Memory-Shaped Optimization

In the multi-well study, removing memory reduced success rate and worsened best gap. The empirical pattern indicates that memory improves success and best gap on multi-well and basin-escape tasks. SHAPE's shaped potential includes a memory-induced term, an anchor term, and an optional barrier or exclusion term. SHAPE uses memory to summarize previously visited regions at each stage. SHAPE is hypothesized to use memory-shaped energy to avoid repeatedly refining uninformative basins. Scalable memory updates remain an open problem for high-dimensional spaces.