Our work derives ideas from learned optimization and adversarial machine learning, and makes an attempt to combine the best features of both aforementioned paradigms.

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional descriptions from high-dimensional data, facilitating comprehension and analysis. We address the challenges posed by real-world data that defy conventional assumptions, such as complex interactions within neural systems or high-dimensional dynamical systems. Leveraging insights from both theoretical physics and machine learning, this work unifies diverse reduction methods under a comprehensive framework, the Deep Variational Multivariate Information Bottleneck. This framework enables the design of tailored reduction algorithms based on specific research questions. We explore and assert the efficacy of simultaneous reduction approaches over their independent reduction counterparts, demonstrating their superiority in capturing covariation between multiple modalities, while requiring less data. We also introduced novel techniques, such as the Deep Variational Symmetric Information Bottleneck, for general nonlinear simultaneous reduction. We show that the same principle of simultaneous reduction is the key to efficient estimation of mutual information. We show that our new method is able to discover the coordinates of high-dimensional observations of dynamical systems. Through analytical investigations and empirical validations, we shed light on the intricacies of dimensionality reduction methods, paving the way for enhanced data analysis across various domains. We underscore the potential of these methodologies to extract meaningful insights from complex datasets, driving advancements in fundamental research and applied sciences. As these methods evolve, they promise to deepen our understanding of complex systems and inform more effective data analysis strategies.

Large language models (LLMs) increasingly serve as the backbone for classifying text associated with distinct domains and simultaneously several labels (classes). When encountering domain shifts, e.g., classifier of movie reviews from IMDb to Rotten Tomatoes, adapting such an LLM-based multi-label classifier is challenging due to incomplete label sets at the target domain and daunting training overhead. The existing domain adaptation methods address either image multi-label classifiers or text binary classifiers. In this paper, we design DALLMi, Domain Adaptation Large Language Model interpolator, a first-of-its-kind semi-supervised domain adaptation method for text data models based on LLMs, specifically BERT. The core of DALLMi is the novel variation loss and MixUp regularization, which jointly leverage the limited positively labeled and large quantity of unlabeled text and, importantly, their interpolation from the BERT word embeddings. DALLMi also introduces a label-balanced sampling strategy to overcome the imbalance between labeled and unlabeled data. We evaluate DALLMi against the partial-supervised and unsupervised approach on three datasets under different scenarios of label availability for the target domain. Our results show that DALLMi achieves higher mAP than unsupervised and partially-supervised approaches by 19.9% and 52.2%, respectively.

Recently, a team of researchers from Facebook AI and Tel Aviv University proposed an AI system that solves the multiple-choice intelligence test, Raven's Progressive Matrices. The proposed AI system is a neural network model that combines multiple advances in generative models, including employing multiple pathways through the same network. Raven's Progressive Matrices, also known as Raven's Matrices, are multiple-choice intelligence tests. The test is used to measure abstract reasoning and is regarded as a non-verbal estimate of fluid intelligence. In this test, a person tries to finish the missing location in a 3X3 grid of abstract images.

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially to discern ground-truth images from unregularized reconstructions. Convexity of the regularizer is attractive since (i) one can establish analytical convergence guarantees for the corresponding variational reconstruction problem and (ii) devise efficient and provable algorithms for reconstruction. In particular, we show that the optimal solution to the variational problem converges to the ground-truth if the penalty parameter decays sub-linearly with respect to the norm of the noise. Further, we prove the existence of a subgradient-based algorithm that leads to monotonically decreasing error in the parameter space with iterations. To demonstrate the performance of our approach for solving inverse problems, we consider the tasks of deblurring natural images and reconstructing images in computed tomography (CT), and show that the proposed convex regularizer is at least competitive with and sometimes superior to state-of-the-art data-driven techniques for inverse problems.