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.
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arXiv:2607. 15107v1 Announce Type: new Abstract: This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting.
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
arXiv:2607. 08843v1 Announce Type: new Abstract: In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space.
arXiv:2607. 11289v1 Announce Type: cross Abstract: Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs.
arXiv:2608. 03921v2 Announce Type: replace Abstract: This paper offers a new interpretation of the Transformer during inference.
arXiv:2609.06546v1 Announce Type: cross Abstract: Although machine learning can be used to predict the evolution of physical systems from data, a formulation that learns only the system state at each...