ThinQuant: Scalable Rotation Learning for Weight and Activation Quantization of LLMs

Learned rotations play an important role in enabling low-bit weight and activation quantization of large language models by smoothing outliers in the activation distribution. State-of-the-art approaches include gradient-based procedures such as SpinQuant and computationally friendlier gradient-free approaches such as DartQuant, but both remain hard to scale to the largest architectures. To address the computational bottlenecks in gradient-free rotation learning, we introduce two ideas for efficiency, (i) a data selection procedure which reduces the required number of calibration data points, and (ii) an exact reduction of the associated optimization on this reduced calibration set. Our data selection procedure exploits the geometric structure of the convex hull of the activations. Using this idea, we show that a carefully selected calibration set with several orders of magnitude fewer activations than state-of-the-art rotation-based methods can match their performance in low-bit quantization settings. Under this extreme data efficiency, the selected activations span an r-dimensional subspace with r<d, making optimization over a d× d rotation equivalent to optimizing a d× r matrix on the Stiefel manifold. We solve this reduced problem using an efficient ADMM algorithm that iteratively employs thin matrix updates at every step, hence the name ThinQuant. For Llama-3-70B with W4A4KV4 quantization, ThinQuant completes the entire rotation calibration in under 12 minutes and achieves a WikiText-2 perplexity of 5.63, compared with 7.55 for DartQuant, which requires 111 minutes. Unlike SpinQuant and DartQuant, ThinQuant also scales to Llama-3.1-405B on a single H200 GPU, completing rotation calibration in just over 2 hours and achieving WikiText-2 perplexity of 2.97 at W4A4, compared with 3.48 for GPTAQ+QuaRoT.