相关论文: On the Relationship Between Representation Geometr…

The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…

Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

Recent results in the literature suggest that the penultimate (second-to-last) layer representations of neural networks that are trained for classification exhibit a clustering property called neural collapse (NC). We study the implicit…

Data augmentation is widely recognized for improving generalization in deep networks, yet its impact on the geometry of learned representations remains poorly understood. In this work, we characterize how different data augmentation…

Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their…

Deep neural networks have been used in various fields, but their internal behavior is not well known. In this study, we discuss two counterintuitive behaviors of convolutional neural networks (CNNs). First, we evaluated the size of the…

Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

Neural Representations have recently been shown to effectively reconstruct a wide range of signals from 3D meshes and shapes to images and videos. We show that, when adapted correctly, neural representations can be used to directly…

It is widely believed that natural image data exhibits low-dimensional structure despite the high dimensionality of conventional pixel representations. This idea underlies a common intuition for the remarkable success of deep learning in…

Deep Neural Networks can generalize despite being significantly overparametrized. Recent research has tried to examine this phenomenon from various view points and to provide bounds on the generalization error or measures predictive of the…

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…

The internal representations learned by deep networks are often sensitive to architecture-specific choices, raising questions about the stability, alignment, and transferability of learned structure across models. In this paper, we…

Why do deep neural networks (DNNs) benefit from very high dimensional parameter spaces? Their huge parameter complexities vs stunning performance in practice is all the more intriguing and not explainable using the standard theory of model…

Deep neural networks have recently drawn considerable attention to build and evaluate artificial learning models for perceptual tasks. Here, we present a study on the performance of the deep learning models to deal with global optimization…

Current state-of-the-art deep neural networks for image classification are made up of 10 - 100 million learnable weights and are therefore inherently prone to overfitting. The complexity of the weight count can be seen as a function of the…