相关论文: Guaranteed Recovery of One-Hidden-Layer Neural Net…

We investigate the convergence guarantee of two-layer neural network training with Gaussian randomly masked inputs. This scenario corresponds to Gaussian dropout at the input level, or noisy input training common in sensor networks,…

We analyze speed of convergence to global optimum for gradient descent training a deep linear neural network (parameterized as $x \mapsto W_N W_{N-1} \cdots W_1 x$) by minimizing the $\ell_2$ loss over whitened data. Convergence at a linear…

Deep neural networks have shown incredible performance for inference tasks in a variety of domains. Unfortunately, most current deep networks are enormous cloud-based structures that require significant storage space, which limits scaling…

In this paper, we propose a geometric framework to analyze the convergence properties of gradient descent trajectories in the context of linear neural networks. We translate a well-known empirical observation of linear neural nets into a…

Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training…

This paper considers the problem of label recovery in random graphs and matrices. Motivated by transitive behavior in real-world networks (i.e., ``the friend of my friend is my friend''), a recent line of work considers spatially-embedded…

How can local-search methods such as stochastic gradient descent (SGD) avoid bad local minima in training multi-layer neural networks? Why can they fit random labels even given non-convex and non-smooth architectures? Most existing theory…

We prove linear convergence of gradient descent to a global optimum for the training of deep residual networks with constant layer width and smooth activation function. We show that if the trained weights, as a function of the layer index,…

Deep learning models are often successfully trained using gradient descent, despite the worst case hardness of the underlying non-convex optimization problem. The key question is then under what conditions can one prove that optimization…

Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model…

Many modern neural network architectures are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Sufficiently overparameterized neural network architectures in principle have the…

We study norm-based uniform convergence bounds for neural networks, aiming at a tight understanding of how these are affected by the architecture and type of norm constraint, for the simple class of scalar-valued one-hidden-layer networks,…

We present a novel Convolutional Neural Network (CNN) based approach for one class classification. The idea is to use a zero centered Gaussian noise in the latent space as the pseudo-negative class and train the network using the…

In this paper, we study the sample complexity lower bounds for the exact recovery of parameters and for a positive excess risk of a feed-forward, fully-connected neural network for binary classification, using information-theoretic tools.…

We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) on linear neural network training. We propose a tensor formulation of neural networks that includes fully-connected, diagonal, and…

We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training $L$-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations…

Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC), a powerful empirical and theoretical framework which…

Graph neural networks (GNNs) have exhibited prominent performance in learning graph-structured data. Considering node classification task, based on the i.i.d assumption among node labels, the traditional supervised learning simply sums up…

Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…

We continue a long line of research aimed at proving convergence of depth 2 neural networks, trained via gradient descent, to a global minimum. Like in many previous works, our model has the following features: regression with quadratic…