Scientific discovery is a complex cognitive process that has driven human knowledge and technological progress for centuries. While artificial intelligence (AI) has made significant advances in automating aspects of scientific reasoning, simulation, and experimentation, we still lack integrated AI systems capable of performing autonomous long-term scientific research and discovery. This paper examines the current state of AI for scientific discovery, highlighting recent progress in large language models and other AI techniques applied to scientific tasks. We then outline key challenges and promising research directions toward developing more comprehensive AI systems for scientific discovery, including the need for science-focused AI agents, improved benchmarks and evaluation metrics, multimodal scientific representations, and unified frameworks combining reasoning, theorem proving, and data-driven modeling. Addressing these challenges could lead to transformative AI tools to accelerate progress across disciplines towards scientific discovery.

The growing threats of uncertainties, anomalies, and cyberattacks on power grids are driving a critical need to advance situational awareness which allows system operators to form a complete and accurate picture of the present and future state. Simulation and estimation are foundational tools in this process. However, existing tools lack the robustness and efficiency required to achieve the level of situational awareness needed for the ever-evolving threat landscape. Industry-standard (steady-state) simulators are not robust to blackouts, often leading to non-converging or non-actionable results. Estimation tools lack robustness to anomalous data, returning erroneous system states. Efficiency is the other major concern as nonlinearities and scalability issues make large systems slow to converge. This thesis addresses robustness and efficiency gaps through a dual-fold contribution. We first address the inherent limitations in the existing physics-based and data-driven worlds; and then transcend the boundaries of conventional algorithmic design in the direction of a new paradigm -- Physics-ML Synergy -- which integrates the strengths of the two worlds. Our approaches are built on circuit formulation which provides a unified framework that applies to both transmission and distribution. Sparse optimization acts as the key enabler to make these tools intrinsically robust and immune to random threats, pinpointing dominant sources of (random) blackouts and data errors. Further, we explore sparsity-exploiting optimizations to develop lightweight ML models whose prediction and detection capabilities are a complement to physics-based tools; and whose lightweight designs advance generalization and scalability. Finally, Physics-ML Synergy brings robustness and efficiency further against targeted cyberthreats, by interconnecting our physics-based tools with lightweight ML.

This paper addresses hypothesis testing for the mean of matrix-valued data in high-dimensional settings. We investigate the minimum discrepancy test, originally proposed by Cragg (1997), which serves as a rank test for lower-dimensional matrices. We evaluate the performance of this test as the matrix dimensions increase proportionally with the sample size, and identify its limitations when matrix dimensions significantly exceed the sample size. To address these challenges, we propose a new test statistic tailored for high-dimensional matrix rank testing. The oracle version of this statistic is analyzed to highlight its theoretical properties. Additionally, we develop a novel approach for constructing a sparse singular value decomposition (SVD) estimator for singular vectors, providing a comprehensive examination of its theoretical aspects. Using the sparse SVD estimator, we explore the properties of the sample version of our proposed statistic. The paper concludes with simulation studies and two case studies involving surveillance video data, demonstrating the practical utility of our proposed methods.

Multi-modal large language models (MLLMs) have demonstrated promising capabilities across various tasks by integrating textual and visual information to achieve visual understanding in complex scenarios. Despite the availability of several benchmarks aims to evaluating MLLMs in tasks from visual question answering to complex problem-solving, most focus predominantly on mathematics or general visual understanding tasks. This reveals a critical gap in current benchmarks, which often overlook the inclusion of other key scientific disciplines such as physics and chemistry. To address this gap, we meticulously construct a comprehensive benchmark, named VisScience, which is utilized to assess the multi-modal scientific reasoning across the three disciplines of mathematics, physics, and chemistry. This benchmark comprises 3,000 questions drawn from K12 education - spanning elementary school through high school - equally distributed across three disciplines, with 1,000 questions per discipline. The questions within VisScience span 21 distinct subjects and are categorized into five difficulty levels, offering a broad spectrum of topics within each discipline. With VisScience, we present a detailed evaluation of the performance of 25 representative MLLMs in scientific reasoning. Experimental results demonstrate that closed-source MLLMs generally outperform open-source models. The best performance observed include a 53.4\% accuracy in mathematics by Claude3.5-Sonnet, 38.2\% in physics by GPT-4o, and 47.0\% in chemistry by Gemini-1.5-Pro. These results underscore the strengths and limitations of MLLMs, suggesting areas for future improvement and highlighting the importance of developing models that can effectively handle the diverse demands of multi-modal scientific reasoning.

