Calculating Hopfield Stable States
- If you know the stable states that you want, you can easily calculate
them in a Hopfield Net
- A stable state in a N-node Hopfield net is an N-arity bit string
- You can have N stable states
- The states have to differ by more than one node/bit
- A stable state will have the nodes associated with the 1 bits on, and
those associated with the 0 bits off
- Once the stable state occurs, the next cycle will repeat that state,
and then that state will continue
- For a stable state to occur, all that has to happen is the inputs to
the on nodes have to exceed their thresholds and the inputs to
the off nodes have to be lower
- So, to represent the bit pattern 101, all that is needed is a topology
where the input W13>T1, W13>T3, and W12+W23 < T2
- If another pattern were also stored, a similar equation would be
added
- Energy Calculations
- We started this work thinking about Hopfield Energy Calculations
- There is an energy state for each pattern and you can show
that running a net will lead to a lower energy state
- This energy metric informs learning rules that enables the system
to learn the stable states
- However, we couldn't see how that would directly help us
