Hopfield Pattern Recovery

Stored pattern

The reference pattern already encoded in the network's connection weights.

Degraded input

A damaged version of the stored pattern. Some unit states have been flipped.

Recovered pattern

The network's final state after recurrent updates. This stays empty until recovery runs.

What does Run recovery do?

Run recovery repeatedly applies the update rule to the degraded pattern. The network stops when two consecutive states are the same, or after 20 updates.

Store the pattern
wij = 1 N ξiξj

Relationships between stored unit states become connection weights.

→
Use the damaged input
hi = Σj wijsj

Each unit combines activity from the others, scaled by their weights.

→
Update the state
si(t+1) = f(hi(t) - θi)

The weighted input is compared with a threshold to determine the unit's next state.

In this demo: θi = 0, and f is the sign rule: positive input gives +1; negative input gives −1.