Related papers: Jeffrey's prior sampling of deep sigmoidal network…

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the…

Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…

In this paper, we present a local geometric analysis to interpret how deep feedforward neural networks extract low-dimensional features from high-dimensional data. Our study shows that, in a local geometric region, the optimal weight in one…

Even though Deep Neural Networks (DNNs) are widely celebrated for their practical performance, they possess many intriguing properties related to depth that are difficult to explain both theoretically and intuitively. Understanding how…

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

To increase the flexibility and scalability of deep neural networks for image reconstruction, a framework is proposed based on bandpass filtering. For many applications, sensing measurements are performed indirectly. For example, in…

We present the self-encoder, a neural network trained to guess the identity of each data sample. Despite its simplicity, it learns a very useful representation of data, in a self-supervised way. Specifically, the self-encoder learns to…

We study the multiple manifold problem, a binary classification task modeled on applications in machine vision, in which a deep fully-connected neural network is trained to separate two low-dimensional submanifolds of the unit sphere. We…

While both shape and texture are fundamental to visual recognition, research on deep neural networks (DNNs) has predominantly focused on the latter, leaving their geometric understanding poorly probed. Here, we show: first, that optimized…

We demonstrate the use of deep learning for fast spectral deconstruction of speckle patterns. The artificial neural network can be effectively trained using numerically constructed multispectral datasets taken from a measured spectral…

Why do deep neural networks (DNNs) benefit from very high dimensional parameter spaces? Their huge parameter complexities vs stunning performance in practice is all the more intriguing and not explainable using the standard theory of model…

Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in MMFs is a serious challenge. Several groups…

Previous literature suggests that perceptual similarity is an emergent property shared across deep visual representations. Experiments conducted on a dataset of human-judged image distortions have proven that deep features outperform…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…