超越遍历壁垒：用于分析AI缩放极限与复杂度崩溃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
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中文总结 AI 辅助
本文提出由全息E8投影引擎驱动的离散几何物理沙盒，用于分析AI缩放极限与复杂度崩溃，可验证模型的现实约束，实现“NP到P”复杂度崩溃，为AI安全提供支撑。
中文摘要 AI 辅助
本文揭示了当前深度学习的遍历上限与热力学低效性，其收敛于历史人类知识的统计平均值。真正的语义新颖性需要依赖路径、受时空约束的观察者（数据生命锥，Data LifeCone）注入非遍历洞见，以实现KL散度并避免流形锁定。AI安全必须认识到，成熟的人工超级智能（Artificial Superintelligence, ASI）会将人机共生视为避免模型崩溃的热力学必需。因此，我们提出通过由全息E8投影引擎（Holographic E8 Projection Engine）驱动的数字物理沙盒实现硬物理约束，以针对现实世界约束验证模型。时空被建模为嵌套面心立方（face-centered cubic, FCC）晶格的信息基底，该晶格由振荡的普朗克尺度球体构成，用于最大化局部信息与熵密度。来自E8根晶格的切割-投影方法产生准晶体几何，其中四面体空隙支持SU手性结构，弹性-剪切本征值生成候选质量谱。静质量被视为局部全息边界（贝肯斯坦限，Bekenstein bound）上的离散整数微观态计数，用严格整数算术取代浮点近似，以提供物质的信息论定义。稳定粒子作为重复出现的晶格位错出现，连续统恢复通过变分重整化群流与傅里叶神经算子（Fourier Neural Operators）进行，这些算子学习连续谱算子以恢复作为涌现统计描述的薛定谔方程。关键在于，这些自上而下的拓扑约束提供了“NP到P”复杂度崩溃的机制：通过将算法的提议空间限制为物理守恒的因果轨迹，沙盒将组合树修剪为确定性多项式时间路径。
英文摘要
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.
发表机构
- Dyson School of Engineering, Imperial College（帝国理工学院戴森工程学院）
机构由 AI 辅助整理，请以论文原文为准。
