Maximum Hidden Irreversibility Reveals Latent Rotational Dynamics and Predicts Emergent Grokking in Neural Networks

We introduce Maximum Hidden Irreversibility (MHI), a geometric measure of learning dynamics that isolates latent rotational structure in neural networks. Unlike standard diagnostics based on loss, divergence, or spectral norms, MHI captures antisymmetric components of hidden-state Jacobians corresponding to cyclic, non-gradient flows. We show that increasing MHI consistently precedes sudden improvements in generalization (grokking) across toy models and controlled neural systems, acting as an early-warning signal of emergent representational reorganization. Systems with identical contraction or loss trajectories can exhibit fundamentally different global behavior, which MHI uniquely distinguishes. The framework is: • Geometric (Jacobian-level, coordinate-invariant), • Mechanistic (linked to non-normal operators, transient amplification, and Mori–Zwanzig projections), • Reproducible (explicit decomposition into symmetric and antisymmetric components). These results suggest that hidden rotational dynamics play a critical role in delayed generalization and challenge purely gradient-based interpretations of learning. Note: results presented are proof-of-concept simulations illustrating theoretical predictions. Empirical validation on real training runs is in preparation.