Correcting Stochastic Update Bias in Preconditioned Language Model Optimizers
This work addresses two finite-sample biases inherent in preconditioned optimizers during language model training: coupling bias between gradient and preconditioner estimates due to minibatch approximation, and systematic bias introduced by nonlinear inversion operations. For the first time, these biases are jointly identified and corrected through a unified single-batch bias-correction framework. The proposed method employs cross-fitting to decouple gradient and preconditioner estimation and incorporates a Delta-method-based variance correction to mitigate nonlinearity-induced bias. Compatible with mainstream optimizers such as AdamW, Sophia, and Shampoo, the approach reduces validation loss by 0.15, 0.07, and 0.11 nats, respectively, in Qwen2.5-0.5B pretraining, while maintaining or improving downstream instruction-tuning performance—demonstrating markedly enhanced training stability and efficiency.