ReRound: Reconstructive Rounding to Resolve Midpoint Ambiguity in Calibration-Free LLM Quantization
Authors: name: He-Yen Hsieh, name: H. T. Kung
Organization: Harvard University

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.