Download Breaking the Neural Code

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