WinQ: Accelerating Quantization-Aware Training of Language Models Around Saddle Points

Quantization-aware training (QAT) is widely adopted to quantize language models by training full-precision weights using gradients from the quantized model. The main bottleneck is its slow convergence and early performance plateau, particularly below 4-bit-widths. While this problem has been observed in prior work, its precise cause remains unclear. In this paper, we analyze the convergence of QAT by estimating the spectrum of the loss-surface Hessians. We find that the weights converge to flat regions around saddle points, where a large fraction of the Hessian eigenvalues are both positive and negative. During training, an increasing fraction of Hessian eigenvalues concentrates around zero, whose magnitude decreases. At lower bit-widths, the magnitude of eigenvalues in the Hessian spectrum is significantly smaller. To mitigate these issues, we propose an algorithm called WinQ to accelerate QAT, which involves: (1) periodically resetting weights to the linear interpolation of full-precision and quantized weights, reducing the distance to the quantization grid and increasing eigenvalue magnitude, and (2) computing gradients of noise-injected weights to regularize the Hessian. Extensive experiments show that WinQ accelerates QAT by up to 4$\times$ across various quantization methods and models. Under the same training cost, WinQ improves state-of-the-art sub-4-bit quantization by up to 8.8%. These results are consistent across 16 settings with different language models, quantization methods, and bit widths.

Language models can be expensive to run, and quantization reduces this cost by storing them in lower precision. A common approach is to train the model while repeatedly simulating how it behaves after its values are rounded. However, at extremely low precision, this training often slows down or stalls, and the reason has not been well understood. We found that low-precision training can settle into flat regions where standard updates make little progress, especially when the model is compressed more aggressively. To address this, we introduce a training method that periodically moves the model closer to its rounded values while adding small random noise during training. Across many language models and compression settings, our method speeds up training and produces more accurate low-precision models, enabling more efficient AI systems.