相关论文: Minimum norm interpolation by perceptra: Explicit …

We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings of $d = n^{\alpha}$, $\alpha\in(0,1)$, for the input…

We show implicit filter level sparsity manifests in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization or weight decay.…

It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness…

We study the dynamics and implicit bias of gradient flow (GF) on univariate ReLU neural networks with a single hidden layer in a binary classification setting. We show that when the labels are determined by the sign of a target network with…

We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as…

In this paper, a novel multi-head multi-layer perceptron (MLP) structure is presented for implicit neural representation (INR). Since conventional rectified linear unit (ReLU) networks are shown to exhibit spectral bias towards learning…

This paper provides elementary analyses of the regret and generalization of minimum-norm interpolating classifiers (MNIC). The MNIC is the function of smallest Reproducing Kernel Hilbert Space norm that perfectly interpolates a label…

While regression tasks aim at interpolating a relation on the entire input space, they often have to be solved with a limited amount of training data. Still, if the hypothesis functions can be sketched well with the data, one can hope for…

A common strategy to train deep neural networks (DNNs) is to use very large architectures and to train them until they (almost) achieve zero training error. Empirically observed good generalization performance on test data, even in the…

We study the effects of mild over-parameterization on the optimization landscape of a simple ReLU neural network of the form $\mathbf{x}\mapsto\sum_{i=1}^k\max\{0,\mathbf{w}_i^{\top}\mathbf{x}\}$, in a well-studied teacher-student setting…

We investigate the out-of-domain generalization of random feature (RF) models and Transformers. We first prove that in the `generalization on the unseen (GOTU)' setting, where training data is fully seen in some part of the domain but…

We consider bounds on the generalization performance of the least-norm linear regressor, in the over-parameterized regime where it can interpolate the data. We describe a sense in which any generalization bound of a type that is commonly…

We examine the implicit bias of mirror flow in univariate least squares error regression with wide and shallow neural networks. For a broad class of potential functions, we show that mirror flow exhibits lazy training and has the same…

The practice of deep learning has shown that neural networks generalize remarkably well even with an extreme number of learned parameters. This appears to contradict traditional statistical wisdom, in which a trade-off between model…

Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training of deep neural networks. Despite its empirical success, a full theoretical understanding of BN is yet to be developed. In this work, we analyze BN…

We study the structural and statistical properties of $\mathcal{R}$-norm minimizing interpolants of datasets labeled by specific target functions. The $\mathcal{R}$-norm is the basis of an inductive bias for two-layer neural networks,…

In this paper, we investigate interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that employing subspace conditions from the standard state space settings to…

We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function $\alpha$ before being multiplied by input vectors. We give an example of continuous, piecewise linear…

In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…

This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of…