Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Store a convex object as a direction-indexed vertex tuple and implement composition of objects through componentwise Minkowski addition and nonnegative scaling. This creates a structured residual or compositional layer where convexification is nonexpansive, making perturbation amplification controllable and avoiding repeated generic geometric optimization.
Replace random Fourier features or a dense sinusoidal positional encoding with a compact bank whose frequencies are the continued-fraction denominators of an irrational number. Inverse-frequency amplitudes provide multiscale structure with a controlled sub-Lipschitz regularity profile, while lacunarity reduces the number of frequencies needed to represent oscillatory structure.
Use an approximate decision diagram to select a structured subset of neurons, channels, attention heads, or attention edges when their quadratic interactions are sparse or inverse-sparse. Merge states that agree on a local interaction boundary and accept a tunable epsilon loss in the pruning objective, obtaining a representation whose size is linear in model width for fixed accuracy tolerance.