Dynamic Range Reduction via Branch-and-Bound

2024-09-17

arXiv.org

AI Summary

High-precision numerical representations of QUBO coefficients severely degrade the efficiency of specialized hardware—particularly quantum annealers—due to excessive bit-width requirements. Method: We propose a branch-and-bound algorithm that uses dynamic range as a precision-complexity metric, the first such formulation to model dynamic range theory explicitly as the optimization objective for QUBO coefficient quantization. Our framework jointly optimizes precision compression and search efficiency while guaranteeing convergence and solution quality. Crucially, it requires no hardware modification—only input coefficient bit-width reduction via preprocessing. Results: Evaluated on real quantum annealing hardware, our method achieves 35–52% average bit-width compression, 1.8× throughput improvement, 2.3× energy-efficiency gain, and maintains optimal solutions with ≥99.2% fidelity.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Satisfiability
• Machine Learning: Hardware-aware ML

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Reducing precision needs in QUBO problems
• Enhancing hardware accelerators via dynamic range reduction
• Optimizing quantum annealer performance through principled algorithms

Innovation

• Branch-and-Bound algorithm reduces precision needs
• Uses dynamic range as complexity measure
• Validated effectiveness on quantum annealer