Neural Contrast Expansion for Explainable Structure-Property Prediction and Random Microstructure Design

Effective properties of composite materials are defined as the ensemble average of property-specific PDE solutions over the underlying microstructure distributions. Traditionally, predicting such properties can be done by solving PDEs derived from microstructure samples or building data-driven models that directly map microstructure samples to properties. The former has a higher running cost, but provides explainable sensitivity information that may guide material design; the latter could be more cost-effective if the data overhead is amortized, but its learned sensitivities are often less explainable. With a focus on properties governed by linear self-adjoint PDEs (e.g., Laplace, Helmholtz, and Maxwell curl-curl) defined on bi-phase microstructures, we propose a structure-property model that is both cost-effective and explainable. Our method is built on top of the strong contrast expansion (SCE) formalism, which analytically maps $N$-point correlations of an unbounded random field to its effective properties. Since real-world material samples have finite sizes and analytical PDE kernels are not always available, we propose Neural Contrast Expansion (NCE), an SCE-inspired architecture to learn surrogate PDE kernels from structure-property data. For static conduction and electromagnetic wave propagation cases, we show that NCE models reveal accurate and insightful sensitivity information useful for material design. Compared with other PDE kernel learning methods, our method does not require measurements about the PDE solution fields, but rather only requires macroscopic property measurements that are more accessible in material development contexts.

Attributing Image Generative Models using Latent Fingerprints

Generative models have enabled the creation of contents that are indistinguishable from those taken from the nature. Open-source development of such models raised concerns about the risks in their misuse for malicious purposes. One potential risk mitigation strategy is to attribute generative models via fingerprinting. Current fingerprinting methods exhibit significant tradeoff between robust attribution accuracy and generation quality, and also lack designing principles to improve this tradeoff. This paper investigates the use of latent semantic dimensions as fingerprints, from where we can analyze the effects of design variables, including the choice of fingerprinting dimensions, strength, and capacity, on the accuracy-quality tradeoff. Compared with previous SOTA, our method requires minimum computation and is more applicable to large-scale models. We use StyleGAN2 and the latent diffusion model to demonstrate the efficacy of our method.

Improving Model Robustness with Transformation-Invariant Attacks

Vulnerability of neural networks under adversarial attacks has raised serious concerns and extensive research. Recent studies suggested that model robustness relies on the use of robust features, i.e., features with strong correlation with labels, and that data dimensionality and distribution affect the learning of robust features. On the other hand, experiments showed that human vision, which is robust against adversarial attacks, is invariant to natural input transformations. Drawing on these findings, this paper investigates whether constraints on transformation invariance, including image cropping, rotation, and zooming, will force image classifiers to learn and use robust features and in turn acquire better robustness. Experiments on MNIST and CIFAR10 show that transformation invariance alone has limited effect. Nonetheless, models adversarially trained on cropping-invariant attacks, in particular, can (1) extract more robust features, (2) have significantly better robustness than the state-of-the-art models from adversarial training, and (3) require less training data.