QuIP: 2-Bit Quantization of Large Language Models With Guarantees (2307.13304v2)

Abstract: This work studies post-training parameter quantization in LLMs. We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from $\textit{incoherent}$ weight and Hessian matrices, i.e., from the weights being even in magnitude and the directions in which it is important to round them accurately being unaligned with the coordinate axes. QuIP consists of two steps: (1) an adaptive rounding procedure minimizing a quadratic proxy objective; (2) efficient pre- and post-processing that ensures weight and Hessian incoherence via multiplication by random orthogonal matrices. We complement QuIP with the first theoretical analysis for an LLM-scale quantization algorithm, and show that our theory also applies to an existing method, OPTQ. Empirically, we find that our incoherence preprocessing improves several existing quantization algorithms and yields the first LLM quantization methods that produce viable results using only two bits per weight. Our code can be found at https://github.com/Cornell-RelaxML/QuIP.

• The paper presents a method that leverages incoherence in weight and Hessian matrices to achieve optimal 2-bit quantization.
• It employs adaptive rounding with a quadratic proxy objective and uses random orthogonal matrices to ensure even error distribution.
• Empirical results demonstrate significant efficiency gains and minimal performance degradation in large-scale LLMs.

Analysis of "QuIP: 2-Bit Quantization of LLMs With Guarantees"

The paper "QuIP: 2-Bit Quantization of LLMs With Guarantees" presents a method for post-training quantization in LLMs specifically aiming to achieve two-bit quantization. The proposed technique, Quantization with Incoherence Processing (QuIP), is based on the insight that incoherence in weight and Hessian matrices can be leveraged to benefit quantization. This method involves pre- and post-processing with adaptive rounding to minimize a quadratic proxy objective.

Methodology

QuIP operates in two stages:

1. Adaptive Rounding: This involves using an adaptive rounding procedure that minimizes the quadratic proxy objective:

$$\ell(\hat W) = \operatorname{tr}((\hat W - W) H (\hat W - W)^T)$$

Here, $H$ is a proxy Hessian, and $\hat W$ are the quantized weights.

1. Incoherence Processing: This step ensures that weight and Hessian matrices are incoherent, utilizing random orthogonal matrices to make matrices evenly distributed in magnitude and unaligned with coordinate axes. The paper provides a theoretical underpinning for these steps and their improvement on quantization quality.

Theoretical Contributions

The paper introduces a theoretical analysis establishing QuIP's quantization procedure as optimal within a class of rounding methods. The analysis provides insight into how incoherence leads to improved quantization by bounding the error using spectral properties of the Hessian matrix. Furthermore, the analysis reveals that QuIP without incoherence processing is equivalent to an existing OPTQ, offering a more efficient implementation and new theoretical insights into OPTQ's performance.

Empirical Results

QuIP demonstrates marked improvements in quantization, particularly notable at two bits per weight, even for large LLMs exceeding 2 billion parameters. In practice, this translates to significant efficiency gains with minimal performance degradation, making two-bit inference feasible for LLMs. The empirical investigations validate that incorporating incoherency results in substantial quantization quality improvements, drawing closer to full-precision performance than previous methods.

Implications and Speculations

The results imply that model weights can be effectively quantized to two bits without a significant loss of accuracy, proving the feasibility of efficient low-bit inference. This development is a considerable stride toward reducing computational and storage requirements for deploying large-scale models, likely encouraging further research into finer-grained quantization and deployment strategies.

Future research could explore combining QuIP with other model compression techniques or extending the incoherence concept to other model architectures beyond LLMs. Additionally, while the current work primarily focuses on post-training quantization, exploring the potential synergies between QuIP and training-aware quantization could open new avenues for model efficiency.

Conclusion

QuIP represents a significant contribution to the quantization field by presenting the first viable 2-bit solution suitable for LLMs. Its strong theoretical and empirical foundations make it a compelling choice for applications requiring efficient and effective model deployment. The potential of QuIP to harmonize model accuracy with reduced computational resources has far-reaching implications in the practical deployment of large-scale AI systems.