Related papers: Implicit Regularization in ReLU Networks with the …
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…
Deep (neural) networks have been applied productively in a wide range of supervised and unsupervised learning tasks. Unlike classical machine learning algorithms, deep networks typically operate in the \emph{overparameterized} regime, where…
A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target…
Using weight decay to penalize the L2 norms of weights in neural networks has been a standard training practice to regularize the complexity of networks. In this paper, we show that a family of regularizers, including weight decay, is…
Gradient-based deep-learning algorithms exhibit remarkable performance in practice, but it is not well-understood why they are able to generalize despite having more parameters than training examples. It is believed that implicit bias is a…
A neural network with one hidden layer or a two-layer network (regardless of the input layer) is the simplest feedforward neural network, whose mechanism may be the basis of more general network architectures. However, even to this type of…
Algorithmic approaches endow deep learning systems with implicit bias that helps them generalize even in over-parametrized settings. In this paper, we focus on understanding such a bias induced in learning through dropout, a popular…
Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut…
In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to $\mathit{local~strong~convexity}$ in the neighborhood of the ground-truth…
We study the implicit bias of ReLU neural networks trained by a variant of SGD where at each step, the label is changed with probability $p$ to a random label (label smoothing being a close variant of this procedure). Our experiments…
Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their…
Deep neural networks tend to underestimate uncertainty and produce overly confident predictions. Recently proposed solutions, such as MC Dropout and SDENet, require complex training and/or auxiliary out-of-distribution data. We propose a…
We establish the asymptotic implicit bias of gradient descent (GD) for generic non-homogeneous deep networks under exponential loss. Specifically, we characterize three key properties of GD iterates starting from a sufficiently small…
We study the implicit bias towards low-rank weight matrices when training neural networks (NN) with Weight Decay (WD). We prove that when a ReLU NN is sufficiently trained with Stochastic Gradient Descent (SGD) and WD, its weight matrix is…
We study the realization map of deep ReLU networks, focusing on when a function determines its parameters up to scaling and permutation. To analyze hidden redundancies beyond these standard symmetries, we introduce a framework based on…
We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…
Injectivity is the defining property of a mapping that ensures no information is lost and any input can be perfectly reconstructed from its output. By performing hard thresholding, the ReLU function naturally interferes with this property,…
Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically. In this paper, we explore theoretical analysis on training two-layer ReLU neural networks in a…
Large neural networks have proved remarkably effective in modern deep learning practice, even in the overparametrized regime where the number of active parameters is large relative to the sample size. This contradicts the classical…
Recently, a spate of papers have provided positive theoretical results for training over-parameterized neural networks (where the network size is larger than what is needed to achieve low error). The key insight is that with sufficient…