Quamba2: A Robust and Scalable Post-training Quantization Framework for
  Selective State Space Models
Authors: name: Hung-Yueh Chiang, name: Chi-Chih Chang, name: Natalia Frumkin, name: Kai-Chiang Wu, name: Mohamed S. Abdelfattah, name: Diana Marculescu
Organization: Energy-Aware Computing Lab @ UT ECE

State Space Models (SSMs) are emerging as a compelling alternative to
Transformers because of their consistent memory usage and high performance.
Despite this, scaling up SSMs on cloud services or limited-resource devices is
challenging due to their storage requirements and computational power. To
overcome this, quantizing SSMs with low bit-width data formats can reduce model
size and benefit from hardware acceleration. As SSMs are prone to
quantization-induced errors, recent efforts have focused on optimizing a
particular model or bit-width for efficiency without sacrificing performance.
However, distinct bit-width configurations are essential for different
scenarios, like W4A8 for boosting large-batch decoding speed, and W4A16 for
enhancing generation speed in short prompt applications for a single user. To
this end, we present Quamba2, compatible with W8A8, W4A8, and W4A16 for both
Mamba1 and Mamba2 backbones, addressing the growing demand for SSM deployment
on various platforms. Based on the channel order preserving and activation
persistence of SSMs, we propose an offline approach to quantize inputs of a
linear recurrence in 8-bit by sorting and clustering for input x, combined
with a per-state-group quantization for input-dependent parameters B and C.
To ensure compute-invariance in the SSM output, we rearrange weights offline
according to the clustering sequence. The experiments show that Quamba2-8B
outperforms several state-of-the-art SSM quantization methods and delivers
1.3times and 3times speed-ups in the pre-filling and generation stages,
respectively, while offering 4times memory reduction with only a 1.6%
average accuracy drop. The evaluation on MMLU shows the generalizability and
robustness of our framework. The code and quantized models will be released at:
https://github.com/enyac-group/Quamba.