one of the learned stimuli

Activity of a single neuron in the cortex one of the learned stimuli new stimulus

Hebbian plasticity “When an axon of cell A is near enough to excite cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased” Donald Hebb, 1949 “Neurons that fire together wire together”

A cortical network

Hebbian plasticity

A cortical network Network can sustain activity even in the absence of input

Specificity of sustained activity

A model of associative memory

‘Biological’ memories • Associative: recall is based on content rather than on the address • A transient cue induces a sustained recall • Robust to minor failures of the hardware • Distributed

The mathematical model I will use a slightly different model than the one presented in the last 10 minutes of Wednesday’s class

The mathematical model Neurons are binary: The activity of neuron i, Si= 0,1 at time t+1 input to neuron i at time t

The mathematical model 5 J51 4 1 J21 2 3 J32

The mathematical model A memory pattern is a vector of desired neural activities 5 For example: 4 1 2 3

The Hopfield model trialn +1

The Hopfield model

The Hopfield model 5 J51 4 1 • local learning rule • incremental, on-line J21 2 3 J32 “Neurons that fire together wire together”

The Hopfield model Network connections are symmetrical. It can be shown that with asynchronous updating, the dynamics necessarily converge to a fixed point. • Questions: • What are the fixed points of the dynamics? • What is their relation with the memory pattern?

one of the learned stimuli