2581 valuable arXiv mathematics papers the pipeline has analyzed — each with a short note on what its math gives to machine learning.
The paper proves an exact identifiability theorem for sets from Fourier samples taken on a dual lattice. For connected finite unions of convex bodies satisfying an alias-free sparse-lattice condition, equality of all sampled indicator…
The paper isolates a useful decomposition for entropic transport estimation: empirical operator fluctuations scale as n^(-1/2), while inverse stability of the population Sinkhorn fixed point controls how strongly those fluctuations are…
The paper provides a transferable numerical-dynamics mechanism: a discretization of a stochastic continuous-time system can preserve both its random attractor and the sign of the almost-sure Lyapunov exponent of a distinguished invariant…
The paper gives a constructive way to build nonnegative rational temporal kernels that approximate a deterministic delay with substantially lower variance than Erlang/gamma cascades at the same polynomial order. The transferable asset is…
The paper provides a uniform statistical-stability mechanism for deterministic, nonstationary compositions of heterochaos baker maps: despite arbitrary admissible parameter variation, sufficiently regular initial distributions lose memory…
The paper offers a transferable decentralized optimization mechanism: stochastic proximal best responses are combined with Krasnoselskii relaxation and variable sample sizes, with mean-square convergence to a unique Nash equilibrium under…
The paper identifies a transferable mechanism: periodic driving plus dissipation produces a static force with a genuinely nonconservative component, characterized by nonzero circulation around closed loops in collective-coordinate space…
The paper offers a transferable representation-learning principle for systems whose dynamics are only locally linearizable: make the Koopman latent state sparse, so the active-coordinate support becomes an unsupervised regime variable. The…
The paper constructs an explicit finite-dimensional representation of the braid group using local, invertible 2-by-2 crossing operators, and proves that these operators satisfy braid and far-commutativity relations exactly. The…
The paper develops geometric-attraction criteria for iterated function systems whose transformation families and selection probabilities change with time. Its transferable mechanism is a quantitative contraction condition on products of…
The paper gives a sharp, dimension-independent certificate for deleting off-diagonal blocks from a Hermitian matrix: the induced eigenvalue displacement is controlled by both the cross-block norm and the spectral separation between…
The paper introduces divisibility-constrained integer weights on simplices and uses them to modify boundary and coboundary operators while preserving the chain-complex identity \(\partial^w\partial^w=0\). This yields incidence operators…
The paper provides a certified counterexample showing that geodesic strong convexity and an interior minimizer do not imply forward invariance of a geodesic trust region under gradient flow on \(\mathrm{SO}(3)\). Its transferable mechanism…
The paper provides a transferable dissipativity mechanism for quantifying how measurement and actuation delays amplify external perturbations: a delay-dependent Lyapunov–Krasovskii functional yields LMIs certifying an upper bound on…
The paper gives a concrete, numerically stable alternative to Gram–Schmidt for constructing an adaptively sized low-rank basis: draw Gaussian test blocks, factor each sampled residual block with blocked Householder reflectors, and stop…
The paper gives a deterministic quadratic-phase sequence whose diffraction is purely absolutely continuous for every nonzero amplitude, irrational quadratic coefficient, and phase offsets. This is a concrete source of structured…
The paper addresses a failure mode of standard implicit differentiation: an inner optimization problem may have multiple minimizers, so its Jacobian is singular even though a stable, canonical solution can be selected. Its transferable…
The paper provides a concrete projective-dynamics mechanism for complete affine torus tilings: affine holonomy elements with sufficiently large positive translational invariant drive almost every initial direction toward one of two…
The paper supplies a structured change-of-basis framework in which polynomial coefficient matrices are replaced by production matrices, with orthogonal-polynomial recurrences appearing as tridiagonal operators and d-orthogonal recurrences…
The paper provides an entropy-dissipation framework for particle systems combining deterministic Stein transport with Langevin diffusion. The transferable asset is that both components reduce the same relative entropy through distinct…
The paper supplies a strong spectral balancing principle: a collection of individually bounded symmetric operators can be assigned signs so that their aggregate operator norm grows only as the square root of the number of operators, with…
The paper introduces a powered ratio-of-norms penalty, R_p(X) = ||X||_1^p / ||X||_F, which is a nonconvex sparsity surrogate that distinguishes concentrated representations from diffuse ones more sharply than an ordinary L1 penalty. Its…
The paper gives a constructive representation of functions as positive cosine mixtures on a frequency lattice, together with a scaling law linking lattice spacing, polynomial degree, and spectral bandwidth. The transferable asset is the…
The paper gives a constructive characterization of a class of positive-definite quadratic forms as nonnegative sums of integral rank-one forms whose covectors have unimodular, regular-matroid support. This suggests replacing an…