Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Use a local chaining complexity computed from an empirical input metric to predict stochastic output error for each individual input. Easy, locally concentrated inputs can use fewer dropout, ensemble, or diffusion samples, while high-complexity inputs receive additional computation; unlike a global confidence threshold, the allocation varies with the input.
Add a per-feature or per-token state that accumulates recent stimulation and decays when stimulation is absent, then use a nonlinear decreasing gain to suppress repeatedly activated features. This creates short-term adaptation without changing the core transformer or recurrent weights: familiar inputs are processed with reduced gain, while novel inputs recover their full response.
Remove a latent relay or hub token from an attention or graph layer and replace its two-hop influence by direct effective edges between retained tokens. The correction is a normalized rank-one update, so it can preserve hub-mediated communication while reducing the number of stored and processed states.
Augment a causal sequence model with a small hierarchy of prefix summaries weighted by powers of the logarithmic rank of each preceding token. The summaries retain order-sensitive deviations from a baseline representation while costing O(KNd) for sequence length N, hierarchy width K, and hidden dimension d, instead of O(N^2d) dense attention.
Replace a fixed top-k expert count with a stochastic, token-specific fanout generated by a supercritical binary branching process stopped at a geometric time. The resulting number of active experts has finite mean but a power-law tail with log-periodic modulation, allowing most tokens to use little compute while reserving larger computation for difficult or ambiguous tokens.