Output Embedding Centering for Stable LLM Pretraining

TL;DR

This paper introduces output embedding centering (OEC) to improve stability in large language model pretraining by addressing output logit divergence caused by anisotropic embeddings.

Contribution

The paper proposes a novel embedding centering method, OEC, with deterministic and regularization variants, outperforming existing mitigation strategies for training stability.

Findings

OEC suppresses output logit divergence effectively.

Both OEC variants outperform z-loss in stability.

μ-loss is less sensitive to hyperparameter tuning.

Abstract

Pretraining of large language models is not only expensive but also prone to certain training instabilities. A specific instability that often occurs at the end of training is output logit divergence. The most widely used mitigation strategies, z-loss and logit soft-capping, merely address the symptoms rather than the underlying cause of the problem. In this paper, we analyze the instability from the perspective of the output embeddings' geometry and identify anisotropic embeddings as its source. Based on this, we propose output embedding centering (OEC) as a new mitigation strategy, and demonstrate that it suppresses output logit divergence. OEC can be implemented in two different ways: as a deterministic operation called $\mu$-centering, or a regularization method called $\mu$-loss. Our experiments show that both variants outperform z-loss in terms of training stability, while being on par with logit soft-capping. This holds true both in the presence and the absence of weight tying. As a secondary result, we find that $\mu$-loss is significantly less sensitive to regularization hyperparameter tuning than z-loss.