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Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…
One of the central questions in the theory of deep learning is to understand how neural networks learn hierarchical features. The ability of deep networks to extract salient features is crucial to both their outstanding generalization…
With the advent of deep learning, the number of works proposing new methods or improving existent ones has grown exponentially in the last years. In this scenario, "very deep" models were emerging, once they were expected to extract more…
Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…
Modern neural network training relies on piece-wise (sub-)differentiable functions in order to use backpropagation to update model parameters. In this work, we introduce a novel method to allow simple non-differentiable functions at…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
We consider the use of deep learning for covariance estimation. We propose to globally learn a neural network that will then be applied locally at inference time. Leveraging recent advancements in self-supervised foundational models, we…
Despite the remarkable progress facilitated by learning-based stereo-matching algorithms, disparity estimation in low-texture, occluded, and bordered regions still remains a bottleneck that limits the performance. To tackle these…
In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model…
We propose a differential radial basis function (RBF) network termed RBF-DiffNet -- whose hidden layer blocks are partial differential equations (PDEs) linear in terms of the RBF -- to make the baseline RBF network robust to noise in…
Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…
In this paper we introduce a novel method of gradient normalization and decay with respect to depth. Our method leverages the simple concept of normalizing all gradients in a deep neural network, and then decaying said gradients with…
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…
During the last decades, many studies have been dedicated to improving the performance of neural networks, for example, the network architectures, initialization, and activation. However, investigating the importance and effects of…
Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…
By redefining the conventional notions of layers, we present an alternative view on finitely wide, fully trainable deep neural networks as stacked linear models in feature spaces, leading to a kernel machine interpretation. Based on this…
Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…
Semi-supervised segmentation methods have demonstrated promising results in natural scenarios, providing a solution to reduce dependency on manual annotation. However, these methods face significant challenges when directly applied to…
Monocular depth estimation has drawn widespread attention from the vision community due to its broad applications. In this paper, we propose a novel physics (geometry)-driven deep learning framework for monocular depth estimation by…
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…