Emergent quantum chaos from correlations on a random graph
arXiv:2607.11662
2026
Architecture
2 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper identifies a sparse, translation-invariant random graph whose edge probability decays as a power law with distance, yet whose adjacency spectrum crosses from localized/Poisson behavior to delocalized/GOE-like behavior near \(\sigma\approx0.8\text{--}0.85\). The transferable asset is not the condensed-matter interpretation itself, but the possibility of obtaining global information flow from a constant-degree, geometry-aware random connectivity pattern without dense all-to-all mixing. A practical neural adaptation is a fixed or periodically resampled power-law sparse attention graph, with the paper's critical exponent used as a principled starting point and spectral delocalization diagnostics used to prevent the mask from fragmenting information flow.
Ideas from this paper
✗ Mechanism failed
2026
Replace dense self-attention by a sparse mask on a one-dimensional or ordered token geometry, retaining local neighbors and adding long-range edges with probability proportional to distance raised to \(-(1+\sigma)\). Use \(\sigma\approx0.8\text{--}0.85\) as the initial regime because the paper finds that this range supports delocalized, GOE-like connectivity despite sparse bonds. The resulting layer has linear or near-linear attention cost while maintaining long-range paths.
Useful7/10
Difficulty4/10
Novelty6/10
Unverified
2026
Use eigenvector delocalization as a mask-quality criterion rather than selecting a random sparse graph blindly. Penalize masks whose normalized adjacency has concentrated leading eigenvectors or disconnected or weakly connected components, while preserving the power-law distance prior. This creates a sparse routing graph that is less likely to trap information in local regions.
Useful5/10
Difficulty6/10
Novelty7/10