ReRound: Reconstructive Rounding to Resolve Midpoint Ambiguity in Calibration-Free LLM Quantization
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Computer Science > Machine Learning
arXiv:2608.11045 (cs)
[Submitted on 11 Aug 2026]
Title:ReRound: Reconstructive Rounding to Resolve Midpoint Ambiguity in Calibration-Free LLM Quantization
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Abstract:ReRound (Reconstructive Rounding) is a post-training quantization method that addresses the midpoint ambiguity inherent in standard round-to-nearest (RTN) schemes when quantizing weights near the centers of quantization intervals.
Starting from a pretrained LLM, ReRound trains a conditional diffusion model to produce continuous reconstructions of low-bit weights for the LLM. These reconstructed weights act as a guidance signal to disambiguate the rounding direction of weights located close to interval midpoints.
To integrate this reconstruction-guided rounding with conventional RTN, ReRound introduces a tolerance metric measuring how far the quantized weight (not the final quantized integer) is away from the midpoint: quantized weights within a tolerance region around midpoints are quantized using diffusion-based reconstructions, whereas weights closer to quantization boundaries are quantized with RTN. By sweeping the tolerance parameter, ReRound generates multiple candidate quantized integer weight matrices and selects the de-quantized weight matrix candidate whose leading singular values most closely match those of the original full-precision weights. This selected candidate determines the tolerance parameter ReRound uses.
ReRound is particularly effective for smaller LLMs. Across a range of such models, it consistently outperforms standard RTN for 3-bit and 4-bit weight quantization. ReRound achieves superior accuracy compared to an extensive set of calibration-free methods, remains competitive with calibration-dependent approaches, and operates entirely offline, introducing no additional overhead during low-bit inference.
The ReRound strategy represents a new approach for low-bit quantization. The method applies to AI models beyond LLMs. This paper focuses on its applications to small LLMs.
| Comments: | 16 pages, 8 figures |
| Subjects: | Machine Learning (cs.LG); Computation and Language (cs.CL) |
| Cite as: | arXiv:2608.11045 [cs.LG] |
| (or arXiv:2608.11045v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.11045
arXiv-issued DOI via DataCite (pending registration)
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View a PDF of the paper titled ReRound: Reconstructive Rounding to Resolve Midpoint Ambiguity in Calibration-Free LLM Quantization, by He-Yen Hsieh and 1 other authors
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