Study bounds graph neural networks' over-parameterized error.
problem Understanding graph neural networks' performance in over-parameterized regimes.
method Developed mean-field regime bounds for graph convolutional and message passing neural networks.
result Established upper bounds with a convergence rate of O(1/n) for generalization error. Local convergence theory for mildly over-parameterized neural nets.
problem Understanding why over-parameterization works in neural networks.
method Developed a local convergence theory for two-layer neural nets, showing neuron convergence under certain conditions.
result All student neurons converge to one of teacher neurons when the loss is below a threshold.
Recently, over-parameterized neural networks have been extensively analyzed in the literature. However, the previous studies cannot satisfactorily explain why fully trained neural networks are successful in practice. In this paper, we present a new theoretical framework for analyzing over-parameterized neural networks …
This paper proves SGD converges to global minimum for over-parameterized ReLU networks.
problem Theoretical understanding of implicit neural networks is limited.
method Gradient flow analysis of ReLU activated implicit neural networks.
result Randomly initialized gradient descent converges to global minimum at a linear rate for square loss function in over-parameterized ReLU networks.
New framework analyzes deep neural networks using feature probabilities.
problem Degenerate situation in over-parameterized DNNs.
method Mean-field framework representing DNNs by feature probabilities and functions.
result Global convergence proof for over-parameterized Res-Net training.
This work proposes a mathematical framework for loss landscapes and optimization in deep neural networks.
problem The effectiveness of gradient-based optimization in over-parameterized neural networks.
method A modern view and mathematical framework of loss landscapes and efficient optimization in over-parameterized machine learning models.
result Wide neural networks satisfy the PL∗ condition, explaining (S)GD convergence to a global minimum. This paper explores adaptive methods in over-parameterized linear regression.
problem Understanding why neural networks generalize well in over-parameterized settings.
method Characterizes two sub-classes of adaptive methods and their generalization performance.
result Adaptive methods in over-parameterized linear regression converge to the minimum norm solution.
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 prevents the network from overfitting. In this work, we introduce the gradient gap d…
Over-parameterization makes optimization easier for simple neural networks, even with minor extra neurons.
problem Understanding the impact of over-parameterization on optimization landscapes of shallow neural networks.
method Analyzing a simple ReLU neural network with Gaussian inputs, focusing on optimization properties and landscape changes.
result Over-parameterization makes the objective function one-point strongly convex in most directions, aiding optimization.
DebiNet uses over-parameterized neural networks to improve linear model performance and debiasing.
problem Improving linear model performance and debiasing in high-dimensional settings.
method Incorporates over-parameterized neural networks into semi-parametric models to estimate parameters consistently.
result DebiNet offers valid inference and accurate prediction by leveraging neural networks' universal approximation and linear model's interpretability.
This work improves the lottery ticket hypothesis by reducing over-parameterization requirement.
problem Approximating a neural network by pruning a randomly over-parameterized network.
method Connecting pruning ReLU networks to extsc{SubsetSum} problem, showing logarithmic over-parameterization sufficiency.
result Logarithmic over-parameterization is sufficient for approximating any target neural network.
Empirical studies show that gradient-based methods can learn deep neural networks (DNNs) with very good generalization performance in the over-parameterization regime, where DNNs can easily fit a random labeling of the training data. Very recently, a line of work explains in theory that with over-parameterization and p…
Over-parameterized CNNs show U-shaped test risk with depth increase.
problem Understanding the impact of depth on test risk in over-parameterized CNNs.
method Empirical image classification experiments and linear regression framework.
result Test risk is U-shaped with increasing depth in over-parameterized CNNs.
A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the condition on the width of the neural network to ensure the global convergence is very s…
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 error ε−1, deep neural networks learned by (stochastic) gradient descent enjoy …
In this paper, we analyze the effects of depth and width on the quality of local minima, without strong over-parameterization and simplification assumptions in the literature. Without any simplification assumption, for deep nonlinear neural networks with the squared loss, we theoretically show that the quality of local…
New NTK bounds show deep networks with minimum over-parameterization can still memorize and optimize.
problem Understanding memorization and optimization in sub-linear over-parameterized deep networks.
method Lower bound on NTK eigenvalues for deep networks with minimum over-parameterization.
result Deep networks with minimum over-parameterization can still be powerful memorizers and optimizers.
Over-parameterized models can memorize noisy labels and still generalize well, revealing a hidden structure.
problem Understanding how over-parameterized models can simultaneously memorize noisy labels and generalize well.
method Investigated through modular arithmetic tasks with label noise using two-layer neural networks.
result Over-parameterized models can achieve near-perfect test accuracy with 80% label noise by extracting an internal generalization structure.
