OJBKQ: Objective-Joint Babai-Klein Quantization

TL;DR

OJBKQ introduces a joint optimization approach for post-training quantization of large language models, effectively reducing model size with minimal performance loss at low-bit quantization levels.

Contribution

It formulates weight quantization as a joint optimization problem and applies novel algorithms to find sub-optimal solutions, improving low-bit quantization performance.

Findings

Achieves lower perplexity at 3-4 bits compared to existing methods.

Maintains comparable computational cost with improved quantization quality.

Demonstrates effectiveness on large language models.

Abstract

Post-training quantization (PTQ) is widely used to compress large language models without retraining. However, many existing weight-only methods rely on heuristic objectives and greedy rounding, thus leading to noticeable degradation under low-bit quantization. In this work, we introduce OJBKQ (Objective-Joint Babai-Klein Quantization with K-Best Sampling), a layer-wise PTQ method that formulates weight quantization as a joint optimization problem over activations and weights. This formulation results in a multiple-right-hand-side box-constrained integer least squares (BILS) problem in each layer, which is NP-hard. For each column of the weight matrix, we apply an extended Babai nearest-plane algorithm and an extended version of Klein's randomized Babai algorithm to find the minimum-residual Babai-Klein point, a sub-optimal solution to the BILS problem. Experimental results on large language models show that OJBKQ achieves lower perplexity at 3-4 bits compared to existing PTQ approaches, while maintaining comparable computational cost.