Title:Towards Physical Intuitions for Alignment Dynamics: A Case Study With Randomness Crystallization

Abstract:The alignment of language models is typically studied through the lens of capability benchmarks, but the dynamics of how models change during post-training remain poorly understood. We argue that the physical sciences, and thermodynamic phase-transition theory in particular, offer a principled and underexplored vocabulary for reasoning about these dynamics. As a case study, we instantiate this position through the lens of material Crystallization, which is a well-studied thermodynamic phase transition. For tasks like random number generation, this breaks into 3 phases: (1) the high entropy liquid phase in the pretrained model, with many distinct sampling distributions promptable from the model; (2) the nucleation phase caused by supervised finetuning, in which behavior collapses onto a single seed distribution present in the pretrained LLM; and (3) a settling phase in which reinforcement learning techniques redistribute probability of the collapsed distribution, but largely keep it concentrated on the same options as the seed distribution. We propose intuitive metrics to verify the transitions between these phases, and validate the idea across a range of random tasks. Crystallization is one instance of a broader class of physical frameworks we believe alignment research should import to answer questions about where alignment-induced structure comes from, why it converges where it does, and what it fundamentally cannot change.

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