# LogiC-Diff: Embedding Security Properties Into AI-Enabled Cyber-Physical Systems

arXiv: https://arxiv.org/abs/2609.38381 · HTML: https://mlsanity.com/paper/2609.38381/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 55 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Learning from Multiple Cities: A Meta-Learning Approach for Spatial-Temporal Prediction](https://mlsanity.com/paper/1901.08518/) (2019)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspective](https://mlsanity.com/paper/2206.12227/) (2022)
- [Adversarial Attacks on Time Series](https://mlsanity.com/paper/1902.10755/) (2019)
- [Practical Adversarial Attacks on Spatiotemporal Traffic Forecasting Models](https://mlsanity.com/paper/2210.02447/) (2022)
- [Defending against Adversarial Audio via Diffusion Model](https://mlsanity.com/paper/2303.01507/) (2023)
- [Improving Certified Robustness via Statistical Learning with Logical Reasoning](https://mlsanity.com/paper/2003.00120/) (2020)
- [Benchmarking adversarial attacks and defenses for time-series data](https://mlsanity.com/paper/2008.13261/) (2020)
- [ALFA: A Dataset for UAV Fault and Anomaly Detection](https://mlsanity.com/paper/1907.06268/) (2019)
- [Robust Multivariate Time-Series Forecasting: Adversarial Attacks and Defense Mechanisms](https://mlsanity.com/paper/2207.09572/) (2022)
- [CitySpec with Shield: A Secure Intelligent Assistant for Requirement Formalization](https://mlsanity.com/paper/2302.09665/) (2023)
- [Formal Logic Enabled Personalized Federated Learning Through Property Inference](https://mlsanity.com/paper/2401.07448/) (2024)
- [Temporal Logic-Based Multi-Vehicle Backdoor Attacks against Offline RL Agents in End-to-end Autonomous Driving](https://mlsanity.com/paper/2509.16950/) (2025)

## Abstract (arXiv)

AI-enabled Cyber-Physical Systems (CPS) are highly vulnerable to adversarial and anomalous inputs, where small perturbations can induce cascading errors and unsafe control actions. Existing approaches, such as rule-based filtering, training-time regularization, or diffusion-based reconstruction, either operate outside the model or lack mechanisms to incorporate formal security specifications into the prediction process. In this paper, we take the first step toward embedding security properties directly into AI-enabled CPS, enabling predictive models to enforce system-level constraints during inference rather than relying on external defenses. We introduce a logic-conditioned bi-stage diffusion framework that integrates Signal Temporal Logic (STL) specifications into forecasting. STL serves as a first-class conditioning signal that guides both an input repair stage and an output refinement stage, allowing the model to jointly mitigate adversarial perturbations and enforce desired temporal behaviors to satisfy security-critical properties. We evaluate our approach on two real-world multivariate CPS forecasting datasets under a diverse set of physical sensor and cyber attacks. Across sensor faults, gradient-based attacks, adaptive attacks, and varying attack strengths, our method consistently improves robustness and specification compliance, degrades more gracefully as attack strength increases, and generalizes better to unseen attacks. Ablation studies on specification coverage and quality further show that embedding logical security properties yields gains unattainable by reconstruction-based methods alone, highlighting a new direction for integrating formal methods with generative models in secure CPS.