Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Train decentralized agents using only individual rewards for discovering replenishable targets, while their observations contain conspecifics but not target locations. Give the policy a tunable visual or attention radius and test whether aggregation and improved search emerge above the predicted crossover, without adding alignment, proximity, or group rewards. This creates a controllable collective phase that can reduce redundant exploration and improve multi-agent resource discovery.
Choose the neural operator's input-history length from the measured correlation time of the unresolved closure signal produced by coarse-graining. This avoids under-memory, which causes systematic closure error, and over-memory, which increases attention cost and can destabilize training. The same diagnostic can drive adaptive memory truncation across physical regimes.
Use a learned scalar ordering function to turn a symmetric local Gaussian graph kernel into a directed, row-stochastic message-passing operator. The asymmetric tilt lets neighboring nodes communicate preferentially along an inferred dynamical direction, while the Gaussian factor retains locality and diffusion-like smoothing.
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.
Replace quadratic self-attention over a sequence with a bank of K auxiliary exponentially decaying states whose rates are fitted directly from the empirical autocorrelation of the sequence features. Each mode captures a distinct time scale, so the module can represent short- and long-range dependencies with O(TK) computation and O(K) recurrent memory rather than storing all previous tokens. Constrain decay rates to be positive and use the paper's extended Markovian block structure to obtain a…
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.
Construct a sparse attention layer by sampling backward token histories as a continuous-time branching process rather than allowing every query to attend to every key. Each active ancestor either dies or branches into a bounded number of candidate ancestors, with branching probability controlled by a small parameter. The branch-out penalty predicts exponentially small probability of long, highly branching histories, providing a direct knob for receptive-field size and attention FLOPs.
Replace iid dropout or iid activation noise on spatial tokens with fluctuations generated by a conserved diffusing density. Each token receives a positive mass variable whose total mass is preserved, while Poissonian stochastic flux produces correlated perturbations that explore coherent local patterns rather than independently corrupting every feature. The density is autonomous and detached from autograd, so the regularizer adds little computational overhead.
Replace scalar entropy penalties on attention maps with a matrix-valued heat-flow regularizer over a circular or periodic token coordinate. Each position stores a positive semidefinite matrix describing coupled heads, experts, or channels; heat smoothing is constrained by the sharp modified log-Sobolev and Bogoliubov–Kubo–Mori contraction rather than an arbitrary smoothing coefficient. This should suppress high-frequency routing noise while preserving positive matrix structure and reducing…