Related papers: Deep Neural Networks with Symplectic Preservation …

Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…

Deep neural networks have been demonstrated impressive results in various cognitive tasks such as object detection and image classification. In order to execute large networks, Von Neumann computers store the large number of weight…

We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…

We propose a \emph{hybrid} real- and complex-valued \emph{neural network} (HNN) architecture, designed to combine the computational efficiency of real-valued processing with the ability to effectively handle complex-valued data. We…

Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…

Image segmentation with a volume constraint is an important prior for many real applications. In this work, we present a novel volume preserving image segmentation algorithm, which is based on the framework of entropic regularized optimal…

Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…

In this paper we address the importance and the impact of employing structure preserving neural networks as surrogate of the analytical physics-based models typically employed to describe the rheology of non-Newtonian fluids in Stokes…

Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…

Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous…

Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…

We investigate the potential of stochastic neural networks for learning effective waveform-based acoustic models. The waveform-based setting, inherent to fully end-to-end speech recognition systems, is motivated by several comparative…

In this paper, we present neural networks learning mechanical systems that are both symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid body). Mechanical systems have Hamiltonian evolution, which…

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend…

This is a master's thesis concerning the theoretical ideas of geometric deep learning. Geometric deep learning aims to provide a structured characterization of neural network architectures, specifically focused on the ideas of invariance…

Artificial Neural Network computation relies on intensive vector-matrix multiplications. Recently, the emerging nonvolatile memory (NVM) crossbar array showed a feasibility of implementing such operations with high energy efficiency, thus…

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems…

We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy,…