artificial spiking neural networks sander m. bohte cwi amsterdam the netherlands
TRANSCRIPT
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
Binding
• representing multiple objects?
• like language without grammar! (i.e. no predicates)
or
?
?
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:
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:
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
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