1. Artificial Spiking Neural Networks
Sander M. Bohte
CWI
Amsterdam
The Netherlands

2. 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

3. 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

4. Real Neurons
Real cortical neurons communicate with spikes or action potentials

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

6. 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)

7. 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

8. Dynamic Feature Binding
“bind” local features into coherent percepts:

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

10. Binding
Conjunction coding:

11. Binding
Synchronizing spikes?

12. 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

13. 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]

14. Artificial Spiking Neuron
The “state” (= membrane potential) is a weighted sum of impinging spikes
spike generated when potential crosses threshold, reset potential

15. Artificial Spiking Neuron
Spike-Response Model:
where ε(t) is the kernel describing how a single spike changes the potential:

16. Artificial Spiking Neural Network
Network of spiking neurons:

17. Error-backpropagation in ASNN
Encode “X-OR” in (relative) spike-times

18. 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)

19. 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)

20. 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)

21. STDP from variance reduction
neurons fire stochastically as a function of membrane potential
Good idea to minimize response variability:
response entropy:
gradient:

22. STDP?
Spike-timing dependent plasticity:

23. Variance Reduction Simulate STDP experiment (Bohte&Mozer,2005):
predicts dependence shape STDP -> neuron parameters

24. 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

25. Hidden Markov Model
Bayesian inference in simple single level (Rao, NIPS 2004):
hidden state of model at time t

26. Let be the observable output at time t
probability:
forward component of belief propagation:

27. Bayesian SNN
Recurrent spiking neural network:

28. Bayesian SNN
Equivalence: SNN HMM

29. 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

30. 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