Hopfield Nets

• The units of a Hopfield Nets are integrate and fire neurons.
• The net is well connected, and the connections are bidirectional.
• They can be continuous or discrete, but we'll consider discrete.
• Here's an example; the missing arcs are 0.
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• If you turn on some units, the net will run and settle into a stable state (or a two state oscillator).
• 00111->00111
• So, it is an auto-associative memory.
• It retrieves patterns from the inputs.
• Here, if you put in a corrupted pattern, you get the original.
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• This is a spin-glass model from Physics.
• There is a lot of work with statistical mechanics that you can use to prove things about these and related nets.
• You can use Hebbian learning rules to store the patterns. You can store up to N patterns that differ by more than one bit in a net of N Hopfield units.