This October 5 2025 paper presents the first mechanistic explanation for a persistent training instability experienced when using low-precision arithmetic (specifically BF16) with the Flash Attention algorithm in transformer models. The paper identifies the core problem as a "catastrophic loss explosion" caused by two interacting phenomena: the emergence of similar low-rank representations within the attention mechanism and the accumulation of biased rounding errors inherent to BF16 addition during the attention output calculation. This bias leads to a systematic error in the gradient updates, causing the spectral norm of weights to increase and derailing the training process. To validate this analysis, the authors introduce a minimal modification to the softmax computation in Flash Attention that mitigates the rounding bias and successfully stabilizes the training, offering a practical solution to this long-standing issue. Source: https://arxiv.org/pdf/2510.04212