相关论文: Global Convergence and Geometric Characterization …

We consider the dynamics of gradient descent (GD) in overparameterized single hidden layer neural networks with a squared loss function. Recently, it has been shown that, under some conditions, the parameter values obtained using GD achieve…

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…

We study the convergence properties of gradient descent for training deep linear neural networks, i.e., deep matrix factorizations, by extending a previous analysis for the related gradient flow. We show that under suitable conditions on…

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…

Graph Neural Networks (GNNs) are powerful tools for addressing learning problems on graph structures, with a wide range of applications in molecular biology and social networks. However, the theoretical foundations underlying their…

We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…

In this paper, we theoretically prove that gradient descent can find a global minimum of non-convex optimization of all layers for nonlinear deep neural networks of sizes commonly encountered in practice. The theory developed in this paper…

A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the…

We investigate the generalization and optimization properties of shallow neural-network classifiers trained by gradient descent in the interpolating regime. Specifically, in a realizable scenario where model weights can achieve arbitrarily…

A surprising phenomenon in the training of neural networks is the ability of gradient descent to find global minimizers of the training loss despite its non-convexity. Following earlier works, we investigate this behavior for wide shallow…

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…

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…

In this paper, we present some theoretical work to explain why simple gradient descent methods are so successful in solving non-convex optimization problems in learning large-scale neural networks (NN). After introducing a mathematical tool…

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,…

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…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing…

We introduce a novel framework for learning in neural networks by decomposing each neuron's weight vector into two distinct parts, $W_1$ and $W_2$, thereby modeling contrastive information directly at the neuron level. Traditional gradient…

It has been observed that design choices of neural networks are often crucial for their successful optimization. In this article, we therefore discuss the question if it is always possible to redesign a neural network so that it trains well…