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Recently, formal verification of deep neural networks (DNNs) has garnered considerable attention, and over-approximation based methods have become popular due to their effectiveness and efficiency. However, these strategies face challenges…
Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…
This paper presents a new method for reconstructing regions of interest (ROI) from a limited number of computed tomography (CT) measurements. Classical model-based iterative reconstruction methods lead to images with predictable features.…
Radial basis function (RBF) network is a third layered neural network that is widely used in function approximation and data classification. Here we propose a quantum model of the RBF network. Similar to the classical case, we still use the…
In recent years, the field of implicit neural representation has progressed significantly. Models such as neural radiance fields (NeRF), which uses relatively small neural networks, can represent high-quality scenes and achieve…
We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…
In the ever-evolving field of digital communication systems, complex-valued neural networks (CVNNs) have become a cornerstone, delivering exceptional performance in tasks like equalization, channel estimation, beamforming, and decoding.…
Deep neural networks (DNNs) suffer from the spectral bias, wherein DNNs typically exhibit a tendency to prioritize the learning of lower-frequency components of a function, struggling to capture its high-frequency features. This paper is to…
Neural scene representations, such as Neural Radiance Fields (NeRF), are based on training a multilayer perceptron (MLP) using a set of color images with known poses. An increasing number of devices now produce RGB-D(color + depth)…
Neural Radiance Fields (NeRFs) increase reconstruction detail for novel view synthesis and scene reconstruction, with applications ranging from large static scenes to dynamic human motion. However, the increased resolution and model-free…
The gradient information of multilayer perceptron with a linear neuron is modified with functional derivative for the global minimum search benchmarking problems. From this approach, we show that the landscape of the gradient derived from…
Neural Radiance Field (NeRF) and its variants have exhibited great success on representing 3D scenes and synthesizing photo-realistic novel views. However, they are generally based on the pinhole camera model and assume all-in-focus inputs.…
Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…
Neural radiance fields (NeRFs) enable novel view synthesis with unprecedented visual quality. However, to render photorealistic images, NeRFs require hundreds of deep multilayer perceptron (MLP) evaluations - for each pixel. This is…
Neural Radiance Fields (NeRFs) are a powerful representation for modeling a 3D scene as a continuous function. Though NeRF is able to render complex 3D scenes with view-dependent effects, few efforts have been devoted to exploring its…
We study ReLU deep neural networks (DNNs) by investigating their connections with the hierarchical basis method in finite element methods. First, we show that the approximation schemes of ReLU DNNs for $x^2$ and $xy$ are composition…
We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning…
Multi-view shape reconstruction has achieved impressive progresses thanks to the latest advances in neural implicit surface rendering. However, existing methods based on signed distance function (SDF) are limited to closed surfaces, failing…
Image resampling is a basic technique that is widely employed in daily applications, such as camera photo editing. Recent deep neural networks (DNNs) have made impressive progress in performance by introducing learned data priors. Still,…
While originally developed for novel view synthesis, Neural Radiance Fields (NeRFs) have recently emerged as an alternative to multi-view stereo (MVS). Triggered by a manifold of research activities, promising results have been gained…