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Primary visual cortex (V1) provides crucial insights into the selectivity and emergence of specific output features such as orientation tuning. Tuning and selectivity of cortical neurons in mouse visual cortex is not equivocally resolved so…

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Capsule networks (CapsNets) were introduced to address convolutional neural networks limitations, learning object-centric representations that are more robust, pose-aware, and interpretable. They organize neurons into groups called…

Optical neural networks (ONNs) are emerging as a promising neuromorphic computing paradigm for object recognition, offering unprecedented advantages in light-speed computation, ultra-low power consumption, and inherent parallelism. However,…

Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…

Despite remarkable progress in computer vision, modern recognition systems remain fundamentally limited by their dependence on rich, redundant visual inputs. In contrast, humans can effortlessly understand sparse, minimal representations…

Due to their intrinsic capabilities on parallel signal processing, optical neural networks (ONNs) have attracted extensive interests recently as a potential alternative to electronic artificial neural networks (ANNs) with reduced power…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

Optical networks with multi-core fibers can replace several electronics networks with a single topology. Each electronic link is replaced by a single fiber, which can save space, weight, and cost, while having better segregation and EMI…

We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…

This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Many cortical areas increase in size considerably during postnatal development, progressively displacing neuronal cell bodies from each other. At present, little is known about how cortical growth affects the development of neuronal…

We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction.…

Deep neural networks have attained remarkable performance when applied to data that comes from the same distribution as that of the training set, but can significantly degrade otherwise. Therefore, detecting whether an example is…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

In recent years, by utilizing optimization techniques to formulate the propagation of deep model, a variety of so-called Optimization-Derived Learning (ODL) approaches have been proposed to address diverse learning and vision tasks.…

Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for…

In this paper, we study the influence of technology, traffic properties and price trends on optimized design of a reference IP-over-WDM network with rich underlying fiber topology. In each network node, we investigate the optimal degree of…

Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is some underlying geometric structure inherent to the data or…