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

Real Neurons The artificial sigmoidal neuron models the rate at which spikes are generated artificial neuron computes function of weighted input:

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)

Binding Conjunction coding:

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:

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 Equivalence: SNN HMM

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