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 concrete delay-induced Hopf mechanism for a proportional-derivative-controlled unstable equilibrium, including a computable characteristic spectrum, a critical-delay stability boundary, nonlinear saturation escape…
The paper supplies a multiscale quasi-Banach sparsity structure for wavelet coefficient pairs, rather than an ordinary coefficient-wise l_p penalty. Its local tent-space square function groups coarse father coefficients with fine mother…
The paper identifies a concrete failure mode in learning-enabled nonlinear observers: the Jacobian of a learned measurement map multiplies the correction gain and can destroy a fixed-gain Euclidean contraction certificate. Its key…
The paper supplies a sharp homogeneous polynomial inequality for eight nonnegative variables indexed by the vertices of a 3-dimensional hypercube. Its right-hand side is the product of six coordinate-facet projection sums, while the…
The paper provides a constructive mechanism for sparse desynchronisation control: an order-parameter feedback law is interpreted as gradient descent on synchrony, while event-triggered updates preserve stabilisation and guarantee a…
The paper supplies a geometric hypocoercivity framework for kinetic diffusion: noise acts only in velocity directions, while transport couples velocity regularity to position regularity and produces global smoothing and exponential…
The paper replaces direct frequency-domain deconvolution, which divides by potentially vanishing input spectra, with a Laguerre-Fourier coordinate system and a circulant FFT-solvable formulation. The transferable asset is not the…
The paper provides a constructive Green-operator mechanism for proving that a nonautonomous linear flow remains topologically, and under stronger variational conditions smoothly, equivalent to a quasilinear perturbation. The transferable…
The paper identifies a concrete failure mode in attention analysis: scalar metrics conflate the probability assigned to a sink token with the relative allocation among content tokens. Aitchison log-ratio geometry supplies an exact…
The paper turns constrained categorical sampling into a likelihood-ratio-like statistic obtained from nested information projections onto linear moment families. Its transferable asset is the combination of exponential-family projections…
The paper provides a constructive deterministic sampling mechanism: a continuous Kronecker flow on a torus, mapped measure-preservingly to a sphere, achieves uniform time-averaging with an explicit rate controlled by observable smoothness…
The paper's transferable asset is a constructive robustness principle: a Gibbs model with a strongly outward-drifting but locally non-convex potential can be represented as a mixture of strictly convex gradient models, retaining…
The paper's transferable construction is to represent a difficult temperature- and pressure-dependent scalar quantity as a pretrained static predictor plus a smooth residual surface. This reduces target dynamic range while preserving the…
The paper gives a concrete FFT factorization that performs the effect of zero-padding without storing the padded array, by splitting indices into short radix blocks and evaluating the padded transform through smaller inner sums. This is…
The useful transferable object is the Sauer–Shelah restriction bound: a set system with VC dimension d induces at most 1+|Y|^d distinct restrictions on any sampled subset Y, even when the ambient universe is large. Thresholded attention…
The paper offers a concrete computational mechanism: represent a nonequilibrium bosonic distribution as a finite sum of Gaussian components so that multidimensional interaction collision integrals become tractable, then solve the…
The paper gives a finite, constructive way to distinguish multivariate polynomials up to orthogonal change of coordinates using joint moments of correlated Gaussian replicas, whereas the marginal output distribution loses important…
The paper turns a fixed-parameter unrolled Douglas–Rachford solver into a feedback-controlled dynamical system: intermediate splitting residuals determine relaxation and objective-drive parameters rather than fixing them for every…
The paper gives a combinatorial certificate that point clouds on an irreducible algebraic surface have few additive collisions unless they concentrate on affine lines. Its transferable asset is the additive-energy viewpoint: the number of…
The paper gives a constructive spectral-design mechanism for directed graphs: every weakly connected digraph can be assigned strictly positive arc weights so that its in-degree Laplacian is diagonalizable, with a semisimple zero eigenvalue…
The paper provides a transferable mechanism for predicting and controlling symmetry-specific oscillatory modes in delayed ring networks. Discrete Fourier decomposition converts the ring dynamics into independent spatial modes, while…
The paper identifies a concrete failure mode in periodic discretizations: representing a Bloch mode as a periodic factor with wavenumber-dependent differential terms can break reciprocal-lattice covariance and create nonphysical phantom…
The paper establishes a dimension-counting identifiability principle for analytic finite-dimensional model classes: if an infinite-data forward map is injective on a d-dimensional analytic class, then 2d+1 independent random scalar…
The paper develops a multidimensional thermodynamic uncertainty relation for arbitrary combinations of counting observables, including currents, traffic, flows, coarse-grained observations, finite observation windows, and time-dependent…