Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Regularize a circular recurrent kernel by directly controlling the growth rate and phase velocity of its Fourier modes. This converts replay-speed selection into a low-dimensional spectral control problem and can suppress unstable or excessively slow modes without adding recurrent parameters.
Replace a conventional scalar activation by a geometrically indexed family of affine pieces whose slope changes with the logarithmic magnitude of the input. The same two endpoint parameters are reused across all scales, giving a compact, explicitly scale-aware activation that can represent different responses for exponentially separated activation magnitudes.
Paper: From two-dimensional continuous maps to one-dimensional discontinuous maps: a novel reduction explaining complex bifurcation structures in piecewise-linear families of mapsarXiv:2512.02291