What can spiking neurons compute?

Kendrick Kay

(with Greg Corrado)

October 5, 2009

• Given neuromorphic spiking hardware, what useful things can we compute?

• Think about computation in terms of input/output

• Literature on spiking neurons not large; hard to subject spiking neurons to theoretical analysis

• Approach: Simulate neuromorphic spiking hardware (in MATLAB) and see what happens

The big picture

• Oja’s rule applied to a perceptron leads to computation of the first principal component of the data (Oja 1982)

Example of a result

• FNS: “Framework for Neural Simulation”– a modular code architecture (in MATLAB) that allows

different flavors of synapses, membranes, and spikers to be interchanged and reused

– includes a variety of neuronal models as special cases

Let’s get started: FNS

• Can we design a general-purpose neural network that can learn appropriate behaviors when embedded in a closed-loop system (input: sensory, output: action)?

• Example:– learn to play Pong based on raw video input

– or maybe more vision-type stuff

What kind of neural network to build?

• Perceptron– Hmm... notice that input, output, network can each be binary

or continuous (8 possible combinations)

Some initial results

Things to tackle:• The world is analog, but spiking neurons propagate digital

signals.• The world evolves over time, but artificial neural networks

tend to deal with static data points.

Is this going to work at all?• Multi-layer perceptrons already can compute any function.• What does spiking computation really offer? Surely not

computational capacity, but efficiency?

Open issues, things to do