Output Embedding Centering for Stable LLM Pretraining

Reinforcement learning (RL) of large language models is notoriously sensitive to small differences between training and inference engines, often referred to as the training-inference mismatch (TIM). However, completely eliminating TIM is impractical, as it would come at a major cost to rollout efficiency. In this paper, we show that the instability of RL under TIM is primarily caused by drift: a persistent bias between training and inference engines that accumulates with every training step. We derive an additive "score centering" correction term that stabilizes RL under TIM by canceling drift. When training models from 0.6B to 30B parameters, score centering alone matches or outperforms methods based on importance sampling under quantization, with the gap growing as the mismatch becomes more severe. Because the correction is additive, score centering also composes with importance sampling -- their composition outperforms pure importance-sampling baselines in our staleness experiments.

We identify a previously overlooked failure mode of ALiBi positional encoding: its linear bias scaling underflows floating-point precision, which zeroes out a large fraction of attention weights and renders the affected attention heads partially blind. We analyze this failure mode, characterize its impact, and examine four mitigation strategies. We further demonstrate its occurrence in state-of-the-art pretrained models based on ALiBi. Comprehensive pretraining experiments with 148M-parameter decoder models help us to disentangle its effects from out-of-context degradation. We find that ALiBi's failure mode can substantially impair token retrieval while having only a minor effect on standard decoder benchmarks. We propose four training-time mitigation strategies and evaluate them individually and in combinations, finding that log-scaled distances yield the most consistent improvements in passkey retrieval. Despite this problem, default ALiBi slopes remain a surprisingly strong baseline, particularly for needle-in-a-haystack retrieval. Based on these findings we provide concrete recommendations on how to train models with ALiBi.

We propose a preconditioning (PC) layer, a weight parameterization via polynomial preconditioner that ensures stable weight conditioning throughout LLM training. The PC module reshapes the singular-value spectrum of weight matrices via low-degree polynomial preconditioning. After training, the preconditioned weights can be merged back into the original architecture, incurring no inference overhead. We demonstrate the advantage of the proposed PC layer over standard transformers in Llama-1B pre-training, for both the AdamW and Muon optimizers. Theoretically, we justify this spectrum-control principle by proving that uniformly bounding each layer's singular values ensures geometric convergence of gradient descent to global minima, for certain deep linear networks. Our code is available at https://github.com/Empath-aln/PC-layer.