Artificial Spiking Neural Networks

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Artificial Spiking Neural Networks

• Sander M. Bohte
• CWI
• Amsterdam
• The Netherlands

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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

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Of neurones and neurons

• Artificial Neural Networks
• (neuro)biology -gt Artificial Intelligence (AI)
• Model of how we think the brain processes
  information
• New data on how the brain works!
• Artificial Spiking Neural Networks

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Real Neurons

• Real cortical neurons communicate with spikes or
  action potentials

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Real Neurons

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

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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)

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ANNs

• 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

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Dynamic Feature Binding

• bind local features into coherent percepts

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Binding

• representing multiple objects?
• like language without grammar! (i.e. no
  predicates)

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Binding

• Conjunction coding

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Binding

• Synchronizing spikes?

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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 lt 1ms
• Spikes are rare average brain activity lt 1Hz
• rates are not energy efficient

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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

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Artificial Spiking Neuron

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

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Artificial Spiking Neuron

• Spike-Response Model
• where e(t) is the kernel describing how a single
  spike changes the potential

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Artificial Spiking Neural Network

• Network of spiking neurons

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Error-backpropagation in ASNN

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

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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)

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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)

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From Neurons to Neurones

• artificial spiking neurons are fairly accurate
  model of real neurons
• learning rules -gt predictions for real neuronal
  behavior
• example reducing response variance in stochastic
  spiking neuron yields learning rule like biology
  (Bohte Mozer, NIPS 2004)

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STDP from variance reduction

• neurons fire stochastically as a function of
  membrane potential
• Good idea to minimize response variability
• response entropy
• gradient

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STDP?

• Spike-timing dependent plasticity

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Variance Reduction

• Simulate STDP experiment (BohteMozer,2005)
• predicts dependence shape STDP -gt neuron
  parameters

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STDP -gt 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

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Hidden Markov Model

• Bayesian inference in simple single level (Rao,
  NIPS 2004)
• hidden state of model at time t

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• Let be the observable output at time t
• probability
• forward component of belief propagation

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Bayesian SNN

• Recurrent spiking neural network

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Bayesian SNN

• Equivalence SNN HMM

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Bayesian SNN

• Current spike-rate
• The probability of spiking is directly
  proportional to the posterior probability of the
  neurons preferred state and the current input
  given all past inputs
• Generalizes to Hierarchical Inference

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Conclusion

• new neural networks Artificial Spiking Neural
  Networks
• can do what traditional ANNs 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