The energy landscape in 2-D: click to start, change β to merge the valleys
β (inverse temperature)
β = 0.05
β = 1
β = 20
or drag the slider; click on the map to place the state ξ
stored patterns
same length (on a circle)
different lengths
stored pattern (size: its weight at the end)
path of ξ, one dot per update
fixed points (minima)
darker = lower energy
Weights p = softmax(β Xᵀξ) at the end
The 8 shapes that broke the classical network, under steeper energies
1. Stored shapes (click to toggle; all 8 by default)
2. energy
β for the softmax update
3. start from
noise: pixels flipped
↻ New corruption
▶ Recall
Cue
Result
Overlap with each stored shape
Capacity: how many random patterns can be recalled from 10% noise?
Against the number of neurons d (largest N recalled at least 90% of the time)
At d = 64, for different interaction functions F (binary dense associative memory)