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 single global learning rate with mode-dependent rates determined by the static correlation structure of recent parameter updates or hidden-state updates. Correlated modes are treated as collective diffusive modes: their effective relaxation rate is reduced in proportion to their structure-factor amplitude, so the optimizer accelerates weakly correlated modes while damping collective slow modes. The method also supplies a diagnostic for when the Markovian approximation is invalid and…
Paper: The intermediate scattering function of an interacting adlayer as a characteristic function: a closed-form theory of Ising lattice-gas surface diffusionarXiv:2608.03398
Replace an unconstrained recurrent or neural-operator latent transition with a differentiable KPZ cell acting on a spatial latent field. The cell explicitly separates smoothing, nonequilibrium nonlinear steepening, and stochastic forcing, making it suitable for driven dissipative systems and long-horizon roughening that generic networks may fail to reproduce.
Estimate the leading complex resonances of the noise-averaged hidden-state dynamics of a stochastic RNN and use them to detect or control statistically persistent oscillations. The key design principle is to treat resonance radius and Lyapunov growth as independent signals: hidden trajectories can be Lyapunov-stable while the annealed dynamics still produce narrow-band ringing because a transfer-operator eigenvalue lies close to the unit circle.