• Talk and paper presented at the 32nd Annual Meeting of the Cognitive Science Society (CogSci 2010)
  • by Terrence C. Stewart, Xuan Choo, and Chris Eliasmith; Centre for Theoretical Neuroscience, University of Waterloo
  • Slides available in [pdf] and [odp]

Goal

• To create a neural cognitive architecture
  • that is biologically realistic
  • (spiking neurons, anatomical constraints, neural parameters, etc.)
  • and supports high-level cognition
  • (symbol manipulation, cognitive control, etc.)
• Advantages
  • Connect cognitive theory to neural data
  • Neural implementation imposes constraints on theory

Required Components

• Representation
  • Distributed representation of high-dimensional vectors
• Transformation
  • Manipulate and combine representations
• Memory
  • Store representations over time
• Control
  • Apply the right operations at the right time

Representation

• Assumption: Cognition uses high-dimensional vectors for representation
  • [2,4,-3,7,0,2,...]
• Forms the top level of many hierarchical object recognition models
• The vector is compressed information
• Different vectors for each thing that can be represented
  • including DOG, CAT, SQUARE, TRIANGLE, RED, BLUE, SENTENCE, etc.

How can a group of neurons represent vectors?

• We know how this happens in visual and motor cortex
  • (e.g. Georgopoulos et al., 1986)
• Representing a spatial (x,y) location (2-dimensional vector)
  • Distributed representation
  • Each neuron has a preferred direction
  • One direction it fires most strongly for
  • Uniformly distributed around the circle

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• Neural representation
  • Using Leaky Integrate-and-Fire (LIF) neurons
  • Input current is the dot product of the represented vector with the preferred vector times the neuron gain (randomly chosen) plus a constant bias current (randomly chosen)

• How good is this representations?

  • We know how to go from vector to spikes
  • Can we go the other way around?
  • Use the post-synaptic current to recover the original vector

  • Linear decoding

  • Take a weighted sum of neuron outputs to approximate the original input

  • Need decoding weights for optimal estimate
  • (see Eliasmith & Anderson, 2003 for calculations)
  • Extends to higher dimensions
  • Forms the basis of the Neural Engineering Framework
  • Decrease error by increasing number of neurons
  • Distributed representation
  • Robust to noise, neuron loss

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Transformation

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Memory

Control

Sequential Action

Information Routing

Question Answering

Results

Conclusions