CondiQuant: Condition Number Based Low-Bit Quantization for Image Super-Resolution

TL;DR

CondiQuant addresses the accuracy loss in ultra-low-bit post-training quantization for image super-resolution by linking quantization sensitivity to the condition number of weight matrices. The method formulates the quantization error through the condition number and solves a proximal-gradient optimization to reduce conditioning while keeping outputs close to the original, enabling effective activation quantization with minimal weight distortion. By integrating a singular-value based proximal update with gradient steps, CondiQuant achieves significant conditioning reduction (from ~$3{,}000$ to ~28) and, when followed by standard 2D PTQ, yields state-of-the-art SR performance at 2–4 bits with negligible inference overhead. The approach offers practical edge-device benefits, including substantial compression and speedups, demonstrated on SwinIR-light across five SR benchmarks.

Abstract

Low-bit model quantization for image super-resolution (SR) is a longstanding task that is renowned for its surprising compression and acceleration ability. However, accuracy degradation is inevitable when compressing the full-precision (FP) model to ultra-low bit widths (2~4 bits). Experimentally, we observe that the degradation of quantization is mainly attributed to the quantization of activation instead of model weights. In numerical analysis, the condition number of weights could measure how much the output value can change for a small change in the input argument, inherently reflecting the quantization error. Therefore, we propose CondiQuant, a condition number based low-bit post-training quantization for image super-resolution. Specifically, we formulate the quantization error as the condition number of weight metrics. By decoupling the representation ability and the quantization sensitivity, we design an efficient proximal gradient descent algorithm to iteratively minimize the condition number and maintain the output still. With comprehensive experiments, we demonstrate that CondiQuant outperforms existing state-of-the-art post-training quantization methods in accuracy without computation overhead and gains the theoretically optimal compression ratio in model parameters. Our code and model are released at https://github.com/Kai-Liu001/CondiQuant.

Figures (5)

• Figure 1: Comparison with SOTA PTQ methods on five benchmarks. Our CondiQuant gains consistently better performance.
• Figure 2: Distribution of activation ranks along the ($\times 2$) model depth. Most activations are severely rank deficient.
• Figure 3: Overview of our proposed CondiQuant which employs iterative optimization to minimize the condition number of weight matrix while maintaining the output still. The gradient descent step updates the weight matrix with gradients to ensure the output is close to the original. The proximal descent step minimizes the condition number with the proximal operator. The above two steps are conducted iteratively before reaching the convergence criterion, i.e. the max iteration step. We illustrate the effect of both steps. With CondiQuant, the weight matrix is converted into a quantization-friendly and well-conditioned one while the output is close to the original.
• Figure 4: Visual comparison for image SR. We compare our proposed CondiQuant with current competitive quantization methods and the full-precision (FP) model. The visual results illustrate that CondiQuant gains sharper edges and reasonable textures.
• Figure 5: Condition number before and after CondiQuant on $\times 2$ model. Before CondiQuant, the distribution of condition numbers is extremely high, with an average of nearly 3k. After CondiQuant, the average value of condition numbers is significantly reduced to 28.37.