# Inner Product Aware Quantization: Provably Fast, Accurate, and Adaptive Algorithms

arXiv: https://arxiv.org/abs/2606.00289 · HTML: https://mlsanity.com/paper/2606.00289/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 9 of 9)

- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [FlexGen: High-Throughput Generative Inference of Large Language Models with a Single GPU](https://mlsanity.com/paper/2303.06865/) (2023)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [Adaptive Gradient Quantization for Data-Parallel SGD](https://mlsanity.com/paper/2010.12460/) (2020)
- [Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2409.09913/) (2024)
- [NUQSGD: Provably Communication-efficient Data-parallel SGD via Nonuniform Quantization](https://mlsanity.com/paper/1908.06077/) (2019)
- [Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D](https://mlsanity.com/paper/1701.07204/) (2017)
- [A New Pair of GloVes](https://mlsanity.com/paper/2507.18103/) (2025)

## Abstract (arXiv)

Quantization is a fundamental tool used to compress datasets, neural network weights, and memory usage in a range of computational tasks. Many downstream applications of vector quantization perform inner products with arbitrary inputs. This motivates the study of inner product aware quantization schemes that approximately preserve inner products with unseen vectors -- in contrast to simply minimizing the mean-squared error. In this work, we formulate objectives that capture natural desiderata and develop adaptive and unbiased quantization methods that approximately preserve inner products with worst-case and average-case inputs. An analysis of these objectives shows a tight connection with the well-studied notion of Adaptive Stochastic Quantization (ASQ). We develop provably fast exact and approximate algorithms for our objectives. Our theoretical results inspire efficient practical algorithms that perform well across a variety of workload distributions. They also lead to practical algorithms for standard ASQ which are 2-10× faster than prior state-of-the-art methods while maintaining quality. These theoretical and empirical results contribute towards making adaptive quantization techniques more efficient and tractable in practical settings.