BBQ: Boosting Quantization Entropy with Bell Box Quantization

ICLR 2026 Conference Submission4568 Authors

Keywords: Quantization, Quantization-Aware Training, Pre-Training

Abstract:

Quantization-Aware Pre-Training (QAPT) is an effective technique to reduce the compute and memory overhead of
Deep Neural Networks while improving their energy efficiency on edge devices. Existing QAPT methods produce models stored in compute-efficient data types (e.g. integers) that are not information theoretically optimal (ITO). On the other hand, existing ITO data types (e.g. Quantile/NormalFloat Quantization) are not compute-efficient.
We propose BBQ, the first ITO quantization method that is also compute-efficient. BBQ builds on our key insight that since learning is domain-agnostic, the output of a quantizer does not need to reside in the the same domain as its input. BBQ performs ITO quantization in its input domain, and returns its output in a compute-efficient domain where ITO data types are mapped to compute-efficient data types. Without sacrificing compute efficiency, BBQ outperforms prior SOTA QAPT methods by a perplexity reduction of up to 2 points for 4-bit models, up to 4 points for 3-bit models, up to 5 points for 2-bit models , and up to 18 points for 1-bit models.

Primary Area: foundation or frontier models, including LLMs

Submission Number: 4568