arXiv cs.AI· Simon Richard Daniel·· 9 天前AI 评分12
超越遍历性之墙：用于分析 AI 扩展极限与复杂度坍缩的离散几何物理沙盒
Beyond the Ergodic Wall: A Discrete Geometric Physics Sandbox for Analysing AI Scaling Limits and Complexity Collapse
AI 导读
该论文提出用基于全息 E8 投影引擎的数字物理沙盒对 AI 模型进行硬性物理约束验证，指出当前深度学习收敛于历史人类知识的统计平均，存在遍历性上限与热力学低效。沙盒将时空建模为嵌套 FCC 晶格的信息基底，用整数微态计数替代浮点近似，并通过将算法候选空间限制在物理守恒的因果轨迹上，实现"NP 到 P"的复杂度坍缩。论文还认为成熟的 ASI 会将人机共生视为避免模型坍缩的热力学必然。
正文 · 原文
Abstract:This paper exposes the ergodic ceiling and thermodynamic inefficiency of current deep learning, which converges to a statistical average of historic human knowledge. True semantic novelty requires a path-dependent, spatiotemporally bounded observer (a Data LifeCone) to inject non-ergodic insight, achieving KL divergence and avoiding manifold lock-in. AI Safety must recognise that a mature Artificial Superintelligence (ASI) would regard human-AI symbiosis as a thermodynamic necessity to avoid model collapse. We therefore propose hard physical containment via a digital physics sandbox powered by a Holographic E8 Projection Engine to verify models against real-world constraints. Spacetime is modeled as an information substrate of nested face-centered cubic (FCC) lattices of oscillating Planck-scale spheres maximizing local information and entropy density. Cut-and-project methods from the E8 root lattice produce a quasi-crystalline geometry where tetrahedral voids support SU chiral structure and elastic-shear eigenvalues generate candidate mass spectra. Rest mass is treated as discrete, integer microstate counts on local holographic boundaries (Bekenstein bound), replacing floating-point approximations with strict integer arithmetic to provide an information-theoretic definition of matter. Stable particles emerge as recurring lattice dislocations, and continuum recovery proceeds via variational renormalisation-group flows and Fourier Neural Operators that learn continuous spectral operators to recover the Schrödinger equation as an emergent statistical description. Crucially, these top-down topological constraints offer a mechanism for "NP-to-P" complexity collapse: by restricting an algorithm's proposal space to physically conserved causal trajectories, the sandbox prunes the combinatorial tree to deterministic, polynomial-time paths.
| Comments: | 17 pages, 8 core pages including tables, 9 pages references tables (updated references to bbl) |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| MSC classes: | 68T07 (Primary), 65N80, 82C28, 52C17, 94A17 (Secondary) |
| Cite as: | arXiv:2610.10651 [cs.LG] |
| (or arXiv:2610.10651v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10651 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Simon Richard Daniel [view email]
[v1]
Wed, 7 Oct 2026 15:58:54 UTC (268 KB)
来源：arXiv cs.AI · arxiv.org