[2601.02031] Output Embedding Centering for Stable LLM Pretraining

Computer Science > Machine Learning arXiv:2601.02031 (cs) [Submitted on 5 Jan 2026 (v1), last revised 2 Apr 2026 (this version, v2)] Title:Output Embedding Centering for Stable LLM Pretraining Authors:Felix Stollenwerk, Anna Lokrantz, Niclas Hertzberg View a PDF of the paper titled Output Embedding Centering for Stable LLM Pretraining, by Felix Stollenwerk and 2 other authors View PDF HTML (experimental) 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 t...