spikes

• Computing with precisely timed spikes is more powerful than with “rates”.(VC dimension of spiking neuron models)[W. Maass and M. Schmitt., 1999]

• Artificial Spiking Neural Networks??[W. Maass Neural Networks, 10, 1997]

Artificial Spiking Neuron

• The “state” (= membrane potential) is a weighted sum of impinging spikes– spike generated when potential crosses threshold,

reset potential

Artificial Spiking Neuron

• Spike-Response Model:

– where ε(t) is the kernel describing how a single spike changes the potential:

t e (1-t/ )

PS P:

Artificial Spiking Neural Network

• Network of spiking neurons:

Error-backpropagation in ASNN

• Encode “X-OR” in (relative) spike-times

XOR in ASNN

• Change weights according to gradient descent using error-backpropagation (Bohte etal, Neurocomputing 2002)

• Also effective for unsupervised learning(Bohte etal, IEEE Trans Neural Net. 2002)

Computing Graphical Models

• What kind of intelligent computing can we do?

• recent work: computing Hidden Markov Models in noisy recurrent ASNN(Rao, NIPS 2004, Zemel etal, NIPS 2004)

From Neurons to Neurones

• artificial spiking neurons are fairly accurate model of real neurons

• learning rules -> predictions for real neuronal behavior

• example: reducing response variance in stochastic spiking neuron yields learning rule like biology (Bohte & Mozer, NIPS 2004)

STDP from variance reduction

• neurons fire stochastically as a function of membrane potential

• Good idea to minimize response variability: – response entropy:

– gradient:

STDP?

• Spike-timing dependent plasticity:

Variance Reduction

• Simulate STDP experiment (Bohte&Mozer,2005):

• predicts dependence shape STDP -> neuron parameters

STDP -> ASNN

• Variance reduction replicates experimental results.

• Suggests: learning in ASNN based on– (mutual) information maximization– minimum description length (MDL)

(based on similar entropy considerations)

• Suggests: new biological experiments

Hidden Markov Model

• Bayesian inference in simple single level (Rao, NIPS 2004):

• hidden state of model at time t

• Let be the observable output at time t

• probability:

• forward component of belief propagation:

Bayesian SNN

• Recurrent spiking neural network:

Bayesian SNN

• Current spike-rate:

• The probability of spiking is directly proportional to the posterior probability of the neuron’s preferred state and the current input given all past inputs

• Generalizes to Hierarchical Inference

Conclusion

• new neural networks: Artificial Spiking Neural Networks

• can do what traditional ANN’s can• we are researching how to use these networks

in more interesting ways• many open directions:

– Bayesian inference / graphical models in ASNN– MDL/information theory based learning– distributed coding for binding problem in ASNN– applying agent-based reward distribution ideas to

scale learning in large neural nets