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A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We…
We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature…
Deep learning methods based synthetic aperture radar (SAR) image target recognition tasks have been widely studied currently. The existing deep methods are insufficient to perceive and mine the scattering information of SAR images,…
Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large…
Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained…
Deep learning is increasingly being applied in safety-critical domains. For these scenarios it is important to know the level of uncertainty in a model's prediction to ensure appropriate decisions are made by the system. Deep ensembles are…
Predictions for deep Virtual Compton Scattering are obtained in a two-component dipole model of diffraction. The model automatically includes hard and soft components and implicitly allows for ``hadronic'' contributions via large dipoles.…
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…
This paper develops an explainable deep learning model that estimates the remaining useful lives of rotating machinery. The model extracts high-level features from Fourier transform using an autoencoder. The features are used as input to a…
In this paper, a linear model based on multiple measurement vectors model is proposed to formulate the inverse scattering problem of highly conductive objects at one single frequency. Considering the induced currents which are mostly…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…
We consider in this work an inverse acoustic scattering problem when only phaseless data is available. The inverse problem is highly nonlinear and ill-posed due to the lack of the phase information. Solving inverse scattering problems with…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…
We present a model for dihadron fragmentation functions, describing the fragmentation of a quark into two unpolarized hadrons. We tune the parameters of our model to the output of the PYTHIA event generator for two-hadron semi-inclusive…
Acoustic scattering is strongly influenced by boundary geometry of objects over which sound scatters. The present work proposes a method to infer object geometry from scattering features by training convolutional neural networks. The…
Neural networks have been demonstrated to be able to accelerate the modeling and inverse design of optical and electromagnetic devices by serving as fast surrogates for electromagnetic solvers. Nevertheless, such neural networks can be…
Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…