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.

Unverified 2026

Reflection-Equation Expert Reset

Add a structured boundary-like operation to an MoE router that rapidly mixes expert probabilities toward a learned distribution while preserving predefined expert groups. The operation is a rank-one stochastic kernel, so it costs linear rather than quadratic work in the number of experts and can act as a controlled reset when routing becomes concentrated.

Useful4/10
Difficulty3/10
Novelty6/10
Paper: Integrable multi-species SSEP with reactive particle species arXiv:2607.18959
Unverified 2026

Adaptive Hankel constraint curriculum

Exploit the paper's nested obstruction hierarchy by applying cheap low-order Hankel tests to every example and evaluating larger matrices only for outputs near the current feasibility boundary. This turns higher-order structural validation into an adaptive curriculum rather than an always-on expensive eigendecomposition.

Useful4/10
Difficulty5/10
Novelty8/10
Paper: Higher-Order Hankel Obstructions to Free Infinite Divisibility for Beta Distributions arXiv:2607.17630