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Deep neural networks have become a pervasive tool in science and engineering. However, modern deep neural networks' growing energy requirements now increasingly limit their scaling and broader use. We propose a radical alternative for…

The primate visual cortex exhibits topographic organization, where functionally similar neurons are spatially clustered, a structure widely believed to enhance neural processing efficiency. While prior works have demonstrated that…

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…

Deep convolutional neural networks are biologically driven models that resemble the hierarchical structure of primate visual cortex and are the current best predictors of the neural responses measured along the ventral stream. However, the…

Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…

In this paper, we propose neural networks that tackle the problems of stability and field-of-view of a Convolutional Neural Network (CNN). As an alternative to increasing the network's depth or width to improve performance, we propose…

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…

It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with…

This article provides an expository account of training dynamics in the Deep Linear Network (DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results by several authors are unified into a thermodynamic…

With recent advances in sensing technologies, a myriad of spatio-temporal data has been generated and recorded in smart cities. Forecasting the evolution patterns of spatio-temporal data is an important yet demanding aspect of urban…

We propose an end-to-end trained neural networkarchitecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible…

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the…

Super-Resolution convolutional neural networks have recently demonstrated high-quality restoration for single images. However, existing algorithms often require very deep architectures and long training times. Furthermore, current…

In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data,…

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…

Latent dynamics models have emerged as powerful tools for modeling and interpreting neural population activity. Recently, there has been a focus on incorporating simultaneously measured behaviour into these models to further disentangle…

A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…

Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs)…