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On the Impact of Weight Discretization in QUBO-Based SVM Training

Sascha Mücke

TL;DR

This paper addresses how discretizing the dual SVM weights in a QUBO encoding affects predictive performance. It develops a Binary Qubo-SVM and a k-bit Qubo-SVM by binarizing or multi-bit encoding of the dual variables and compares them to LIBSVM on several datasets. The results show that even a 1-bit per weight encoding can achieve competitive accuracy with LIBSVM, and increasing the precision to k>1 mainly widens the feasible range of $C$ rather than consistently improving accuracy; a key takeaway is that selecting the right set of support vectors can be more impactful than weight precision. Hardware constraints currently limit the QUBO size to $N k$, but as quantum devices scale, QA-based SVM training could become a practical approach for larger datasets.

Abstract

Training Support Vector Machines (SVMs) can be formulated as a QUBO problem, enabling the use of quantum annealing for model optimization. In this work, we study how the number of qubits - linked to the discretization level of dual weights - affects predictive performance across datasets. We compare QUBO-based SVM training to the classical LIBSVM solver and find that even low-precision QUBO encodings (e.g., 1 bit per parameter) yield competitive, and sometimes superior, accuracy. While increased bit-depth enables larger regularization parameters, it does not always improve classification. Our findings suggest that selecting the right support vectors may matter more than their precise weighting. Although current hardware limits the size of solvable QUBOs, our results highlight the potential of quantum annealing for efficient SVM training as quantum devices scale.

On the Impact of Weight Discretization in QUBO-Based SVM Training

TL;DR

This paper addresses how discretizing the dual SVM weights in a QUBO encoding affects predictive performance. It develops a Binary Qubo-SVM and a k-bit Qubo-SVM by binarizing or multi-bit encoding of the dual variables and compares them to LIBSVM on several datasets. The results show that even a 1-bit per weight encoding can achieve competitive accuracy with LIBSVM, and increasing the precision to k>1 mainly widens the feasible range of rather than consistently improving accuracy; a key takeaway is that selecting the right set of support vectors can be more impactful than weight precision. Hardware constraints currently limit the QUBO size to , but as quantum devices scale, QA-based SVM training could become a practical approach for larger datasets.

Abstract

Training Support Vector Machines (SVMs) can be formulated as a QUBO problem, enabling the use of quantum annealing for model optimization. In this work, we study how the number of qubits - linked to the discretization level of dual weights - affects predictive performance across datasets. We compare QUBO-based SVM training to the classical LIBSVM solver and find that even low-precision QUBO encodings (e.g., 1 bit per parameter) yield competitive, and sometimes superior, accuracy. While increased bit-depth enables larger regularization parameters, it does not always improve classification. Our findings suggest that selecting the right support vectors may matter more than their precise weighting. Although current hardware limits the size of solvable QUBOs, our results highlight the potential of quantum annealing for efficient SVM training as quantum devices scale.

Paper Structure

This paper contains 10 sections, 10 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Support Vector Machines
  4. QUBO
  5. A QUBO Formulation of SVM Training
  6. Increasing Precision
  7. Experimental Evaluation
  8. Concluding Remarks
  9. Acknowledgments.
  10. Disclosure of Interests.

Figures (2)

  • Figure 1: Example of a conversion from a binary vector of length $k=3$ to a scalar value between $0$ and $C$ through multiplication with a vector $\bm p$; by choosing $p_j=C\cdot 2^{j-1}/(2^k-1)$, the interval $[0,C]$ is sampled evenly.
  • Figure 2: 5-fold cross-validated prediction accuracies of the $k$-bit Qubo-SVM and LIBSVM on the three data sets listed in \ref{['tab:svm:datasets']}, using various values for $C$ and $k$.

Theorems & Definitions (5)

  • definition thmcounterdefinition: Primal SVM hastie.etal.2009a
  • definition thmcounterdefinition: Dual SVM hastie.etal.2009a
  • definition thmcounterdefinition: Qubo
  • definition thmcounterdefinition: Binary Qubo-SVM muecke.etal.2019a
  • definition thmcounterdefinition: $k$-bit Qubo-SVM