用时空类比解释模型重构的计算成本,揭示智能惯性现象。
Intelligence Inertia: Physical Isomorphism and Applications
- 将深度学习动态类比为闵可夫斯基时空,构建非线性成本公式。
- 预测出计算量呈$J$型曲线膨胀,经典方法在此失效。
- 提出惯性感知调度器,防止灾难性遗忘,适合模型演化研究者。
经典框架如费舍尔信息仅能近似低密度状态下的神经适应成本,无法解释深层结构重组时爆发的计算开销。为此,我们引入‘智能惯性’——基于规则与状态间非对易性($[\ς, \u03b3] = i\mathcal{D}$)的启发式数学同构。该同构将深度学习动力学类比为闵可夫斯基时空,作为高维张量演化的有效理论,推导出类似洛伦兹因子的非线性成本公式,预测出相对论式的$J$形通胀曲线——即经典近似失效的计算壁垒。通过三项实验验证:(1) 在高熵噪声下裁定$J$曲线分歧;(2) 绘制架构演化的最优测地线路径;(3) 部署‘惯性感知调度器包装器’,防止灾难性遗忘。该同构提供结构抵抗的精确量化指标,提升智能体的稳定性与效率。
原文摘要 · Abstract (English)
Classical frameworks like Fisher Information approximate the cost of neural adaptation only in low-density regimes, failing to explain the explosive computational overhead incurred during deep structural reconfiguration. To address this, we introduce \textbf{Intelligence Inertia}, a property derived from the fundamental non-commutativity between rules and states ($[\hat{S}, \hat{R}] = i\mathcal{D}$). Rather than claiming a new fundamental physical law, we establish a \textbf{heuristic mathematical isomorphism} between deep learning dynamics and Minkowski spacetime. Acting as an \textit{effective theory} for high-dimensional tensor evolution, we derive a non-linear cost formula mirroring the Lorentz factor, predicting a relativistic $J$-shaped inflation curve -- a computational wall where classical approximations fail. We validate this framework via three experiments: (1) adjudicating the $J$-curve divergence under high-entropy noise, (2) mapping the optimal geodesic for architecture evolution, and (3) deploying an \textbf{inertia-aware scheduler wrapper} that prevents catastrophic forgetting. Adopting this isomorphism yields an exact quantitative metric for structural resistance, advancing the stability and efficiency of intelligent agents.
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