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Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative…
The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…
In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…
The ability of deep neural networks to learn hierarchical features is widely regarded as a key mechanism underlying their success in high-dimensional learning. Existing theory partially supports this view by establishing approximation rates…
In the paper, we show that quantum logic of linear subspaces can be used for recognition of random signals by a Bayesian energy discriminant classifier. The energy distribution on linear subspaces is described by the correlation matrix of…
The embedding space of language models is widely believed to capture the semantic relationships; for instance, embeddings of digits often exhibit an ordered structure that corresponds to their natural sequence. However, the mechanisms…
We study nonparametric clustering of smooth random curves on the basis of the L2 gradient flow associated to a pseudo-density functional and we show that the clustering is well-defined both at the population and at the sample level. We…
We propose a new type of effective densities via the potential distribution theorem. These densities are for the sake of enabling the mapping of the free energy of a uniform fluid onto that of a nonuniform fluid. The potential distribution…
Recently deep learning and machine learning approaches have been widely employed for various applications in acoustics. Nonetheless, in the area of sound field processing and reconstruction classic methods based on the solutions of wave…
In this paper, we describe the Maximum Uniformity of Distribution (MUD) algorithm with the power-law nonlinearity. In this approach, we hypothesize that neural network training will become more stable if feature distribution is not too much…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…
Stochastic microstructure reconstruction has become an indispensable part of computational materials science, but ongoing developments are specific to particular material systems. In this paper, we address this generality problem by…
We propose and demonstrate a generative deep learning approach for the shape recognition of an arbitrary object from its acoustic scattering properties. The strategy exploits deep neural networks to learn the mapping between the latent…
Choosing a deep neural network architecture is a fundamental problem in applications that require balancing performance and parameter efficiency. Standard approaches rely on ad-hoc engineering or computationally expensive validation on a…
The rapid expansion in the size of new datasets has created a need for fast and efficient parameter-learning techniques. Compressive learning is a framework that enables efficient processing by using random, non-linear features to project…
We propose a novel deep learning framework for predicting permeability of porous media from their digital images. Unlike convolutional neural networks, instead of feeding the whole image volume as inputs to the network, we model the…
Mode shape information play the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to…
Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…
While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources…