FidelityQ: Preserving Predictive Fidelity in Ultra-Low-Bit Language Model Quantization

Yujie Chen, Weiyan Zheng, Yiwu Yao, Tianchi Hu, Bo Wang +5

Ultra-low-bit scalar quantization offers a regular arithmetic structure for efficient deployment of large language models, but preserving predictive behavior at extreme precision remains challenging: with only a few reconstruction levels, accurate weight representation must translate into consistent predictions from a small calibration set. We propose FidelityQ, a scalar quantization framework that preserves predictive fidelity at weight precisions down to 2 bits. For accurate quantization, we introduce Information-Aligned Analytic Coding (IAC), which shapes each weight row toward a centered symmetric source via randomized Hadamard mixing and fits a mirrored four-level minimum-distortion quantizer to its empirical weights. Every level set in this family decomposes exactly into two sign-valued bases with associated scales, combining source-adaptive reconstruction with lookup-free decoding compatible with scaled integer arithmetic. Our analysis further shows that residual predictive discrepancies are heavy-tailed and concentrate on tokens the teacher predicts confidently, motivating Knowledge-Intensive Calibration (KIC) for consistent quantization. KIC ranks sequences by the tail…