相关论文: Neural network learns low-dimensional polynomials …

The information exponent ([BAGJ21]) and its extensions -- which are equivalent to the lowest degree in the Hermite expansion of the link function (after a potential label transform) for Gaussian single-index models -- have played an…

In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model…

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…

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…

We study the optimization and sample complexity of gradient-based training of a two-layer neural network with quadratic activation function in the high-dimensional regime, where the data is generated as $f_*(\boldsymbol{x}) \propto…

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar…

We study the complexity of online stochastic gradient descent (SGD) for learning a two-layer neural network with $P$ neurons on isotropic Gaussian data: $f_*(\boldsymbol{x}) = \sum_{p=1}^P a_p\cdot…

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…

We study the problem of learning a low-degree spherical polynomial of degree $\ell_0 = \Theta(1) \ge 1$ defined on the unit sphere in $\RR^d$ by training an over-parameterized two-layer neural network (NN) with channel attention in this…

Neural networks can identify low-dimensional relevant structures within high-dimensional noisy data, yet our mathematical understanding of how they do so remains scarce. Here, we investigate the training dynamics of two-layer shallow neural…

We focus on the task of learning a single index model $\sigma(w^\star \cdot x)$ with respect to the isotropic Gaussian distribution in $d$ dimensions. Prior work has shown that the sample complexity of learning $w^\star$ is governed by the…

According to a popular viewpoint, neural networks learn from data by first identifying low-dimensional representations, and subsequently fitting the best model in this space. Recent works provide a formalization of this phenomenon when…

We study the computational and sample complexity of learning a target function $f_*:\mathbb{R}^d\to\mathbb{R}$ with additive structure, that is, $f_*(x) = \frac{1}{\sqrt{M}}\sum_{m=1}^M f_m(\langle x, v_m\rangle)$, where…

Significant theoretical work has established that in specific regimes, neural networks trained by gradient descent behave like kernel methods. However, in practice, it is known that neural networks strongly outperform their associated…

We consider training over-parameterized two-layer neural networks with Rectified Linear Unit (ReLU) using gradient descent (GD) method. Inspired by a recent line of work, we study the evolutions of network prediction errors across GD…

We prove the first superpolynomial lower bounds for learning one-layer neural networks with respect to the Gaussian distribution using gradient descent. We show that any classifier trained using gradient descent with respect to square-loss…

While it is commonly observed in practice that pruning networks to a certain level of sparsity can improve the quality of the features, a theoretical explanation of this phenomenon remains elusive. In this work, we investigate this by…

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…

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

Understanding the dynamics of feature learning in neural networks (NNs) remains a significant challenge. The work of (Mousavi-Hosseini et al., 2023) analyzes a multiple index teacher-student setting and shows that a two-layer student…