Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems
Authors: Mengke Zhao, Guang-Xing Li, Duo Xu, Keping Qiu
Organizations: School of Astronomy and Space Science, Nanjing University, 163 Xianlin Avenue, Nanjing 210023, Jiangsu, People’s Republic of China · Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023, Jiangsu, People’s Republic of China · South-Western Institute for Astronomy Research, Yunnan University, Kunming 650091, People’s Republic of China · Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
Abstract
Complex physical systems, from supersonic turbulence to the macroscopic structure of the universe, are governed by continuous multiscale dynamics. While modern machine learning architectures excel at mapping the high-dimensional observables of these systems, it remains unclear whether they internalize the governing physical laws or merely interpolate discrete statistical correlations. Standard Explainable AI (XAI) architectures, particularly perturbation-based and gradient-saliency methods, rely on pixel-wise perturbations, which generate unphysical artifacts and push inputs off the valid empirical distribution. To resolve this, we introduce a diagnostic framework driven by Constrained Diffusion Decomposition (CDD), a diffusion-based multiscale data decomposition algorithm that enables physically constrained data generation and model evaluation via scale-aware modifications. Applying this framework to a Denoising Diffusion Probabilistic Model (DDPM), we execute deterministic interventions directly within the continuous, CDD-based scale space. We demonstrate that under moderate physical perturbations, the unconstrained generative model exhibits localized structural freezing and non-linear instability rather than continuous PDE-like responses. The network fails to maintain cross-scale continuity, causing the generative trajectory to diverge when pushed into unseen physical states. By synthesizing a continuum of physically coherent states, this scale-informed methodology establishes a controlled test ground to evaluate algorithmic vulnerabilities, providing the rigorous physical constraints necessary for future architectures to respect the multiscale causality of the natural universe.
The increasing deployment of deep learning systems requires systematic evaluation of their reliability in real-world scenarios. Traditional gradient-based adversarial attacks introduce small perturbations that rarely correspond to realistic failures and mainly assess robustness rather than functional behavior. Generative test generation methods offer an alternative but are often limited to simple datasets or constrained input domains. Although diffusion models enable high-fidelity image synthesis, their computational cost and limited controllability restrict their applicability to large-scale testing. We present HyNeA, a generative testing method that enables direct and efficient control over diffusion-based generation. HyNeA provides dataset-free controllability through hypernetworks, allowing targeted manipulation of the generative process without relying on architecture-specific conditioning mechanisms or dataset-driven adaptations such as fine-tuning. HyNeA employs a distinct training strategy that supports instance-level tuning to identify failure-inducing test cases without requiring datasets that explicitly contain examples of similar failures. This approach enables the targeted generation of realistic failure cases at substantially lower computational cost than search-based methods. Experimental results show that HyNeA improves controllability and test diversity compared to existing generative test generators and generalizes to domains where failure-labeled training data is unavailable.
Oliver Weißl, Vincenzo Riccio, Severin Kacianka +1
Modern GANs often introduce adversarial supervision on intermediate generator outputs and interpret the resulting multi-stage synthesis as coarse-to-fine hierarchical generation. In this work, we challenge this interpretation. We argue that standard scale-wise adversarial supervision does not construct a proper coarse-to-fine hierarchy: each intermediate image is independently pushed toward the real distribution at its own resolution, but this scale-wise realism does not ensure that outputs across stages represent the identical generated sample. Moreover, the scale-specific image produced at each stage is not used as an explicit refinement target for the subsequent stage. Therefore, its adversarial loss can improve a scale-specific output without constraining later stages to preserve the same sample trajectory, allowing them to move toward a different sample rather than refine the previous output. We refer to this problem as a cross-scale trajectory misalignment problem. To resolve it, we propose CAT, a Cross-scale Aligned Transformer for multi-scale adversarial generation. CAT keeps the discriminator scale-wise, so each intermediate output is evaluated at its own resolution, while adding a simple generator-side consistency regularization that aligns intermediate outputs with the final output. On class-conditional ImageNet-256, CAT-H/2 achieves an FID-50K of 1.56 with one-step inference after only 60 training epochs, outperforming strong one-step GAN and diffusion/flow baselines.
Physical AI is being successfully applied to data which does not follow the traditional paradigm of independent and identically distributed (i.i.d.) samples. In fact, physical AI is often trained on data which is not random at all, and is instead derived from chaotic dynamical systems like turbulence. We aim to explain the empirical success of these methods using the example of generative adversarial networks (GANs), whose statistical learning theory under the i.i.d. assumption is generally well understood. We prove that it is possible, using an infinite-dimensional model of generative adversarial learning (GAL), to learn the invariant distribution of a sufficiently chaotic dynamical system from a single deterministically evolving time series of its states or measurements thereof, and give explicit rates for the convergence to the solution in terms of the Jensen-Shannon divergence.