GaugeQuant: Online Learning of Quantization-Optimal Bases from LLM Symmetries

Transformers are known to have internal continuous symmetries that leave outputs invariant, while modifying quantization. GaugeQuant leverages this in-training by introducing a LogSumExp term to the loss that breaks the symmetries, thus selecting a basis that minimizes activation outliers. A stop-gradient operator ensures that only rotation matrices are updated, yielding the language modeling objective completely unaltered. Our quantization strategy requires no specific calibration data, no quantization simulation, and adds negligible training overhead. With the LLaMA-2 7B model under W4A4 quantization with group size 128, perplexity drops from 8.22 to 6.73, competing with post-training methods that require frozen models and calibration datasets. Under W4A16, perplexity drops from 11.16 to 5.45. On downstream reasoning tasks, GaugeQuant slightly improves zero-shot accuracy on Qwen-2.5 0.5B.