The Devil Is in the Reconstruction Loss Scale: Rethinking Optimization in LLM Quantization

Chao Li, Shigeng Wang, Anbang Yao

Post-training quantization (PTQ) methods typically use sequential quantization that partitions a pre-trained LLM into a series of units (e.g., transformer blocks), with one unit quantized at each stage. State-of-the-art PTQ methods are predominantly learning-based, optimizing auxiliary quantization parameters (e.g., scaling factors, rotation matrices, clipping thresholds, and adapters) via gradient descent to minimize a reconstruction loss. A common practice is to use mean squared error (MSE) as the reconstruction loss function, yet its induced optimization behavior remains largely unexplored. In this work, we take a holistic view of sequential quantization and systematically investigate how optimization evolves from the first quantization stage to the last, aiming for a deep understanding of optimization in learning-based PTQ schemes. Through extensive empirical studies spanning representative learning-based PTQ methods, LLM families, model scales, architectures, quantization settings and various tasks, we consistently uncover Optimization Imbalance: reconstruction loss magnitudes vary dramatically across stages, accompanied by highly uneven gradient magnitudes and parameter…