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Despite the increasing prevalence of deep neural networks, their applicability in resource-constrained devices is limited due to their computational load. While modern devices exhibit a high level of parallelism, real-time latency is still…

The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…

Understanding whether deep neural networks are effectively optimized remains challenging, as training occurs in highly nonconvex landscapes and standard metrics provide limited visibility into layer-wise learning quality. This challenge is…

Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…

Recently, deep convolutional neural network methods have achieved an excellent performance in image superresolution (SR), but they can not be easily applied to embedded devices due to large memory cost. To solve this problem, we propose a…

Geometric feature learning for 3D surfaces is critical for many applications in computer graphics and 3D vision. However, deep learning currently lags in hierarchical modeling of 3D surfaces due to the lack of required operations and/or…

When imaging through a semi-reflective medium such as glass, the reflection of another scene can often be found in the captured images. It degrades the quality of the images and affects their subsequent analyses. In this paper, a novel deep…

Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

In this paper, we propose a new optimization framework, the layer separation (LySep) model, to improve the deep learning-based methods in solving partial differential equations. Due to the highly non-convex nature of the loss function in…

This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

The p-adic cellular neural networks (CNNs) are mathematical generalizations of the neural networks introduced by Chua and Yang in the 80s. In this work we present two new types of CNNs that can perform computations with real data, and whose…

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be…

The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…

We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…

Since medical image data sets contain few samples and singular features, lesions are viewed as highly similar to other tissues. The traditional neural network has a limited ability to learn features. Even if a host of feature maps is…

We propose a novel formulation of deep networks that do not use dot-product neurons and rely on a hierarchy of voting tables instead, denoted as Convolutional Tables (CT), to enable accelerated CPU-based inference. Convolutional layers are…

Incorporating geometric transformations that reflect the relative position changes between an observer and an object into computer vision and deep learning models has attracted much attention in recent years. However, the existing proposals…

Deep convolutional classifiers linearly separate image classes and improve accuracy as depth increases. They progressively reduce the spatial dimension whereas the number of channels grows with depth. Spatial variability is therefore…