# Dynamic Range Reduction via Branch-and-Bound

arXiv: https://arxiv.org/abs/2409.10863 · HTML: https://mlsanity.com/paper/2409.10863/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 46 references that are in the map.
- First posted on arXiv 17 Sep 2024.

## Builds on (most cited first, 8 of 8)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [Feature Selection on Quantum Computers](https://mlsanity.com/paper/2203.13261/) (2022)
- [Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management](https://mlsanity.com/paper/1711.04889/) (2017)
- [Taming the Curse of Dimensionality: Discrete Integration by Hashing and Optimization](https://mlsanity.com/paper/1302.6677/) (2013)
- [Digital Annealer for quadratic unconstrained binary optimization: a comparative performance analysis](https://mlsanity.com/paper/2012.12264/) (2020)
- [Faster exact solution of sparse MaxCut and QUBO problems](https://mlsanity.com/paper/2202.02305/) (2022)
- [Solving Subset Sum Problems using Quantum Inspired Optimization Algorithms with Applications in Auditing and Financial Data Analysis](https://mlsanity.com/paper/2211.02653/) (2022)

## Built on by (most cited first, 2 of 2)

- [Hybrid Quantum-Classical Multi-Agent Pathfinding](https://mlsanity.com/paper/2501.14568/) (2025)
- [Kernel k-Medoids as General Vector Quantization](https://mlsanity.com/paper/2506.04786/) (2025)

## Abstract (arXiv)

The demand for high-performance computing in machine learning and artificial intelligence has led to the development of specialized hardware accelerators like Tensor Processing Units (TPUs), Graphics Processing Units (GPUs), and Field-Programmable Gate Arrays (FPGAs). A key strategy to enhance these accelerators is the reduction of precision in arithmetic operations, which increases processing speed and lowers latency - crucial for real-time AI applications. Precision reduction minimizes memory bandwidth requirements and energy consumption, essential for large-scale and mobile deployments, and increases throughput by enabling more parallel operations per cycle, maximizing hardware resource utilization. This strategy is equally vital for solving NP-hard quadratic unconstrained binary optimization (QUBO) problems common in machine learning, which often require high precision for accurate representation. Special hardware solvers, such as quantum annealers, benefit significantly from precision reduction. This paper introduces a fully principled Branch-and-Bound algorithm for reducing precision needs in QUBO problems by utilizing dynamic range as a measure of complexity. Experiments validate our algorithm's effectiveness on an actual quantum annealer.