---
title: "OJBKQ: Objective-Joint Babai-Klein Quantization"
authors:
  - "Xinyu Wang"
  - "Ziyu Zhao"
  - "Peng Lu"
  - "Yu Gu"
  - "Xiao-Wen Chang"
doi: "10.24963/ijcai.2026/264"
url: "https://ijcai.org/proceedings/2026/264"
pdf: "https://ijcai.org/proceedings/2026/0264.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "2373-2381"
track: "Main Track"
keywords:
  - "Constraint Satisfaction and Optimization: Constraint optimization problems"
  - "Natural Language Processing: Language models"
---

# OJBKQ: Objective-Joint Babai-Klein Quantization

Xinyu Wang, Ziyu Zhao, Peng Lu, Yu Gu, Xiao-Wen Chang

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 2373-2381. DOI: [10.24963/ijcai.2026/264](https://doi.org/10.24963/ijcai.2026/264)

## 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 strategies, leading to noticeable degradation under low-bit quantization. We propose OJBKQ, a layer-wise PTQ method that formulates weight quantization as a joint optimization problem over activations and weights, yielding a multiple-right-hand-side box-constrained integer least squares (BILS) problem per layer. To solve this NP-hard problem, we extend Klein’s randomized variant of Babai’s nearest-plane algorithm to handle box constraints and run the extended algorithm K times to generate K box-constrained Klein points. The minimum-residual candidate among these points and the box-constrained Babai point is selected as a suboptimal solution. Experiments on large language models show that OJBKQ achieves lower perplexity at 3–4 bits than existing PTQ methods, while maintaining comparable computational cost.