2581 valuable arXiv mathematics papers the pipeline has analyzed — each with a short note on what its math gives to machine learning.
The paper supplies a principled Sobolev-orthogonal basis whose geometry penalizes both function magnitude and derivative magnitude under a confining weight. This is transferable to neural networks as a fixed or learnable feature basis for…
The paper develops a hard-core polymer-gas representation of the Ising partition function, in which connected subsets interact through a binary compatibility relation and receive exponentially decaying weights. The transferable asset is…
The paper offers a transferable decision-focused mechanism: forecast information or pointwise accuracy is not sufficient to predict the value of a downstream policy when the policy depends on ordinal structure. For storage-like decisions…
The paper provides a transferable mechanism for systems whose continuous allocation variables are implemented on a discrete lattice: a dimensionless granularity ratio controls the loss caused by discretization. Positive homogeneity shows…
The paper offers a transferable physics-informed mechanism for learning degradation under regime changes and abrupt outliers: expose cumulative damage history as an input, enforce the physically expected monotonic degradation direction…
The paper identifies a transferable mechanism for shared-observation conditioning: independent hidden trajectories acquire weak pairwise correlations concentrated in the collective direction visible to an observation. Girsanov conditioning…
The paper supplies an endpoint replacement for Lipschitz flow estimates: when the vector-field Jacobian is only integrable, pairwise distances evolve under an Osgood modulus rather than a uniform Lipschitz constant. This is transferable to…
The paper identifies a concrete failure mode in sampled feedback systems: replacing a derivative by a backward difference adds the previous output as a controller state, producing fast modes that are not predicted by the ideal…
The paper constructs a noncommutative lift of hyperbolic toral automorphisms from integer matrices to volume-preserving diffeomorphisms of \(\mathrm{SU}(2)^2\), using compositions of free-group Nielsen automorphisms rather than naive…
The paper identifies signed multilinear tensors whose operator norm is essentially minimal, with exact equality governed by Hadamard matrices and Hurwitz–Radon families of pairwise anticommuting orthogonal matrices. This gives a directly…
The paper gives a constructive sparse factorization of embeddable 3-state Markov transition matrices into at most seven elementary row-mixing matrices. Its transferable asset is exact stochasticity combined with a bounded sequence of cheap…
The paper offers a nonstandard associative-memory mechanism in which neurons and memories are elements of the Lie group SU(d), while recall can be represented in an auxiliary linear Hilbert space. Its key transferable asset is that…
The paper provides two transferable mechanisms rather than merely a domain-specific application: exact averaging over the 48-element cubic point group to impose symmetry in three-dimensional convolutions, and learning a thermodynamically…
The paper proves a sharp lower bound for the Hardy prefix-averaging operator on the cone of nonincreasing functions: averaging cannot reduce the BMO seminorm by more than the optimal factor alpha_0, and one-jump functions are extremizers…
The paper offers a transferable memory-compression design for attention: apply a structured orthogonal mixing transform to KV vectors before low-bit scalar quantization, then perform attention without reconstructing full-precision cache…
The paper identifies a finite-size noise crossover caused by slow reversible internal states: when the mean number of paused particles is of order one, rare pauses alternate with pause-free transport and large jammed clusters. Its…
The paper provides a constructive representation for conditional laws driven by a shared stochastic path: encode the initial distribution with finitely many Fourier moments, encode the common-noise history with a truncated path signature…
The paper introduces a two-parameter information profile that optimizes a weighted sum of conditional entropies against residual conditional mutual information over auxiliary variables. Its transferable asset is the full convex surface…
The paper provides a rotation-robust diagnostic for detecting anisotropy in short, noisy trajectories: turning-angle statistics retain information about the ratio of intrinsic diffusion coefficients even when the laboratory-frame…
The paper offers a constructive method for computing certified safe operating regions for neural-network-controlled dynamical systems. Its transferable assets are interval inclusion functions, predecessor iteration for maximal controlled…
The paper provides a constructive adaptive representation of continuous stochastic paths: recursively split a dyadic time interval only when its within-interval excursion exceeds a threshold. The transferable asset is the resulting…
The paper gives a sharp spectral explanation of the Barzilai--Borwein method: on strongly convex quadratics, the worst-case asymptotic gradient factor is exactly governed by the active condition number, c_H = (kappa(H)-1)/(kappa(H)+1). Its…
The paper provides a practical two-query estimator for Langevin drift when the target potential can only be evaluated through noisy function values. Its transferable asset is the SPSA perturbation identity: a full-dimensional gradient…
The paper isolates a useful consequence of positive-semidefinite low-rank structure: a quadratic score over a complicated feasible family depends only on a low-dimensional shadow, and an optimum generates its own linear exposure direction…