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Chapter5.3_Multilayernetworks-revisedfor3rdedition.ppt

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Chapter 5.3:
Multilayer networks

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Overview

Introduce backpropogation

Discuss the biological plausibility of neural networks

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

The basic problem

• Multilayer networks can be constructed to compute any Turing-computable function, but cannot be trained using the perceptron convergence rule

• Single unit networks can be trained, but can only compute linearly separable functions

• What was needed was an algorithm for training multilayer networks

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Backpropagation

a.k.a. Generalized delta rule

Information is transmitted forwards through the network

Error is propagated backwards through the network

The backpropagated error signal is used to adjust the weights to/from the hidden units

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Note that this was introduced in chapter 3

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Flow of activation

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Backprop

• The algorithm needs to find a way of calculating error in hidden units that do not have target activation levels

• It does this by calculating for each hidden unit its degree of “responsibility” for error at the output units

• This error value is used to adjust the weights of the hidden units

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

How successful is backprop?

• Multilayer networks can compute any Turing-computable function

• But it is not true that backpropagation will always converge on a solution

• Unlike perceptron convergence rule, which is guaranteed to find a solution where there is one

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Gradient descent learning

• GD learning rules calculate the slope of the error curve at a particular point

• Negative slope means that the weight needs to be increased etc.

• Learning stops when the slope is zero

• Single unit networks always have an error curve with a single error minimum

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Backprop and local minima

• The basic problem with backpropagation is that multilayer networks are not guaranteed to have error curves with a single error minimum (i.e. zero slope)

• The network can get stuck in a local minimum

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

Backprop: Biological plausibility

• No evidence that backpropagation takes place in the brain

• Setting the number of hidden units is crucial - how would the brain determine this?

• No evidence that individual neurons receive error signals from all the neurons to which they are connected

• Very little biological learning seems to involve supervised networks

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020

More biological plausible: local algorithms

An individual unit’s weight changes directly as a function of the inputs to and outputs from that unit, e.g. Hebbian learning rule.

Often used in unsupervised learning networks, e.g. competitive networks (do not require feedback)

The inhibitory connections between the output units allow them to compete with each other

Only the winning unit (the one that fires the most) have their weights increased

Each output fires in response to a set of similar inputs

Cognitive Science  José Luis Bermúdez / Cambridge University Press 2020