Related papers: Gradient Descent Finds Over-Parameterized Neural N…
We study nonparametric regression using an over-parameterized two-layer neural networks trained with algorithmic guarantees in this paper. We consider the setting where the training features are drawn uniformly from the unit sphere in…
There has been a recent surge of interest in understanding the convergence of gradient descent (GD) and stochastic gradient descent (SGD) in overparameterized neural networks. Most previous works assume that the training data is provided a…
We explore the ability of overparameterized shallow neural networks to learn Lipschitz regression functions with and without label noise when trained by Gradient Descent (GD). To avoid the problem that in the presence of noisy labels,…
We analyze the generalization properties of two-layer neural networks in the neural tangent kernel (NTK) regime, trained with gradient descent (GD). For early stopped GD we derive fast rates of convergence that are known to be minimax…
This paper presents a comprehensive study on the convergence rates of the stochastic gradient descent (SGD) algorithm when applied to overparameterized two-layer neural networks. Our approach combines the Neural Tangent Kernel (NTK)…
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 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…
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…
Recently, significant progress has been made in understanding the generalization of neural networks (NNs) trained by gradient descent (GD) using the algorithmic stability approach. However, most of the existing research has focused on…
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…
It is well understood that neural networks with carefully hand-picked weights provide powerful function approximation and that they can be successfully trained in over-parametrized regimes. Since over-parametrization ensures zero training…
Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well…
We revisit on-average algorithmic stability of GD for training overparameterised shallow neural networks and prove new generalisation and excess risk bounds without the NTK or PL assumptions. In particular, we show oracle type bounds which…
We study the complexity of training neural network models with one hidden nonlinear activation layer and an output weighted sum layer. We analyze Gradient Descent applied to learning a bounded target function on $n$ real-valued inputs. We…
Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…
The paper contains approximation guarantees for neural networks that are trained with gradient flow, with error measured in the continuous $L_2(\mathbb{S}^{d-1})$-norm on the $d$-dimensional unit sphere and targets that are Sobolev smooth.…
We explore the ability of overparameterized shallow ReLU neural networks to learn Lipschitz, nondifferentiable, bounded functions with additive noise when trained by Gradient Descent (GD). To avoid the problem that in the presence of noise,…
Empirical studies show that gradient-based methods can learn deep neural networks (DNNs) with very good generalization performance in the over-parameterization regime, where DNNs can easily fit a random labeling of the training data. Very…
The fundamental learning theory behind neural networks remains largely open. What classes of functions can neural networks actually learn? Why doesn't the trained network overfit when it is overparameterized? In this work, we prove that…
We study the problem of learning a low-degree spherical polynomial of degree $k_0 = \Theta(1) \ge 1$ defined on the unit sphere in $\RR^d$ by training an over-parameterized two-layer neural network with augmented feature in this paper. Our…