Compositional Dynamics in Learning and Mechanics
Quick summary
arXiv:2606.28984v2 Announce Type: replace-cross Abstract: We give a single compositional setting in which gradient-based learning and Hamiltonian-style mechanics appear as functorial semantics. The syntax is an operad Arr whose objects are input-output interfaces (pairs of manifolds) and whose morphisms are *smooth adaptive arrangements*, which consist of a responsive parameter space, a lens given by smooth output and input maps, and a real-valued potential. The main technical result of the paper is what we call *lens internalization*, a lax symmetric monoidal functor Lens(C) $\to$ C associate
Key takeaways
- arXiv:2606.28984v2 Announce Type: replace-cross Abstract: We give a single compositional setting in which gradient-based learning and Hamiltonian-style mechanics appear as functorial semantics.
- The syntax is an operad Arr whose objects are input-output interfaces (pairs of manifolds) and whose morphisms are *smooth adaptive arrangements*, which consist of a responsive parameter space, a lens given by smooth output and input maps, and a real-valued potential.
- The main technical result of the paper is what we call *lens internalization*, a lax symmetric monoidal functor Lens(C) $\to$ C associate
Why it matters
“Compositional Dynamics in Learning and Mechanics” highlights the need for repeatable measurement rather than a single impressive demonstration. Independent validation across datasets and clearly stated limitations determine whether a result can guide product decisions.
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