arXiv:2606.28984v1 Announce Type: 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 reactive 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 associated to any s
This research emerges as AI systems become increasingly complex, demanding more principled and compositional approaches to design and understanding. The paper introduces a mathematical framework to bridge gradient-based learning with classical mechanics, suggesting a pathway for more robust and foundational AI architectures.
This work points towards a deeper theoretical unification in AI, potentially leading to more stable, interpretable, and generalizable learning systems. By linking learning to physics, it hints at emergent properties and design principles that could unlock new capabilities in AI.
The understanding of AI learning dynamics could shift from purely statistical methods to those grounded in compositional and mechanistic principles. This offers a new lens for developing and evaluating AI, moving beyond empirical trial-and-error.
- · AI foundational research
- · Deep learning framework developers
- · Advanced AI applications
- · Theoretical computer science
- · Ad-hoc AI development methods
- · AI approaches lacking formal guarantees
- · Systems focused purely on empirical optimization
The proposed compositional framework could inspire new AI architectures that leverage insights from classical mechanics for improved performance and theoretical grounding.
This foundational work might eventually lead to AI systems exhibiting more robust and predictable behaviors, reducing unexpected failures and improving safety.
Long-term, a unified theory of learning and mechanics could enable entirely new forms of AI, perhaps leading to truly emergent and adaptable intelligent systems that deeply interact with physical realities.
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Read at arXiv cs.AI