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

This paper explores the implicit bias of overparameterized neural networks of depth greater than two layers. Our framework considers a family of networks of varying depth that all have the same capacity but different implicitly defined…

While the Implicit Bias(or Implicit Regularization) of standard loss functions has been studied, the optimization geometry induced by discriminative metric-learning objectives remains largely unexplored.To the best of our knowledge, this…

We provide a function space characterization of the inductive bias resulting from minimizing the $\ell_2$ norm of the weights in multi-channel convolutional neural networks with linear activations and empirically test our resulting…

We prove a precise geometric description of all one layer ReLU networks $z(x;\theta)$ with a single linear unit and input/output dimensions equal to one that interpolate a given dataset $\mathcal D=\{(x_i,f(x_i))\}$ and, among all such…

We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix $X$ with gradient descent on a factorization of $X$. We conjecture and provide empirical and theoretical evidence that with small enough…

We study the generalization capability of nearly-interpolating linear regressors: $\boldsymbol{\beta}$'s whose training error $\tau$ is positive but small, i.e., below the noise floor. Under a random matrix theoretic assumption on the data…

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden…

Rates of convergence for empirical risk minimizers have been well studied in the literature. In this paper, we aim to provide a complementary set of results, in particular by showing that after normalization, the risk of the empirical…

Most modern learning problems are over-parameterized, where the number of learnable parameters is much greater than the number of training data points. In this over-parameterized regime, the training loss typically has infinitely many…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…

Modern machine learning models often employ a huge number of parameters and are typically optimized to have zero training loss; yet surprisingly, they possess near-optimal prediction performance, contradicting classical learning theory. We…

We propose and analyze a new family of algorithms for training neural networks with ReLU activations. Our algorithms are based on the technique of alternating minimization: estimating the activation patterns of each ReLU for all given…

Over-parameterized neural networks generalize well in practice without any explicit regularization. Although it has not been proven yet, empirical evidence suggests that implicit regularization plays a crucial role in deep learning and…

Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is insensitive to small perturbations in the training set such…

Neural network (NN) denoisers are an essential building block in many common tasks, ranging from image reconstruction to image generation. However, the success of these models is not well understood from a theoretical perspective. In this…

This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning where data from diverse distributions are available. Min-norm interpolators emerge naturally as implicit regularized limits of…

Understanding implicit bias of gradient descent for generalization capability of ReLU networks has been an important research topic in machine learning research. Unfortunately, even for a single ReLU neuron trained with the square loss, it…

The rule of thumb regarding the relationship between the bias-variance tradeoff and model size plays a key role in classical machine learning, but is now well-known to break down in the overparameterized setting as per the double descent…

Neural networks often operate in the overparameterized regime, in which there are far more parameters than training samples, allowing the training data to be fit perfectly. That is, training the network effectively learns an interpolating…

We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared…