arXiv:2611.13545v1 Announce Type: cross Abstract: BF16 is widely used to pretrain large language models because it has the same dynamic range as FP32 and converges similarly to FP32 training. However, in reinforcement learning with verifiable rewards, where learning rates are typically low, we find that standard mixed-precision BF16 training converges more slowly than FP16 training at the same learning rate. We attribute this gap to weight sticking: when FP32 shadow weights are quantized to BF16 using round-to-nearest, small updates often leave the BF16 weights used for rollout generation and training unchanged. Consequently, several optimizer steps may be needed before updates to the shadow weights are reflected in the BF16 weights. Raising the BF16 learning rate reduces weight sticking and matches FP16's convergence speed, but it also increases the KL divergence from the reference model. We instead apply stochastic rounding when quantizing the FP32 shadow weights to BF16. This approach matches FP16's convergence speed across different models and datasets while reducing the KL divergence relative to BF16 training with a larger learning rate. Unlike FP16, it keeps BF16's wider dynamic range and needs no loss scaling.