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

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.

Selective Mixup Fine-Tuning for Optimizing Non-Decomposable Objectives

The rise in internet usage has led to the generation of massive amounts of data, resulting in the adoption of various supervised and semi-supervised machine learning algorithms, which can effectively utilize the colossal amount of data to train models. However, before deploying these models in the real world, these must be strictly evaluated on performance measures like worst-case recall and satisfy constraints such as fairness. We find that current state-of-the-art empirical techniques offer sub-optimal performance on these practical, non-decomposable performance objectives. On the other hand, the theoretical techniques necessitate training a new model from scratch for each performance objective. To bridge the gap, we propose SelMix, a selective mixup-based inexpensive fine-tuning technique for pre-trained models, to optimize for the desired objective. The core idea of our framework is to determine a sampling distribution to perform a mixup of features between samples from particular classes such that it optimizes the given objective. We comprehensively evaluate our technique against the existing empirical and theoretically principled methods on standard benchmark datasets for imbalanced classification. We find that proposed SelMix fine-tuning significantly improves the performance for various practical non-decomposable objectives across benchmarks.