We embed Hamiltonian/symplectic geometry by making the RNN state dynamics a symplectomorphism, which preserves Legendre duality (information geometry) through time. This yields structure-preserving representations enforced by the latent dynamics, rather than imposed indirectly via the output. （2/2）

Representation learning often emphasizes metric preservation. We instead build Symplectic structural invariance directly into the representation. （1/2）

Symplectic Reservoir Representation of Legendre Dynamics Modern learning systems act on internal representations of data, yet how these representations encode underlying physical or statistical structure is often left implicit. In physics, conservation laws...

Beyond metric preservation: build symplectic structural invariance into representation.

arxiv.org/abs/2512.19409

#ReservoirComputing #RepresentationLearning #InformationGeometry #SymplecticGeometry #HamiltonianDynamics #GeometricDeepLearning #DynamicalSystems #PhysicsInformedML

It was a pleasure presenting our work "Universality of Real Minimal Complexity Reservoirs" at #AAAI2025. Many thanks for your interest. I look forward to further discussions =). #AAAI #AAAI25

Full paper: arxiv.org/pdf/2408.08071

酢くま　#くま