As machine learning becomes more widespread and is used in more critical applications, it's important to provide explanations for these models, to prevent unintended behavior. Unfortunately, many current interpretability methods struggle with faithfulness. Therefore, this Ph.D. thesis investigates the question "How to provide and ensure faithful explanations for complex general-purpose neural NLP models?" The main thesis is that we should develop new paradigms in interpretability. This is achieved by first developing solid faithfulness metrics and then applying the lessons learned from this investigation to develop new paradigms. The two new paradigms explored are faithfulness measurable models (FMMs) and self-explanations. The idea in self-explanations is to have large language models explain themselves, we identify that current models are not capable of doing this consistently. However, we suggest how this could be achieved. The idea of FMMs is to create models that are designed such that measuring faithfulness is cheap and precise. This makes it possible to optimize an explanation towards maximum faithfulness, which makes FMMs designed to be explained. We find that FMMs yield explanations that are near theoretical optimal in terms of faithfulness. Overall, from all investigations of faithfulness, results show that post-hoc and intrinsic explanations are by default model and task-dependent. However, this was not the case when using FMMs, even with the same post-hoc explanation methods. This shows, that even simple modifications to the model, such as randomly masking the training dataset, as was done in FMMs, can drastically change the situation and result in consistently faithful explanations. This answers the question of how to provide and ensure faithful explanations.

Domain-invariant representation learning is a powerful method for domain generalization. Previous approaches face challenges such as high computational demands, training instability, and limited effectiveness with high-dimensional data, potentially leading to the loss of valuable features. To address these issues, we hypothesize that an ideal generalized representation should exhibit similar pattern responses within the same channel across cross-domain images. Based on this hypothesis, we use deep features from the source domain as queries, and deep features from the generated domain as keys and values. Through a cross-channel attention mechanism, the original deep features are reconstructed into robust regularization representations, forming an explicit constraint that guides the model to learn domain-invariant representations. Additionally, style augmentation is another common method. However, existing methods typically generate new styles through convex combinations of source domains, which limits the diversity of training samples by confining the generated styles to the original distribution. To overcome this limitation, we propose an Adaptive Feature Blending (AFB) method that generates out-of-distribution samples while exploring the in-distribution space, significantly expanding the domain range. Extensive experimental results demonstrate that our proposed methods achieve superior performance on two standard domain generalization benchmarks for medical image segmentation.

How many times must a phenomenon occur before it graduates from a coincidence to a pattern? Usually, the answer depends on how unlikely, how far from the ordinary, and how (seemingly) inexplicable the phenomenon is. The more so, the lower the threshold. I was very surprised (and pleased) to read of this year's winners of the Nobel Prize in Physics: John Hopfield, a professor of Molecular Biology and earlier of Chemistry and Biology, together with Geoffrey Hinton, a professor of Computer Science. Their affiliations name three major scientific fields, none of them being Physics!

Adversarial Training (AT) is one of the most effective methods to enhance the robustness of DNNs. However, existing AT methods suffer from an inherent trade-off between adversarial robustness and clean accuracy, which seriously hinders their real-world deployment. While this problem has been widely studied within the current AT paradigm, existing AT methods still typically experience a reduction in clean accuracy by over 10% to date, without significant improvements in robustness compared with simple baselines like PGD-AT. This inherent trade-off raises a question: whether the current AT paradigm, which assumes to learn the corresponding benign and adversarial samples as the same class, inappropriately combines clean and robust objectives that may be essentially inconsistent. In this work, we surprisingly reveal that up to 40% of CIFAR-10 adversarial samples always fail to satisfy such an assumption across various AT methods and robust models, explicitly indicating the improvement room for the current AT paradigm. Accordingly, to relax the tension between clean and robust learning derived from this overstrict assumption, we propose a new AT paradigm by introducing an additional dummy class for each original class, aiming to accommodate the hard adversarial samples with shifted distribution after perturbation. The robustness w.r.t. these adversarial samples can be achieved by runtime recovery from the predicted dummy classes to their corresponding original ones, eliminating the compromise with clean learning. Building on this new paradigm, we propose a novel plug-and-play AT technology named DUmmy Classes-based Adversarial Training (DUCAT). Extensive experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet demonstrate that the DUCAT concurrently improves clean accuracy and adversarial robustness compared with state-of-the-art benchmarks, effectively breaking the existing inherent trade-off.

We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our main results are on the exponential rates of convergence of classification errors at equilibrium, which are analogous to the well-known Chernoff-Stein lemma and Chernoff information that describe the error exponents in the classical binary hypothesis testing problem, but with parameters derived from the adversarial model. The results are validated through numerical experiments.

The majority of our hypothesis tests are based on differentially private versions of the F -statistic for the general linear model framework, which are uniformly most powerful unbiased in the non-private setting. We also present another test for testing mixtures, based on the differentially private nonparametric tests of Couch, Kazan, Shi, Bray, and Groce (CCS 2019), which is especially suited for the small dataset regime. We show that the differentially private F -statistic converges to the asymptotic distribution of its non-private counterpart. Through a suite of Monte Carlo based experiments, we show that our tests achieve desired \textit{significance levels} and have a high \textit{power} that approaches the power of the non-private tests as we increase sample sizes or the privacy-loss parameter. We also show when our tests outperform existing methods in the literature.