A Wasserstein Geometric Framework for Hebbian Plasticity

ArXi:2604.16052v1 Announce Type: cross This variational structure induces a fundamental separation between internal and observable dynamics. Internal memory states evolve along Wasserstein geodesics in a latent curved space, while observable quantities, such as effective synaptic weights, arise through geometric projection maps into external spaces. Simplicial projections recover classical affine schemes (including exponential moving averages and mirror descent), while revealing synaptic competition and pruning as geometric consequences of mass redistribution.