SHARP-Q: Spectral Hessian Alignment and Rectification for Post-training Quantization

Post-training quantization (PTQ) suffers from severe accuracy degradation in ultra-low-bit regimes. To address this challenge, we propose SHARP-Q, a unified framework grounded in Information Geometry that aligns the quantization objective with the intrinsic Fisher geometry. Following a "Rectify-then-Approximate" strategy, SHARP-Q first preconditions the optimization landscape via Hessian-Aware Rectification (HAR) and subsequently approximates the rectified Fisher Information Matrix through Dynamic Fisher-Subspace Compensation (DFSC). Our findings reveal a pivotal insight: precise geometric alignment enables hardware-friendly uniform quantizers to consistently outperform specialized non-uniform designs. Extensive experiments across representative Vision Transformer and convolutional architectures confirm that SHARP-Q establishes new state-of-the-art results, achieving substantial accuracy gains in the challenging W2A2 and W3A3 settings. Code is available in the supplementary material.