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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: xj xj = f(wij xi ) wijxi 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? ? or ? • like language without grammar! (i.e. no predicates) 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: (1 -t/) P S P : te 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