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 constructive Kac–Ward fermionic representation in which a lattice model becomes a finite-dimensional momentum-dependent matrix \(\mathcal A(\mathbf{k})\). Criticality is detected by the exact zero-mode condition…
The paper develops a transferable mechanism for time-varying dynamical systems: asymptotic commutativity, in which the order dependence of maps vanishes at late times, together with proximal relations defined by repeated near-collisions of…
The paper gives a quantitative way to turn uniform sampling from a convex body into a rapidly mixing Markov kernel, with a spectral-gap bound controlled by the target distribution's Poincare constant rather than only its outer radius. The…
The paper offers a concrete interference mechanism: an engineered dissipative third terminal can cancel the differential response of the base heat current while emitter and collector currents remain finite, producing a large response ratio…
The paper gives an explicit polyhedral description of feasible joint assignments of vertex-separation variables and pair-separation variables in graph segmentation. Its transferable asset is not the facet characterization itself, but the…
The paper develops subsystem product codes built from polynomial-evaluation codes, combining tensor structure, low-weight local checks, large distance, and transversal algebraic operations. The transferable asset is a redundant tensor-grid…
The paper gives an explicit semidefinite convexification for quadratic functions on the noncompact region where two nonnegative variables satisfy a bounded product. The transferable asset is the construction of a small lifted moment…
The paper establishes a quantitative relation between finite systems of contractive similitudes, their attractor dimension, and branch separation. If contraction ratios r_i satisfy the similarity-dimension equation sum_i r_i^s = 1, then…
The paper derives sharp weighted Caffarelli–Kohn–Nirenberg inequalities and stability deficits on half-spaces and orthants. Their transferable asset is a scale-aware relation between weighted feature magnitude and weighted input…
The paper supplies a constructive positivity-preserving fourth-order diffusion whose maximal-monotone semigroup is contractive in Hellinger geometry rather than ordinary Euclidean distance. This suggests a differentiable implicit…
The paper presents a constructive method for inferring a design structure matrix, equivalent to a directed adjacency matrix, from observed dynamical data instead of relying only on expert knowledge. Its transferable mechanism is sparse…
The paper supplies a noncommutative functional calculus for applying a scalar function to two self-adjoint matrices that do not commute, together with a sharp qualitative divide between Schatten classes p<=2 and p>2. The transferable asset…
The paper develops an explicit two-point construction that reconstructs metric-affine geometry from a local parallelism induced by parallel transport, without assuming a Levi-Civita connection or imposing curvature or torsion constraints…
The paper identifies a concrete failure mode of collapsing signed fast inputs into their weak limit: threshold-reset dynamics can retain the microscopic order of excitatory and inhibitory arrivals even when both synaptic kernels converge…
The paper identifies a sparse-graph spectral operator whose negative eigenspace remains informative down to the percolation regime, where ordinary adjacency or Laplacian embeddings can be dominated by degree noise. The transferable asset…
The paper provides a concrete projected stochastic flow on the sphere in which multiplicative random quadratic dynamics preserve antipodal symmetries, while arbitrarily small independent tangent forcing eventually breaks those symmetries…
The paper develops a quantitatively controlled repulsive particle flow whose useful transferable ingredients are singular repulsion, a density-dependent interaction scale, and an explicit decay envelope for effective density. These…
The paper provides a concrete spectral mechanism: folding a Gaussian frequency through \(\omega=|\xi|\) creates a nonzero density at zero frequency, producing soft modes without a Lifshitz-tail mechanism. The transferable asset is that a…
The paper identifies a quantitative mechanism in which transitions are caused by finite, subcritical relocation cascades rather than critical long-range correlations. A branching ratio R below one predicts a finite mean cascade size of…
The paper provides a realization theorem showing that arbitrary ergodic measurable R^d dynamics can be encoded by a Delone point process with arbitrarily strong finite-order suppression of low-frequency fluctuations, while retaining the…
The paper gives a reference-free method for selecting neural PDE checkpoints without knowing the exact solution. Its central construction is a conforming Riesz reconstruction of each candidate's variational residual, whose energy norm…
The paper develops measure-theoretic matroid intersection and union, preserving rank-based min–max formulas on atomless spaces. The transferable asset is a principled way to combine several global independence, capacity, and diversity…
The paper provides a principled way to measure prompt value as the reduction in resource-bounded description complexity of a target artifact, rather than merely measuring likelihood under one decoding run. Its transferable asset is the…
The paper offers a constructive hybrid-rollout mechanism: use a provably contracting nominal predictor inside a calibrated uncertainty region, and activate a flexible excursion predictor only when epistemic uncertainty exceeds a threshold…