S-DPQ: Block-Level Angular and Norm Matching for Data-Free Ternary Quantization

Post-Training Quantization (PTQ) below 4 bits often causes severe accuracy degradation because scalar range-based scaling can distort the geometry of weight blocks. We introduce Spatial-Directional Preserving Quantization (S-DPQ), a data-free ternary method that selects discrete block structures by maximizing cosine alignment and sets their scale by matching the Frobenius norm. The method additionally protects 5% of salient input channels in 16-bit precision. On DistilBERT, S-DPQ improves over AbsMax RTN by up to 38.23 percentage points on MRPC while using approximately 3.65 effective bits per parameter for the targeted linear layers. On RoBERTa-Large, however, we observe task-dependent collapse on MRPC despite improved SST-2 accuracy. This failure, together with the positive results on shallower models, highlights an empirical limitation of local geometric constraints in data-free sub-4-bit quantization and motivates activation-aware calibration.