CogSci2013

How can we learn the connection weights
in the spiking neural networks in Spaun?

This is that full scale model. We call it Spaun. Spaun is a network of 2.5 million simulated spiking neurons that is able to do several high-level cognitive tasks. In this video, Spaun is solving a problem that you might find on an IQ test. As it gets information about each cell, it's trying to infer the transformation between cells in each row. Then, when we get to the last cell in the last row, we ask Spaun what it thinks should go in that cell, and it writes 333, which is the correct answer. Spaun is able to accomplish this and other tasks by representing information in populations of spiking neurons, and transforming that information through connections between populations of neurons. In order to create Spaun, we analytically solve for the connection weights between each neural population. I wanted to know: Can the connection in Spaun be the result of some learning process? Could Spaun be the result of nurture? Or would Spaun have to be hard-coded by nature?

1. Cognitive functions

Vector Symbolic Architecture (Plate, 2003)

$\circ{5} \Rightarrow \left[ 0.12, 0.56, 0.48 \right] \Rightarrow$ 3d point

$= \text{COUNT} \circledast \circ{1} + \text{NUMBER} \circledast \circ{5}$

$= \text{COUNT} \circledast \circ{2} + \text{NUMBER} \circledast \circ{5}$

$= \text{COUNT} \circledast \circ{3} + \text{NUMBER} \circledast \circ{5}$

How can we learn the binding function $\circledast$?

2. In spiking neurons

Neural Engineering Framework
(Eliasmith & Anderson, 2003)

$X$, $\;e_i$, $\quad a_i = f(e_i \cdot X)$

$\hat{X} = \sum_i \color{red}{d_i} a_i$

$\omega_{ij} \propto e_i d_j$

3. Learning

Random initial $\omega_{ij}$

Supervised learning

Given error $\color{red}{E} = X - \hat{X}$,

$\Delta \omega_{ij} \propto a_i \, e_j \cdot E$

Unsupervised learning

$\Delta \omega_{ij} \propto a_i \; \underbrace{a_j (a_j - E[a_j])}$

Bi & Poo (2001)

Kirkwood, Rioult & Bear (1996)

Combined learning

$\Delta \omega_{ij} \propto a_i [\color{red}{S} \underbrace{e_j \cdot E}_{\color{blue}{\text{ Supervised}}} + \color{red}{(1 - S)} \, \underbrace{a_j (a_j - \theta)}_{\color{blue}{\text{ Unsupervised}}}]$

Sparsity

0.18 0.51

Given an error signal, $E$, we can learn binding.

How are error signals generated?

Thanks to CNRGlab members, NSERC, CRC, CFI and OIT.

Simultaneous unsupervised and supervised learning of cognitive functions
in biologically plausible spiking neural networks

bekolay.org/cogsci2013-pres

tbekolay/cogsci2013

tbekolay/cogsci2013-pres

Learning transmission

Learning parameters

Neurons per dimension, learning rate, supervision ratio ($S$)

jaberg/hyperopt