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We consider the problem of graph-matching on a network of 3D shapes with uncertainty quantification. We assume that the pairwise shape correspondences are efficiently represented as \emph{functional maps}, that match real-valued functions…
Semantic segmentation of high-resolution remote sensing images plays a crucial role in land-use monitoring and urban planning. Recent remarkable progress in deep learning-based methods makes it possible to generate satisfactory segmentation…
Explanations in Computer Vision are often desired, but most Deep Neural Networks can only provide saliency maps with questionable faithfulness. Self-Explaining Neural Networks (SENN) extract interpretable concepts with fidelity, diversity,…
Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…
A three-hidden-layer neural network with super approximation power is introduced. This network is built with the floor function ($\lfloor x\rfloor$), the exponential function ($2^x$), the step function ($1_{x\geq 0}$), or their compositions…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
Operator learning has emerged as a promising paradigm for approximating solution operators of partial differential equations (PDEs). However, conventional approaches typically rely on pointwise function discretizations, which often suffer…
Fast linear algebra in deep learning usually comes with a choice: fixed geometry and exact computation, as in the Fourier transform, or adaptive geometry paid for by dense parameters, random features, or low-rank surrogates. To move beyond…
Understanding and predicting the human visual attentional mechanism is an active area of research in the fields of neuroscience and computer vision. In this work, we propose DeepFix, a first-of-its-kind fully convolutional neural network…
Semantic segmentation for lightweight object parsing is a very challenging task, because both accuracy and efficiency (e.g., execution speed, memory footprint or computational complexity) should all be taken into account. However, most…
Convolutional neural networks (CNNs) excel in local feature extraction while Transformers are superior in processing global semantic information. By leveraging the strengths of both, hybrid Transformer-CNN networks have become the major…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
Random Ferns -- as a less known example of Ensemble Learning -- have been successfully applied in many Computer Vision applications ranging from keypoint matching to object detection. This paper extends the Random Fern framework to the…
On general regular simplicial partitions $\mathcal{T}$ of bounded polytopal domains $\Omega \subset \mathbb{R}^d$, $d\in\{2,3\}$, we construct \emph{exact neural network (NN) emulations} of all lowest order finite element spaces in the…
Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics,…
Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…
Despite recent advances in multi-scale deep representations, their limitations are attributed to expensive parameters and weak fusion modules. Hence, we propose an efficient approach to fuse multi-scale deep representations, called…
Weakly supervised semantic segmentation has been a subject of increased interest due to the scarcity of fully annotated images. We introduce a new approach for solving weakly supervised semantic segmentation with deep Convolutional Neural…
We propose a custom learning algorithm for shallow over-parameterized neural networks, i.e., networks with single hidden layer having infinite width. The infinite width of the hidden layer serves as an abstraction for the…
In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…