Table of Contents
Activations, attractors, and associators
Toets
Overview
Much of perception is dealing with ambiguity
Many interpretations are processed in parallel
The final interpretation must satisfy many constraints
PPT Slide
i. Only one word can occur at a given position
ii. Only one letter can occur at a given position
iii. A letter-on-a-position activates a word
iv. A feature-on-a-position activates a letter
Recognition of a letter is a process of constraint satisfaction
Recognition of a letter is a process of constraint satisfaction
Recognition of a letter is a process of constraint satisfaction
Recognition of a letter is a process of constraint satisfaction
Recognition of a letter is a process of constraint satisfaction
Hopfield (1982)
Energy of a Hopfield network
Given a net input, netj, find aj so that -? netjaj is minimized .
Attractor
Attractor
Example: 8-Queens problem
The constraints are satisfied by inhibitory connections
Problem: how to ensure that exactly 8 nodes are 1?
Traveling Salesman Problem
The energy minimization question can also be turned around
Hebb and Hopfield
Bidirectional Associative Memories (BAM, Kosko 1988)
BAM
Linear Associative Networks.
Associating an input vector p with an output vector q
Inner product pTp gives a scalar
Outer product qpT gives a matrix
Final weight matrix W = ?qpT
Recall: Wp = q
Storing n patterns
Conclusion
LANs have limited representational power
Summing up
Summing up
PPT Slide
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University of Amsterdam
