Q-STRONG: Quantum-Statistical Robustness with Noise-Guarded Dynamics for Learning

Anand Paul

Keywords: Quantum machine learning, Robust M-estimation, Dynamic gradient clipping, Randomized smoothing, Certified robustness, Noise resilience, Spectral gap, Quantum state embeddings, Adversarial robustness, NISQ hardware

TL;DR: Q-STRONG unifies robust M-estimation, quantile-clipped optimization, and gap-adaptive randomized smoothing in a quantum-state framework to deliver certified, noise-resilient learning on MNIST/CIFAR.

Abstract: State-of-the-art learners remain fragile under heavy-tailed noise, adversarial perturbations and decoherence. We propose \emph{Q-STRONG}, a quantum–statistical framework for certified robust learning that uses the spectral structure of a learned state representation as a stability signal. Inputs are embedded into a normalized quantum state space, and a task-aligned Hamiltonian induces a low-energy representation whose spectral gap $\Delta_\theta(x)$ quantifies local stability. This gap steers both training and certification: during optimization, robust losses and quantile-based clipping reduce gradient tail effects; at inference, a gap-adaptive randomized smoothing scheme chooses the noise level $\sigma(x)=\kappa \Delta_\theta(x)^{-\beta}$, yielding larger certified $\ell_2$ radii exactly where the representation is stable. We provide non-asymptotic guarantees for quantile-clipped robust SGD, stability-based generalization bounds with improved effective smoothness, and gap-adaptive extensions of randomized-smoothing certificates tied to $\Delta_\theta(x)$. Empirically, Q-STRONG attains a favorable accuracy–robustness frontier on MNIST and CIFAR-10 under label noise and common corruptions, and on synthetic manifolds that stress intrinsic dimension and outliers, while adding modest overhead and thus offers a practical, theoretically grounded route to certified, noise-resilient learning.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 20847