2581 valuable arXiv mathematics papers the pipeline has analyzed — each with a short note on what its math gives to machine learning.
The paper gives a transferable finite-horizon observability mechanism for recurrent networks. Its strongest result is that general real-valued ReLU dynamics can lose state information through activation masks, yielding a global lower bound…
The paper provides a constructive theory of nonzero-frequency relative equilibria in directed Kuramoto networks, including existence conditions, orbital stability modulo the global phase direction, invariant neighborhoods, and exact…
The paper's transferable asset is a reciprocal primal-dual representation in which an inequality constraint g(x)<0 is paired with a positive multiplier through the explicit manifold \(\lambda=-k/g(x)\). This converts constrained…
The paper classifies finite-dimensional operators satisfying polynomial relations in the inner derivation \(\operatorname{ad}_A(T)=AT-TA\), showing that the root geometry of the polynomial determines when \(T\) and its commutators are…
The paper provides a small-gain-like construction for large-signal stability of interconnected nonlinear subsystems: individual dissipation or gain bounds are assembled into a global stability certificate. Its most transferable asset is a…
The paper constructs ergodic ×p-invariant measures whose mass in every planar tube of width w is O(w^s), so no line projection loses dimension, even when the projected iterated-function system has exact overlaps. The transferable…
The paper provides a constructive statistical geometry for projecting a distribution onto the cone of measures below a reference distribution in convex order, using an optimal-transport cost. The transferable asset is that convex order…
The paper provides a constructive way to extend split-conformal coverage from randomly sampled trajectory points to an entire continuous-time path by combining a discrete conformal residual with a bound on trajectory regularity. Its key…
The paper provides a decision-focused way to handle uncertain quality estimates: instead of requiring the entire model-quality table to be identified, test whether the same budget-feasible allocation remains optimal over an explicitly…
The paper contains a constructive reduction for learning controlled free-boundary dynamics: under quasi-static Darcy filling, the filled region at a fixed time depends on the cumulative, rather than pointwise, gate-pressure history. This…
The paper identifies the positive branch of the quadratic Hessian operator as a useful nonlinear spectral map: G(A)=sqrt(sigma_2(A)) is elliptic, concave, and positively homogeneous on the cone Gamma_2. These properties can be transferred…
The paper identifies a structural limitation of standard passivity analysis: a nonzero passive transfer relation under the usual supply rate must have relative degree no greater than one, so high-fidelity models with electromagnetic or…
The paper introduces an optimizer geometry that uses two points on the same objective level set and the intersection of their normal directions as an ellipcenter. For a strictly convex quadratic, the equal-value second point can be…
The paper provides a constructive sensitivity mechanism for controls that are frozen between discrete review epochs: the fluid value can be nonmonotone for short review periods and, after a threshold, develop monotone nondecreasing, convex…
The paper turns task-aware robustness into a distance-design problem: messages that differ in the prescribed function value must be mapped to codewords that are far apart, while messages with the same function value need not be separated…
The paper proves a sharp higher-order inequality on the Hamming cube: the average L^p magnitude of a conditional projection onto a random k-coordinate subset is controlled by coordinate-wise discrete derivatives and the global centered L^p…
The paper offers a constructive pipeline for learning feedback policies for unknown nonlinear dynamics: identify a model from offline data, jointly synthesize a neural controller and neural Lyapunov function, enforce inputs with hard…
The paper provides a practical way to make limited-memory quasi-Newton training robust to locally indefinite curvature without eigendecompositions, Krylov searches, or costly isotropic damping. Its key transferable asset is a minimal…
The paper offers a transferable uncertainty-propagation mechanism: represent nonlinear stochastic rollouts with a finite Gaussian mixture rather than collapsing uncertainty into one Gaussian, while controlling approximation error in…
The paper provides a constructive Monte Carlo factorization for translation-invariant kernels whose Fourier transform is signed rather than nonnegative. This is useful beyond KDE because many neural architectures implicitly require…
The paper separates geometry from local physical variables by evolving a weighted state and using a geometry-weighted mean as the admissible anchor. This suggests a transferable postprocessing layer for mesh and graph neural operators…
The paper gives an exact construction for bounded, finite-correlation-time nonequilibrium fluctuations: a stable linear relaxation process driven by independent dichotomous telegraph signals. Its transferable assets are a hard stationary…
The paper's transferable contribution is a tail-focused multifidelity correction strategy: use a cheap global predictor, quantify its finite-sample uncertainty, and spend expensive evaluations only near the estimated risk boundary and…
The paper develops a principled method for bilevel problems where an outer objective selects a solution from the zero set of a monotone inner operator. Its transferable asset is dynamic Tikhonov regularization combined with extragradient…