相关论文: A Scale Invariant Flatness Measure for Deep Networ…

Enforcing orthonormal or isometric property for the weight matrices has been shown to enhance the training of deep neural networks by mitigating gradient exploding/vanishing and increasing the robustness of the learned networks. However,…

This paper proves an abstract theorem addressing in a unified manner two important problems in function approximation: avoiding curse of dimensionality and estimating the degree of approximation for out-of-sample extension in manifold…

The proper initialization of weights is crucial for the effective training and fast convergence of deep neural networks (DNNs). Prior work in this area has mostly focused on balancing the variance among weights per layer to maintain…

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero,…

We study the properties of alignment, a form of implicit regularization, in linear neural networks under gradient descent. We define alignment for fully connected networks with multidimensional outputs and show that it is a natural…

The stochastic gradient descent (SGD) method is most widely used for deep neural network (DNN) training. However, the method does not always converge to a flat minimum of the loss surface that can demonstrate high generalization capability.…

Recent experiments have shown that, often, when training a neural network with gradient descent (GD) with a step size $\eta$, the operator norm of the Hessian of the loss grows until it approximately reaches $2/\eta$, after which it…

Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…

Gradient descent on overparameterized neural networks typically operates at the Edge of Stability (EoS), where the largest Hessian eigenvalue hovers around a step-size-dependent threshold. We study how sparse connectivity changes…

Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of H\"{o}lder functions on low-dimensional manifolds using deep…

In this paper we approach the problem of unique and stable identifiability of generic deep artificial neural networks with pyramidal shape and smooth activation functions from a finite number of input-output samples. More specifically we…

Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to…

We study the gradient-based training of large-depth residual networks (ResNets) from standard random initializations. We show that infinite-depth ResNets behave as if they were infinitely wide, regardless of their actual width. More…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

Conventional scaling of neural networks typically involves designing a base network and growing different dimensions like width, depth, etc. of the same by some predefined scaling factors. We introduce an automated scaling approach…

In this paper, we prove that depth with nonlinearity creates no bad local minima in a type of arbitrarily deep ResNets with arbitrary nonlinear activation functions, in the sense that the values of all local minima are no worse than the…

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…

Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large…

Stochastic gradient descent (SGD) and adaptive gradient methods, such as Adam and RMSProp, have been widely used in training deep neural networks. We empirically show that while the difference between the standard generalization performance…

Deep neural networks (DNNs) are so over-parametrized that recent research has found them to already contain a subnetwork with high accuracy at their randomly initialized state. Finding these subnetworks is a viable alternative training…