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 constructive class of symmetry-preserving, probabilistically valid, monotone block transformations for Ising spins, together with an RG interpretation in which repeated coarse-graining follows a low-dimensional dynamical…
The paper offers a constructive Bayesian mechanism for detecting unknown, time-varying feedback delays: represent each candidate delay as a mode, run one Kalman filter per mode, mix their state estimates using Markov transition…
The paper provides a constructive structural test for whether a single-output nonlinear system admits observer-error linearization: a Pascal-triangle pattern in selected Hessian entries together with an identically vanishing lower-right…
The paper replaces scalar utility maximization with a target-distribution objective: choose a stopping time whose stopped diffusion has a prescribed law. Its transferable asset is the coupling between path-dependent stopping rules and…
The paper identifies a strong form of stable iterative dynamics: a disk self-map with boundary multiplier \(\alpha<1\) has exactly linear hyperbolic progress when its Koenigs coordinate remains non-degenerate at the attracting boundary…
The paper offers a transferable mechanism for constructing maximal attractors from trapping regions and for certifying hyperbolic behavior through invariant cone fields. The core neural-network application is to constrain recurrent or…
The paper provides a transferable four-region likelihood that separates inliers, ordinary body observations, and extremes instead of forcing one residual distribution to explain all data. Its generalized Pareto tail gives a principled…
The paper provides a constructive robust-bilevel viewpoint for evaluating congestion when demand is uncertain: an adversary chooses a demand realization while users respond according to a Wardrop equilibrium or a system-optimal flow. The…
The paper offers a parameter-free disturbance-observer mechanism: infer a periodic disturbance and its unknown frequency from inertial measurements and control inputs, then inject an anti-phase correction that dissipates disturbance…
The paper isolates a concrete mechanism by which sequence-pooled normalization creates a global input-to-output dependency even when the convolutional receptive field is local. Its Jacobian gives an exact, task-independent test for whether…
The paper introduces the robust instability radius, defined as the smallest norm of a stable diagonal heterogeneous perturbation that can stabilize an otherwise unstable network. This is a transferable distance-to-stability mechanism for…
The paper gives a constructive way to turn orthogonal transforms into nearly incoherent orthogonal transforms by inserting a uniformly random signed permutation. The resulting product spreads signal energy across coordinates while…
The paper provides an exact robust-instability reduction for networks of identical SISO agents with independent multiplicative uncertainties. For cyclic interaction matrices, the network-level characteristic equation collapses to a scalar…
The paper exposes a useful alternative to fixed-dimensional neural compression: represent a complex matrix by a variable number of physically meaningful rank-one atoms, and let the decoder reconstruct those atoms analytically rather than…
The paper provides a constructive alternative to learning all parameters of a shallow network: prescribe inner weights and biases using quasi-Chebyshev parameter sets, then fit only the output coefficients. Its key transferable asset is a…
The paper's transferable mathematical object is the rearrangement-based hybrid norm Z_E^2, which applies a symmetric-space norm to the largest portion of a signal and an L2 norm to its remaining tail. This provides a principled regularizer…
The paper provides a constructive way to turn output-only interaction into a finite-dimensional recurrent state by stacking delayed inputs and outputs in a companion-form system. Its transferable asset is not the linear-controller result…
The paper gives an exact singular-value characterization of the norm of the two-sided operator S_{a,b}:x maps to axb. Its transferable asset is the coupling of the spectra of the left and right factors through the pointwise product of…
The paper develops a relative variational principle for expanding, possibly nonstationary iterated-function systems: conditional entropy in the fiber, conditioned on an ergodic symbolic base, equals the base-average of fiberwise…
The paper identifies a thresholded weak-type nonlocal interaction whose large-threshold limit is a local Sobolev gradient energy or BV total variation. The transferable asset is that this regularizer can be estimated from sampled pairs of…
The paper gives an exact worst-case chance constraint for a sum of independent nonnegative random variables when only their individual means are known. The transferable asset is not a generic concentration bound: it reduces an…
The paper develops a residual-driven adaptive basis in which nonlinear propagation directions are optimized while linear coefficients are eliminated exactly by variable projection. Its transferable asset is the separation of nonlinear…
The paper provides a nonstandard criterion for robustness of random derivative cocycles: quasi-irreducibility is equivalent, under a simple-top-exponent assumption, to contraction of the projective tangent dynamics, a vertical spectral…
The paper isolates a failure mode for refinement-based samplers: rough potentials can have stable posteriors while their classical derivatives become increasingly resolution-dependent. Its most transferable construction is a…