Three Laws of Semantic Collapse: NLI as Gradient Descent on an Anchor Energy Landscape

We present Livnium, a classification system for Natural Language Inference (NLI) in which inference is modeled as a dynamical process rather than a single forward pass. The hidden state evolves through multiple steps under geometry-aware updates before classification. We discover that the trained system follows three empirical laws:(1) the initial state encodes relational difference,(2) semantic space forms an energy landscape defined by log-sum-exp over cosine similarities to anchor vectors,(3) inference dynamics correspond to gradient descent on this energy. We show that the learned update function can be replaced by an analytical gradient with no loss in accuracy on SNLI. Joint retraining improves consistency between dynamics and classification while increasing neutral recall. This work demonstrates that interpretable physical laws can emerge from trained neural systems.