相关论文: Geometry-induced Regularization in Deep ReLU Neura…

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

This paper investigates the connection between neural networks and sufficient dimension reduction (SDR), demonstrating that neural networks inherently perform SDR in regression tasks under appropriate rank regularizations. Specifically, the…

The success of over-parameterized neural networks trained to near-zero training error has caused great interest in the phenomenon of benign overfitting, where estimators are statistically consistent even though they interpolate noisy…

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

We study the conjectured relationship between the implicit regularization in neural networks, trained with gradient-based methods, and rank minimization of their weight matrices. Previously, it was proved that for linear networks (of depth…

We systematize the approach to the investigation of deep neural network landscapes by basing it on the geometry of the space of implemented functions rather than the space of parameters. Grouping classifiers into equivalence classes, we…

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

We provide a function space characterization of the inductive bias resulting from minimizing the $\ell_2$ norm of the weights in multi-channel convolutional neural networks with linear activations and empirically test our resulting…

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic…

We take a geometrical viewpoint and present a unifying view on supervised deep learning with the Bregman divergence loss function - this entails frequent classification and prediction tasks. Motivated by simulations we suggest that there is…

Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and…

Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…

Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima. The implicit bias refers to the limiting global minimum that is attained by a common optimization…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

Several works have aimed to explain why overparameterized neural networks generalize well when trained by Stochastic Gradient Descent (SGD). The consensus explanation that has emerged credits the randomized nature of SGD for the bias of the…

Implicit Neural Representations (INRs) have emerged as a powerful tool for geometric representation, yet their suitability for physics-based simulation remains underexplored. While metrics like Hausdorff distance quantify surface…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…

We study the generalization of two-layer ReLU neural networks in a univariate nonparametric regression problem with noisy labels. This is a problem where kernels (\emph{e.g.} NTK) are provably sub-optimal and benign overfitting does not…

Recent findings suggest that consecutive layers of neural networks with the ReLU activation function \emph{fold} the input space during the learning process. While many works hint at this phenomenon, an approach to quantify the folding was…