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Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…

Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the…

A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…

Convolutional neural networks (CNNs) can learn directly from raw data, resulting in exceptional performance across various research areas. However, factors present in non-controllable environments such as unlabeled datasets with varying…

The complexity of a learning task is increased by transformations in the input space that preserve class identity. Visual object recognition for example is affected by changes in viewpoint, scale, illumination or planar transformations.…

Neural networks have emerged as promising tools for solving partial differential equations (PDEs), particularly through the application of neural operators. Training neural operators typically requires a large amount of training data to…

Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability -- they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are…

Machine learning (ML) models are often sensitive to carefully crafted yet seemingly unnoticeable perturbations. Such adversarial examples are considered to be a property of ML models, often associated with their black-box operation and…

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based…

In the context of supervised statistical learning, it is typically assumed that the training set comes from the same distribution that draws the test samples. When this is not the case, the behavior of the learned model is unpredictable and…

Exploiting low-precision computations has become a standard strategy in deep learning to address the growing computational costs imposed by ever larger models and datasets. However, naively performing all computations in low precision can…

Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical…

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…

Dynamical systems, prevalent in various scientific and engineering domains, are susceptible to anomalies that can significantly impact their performance and reliability. This paper addresses the critical challenges of anomaly detection,…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…