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Relative Generalization Invariance of LLM Pretraining

Feng-Zhuo Zhang Shu-Che Wang Sheng-Gui Li Tian-Yu Ruan Jian-Liang He Ivor W. Tsang Tian-Yu Pang Chao Du Tian-Wei Zhang Zhuo-Ran Yang
Sep 2026 · 0 citations · 103 references
Computer Science

Abstract

Large Language Model (LLM) pretraining performance is jointly shaped by three components of the training triplet: the optimizer, model architecture, and training data stream. However, how these components influence performance in distinct ways remains unclear. We take a first step toward isolating their effects by studying relative generalization. We introduce Relative Generalization Invariance (RGI), the invariance of the validation-loss difference between any two tokens across models. We show that RGI approximately holds across a wide range of optimizers and moderate architectural variations, suggesting that these choices induce an approximately uniform shift in token-wise losses. In contrast, changing the training data stream can substantially alter relative generalization. We further show that RGI cannot be explained by the neural tangent kernel or mean-field regimes alone and prove that it can emerge in an overparameterized quadratic model. Overall, our work identifies RGI as a new phenomenon in LLM pretraining that helps distinguish the effects of optimizers and architectures from those of training data.

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