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Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…

Single-Hessian Gaussian wavepacket dynamics (GWD) significantly reduces the computational burden of Heller's local harmonic GWD, while maintaining comparable accuracy in approximating vibronic spectra. Here, we provide a new, symplectic…

Many representation systems on the sphere have been proposed in the past, such as spherical harmonics, wavelets, or curvelets. Each of these data representations is designed to extract a specific set of features, and choosing the best fixed…

The existence and uniqueness conditions are a prerequisite for reliable reconstruction of sparse signals from reduced sets of measurements within the Compressive Sensing (CS) paradigm. However, despite their underpinning role for practical…

Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…

Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…

Real-world knowledge is often organized as hierarchies such as product taxonomies, medical ontologies, and label trees, yet learning hierarchical representations is challenging due to asymmetric structure and noisy semantics. We introduce…

In this paper, we investigate a neural network-based learning approach towards solving an integer-constrained programming problem using very limited training. To be specific, we introduce a symmetric and decomposed neural network structure,…

While recent research in image understanding has often focused on recognizing more types of objects, understanding more about the objects is just as important. Recognizing object parts and attributes has been extensively studied before, yet…

We present a novel self-taught framework for unsupervised metric learning, which alternates between predicting class-equivalence relations between data through a moving average of an embedding model and learning the model with the predicted…

In this work, we focus on sampling and recovery of signals over simplicial complexes. In particular, we subsample a simplicial signal of a certain order and focus on recovering multi-order bandlimited simplicial signals of one order higher…

Intrinsic image decomposition is the classical task of mapping image to albedo. The WHDR dataset allows methods to be evaluated by comparing predictions to human judgements ("lighter", "same as", "darker"). The best modern intrinsic image…

We address the general task of learning with a set of candidate models that is too large to have a uniform convergence of empirical estimates to true losses. While the common approach to such challenges is SRM (or regularization) based…

We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial distribution shifts, where the labels can be arbitrary, and the goal is to find a ``best-fit'' function. More precisely, given…

Intrinsic image decomposition, which is an essential task in computer vision, aims to infer the reflectance and shading of the scene. It is challenging since it needs to separate one image into two components. To tackle this, conventional…

An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…

This paper offers a characterization of fundamental limits on the classification and reconstruction of high-dimensional signals from low-dimensional features, in the presence of side information. We consider a scenario where a decoder has…

This paper investigates the problem of reconstructing hyperspectral (HS) images from single RGB images captured by commercial cameras, \textbf{without} using paired HS and RGB images during training. To tackle this challenge, we propose a…

This work proposes a novel method for semi-supervised learning from partially labeled massive network-structured datasets, i.e., big data over networks. We model the underlying hypothesis, which relates data points to labels, as a graph…

This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field.…