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QIBONN: A Quantum-Inspired Bilevel Optimizer for Neural Networks on Tabular Classification

Pedro Chumpitaz-Flores, My Duong, Ying Mao, Kaixun Hua

TL;DR

QIBONN introduces a quantum-inspired bilevel optimizer that encodes feature selection, architectural hyperparameters, and regularization into a qubit-based representation to search neural network hyperparameters for tabular classification under a fixed evaluation budget. It combines deterministic rotations toward a global attractor with stochastic mutations to balance exploration and exploitation, and employs a bilevel framework where inner weight optimization is decoupled from outer hyperparameter tuning. Empirically, QIBONN achieves competitive performance relative to classical and quantum-inspired baselines across eight real-world tabular datasets, with deeper architectures benefiting more, and generalizes to multiclass problems. The method also demonstrates robustness to moderate qubit-level noise in simulations and hardware emulators, suggesting practical viability for scalable HPO on tabular data.

Abstract

Hyperparameter optimization (HPO) for neural networks on tabular data is critical to a wide range of applications, yet it remains challenging due to large, non-convex search spaces and the cost of exhaustive tuning. We introduce the Quantum-Inspired Bilevel Optimizer for Neural Networks (QIBONN), a bilevel framework that encodes feature selection, architectural hyperparameters, and regularization in a unified qubit-based representation. By combining deterministic quantum-inspired rotations with stochastic qubit mutations guided by a global attractor, QIBONN balances exploration and exploitation under a fixed evaluation budget. We conduct systematic experiments under single-qubit bit-flip noise (0.1\%--1\%) emulated by an IBM-Q backend. Results on 13 real-world datasets indicate that QIBONN is competitive with established methods, including classical tree-based methods and both classical/quantum-inspired HPO algorithms under the same tuning budget.

QIBONN: A Quantum-Inspired Bilevel Optimizer for Neural Networks on Tabular Classification

TL;DR

QIBONN introduces a quantum-inspired bilevel optimizer that encodes feature selection, architectural hyperparameters, and regularization into a qubit-based representation to search neural network hyperparameters for tabular classification under a fixed evaluation budget. It combines deterministic rotations toward a global attractor with stochastic mutations to balance exploration and exploitation, and employs a bilevel framework where inner weight optimization is decoupled from outer hyperparameter tuning. Empirically, QIBONN achieves competitive performance relative to classical and quantum-inspired baselines across eight real-world tabular datasets, with deeper architectures benefiting more, and generalizes to multiclass problems. The method also demonstrates robustness to moderate qubit-level noise in simulations and hardware emulators, suggesting practical viability for scalable HPO on tabular data.

Abstract

Hyperparameter optimization (HPO) for neural networks on tabular data is critical to a wide range of applications, yet it remains challenging due to large, non-convex search spaces and the cost of exhaustive tuning. We introduce the Quantum-Inspired Bilevel Optimizer for Neural Networks (QIBONN), a bilevel framework that encodes feature selection, architectural hyperparameters, and regularization in a unified qubit-based representation. By combining deterministic quantum-inspired rotations with stochastic qubit mutations guided by a global attractor, QIBONN balances exploration and exploitation under a fixed evaluation budget. We conduct systematic experiments under single-qubit bit-flip noise (0.1\%--1\%) emulated by an IBM-Q backend. Results on 13 real-world datasets indicate that QIBONN is competitive with established methods, including classical tree-based methods and both classical/quantum-inspired HPO algorithms under the same tuning budget.

Paper Structure

This paper contains 9 sections, 2 theorems, 9 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Quantum-Inspired Optimization
  3. Quantum-Inspired Bilevel Optimizer
  4. Computational Experiments
  5. Numerical Results
  6. Generalization to Multiclass Problems
  7. Robustness to Noise
  8. Conclusion
  9. Limitations and Future Work

Key Result

Proposition 1

For each $h\in H$, the inner problem $\theta^*(h) = \arg\min_{\theta} L(\theta; h)$ is solved independently, and the outer problem $\min_{h \in H} J(h)$ depends solely on validation performance $J(h)$.

Figures (3)

  • Figure 1: QIBONN pipeline
  • Figure 2: Mean ROC-AUC (left) and PR-AUC (right) across three real-world tabular datasets under different noise models. Conditions are ordered as: Noiseless; Bit-flip (0.001–0.01); Depolarizing (0.005–0.02); Amplitude Damping (0.01–0.05); and IBM Q hardware emulators (FakeMontrealV2, FakeBrooklynV2).
  • Figure 3: Training and validation loss versus epochs for QIBONN.

Theorems & Definitions (6)

  • Definition 1: Hyperparameter Space
  • Definition 2: Candidate Encoding and Decoding
  • Definition 3: Evaluation Function
  • Definition 4: Training Phase
  • Proposition 1: Decoupling of Hyperparameter Tuning and Weight Optimization
  • Proposition 2: Quantum-Inspired Update in the Encoded Space