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 an explicit formal-power-series construction of lower-triangular Sprugnoli operators whose square is an aerated Appell operator, including exact involutions. The transferable asset is not the particular combinatorial…
The paper gives an explicit local surgery on quad meshes that splits one cone vertex into two while preserving genus, all other vertices, and the subgroup of rotational holonomy. This is useful as a mathematically controlled…
The paper gives an exact support-function characterization of whether a stationary curve is covered by every translated and rotated copy of a triangle. The transferable asset is the reduction of a global geometric containment condition to…
The paper identifies a failure mode of masked prediction that is directly relevant to masked language models and masked diffusion: schedules exposing almost the entire input can fit local conditionals while remaining exponentially…
The paper provides a constraint-aware Luenberger observer for P-Time Event Graphs, where latent firing times are reconstructed from partial observations while enforcing both causal lower bounds and token-lifetime upper bounds. Its…
The paper identifies U-centering with an explicit least-squares projection that removes additive effects attached to the endpoints of every edge, rather than treating it as an ad hoc dependence-statistic formula. This gives neural networks…
The paper provides an exact rake–compress contraction for quadratic dynamic programs on arbitrary rooted trees, replacing the sequential tree-height dependency of Riccati/message-passing recursions with O(log N) span while preserving…
The paper constructs an entire complex-time flow W_z=e^{zK} whose generator preserves a bilinear form, with complex orthogonality replacing ordinary unitary evolution. This structure transfers to recurrent and state-space neural networks…
The paper identifies chunked-prefill scheduling as a controllable dynamical mechanism for shaping LLM inference power: splitting long-prompt computation into smaller scheduling quanta substantially reduces power ramp rate while leaving…
The paper provides a constructive block-diagonal-dominance (BDD) certificate for decentralized stability: a block matrix is nonsingular when each block row's normalized off-diagonal coupling has infinity norm below one. Its transferable…
The paper constructs H-distributions that record localized correlations between weakly convergent Lp sequences and their conjugate-dual sequences, resolved by Fourier direction. The transferable asset is a non-Hilbert-space directional…
The paper gives a concrete particle gradient flow for the nonsmooth negative-distance kernel K(z)=-|z|^q, together with the essential prescription of removing self-interactions. Its transferable asset is a repulsive-attractive dynamics…
The paper isolates a broadly useful numerical principle: evaluate a high-order rational spectral filter as an additive partial-fraction sum rather than as a recursive product. Although the target application is one-way fluid marching, the…
The paper gives an explicit algebraic certificate for when a structured coefficient-vector code lies in the MDS locus: every maximal Pluecker coordinate factors into the constant coefficient and Schur polynomials indexed by partitions…
The paper develops a compactification for asymmetric metric-measure spaces using one-sided Lipschitz observables, domination by measure-preserving nonexpansive maps, and multiscale lower sets called pyramids. Its most transferable asset is…
The paper supplies an exact global objective for measuring how uniformly a finite set of q-ary codewords covers all Hamming balls, with perfect codes attaining the minimum whenever they exist. This is transferable as a structured…
The paper provides a constructive multistability mechanism in three-dimensional quadratic zero-one mass-action networks: among minimal six-reaction motifs, positive steady states occur in an alternating stability pattern, with consecutive…
The paper contributes a practical way to optimize piecewise-linear maps while explicitly preventing orientation reversals: first restore feasibility, then minimize a strictly feasible logarithmic barrier with a line search. Its most…
This paper gives a sharp, algorithm-dependent characterization of post-adaptive-sampling bias rather than treating bandit samples as iid. The transferable object is the effective exploration rate: for generalized UCB indices x +…
The paper gives an exact example where interpolation is statistically inferior to deliberate training misfit: a shared high-variance signal is represented in the training span only together with orthogonal nuisance directions. The useful…
The paper provides a constructive way to estimate a nonlinear system's domain of attraction by converting the Zubov function into a unique invariant element of a Koopman-like operator acting on an RKHS. Its key transferable mechanism is…
The paper gives an explicit sparse, skew-symmetrizable exchange system produced by folding a larger quiver under a transpose involution. Its transferable value is the combination of sparse signed interactions, orbit-based parameter tying…
The paper provides a sharp shadowing criterion for compact-group endomorphisms: after reduction to the surjective stable image, every finite-dimensional invariant sector of the rational dual dynamics must be hyperbolic, and the induced map…
The paper gives a constructive route to recover outlying eigenspaces of a large bounded symmetric matrix from only a small uniformly sampled set of columns, with the approximation living in the span of those columns. The transferable asset…