相关论文: Nonparametric Regression with Shallow Overparamete…

A recent line of work has shown that an overparametrized neural network can perfectly fit the training data, an otherwise often intractable nonconvex optimization problem. For (fully-connected) shallow networks, in the best case scenario,…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

Early stopping methods in deep learning face the challenge of balancing the volume of training and validation data, especially in the presence of label noise. Concretely, sparing more data for validation from training data would limit the…

While implicit regularization facilitates benign overfitting in low-noise regimes, recent theoretical work predicts a sharp phase transition to harmful overfitting as the noise-to-signal ratio increases. We experimentally isolate the…

A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated. General initialization schemes as well as general…

When random label noise is added to a training dataset, the prediction error of a neural network on a label-noise-free test dataset initially improves during early training but eventually deteriorates, following a U-shaped dependence on…

Deep Neural Networks (DNNs) have been shown to be susceptible to memorization or overfitting in the presence of noisily-labelled data. For the problem of robust learning under such noisy data, several algorithms have been proposed. A…

Modern neural networks have the capacity to overfit noisy labels frequently found in real-world datasets. Although great progress has been made, existing techniques are limited in providing theoretical guarantees for the performance of the…

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical…

We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with…

Collecting large-scale data with clean labels for supervised training of neural networks is practically challenging. Although noisy labels are usually cheap to acquire, existing methods suffer a lot from label noise. This paper targets at…

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…

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…

Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they…

Label Ranking (LR) corresponds to the problem of learning a hypothesis that maps features to rankings over a finite set of labels. We adopt a nonparametric regression approach to LR and obtain theoretical performance guarantees for this…

The behavior of the gradient descent (GD) algorithm is analyzed for a deep neural network model with skip-connections. It is proved that in the over-parametrized regime, for a suitable initialization, with high probability GD can find a…

Neural networks trained with stochastic gradient descent exhibit an inductive bias towards simpler decision boundaries, typically converging to a narrow family of functions, and often fail to capture more complex features. This phenomenon…

Noisy training set usually leads to the degradation of generalization and robustness of neural networks. In this paper, we propose using a theoretically guaranteed noisy label detection framework to detect and remove noisy data for Learning…

In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss…

We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a…