Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Replace a fragile learned similarity score for continuous object coordinates with a projection residual against a learned signal subspace. Candidate coordinates are represented by normalized Fourier or positional feature vectors, and the score is the fraction of feature energy outside the estimated subspace. The score remains useful even when the estimated subspace is adversarially rotated, because the perturbation is controlled directly by a sine-theta distance rather than by assumptions about…
Make a neural network predict a positive Gaussian-mixture representation of the distribution function rather than independent values on a momentum grid. Use the mixture parameters inside a differentiable Boltzmann collision operator, so training directly enforces the interaction mechanism and exposes the relaxation spectrum responsible for ballistic-to-hydrodynamic crossover.
Use a convergent kernel approximation of the Zubov invariant as a trust-region monitor for a learned dynamics model. The estimated Zubov sublevel sets become an inference-time gate that rejects, shortens, or dampens transitions predicted to leave the learned attraction region.
Initialize a recurrent or state-space transition matrix with weak Wigner noise plus a shared cumulative-sum correlation structure. Increasing the correlation strength produces recurrent eigenmodes one at a time at analytically predicted BBP thresholds, yielding a controllable hierarchy of short- and long-memory modes. The matrix should then be globally rescaled or constrained so that all active modes remain inside the desired stability radius.
Replace the unconstrained transition of a recurrent or state-space neural network with a DMDc-initialized linear latent transition plus a learned nonlinear residual. Estimate the transition from a short warm-up dataset using Hankel delay coordinates, retain eigenmodes with decay rates near the unit circle for long-term memory, and let the neural residual model dynamics not explained by the linear backbone. This should make long-horizon prediction and slowly varying signals easier to learn while…
Replace magnitude-based channel or expert pruning with a subset-selection objective that maximizes the weakest direction in the candidates' activation span. Relax the binary mask to continuous gates, optimize an entropic soft minimum eigenvalue, and round the gates to retain a fixed number of channels or experts. This should preserve diverse representations and reduce redundant feature directions.
Use the diffusion graph's Dirichlet energy and almost-isometry inequalities to score whether a candidate minibatch preserves the low-frequency structure of losses, logits, or gradients over the dataset. Reject or augment batches that distort these quantities, producing a geometry-aware batch acceptance rule rather than relying only on random or loss-based sampling.