# Quantum Tunneling-Aware Machine Learning: Physics-Derived Noise Models for Robust Deployment

arXiv: https://arxiv.org/abs/2606.00741 · HTML: https://mlsanity.com/paper/2606.00741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 11 of 11)

- [Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift](https://mlsanity.com/paper/2006.10963/) (2020)
- [Hardware-aware training for large-scale and diverse deep learning inference workloads using in-memory computing-based accelerators](https://mlsanity.com/paper/2302.08469/) (2023)
- [Aegis: Mitigating Targeted Bit-flip Attacks against Deep Neural Networks](https://mlsanity.com/paper/2302.13520/) (2023)
- [RA-BNN: Constructing Robust & Accurate Binary Neural Network to Simultaneously Defend Adversarial Bit-Flip Attack and Improve Accuracy](https://mlsanity.com/paper/2103.13813/) (2021)
- [CorrectNet: Robustness Enhancement of Analog In-Memory Computing for Neural Networks by Error Suppression and Compensation](https://mlsanity.com/paper/2211.14917/) (2022)
- [Quantum-tunnelling deep neural network for optical illusion recognition](https://mlsanity.com/paper/2407.11013/) (2024)
- [Universal Scaling Laws of Absorbing Phase Transitions in Artificial Deep Neural Networks](https://mlsanity.com/paper/2307.02284/) (2023)
- [MoRS: An Approximate Fault Modelling Framework for Reduced-Voltage SRAMs](https://mlsanity.com/paper/2110.05855/) (2021)
- [Harden Deep Neural Networks Against Fault Injections Through Weight Scaling](https://mlsanity.com/paper/2411.18993/) (2024)
- [Sensitivity-Aware Finetuning for Accuracy Recovery on Deep Learning Hardware](https://mlsanity.com/paper/2306.03076/) (2023)
- [Analog Bayesian neural networks are insensitive to the shape of the weight distribution](https://mlsanity.com/paper/2501.05564/) (2025)

## Abstract (arXiv)

Transistor scaling is approaching a quantum-mechanical limit, as thin gate oxides induce electron leakage through quantum tunneling. Unlike conventional digital systems, AI inference can tolerate such errors provided their structure is modeled correctly. In this paper, we introduce quantum tunneling-aware machine learning (QTAML). We derive the deployment-time weight-error distribution from first principles using the Wentzel-Kramers-Brillouin (WKB) approximation and show that it has structure that generic Gaussian noise models miss: an exact affine mean drift, a per-bit variance hierarchy dominated by the most-significant bit, and a per-layer dependence on |Wℓ|_∞ and the trained-network Jacobian. We package these three structural properties into a single deployment-time algorithm, Tunneling-Aware Compensation (TAC), that combines closed-form mean correction with an optimal layer-adaptive bit-budget allocation derived from the WKB variance decomposition. Across four convolutional architectures at pflip=0.10 and a transformer encoder at pflip=0.05, TAC reaches 95% of clean accuracy with 3.4× to 33.6× less ECC overhead than Uniform-MSP, the natural baseline derived from the same physics. The closed-form saturation ratio ρ^* predicts these gains in advance, and on heterogeneous architectures WKB-derived scoring outperforms magnitude-based allocation by up to 24 percentage points at small budgets. The algorithm requires no retraining, no labels, and no inference-time overhead. We also verify the WKB-derived distributional theorems to Monte Carlo precision. These results connect WKB tunneling physics with noise-aware deep learning and suggest a principled path toward hardware--software co-design beyond conventional scaling limits.