arXiv research

Over-parametrization speeds up learning a single neuron model.

The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.

We improve the over-parametrization size over two beautiful results [Li and Liang' 2018] and [Du, Zhai, Poczos and Singh' 2019] in deep learning theory.

Large over-parametrized models learned via stochastic gradient descent (SGD) methods have become a key element in modern machine learning. Although SGD methods are very effective in practice, most theoretical analyses of SGD suggest slower convergence than what is empirically observed. In our recent work [8] we analyze…

SMD outperforms SGD in over-parametrized linear models for certain data distributions.

Dr. of Crosswise proposes a new architecture to reduce over-parametrization in Neural Networks. It introduces an operand for rapid computation in the framework of Deep Learning that leverages learned weights. The formalism is described in detail providing both an accurate elucidation of the mechanics and the theoretica…

Paper shows faster convergence to local-minimizers in over-parametrized models under interpolation-like conditions.

The paper shows over-confidence in models isn't just due to over-parametrization.

Despite existing work on ensuring generalization of neural networks in terms of scale sensitive complexity measures, such as norms, margin and sharpness, these complexity measures do not offer an explanation of why neural networks generalize better with over-parametrization. In this work we suggest a novel complexity m…

A recent line of work has shown that an overparametrized neural network can perfectly fit the training data, an otherwise often intractable nonconvex optimization problem. For (fully-connected) shallow networks, in the best case scenario, the existing theory requires quadratic over-parametrization as a function of the …

New function class characterizes loss landscape of deep neural networks without over-parametrization.

We provide new theoretical insights on why over-parametrization is effective in learning neural networks. For a $k$ hidden node shallow network with quadratic activation and $n$ training data points, we show as long as $k \ge \sqrt{2n}$, over-parametrization enables local search algorithms to find a \emph{globally} op…

We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural network model and the residual network model. We proved that for all three models, the generalization error for the minimum-norm solution is compa…

Gradient descent learns over-param neural nets better than NTK.

New method reduces over-parametrization in neural networks, ensuring sparsity and finite network size.

Convolutional neural networks converge quickly with gradient descent.

Study shows neural network parameters converge to ridgelet spectrum.

We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. Under some general conditions, we show that this transition is sharp for the hinge loss. In the whole over-parametrized regime, poor minima of the loss are not encounte…

Improved complexity for machine learning optimization methods.

ADA augments data using AR replicas for robust regression.

Interpolation improves performance in nearest neighbor algorithms without over-parametrization.

Adaptive gradient methods like AdaGrad are widely used in optimizing neural networks. Yet, existing convergence guarantees for adaptive gradient methods require either convexity or smoothness, and, in the smooth setting, only guarantee convergence to a stationary point. We propose an adaptive gradient method and show t…

Noether's theorem clarifies how symmetries in neural networks influence learning.

Estimates how much samples inform neural network training and function.

Improved DNN calibration without sacrificing accuracy.

Gradient descent can find better tensor decompositions than lazy training in over-parameterized settings.

Gradient descent trains shallow neural networks to approximate functions in 1D.

New study shows how model complexity affects test risk, challenging classical theory.

Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the empirical performance of neural networks are observed to exceed their linearized …

Deep neural networks without regularization can achieve consistent estimates with good convergence rates.

Study linear transformations' effects on data augmentation for improved estimation.

Study on neural networks with quadratic activation functions, focusing on optimization and generalization.

We analyze ridge interpolators in correlated factor regression models using RDT.

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 technique to avoid overfitting in deep learning. For single hidden-layer linear neural …

Gradient descent in neural networks analyzed using RKBS for broader applicability.

Deep neural networks are often trained in the over-parametrized regime (i.e. with far more parameters than training examples), and understanding why the training converges to solutions that generalize remains an open problem. Several studies have highlighted the fact that the training procedure, i.e. mini-batch Stochas…

This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive over-parametrization with shrinkage to incorporate variable dependencies into the criterion. An ite…

New law establishes robustness for neural networks with bounded weights.

In this paper we aim to formally explain the phenomenon of fast convergence of SGD observed in modern machine learning. The key observation is that most modern learning architectures are over-parametrized and are trained to interpolate the data by driving the empirical loss (classification and regression) close to zero…

Traditionally in regression one minimizes the number of fitting parameters or uses smoothing/regularization to trade training (TE) and generalization error (GE). Driving TE to zero by increasing fitting degrees of freedom (dof) is expected to increase GE. However modern big-data approaches, including deep nets, seem to…

Lazy neural networks are vulnerable to adversarial attacks.

It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing works, we investigate the gradient descent method for training two-layer neural ne…

We consider complexity of Deep Neural Networks (DNNs) and their associated massive over-parameterization. Such over-parametrization may entail susceptibility to adversarial attacks, loss of interpretability and adverse Size, Weight and Power - Cost (SWaP-C) considerations. We ask if there are methodical ways (regulariz…

To better understand the interplay of censoring and sparsity we develop finite sample properties of nonparametric Cox proportional hazard's model. Due to high impact of sequencing data, carrying genetic information of each individual, we work with over-parametrized problem and propose general class of group penalties s…

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces biases that will lead to convergence to specific minimizers of the objective. Consequ…

New estimates for the population risk are established for two-layer neural networks. These estimates are nearly optimal in the sense that the error rates scale in the same way as the Monte Carlo error rates. They are equally effective in the over-parametrized regime when the network size is much larger than the size of…

We use smoothed analysis techniques to provide guarantees on the training loss of Multilayer Neural Networks (MNNs) at differentiable local minima. Specifically, we examine MNNs with piecewise linear activation functions, quadratic loss and a single output, under mild over-parametrization. We prove that for a MNN with …

Deep neural networks learn spatially heterogeneous patterns from input data.