Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Treat the maximum dependency distance faithfully modeled by a finite neural architecture as an emergent correlation length, and estimate how it grows with depth, state size, or attention span. Fit the exponent \(\kappa\) and use it as an architecture-selection signal: a model with larger \(\kappa\) should acquire long-range competence more efficiently at equal parameter or FLOP budget.
Replace softmax attention or dense MoE routing with a normalized Rayleigh–Jeans distribution over tokens or experts. If an item's energy is close to the chemical potential, its probability becomes disproportionately large, creating controllable low-energy condensation instead of the exponentially smooth allocation produced by softmax.
Construct a finite menu of experts or LoRA adapters by quantizing the oracle action manifold under a task-aware Fisher-information distortion rather than Euclidean parameter distance. The router can choose an installed expert after observing the input, but only k experts are stored or evaluated. The paper's frontier rate gives a falsifiable accuracy-versus-menu-size prediction.