Research ideas

Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.

74 ideas found

Solves: Scalability ML: Rnn Clear all

Unverified 2026

Prime-Gated Maximal-Length Binary Reservoir

Replace a learned recurrent transition with a sparse binary reservoir compiled from prime-count gates. Three permanently active control vertices implement copy and XNOR transitions, allowing the signal state to realize an affine feedback register over \(\mathbb F_2\) with period \(2^m-1\) using only \(O(m)\) edges and bounded in-degree. Train only an input projection and readout, or use straight-through estimators if end-to-end adaptation is required.

Useful5/10

Difficulty5/10

Novelty6/10

Architecture Memory Scalability Sample efficiency

Paper: Pulse Graphs: Prime-Activated Boolean Dynamics on Directed Graphs arXiv:2607.10453

Unverified 2026

Quasiperiodic Additive State Module

Use the paper's skew product as a parameter-free recurrent state: one phase rotates by an irrational increment and a second state accumulates a lacunary Fourier readout of that phase. This supplies deterministic long-range memory with only scalar updates, avoiding a learned recurrent transition matrix and its potentially unstable spectrum.

Useful5/10

Difficulty5/10

Novelty6/10

Dynamics Memory Scalability Stability

Paper: Regularity, quantitative deviation, and non-rigidity of a lacunary skew product arXiv:2608.25821