Quantization of Large Language Models (LLMs) has be- coming increasingly important for reducing the computa- tional costs and resource requirements for practical deploy- ment.Growinginterestinthisareahasmotivatedthecommu- nity to move beyond 8-bit quantization towards 4-bit preci- sion, leading to the development of customized 4-bit formats such as MXFP4 and NVFP4. Recently, HiFloat4 (HiF4) has emerged as a competitive alternative which adopts a Block Floating-Point(BFP)formatwithathree-levelscalinghierar- chy, thereby achieving a significantly larger dynamic range. While quantization can substantially reduce memory usage and accelerate inference, it frequently introduces accuracy degradation. Calibration is therefore essential for narrowing theperformancegapbetweenlow-precisionquantizedmodels and their full-precision counterparts. Nevertheless, existing calibration methods are mainly designed and validated us- ing integer-precision formats, such as INT4, lacking support for HiF4 due to its hierarchical BFP structure. In this paper, weinvestigatethreecalibrationapproaches,namelyHiGPTQ, HiAutoRound, and HiFlatQuant, to further enhance model quantizationbasedontheHiF4format.Extensiveexperiments demonstratethatallthreeproposedapproachesimproveinfer- ence accuracy compared with direct HiF4 conversion, reduc- ing the gap between HiF4 and BF16 to less than 1% and out- performing the state-of-the-art NVFP4 format across various models and downstream tasks.

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