  Low-bit quantization has become widespread for compressing image
super-resolution (SR) models for edge deployment, which allows advanced SR
models to enjoy compact low-bit parameters and efficient integer/bitwise
constructions for storage compression and inference acceleration, respectively.
However, it is notorious that low-bit quantization degrades the accuracy of SR
models compared to their full-precision (FP) counterparts. Despite several
efforts to alleviate the degradation, the transformer-based SR model still
suffers severe degradation due to its distinctive activation distribution. In
this work, we present a dual-stage low-bit post-training quantization (PTQ)
method for image super-resolution, namely 2DQuant, which achieves efficient and
accurate SR under low-bit quantization. The proposed method first investigates
the weight and activation and finds that the distribution is characterized by
coexisting symmetry and asymmetry, long tails. Specifically, we propose
Distribution-Oriented Bound Initialization (DOBI), using different searching
strategies to search a coarse bound for quantizers. To obtain refined quantizer
parameters, we further propose Distillation Quantization Calibration (DQC),
which employs a distillation approach to make the quantized model learn from
its FP counterpart. Through extensive experiments on different bits and scaling
factors, the performance of DOBI can reach the state-of-the-art (SOTA) while
after stage two, our method surpasses existing PTQ in both metrics and visual
effects. 2DQuant gains an increase in PSNR as high as 4.52dB on Set5 (x2)
compared with SOTA when quantized to 2-bit and enjoys a 3.60x compression ratio
and 5.08x speedup ratio. The code and models will be available at
https://github.com/Kai-Liu001/2DQuant.
