Jacob H. Seidman

Jacob H. Seidman, Georgios Kissas, Paris Perdikaris et al.

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost.

Sepehr Dehdashtian, Jacob H Seidman, Vishnu N Boddeti et al.

Audio deepfake detection (ADD) models are critical for countering the malicious use of text-to-speech (TTS) models. Evaluating and strengthening ADD models requires developing datasets that span the space of generated audio and highlight high-error regions. Existing dataset development strategies face two challenges: (i) manual collection, and (ii) inefficient discovery of blind spots in the ADD models. To address these challenges, we propose FoeGlass, the first black-box automated red-teaming method for ADDs, which effectively discovers ADD failure modes in the space of generated audio underexplored by state-of-the-art deepfake benchmarks. FoeGlass uses the in-context learning capabilities of an LLM to explore the input space of a TTS model, generating audio samples that fool the target ADD using only black-box access to all components. By using a carefully designed context based on diversity measurements, FoeGlass mitigates the common problem of mode collapse in automated red-teaming systems. Empirical evaluations on several open-source ADD and TTS models demonstrate that data generated from FoeGlass substantially improves the false negative rates over unconditional sampling baselines and recent spoofing datasets by up to 94%, while requiring no manual supervision. Furthermore, we show that the attacks generated by FoeGlass are transferable across different target ADDs, demonstrating its broad applicability and ease of use for the automated red teaming of ADD systems. Finally, fine-tuning ADD models on FoeGlass-generated samples notably enhances the robustness of the detectors (up 41%).

Jacob H. Seidman, Georgios Kissas, George J. Pappas et al.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

Sifan Wang, Hanwen Wang, Jacob H. Seidman et al.

Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals. However, training them to capture fine details in multi-scale signals is difficult and computationally expensive. Here we propose random weight factorization as a simple drop-in replacement for parameterizing and initializing conventional linear layers in coordinate-based multi-layer perceptrons (MLPs) that significantly accelerates and improves their training. We show how this factorization alters the underlying loss landscape and effectively enables each neuron in the network to learn using its own self-adaptive learning rate. This not only helps with mitigating spectral bias, but also allows networks to quickly recover from poor initializations and reach better local minima. We demonstrate how random weight factorization can be leveraged to improve the training of neural representations on a variety of tasks, including image regression, shape representation, computed tomography, inverse rendering, solving partial differential equations, and learning operators between function spaces.

Kaixiang Zheng, Jacob H. Seidman

As synthetic images become increasingly realistic, reliable synthetic image detection techniques are of pressing need to prevent their misuse. Despite satisfactory in-distribution performance, deep neural network-based synthetic image detectors (SIDs) lack reliability in deployment and often fail in the presence of common covariate shifts, resulting in poor detection accuracy. To avoid the risk caused by potential errors, we adopt a selective classification (SC) strategy by allowing SIDs to abstain from making low confidence predictions. For practicality, we focus on post-hoc methods which perform confidence estimation on a given SID without retraining. However, we show that conventional logit-based confidence score functions (CSFs) exhibit pathological behavior under covariate shifts, leading to SC performance close to or even worse than random guessing. To address this, we propose a simple yet effective SC framework for Reliable Synthetic Image Detection (ReSIDe). First, we generalize the notion of logits to an SID's intermediate layers from a centroid matching perspective, extending the use of logit-based CSFs to any layer of an SID. Then, we introduce a preference optimization algorithm that aggregates confidence scores extracted from different layers to a final confidence estimate by minimizing an upper bound of the area under the risk-coverage curve (AURC). Extensive experimental results show that ReSIDe significantly boosts the SC performance of various logit-based CSFs under common covariate shifts, achieving up to 69.55% AURC reduction.

Sifan Wang, Jacob H Seidman, Shyam Sankaran et al.

Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various physical domains. Here we introduce the Continuous Vision Transformer (CViT), a novel neural operator architecture that leverages advances in computer vision to address challenges in learning complex physical systems. CViT combines a vision transformer encoder, a novel grid-based coordinate embedding, and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. This design allows for flexible output representations and consistent evaluation at arbitrary resolutions. We demonstrate CViT's effectiveness across a diverse range of partial differential equation (PDE) systems, including fluid dynamics, climate modeling, and reaction-diffusion processes. Our comprehensive experiments show that CViT achieves state-of-the-art performance on multiple benchmarks, often surpassing larger foundation models, even without extensive pretraining and roll-out fine-tuning. Taken together, CViT exhibits robust handling of discontinuous solutions, multi-scale features, and intricate spatio-temporal dynamics. Our contributions can be viewed as a significant step towards adapting advanced computer vision architectures for building more flexible and accurate machine learning models in the physical sciences.

Sepehr Dehdashtian, Mashrur M. Morshed, Jacob H. Seidman et al.

Synthetic image detectors (SIDs) are a key defense against the risks posed by the growing realism of images from text-to-image (T2I) models. Red teaming improves SID's effectiveness by identifying and exploiting their failure modes via misclassified synthetic images. However, existing red-teaming solutions (i) require white-box access to SIDs, which is infeasible for proprietary state-of-the-art detectors, and (ii) generate image-specific attacks through expensive online optimization. To address these limitations, we propose PolyJuice, the first black-box, image-agnostic red-teaming method for SIDs, based on an observed distribution shift in the T2I latent space between samples correctly and incorrectly classified by the SID. PolyJuice generates attacks by (i) identifying the direction of this shift through a lightweight offline process that only requires black-box access to the SID, and (ii) exploiting this direction by universally steering all generated images towards the SID's failure modes. PolyJuice-steered T2I models are significantly more effective at deceiving SIDs (up to 84%) compared to their unsteered counterparts. We also show that the steering directions can be estimated efficiently at lower resolutions and transferred to higher resolutions using simple interpolation, reducing computational overhead. Finally, tuning SID models on PolyJuice-augmented datasets notably enhances the performance of the detectors (up to 30%).

Jacob H. Seidman, Mahyar Fazlyab, Victor M. Preciado et al.

The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This mechanism can be formulated as a min-max optimization problem, where the adversary seeks to maximize the loss function using an iterative first-order algorithm while the learner attempts to minimize it. However, finding adversarial examples in this way causes excessive computational overhead during training. By interpreting the min-max problem as an optimal control problem, it has recently been shown that one can exploit the compositional structure of neural networks in the optimization problem to improve the training time significantly. In this paper, we provide the first convergence analysis of this adversarial training algorithm by combining techniques from robust optimal control and inexact oracle methods in optimization. Our analysis sheds light on how the hyperparameters of the algorithm affect the its stability and convergence. We support our insights with experiments on a robust classification problem.