Intelligence Inertia: Physical Principles and Applications

Abstract

While Landauer's principle establishes the fundamental thermodynamic floor for information erasure and Fisher Information provides a metric for local curvature in parameter space, these classical frameworks function effectively only as approximations within regimes of sparse rule-constraints. They fail to explain the super-linear, and often explosive, computational and energy costs incurred when maintaining symbolic interpretability during the reconfiguration of advanced intelligent systems. This paper introduces the property of intelligence inertia and its underlying physical principles as foundational characteristics for quantifying the computational weight of intelligence. We demonstrate that this phenomenon is not merely an empirical observation but originates from the fundamental non-commutativity between rules and states, a root cause we have formally organized into a rigorous mathematical framework. By analyzing the growing discrepancy between actual adaptation costs and static information-theoretic estimates, we derive a non-linear cost formula that mirrors the Lorentz factor, characterizing a relativistic J-shaped inflation curve -- a "computational wall" that static models are blind to. The validity of these physical principles is examined through a trilogy of decisive experiments: (1) a comparative adjudication of this J-curve inflation against classical Fisher Information models, (2) a geometric analysis of the "Zig-Zag" trajectory of neural architecture evolution, and (3) the implementation of an inertia-aware scheduler wrapper that optimizes the training of deep networks by respecting the agent's physical resistance to change. Our results suggest a unified physical description for the cost of structural adaptation, offering a first-principle explanation for the computational and interpretability-maintenance overhead in intelligent agents.

Figures (9)

• Figure 1: Geometric Partition of Logical Action. A particle collision with total action $l$ is decomposed by a microscopic slant. The component $l_R = l \sin\theta$ is absorbed by the adiabatic rule-manifold, while the normal component $l_S$ governs state-expression. Heat emission is only registered when the cumulative normal action matches a full vertical collision relative to the system's local energy level, naturally inducing the relationship $l^2 = l_S^2 + l_R^2$.
• Figure 2: Comparative Adjudication of Reference Frame Sensitivity and Model Robustness. Arena 1 (Left) demonstrates the sensitivity of the classical FIM model to coordinate shifts; the model fails to track the data trend in absolute coordinates. Arena 2 (Right) illustrates the Intelligence Inertia model, where the relativistic curves remain covariant and highly accurate regardless of the reference frame, maintaining an RMSE between 18.5 and 19.6.
• Figure 3: Ablation Analysis of Relativistic Velocity Addition vs. Mass Expansion. Arena 3 (Left) contrasts the Galilean-shifted FIM against the relativistic mass model, showing the clear failure of the quadratic assumption at high speeds; Arena 4 (Right) introduces a "Hybrid FIM" model, which applies the relativistic Lorentz velocity transformation but retains the classical quadratic cost formula, highlighting that velocity correction alone is insufficient to explain the "J-Curve" inflation.
• Figure 4: 3D Reachability Topography and the Zig-Zag Evolutionary Geodesic. This 3D surface plots the Reachability Limit ($\mathcal{L}_{min}$) as a function of improvements in internal manifold smoothing ($dS_R$-axis) and external structural bias ($dS_{ext}$-axis). The red nodes represent measured architectures from our matrix, while the blue line illustrates the "Zig-Zag Geodesic," representing the path of maximum efficiency. The topography exhibits a distinct saddle shape, where the steepest descent occurs along the diagonal of balanced development.
• Figure 5: Velocity Deviation Topography and the Dynamical Riverbed. This 3D surface maps the absolute deviation of system velocity from the $0.5$ golden axis. The resulting "V-shaped" valley—the Dynamical Riverbed—approximately aligns with the optimal evolutionary path, identifying the minimization of velocity deviation as the physical objective of architectural progress.