A Wasserstein Geometric Framework for Hebbian Plasticity
We introduce the Tan-HWG framework (Hebbian-Wasserstein-Geometry), a geometric theory of Hebbian plasticity in which memory states are modeled as probability measures evolving through Wasserstein minimizing movements. Hebbian learning rules are formalized as Hebbian energies satisfying a sequential stability condition, ensuring well-posed fiberwise JKO updates, optimal-transport realizations, and an energy descent inequality. 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 ge...
| Authors | Ulrich Tan |
|---|---|
| Primary category | math.OC |
| Published | 17 April 2026 |
| Last updated at source | 17 April 2026 |
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