EMA Without the Lag: Bias-Corrected Iterate Averaging Schemes

Stochasticity in language model fine-tuning, often caused by the small batch sizes typically used in this regime, can destabilize training by introducing large oscillations in generation quality. A popular approach to mitigating this instability is to take an Exponential moving average (EMA) of weights throughout training. While EMA reduces stochasticity, thereby smoothing training, the introduction of bias from old iterates often creates a lag in optimization relative to vanilla training. In this work, we propose the Bias-Corrected Exponential Moving Average (BEMA), a simple and practical augmentation of EMA that retains variance-reduction benefits while eliminating bias. BEMA is motivated by a simple theoretical model wherein we demonstrate provable acceleration of BEMA over both a standard EMA and vanilla training. Through a suite of experiments on Language Models, we show that BEMA leads to improved convergence rates over both EMA and vanilla training in a variety of LM benchmarks, making BEMA a practical and theoretically motivated intervention for more stable and efficient fine-tuning.