Related papers: Learning Smooth Neural Functions via Lipschitz Reg…

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…

The last decade has witnessed the breakthrough of deep neural networks (DNNs) in many fields. With the increasing depth of DNNs, hundreds of millions of multiply-and-accumulate (MAC) operations need to be executed. To accelerate such…

Modern deep neural networks require a tremendous amount of data to train, often needing hundreds or thousands of labeled examples to learn an effective representation. For these networks to work with less data, more structure must be built…

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…

Large learning rates, when applied to gradient descent for nonconvex optimization, yield various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang et al., 2022), and catapult (Lewkowycz et al., 2020).…

Neural Radiance Fields (NeRF) has emerged as a compelling framework for scene representation and 3D recovery. To improve its performance on real-world data, depth regularizations have proven to be the most effective ones. However, depth…

Recent research on learnable neural representations has been widely adopted in the field of 3D scene reconstruction and neural rendering applications. However, traditional feature grid representations often suffer from substantial memory…

Deep implicit functions (DIFs), as a kind of 3D shape representation, are becoming more and more popular in the 3D vision community due to their compactness and strong representation power. However, unlike polygon mesh-based templates, it…

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…

Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework…

Recently, neural fields, also known as coordinate-based MLPs, have achieved impressive results in representing low-dimensional data. Unlike CNN, MLPs are globally connected and lack local control; adjusting a local region leads to global…

In this paper, we consider one dimensional (shallow) ReLU neural networks in which weights are chosen randomly and only the terminal layer is trained. First, we mathematically show that for such networks L2-regularized regression…

Neural Radiance Fields (NeRF) have significantly advanced the generation of highly realistic and expressive 3D scenes. However, the task of editing NeRF, particularly in terms of geometry modification, poses a significant challenge. This…

Neural implicit reconstruction via volume rendering has demonstrated its effectiveness in recovering dense 3D surfaces. However, it is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with…

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…

We propose a neural regularization method that refines the noisy 3D semantic field produced by lifting multi-view inconsistent 2D features, in order to obtain an accurate and robust 3D semantic Gaussian Splatting. The 2D features extracted…

Mathematically characterizing the implicit regularization induced by gradient-based optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is that a characterization based on minimization of norms may…

Tomographic imaging reveals internal structures of 3D objects and is crucial for medical diagnoses. Visualizing the morphology and appearance of non-planar sparse anatomical structures that extend over multiple 2D slices in tomographic…

We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight…

Neural implicit representations have shown substantial improvements in efficiently storing 3D data, when compared to conventional formats. However, the focus of existing work has mainly been on storage and subsequent reconstruction. In this…