2581 valuable arXiv mathematics papers the pipeline has analyzed — each with a short note on what its math gives to machine learning.
The paper provides a quantitative characterization of null dynamical systems through maximal pattern complexity: vanishing sequence entropy is equivalent to polynomial growth of observable orbit patterns for every finite open cover, while…
The paper identifies a concrete collective-search mechanism: when many agents compete for depleted targets under finite-range eligibility, the assignment policy can dominate the individual agents’ persistence dynamics…
The paper's central constructive object represents a graph as the intersection of two constraints: adjacency in a base graph H and overlap between one of d vertex label sets. This gives a factorized Boolean edge mask that can replace an…
The paper provides a transferable construction for a measurement-conditioned effective Hamiltonian: a local inverse-temperature profile is fixed by geometry and vanishes with a square-root law at measurement-region endpoints, while a local…
The paper provides a transferable way to treat an iterative multi-agent or recurrent neural computation as a dynamical system while replacing nonlinear state evolution with a linear operator on observables. The useful asset is not merely…
The paper develops a stability certificate for stochastic linear dynamics with state- and control-dependent multiplicative noise, where ordinary Hurwitz stability of the drift is insufficient. Its transferable asset is the stochastic…
The paper identifies an exact computational shortcut for Lin–Lu–Yau curvature: on weighted graphs, for every edge and every idleness parameter p greater than or equal to 1/2, Ollivier curvature is linear in 1-p, so the derivative-like…
The paper identifies a nontrivial dynamic-scaling mechanism for a system driven periodically through a continuous transition: time enters through the phase \(\tau=t/P\), while forcing amplitude and period combine into the scaling variable…
The paper identifies a nonstandard failure of invasion-based stability reasoning in spatial replicator systems: the principal eigenvalue of the linearized invasion operator can be negative while a stable finite-amplitude coexistence state…
The paper provides a robust, distribution-level notion of representation complexity based on how many metric balls cover almost all probability mass. This is transferable to neural networks as a scale-dependent intrinsic-dimension…
The paper gives a constructive algebraic criterion for when a nonlinear formal map or vector field can be removed by a near-identity change of coordinates: linearisation is equivalent to the existence of a splitting map into coderivations…
The paper gives a quantitative finite-sample bound showing that a normalized free sum of centered self-adjoint variables is close to the standard semicircle law, with error controlled by the aggregate normalized (2+δ)-moment. The…
The paper derives a concrete noise-induced renormalization mechanism: Gaussian spin-wave fluctuations dress a nonlinear activity coupling by an exponential Debye-Waller factor, causing the effective nonlinearity to collapse when…
The paper isolates a useful failure mode of Bregman regression: convexity of the scalar potential phi does not imply convexity of the parameterized objective because residuals enter the curvature coefficient. Its Hessian is a weighted Gram…
The paper supplies a constructive family of causal Gaussian Volterra kernels whose power exponents separately control local roughness, fixed-time fluctuation scale, and global self-similar scaling. This is transferable to sequence models…
The paper identifies a counterintuitive failure mode of graph augmentation: adding edges or cliques can increase Kemeny’s constant, the stationary-distribution-weighted average hitting time of a random walk. This is directly relevant to…
The paper transfers Ruelle–Pollicott resonance theory from deterministic maps to iid random dynamical systems by replacing a single transfer or Koopman operator with an annealed operator obtained by averaging over random maps. Its key…
The paper provides a useful nonlinear coordinate for coefficients that may approach a singular boundary: an unconstrained field ν is mapped to a Beltrami coefficient μ with |μ|<1 and distortion K=1+|ν|. Its most transferable asset is…
The paper develops a two-scale asymptotic decomposition in which a coarse homogenized solution is corrected by explicitly parameterized first- and second-order local fluctuation fields. The transferable asset is not the…
The paper develops projected dynamical systems with a state-dependent positive-definite matrix metric, extending beyond fixed Euclidean metrics and Hessian-generated metrics. The transferable asset is a stability framework linking strong…
The paper provides a constructive way to build tangent-valued, surface-divergence-free matrix kernels from scalar zonal kernels, while avoiding repeated explicit surface differential operators in the final representation. The transferable…
The paper provides a constructive irreversible threshold process in which each binary site can correct a local minority error at most once and then becomes inert. Its transferable mechanism is finite-use, state-dependent updating that…
The paper offers a transferable passivity certificate for momentum-based optimization: a sector-bounded gradient map becomes output strictly passive after a feedthrough loop transformation. For an L-smooth objective, subtracting D times…
The paper proposes a biologically local alternative to backpropagation in which each layer learns from paired and mismatched input-label examples, while recurrent bottom-up, top-down, and lateral signals create a layered surprise state…