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Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…

The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of…

The memorization effect of deep neural networks (DNNs) plays a pivotal role in recent label noise learning methods. To exploit this effect, the model prediction-based methods have been widely adopted, which aim to exploit the outputs of…

This paper develops a new mathematical framework for denoising in blind two-dimensional (2D) super-resolution upon using the atomic norm. The framework denoises a signal that consists of a weighted sum of an unknown number of time-delayed…

This review addresses the problem of learning abstract representations of the measurement data in the context of Deep Reinforcement Learning (DRL). While the data are often ambiguous, high-dimensional, and complex to interpret, many…

Falsely annotated samples, also known as noisy labels, can significantly harm the performance of deep learning models. Two main approaches for learning with noisy labels are global noise estimation and data filtering. Global noise…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Most deep metric learning (DML) methods employ a strategy that forces all positive samples to be close in the embedding space while keeping them away from negative ones. However, such a strategy ignores the internal relationships of…

Discovering compact governing equations from experimental observations is one of the defining objectives of quantitative science, yet practical discovery pipelines routinely fail when measurements are noisy, relevant state variables are…

As our ability to sense increases, we are experiencing a transition from data-poor problems, in which the central issue is a lack of relevant data, to data-rich problems, in which the central issue is to identify a few relevant features in…

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

Supervised learning results typically rely on assumptions of i.i.d. data. Unfortunately, those assumptions are commonly violated in practice. In this work, we tackle such problem by focusing on domain generalization: a formalization where…

In differential equation discovery algorithms, numerical differentiation is usually a fixed preliminary step. Current methods improve robustness with data subsampling and sparsity but often ignore the variability from the differentiation…

Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…

Real-world large-scale datasets are heteroskedastic and imbalanced -- labels have varying levels of uncertainty and label distributions are long-tailed. Heteroskedasticity and imbalance challenge deep learning algorithms due to the…

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically…

The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…

Large training datasets almost always contain examples with inaccurate or incorrect labels. Deep Neural Networks (DNNs) tend to overfit training label noise, resulting in poorer model performance in practice. To address this problem, we…

The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…

The ability of learning from noisy labels is very useful in many visual recognition tasks, as a vast amount of data with noisy labels are relatively easy to obtain. Traditionally, the label noises have been treated as statistical outliers,…