Backpropagation for PopulationTemporal Coded Spiking Neural Networks

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Backpropagation for Population-Temporal Coded
Spiking Neural Networks

• July 18 2006 - WCCI/IJCNN 2006
• Benjamin Schrauwen and Jan Van Campenhout
• Electronics and Information Systems Department
• Ghent University
• www.elis.UGent.be/SNN/

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Problem

• Current learning rules for Spiking Neurons have
  convergence problems and only support a single
  coding scheme.

Outline

• Introduction
• Population-Temporal Coding
• Analog Spiking Neuron Approximation
• ASNA-Prop learning rule
• Results
• Conclusions

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Introduction

• Spiking Neural Networks
• Uses spikes to communicate
• Neuron model is approx. leaky integrator with
  threshold
• Computationally more powerfull as analog neurons
  Maass
• Intrinsically able to process temporal
  information
• Biologically more plausible

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Introduction

• But learning is still a problem. Already
  published
• Unsupervised Spike Timing Dependent Plasticity
• Genetic Algorithm, Evolutionary Strategy and
  Simulated Annealing
• Correlation based ALOPEX algorithm
• Supervised, gradient-based SpikeProp learning
  rule
• Only supports time-to-first-spike coding
• Troubled by convergence problems
• Sensitive to exact weight initialisation
• Only able to move spikes, has no notion of
  creation and removal of spikes due to parameter
  changes

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Introduction
SpikeProp
Very discontinous error landscape, resulting in
convergence problems
Desired spike times
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Population-Temporal Coding

• Many spike coding hypothesis exist rate,
  population, time-to-first-spike, rank, filter,
  ...
• This work uses Population-Temporal Coding
• A combination of both temporal and population
  representation
• Embodies a large range of different coding
  possibilities

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Analog Spiking Neuron Approximation

• To solve the SpikeProp problems due the hard
  thresholding
• Approximate SNNs by analog approximation with a
  'soft' threshold
• Allows the calculation of gradients at every time
  step
• Use this model to contstruct learning rule, but
  apply this to the original spiking neuron model
• Analog approximation does not need to be
  simulated!

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Analog Spiking Neuron Approximation
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ASNA-Prop learning rule

• Analog spiking neuron approximation is similar to
  a Output Feedback, Locally Recurrent, Globally
  Feed-forward neural network
• Learning rules for OF-LRNN presented by
  Campolucci and Piazza
• Used these ideas, but constructed new rules for
  ASNA
• ASNA-Prop is derived from analog approximation
  but applied to spiking model !
• See publication for actual math...

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ASNA-Prop learning rule

• ASNA-Prop has notion of spike removal and
  creation
• Supports multiple coding schemes
• Smooth convergence
• Improved performance greatly by using Resilient
  PROPagation
• Heuristic first order backpropagation speedup
• Was also tried for SpikeProp but didn't work due
  to discontinous error landscape
• Not sensitive to weight initialisation

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Results

• SpikeProp's time-to-first spike coding only
  allows timeless functions yf(x). Implicit
  temporal processing not used.
• PTR coding allows temporal processing input and
  output are function of time
• First test non-temporal XOR
• Rate based input coding (length 0.1s, 1 is coded
  as 500 Hz, 0 by no signal)
• Output PTR one output, with Gaussian temporal
  filtering
• 3-4-1 architecture
• Converges in 80 epochs, enhanced SpikeProp in 120
  epochs (but has 16 times more connections !)

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Results
20 runs
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Results

• Temporal XOR
• 40 XORs per example, length 50 ms

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Results

• Transcoding ISI encoding as input, PTR as output
• Spiking neurons can speak multiple languages

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Conclusions

• New learning rules that eliminates all the
  problems of SpikeProp
• Support broad range of coding schemes
• Performance is much better than SpikeProp
• Future work
• Apply to much larger benchmark problems
• Implement rules for other coding schemes (ttfs,
  ISI, ...)
• Train more parameters to improve performance
• Influence of alpha need to be further
  investigated
• www.elis.UGent.be/SNN/