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

ICLR 2026 Conference Submission20847 Authors

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—on NISQ devices—intrinsic stochasticity. We present \emph{Q-STRONG}, a quantum–statistical framework that couples (i) robust M–estimation, (ii) quantile–scheduled gradient clipping, and (iii) gap–adaptive randomized smoothing. Inputs are encoded as quantum states; a task-aligned Hamiltonian yields a representation whose spectral gap acts as a stability signal. During training, bounded-influence losses and per-sample clipping suppress rare gradient spikes. At inference, we certify predictions with instance-adaptive noise $\sigma(x)=\kappa\,\Delta(x)^{-\beta}$, producing larger $\ell_2$ radii where the representation is stable.

We prove non-asymptotic guarantees: convergence of clipped SGD to first-order stationarity for weakly smooth robust objectives; a stability-based generalization bound with an \emph{effective} Lipschitz constant lowered by clipping and robustification; gap-adaptive extensions of randomized-smoothing certificates; and parameter-noise resilience that scales inversely with the gap. Empirically, Q-STRONG achieves a favorable accuracy–robustness frontier on MNIST and CIFAR-10 with label noise and common corruptions, and on synthetic manifolds stressing intrinsic dimension and outliers. Ablations isolate the roles of each component. The approach is hardware-agnostic (classical or NISQ), plug-compatible with standard models, and adds minimal overhead. Q-STRONG 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