This paper analyzes the landscape of supervised contrastive loss in over-parameterized networks.
problem Understanding the structure of solutions in over-parameterized networks under supervised contrastive loss.
method Analytical approach using unconstrained features model (UFM) to study the solutions of SC loss minimization.
result All local minima of SC loss are global minima in over-parameterized networks, and the minimizer is unique (up to rotation).
Single wide layer followed by a pyramidal structure ensures global convergence in deep networks.
problem Ensuring global convergence in deep neural networks with limited width constraints.
method Proves that a single wide layer followed by a pyramidal structure guarantees global convergence for over-parameterized networks.
result Single wide layer of width N suffices for global convergence in deep networks with constant-width remaining layers. A new algorithm for learning shallow neural networks with infinite width.
problem Learning shallow over-parameterized neural networks.
method Sinkhorn proximal algorithm approximating mean field learning dynamics.
result The algorithm performs gradient descent of the free energy associated with the risk functional.
Bayesian neural networks ignore data in infinite units limit.
problem Pathological behavior of posterior in over-parameterized networks.
method Mean-field variational inference in infinite hidden units limit.
result Posterior mean converges to zero, ignoring data.
Topological constraints improve neural network generalization.
problem Improving generalization in neural networks with limited data.
method Imposing topological constraints on internal representations of neural networks.
result Topological constraints lead to better mass concentration around training instances, improving generalization.
Gradient descent trains neural networks to match kernel regression's sharp generalization rate.
problem Training over-parameterized neural networks for nonparametric regression.
method Gradient descent with early stopping on over-parameterized two-layer neural networks.
result Trained neural networks achieve sharp generalization rate of O(εn2). New method reduces uncertainty in deep neural networks with minimal computation.
problem Uncertainty in over-parameterized neural networks hinders reliability and statistical guarantees.
method Procedural-noise-correcting (PNC) predictor and resampling methods.
result Asymptotically exact-coverage confidence intervals constructed with minimal computation.
Proposes a new approach to generate sparse models from deep networks.
problem Training small networks can get stuck in local optima; over-parameterized models are preferred.
method Differential inclusion paths to generate a family of models from simple to complex.
result Algorithm converges to a critical point of empirical risks from any initializations.
Recently, several studies have proven the global convergence and generalization abilities of the gradient descent method for two-layer ReLU networks. Most studies especially focused on the regression problems with the squared loss function, except for a few, and the importance of the positivity of the neural tangent ke…
Study explores grokking in neural networks, revealing transition from memorization to generalization.
problem Understanding the transition from memorization to generalization in over-parameterized neural networks.
method Extensive experiments and exploration of various viewpoints on grokking mechanism.
result Sharp transition from no generalization to perfect generalization observed during prolonged training.
Gradient descent can find better tensor decompositions than lazy training in over-parameterized settings.
problem Finding better tensor decompositions in over-parameterized settings.
method Gradient descent on over-parameterized tensor decomposition problems.
result Gradient descent can find an approximate tensor decomposition with rank m=O∗(r2.5llogd), while lazy training requires m=Ω(dl−1). A remarkable recent discovery in machine learning has been that deep neural networks can achieve impressive performance (in terms of both lower training error and higher generalization capacity) in the regime where they are massively over-parameterized. Consequently, over the past year, the community has devoted growin…
Improves understanding of neural network predictions using influence functions.
problem Challenges in understanding neural network predictions.
method Utilized NTK theory to calculate influence functions for over-parameterized neural networks.
result Proved that the approximation error of IF can be arbitrarily small in the over-parameterized regime.
Gradient Descent with Projection learns low-degree polynomials efficiently.
problem Learning low-degree spherical polynomials with neural networks.
method Over-parameterized two-layer neural network with Gradient Descent with Projection.
result Achieves nearly minimax optimal sample complexity and risk bound.
Deep neural networks can learn smooth functions without parameters.
problem Learning smooth functions from shallow ReLU neural networks.
method Using over-parameterized shallow ReLU neural networks with norm constraints.
result Least squares estimators based on shallow neural networks are minimax optimal.
Study shows how over-parameterized classifiers can still perform well on noisy data.
problem Understanding how maximum margin classifiers perform in over-parameterized settings with noisy data.
method Analyzes maximum margin classifiers on sub-Gaussian mixtures, providing risk bounds.
result Characterizes conditions for 'benign overfitting' in linear classification problems.
OPT framework improves neural network generalization by learning an orthogonal transformation.
problem Improving neural network generalization.
method Orthogonal over-parameterized training (OPT) framework that minimizes hyperspherical energy.
result OPT framework provably minimizes hyperspherical energy and improves empirical generalization.
Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural networks with one hidden layer. The theory of multi-layer networks remains largely …
FedAvg converges linearly to global minimum in federated learning with partial participation.
problem Challenges in federated learning with partial client participation.
method Federated averaging (FedAvg) method for over-parameterized neural networks.
result FedAvg converges to global minimum at a linear rate after t iterations.
Optimal rates for shallow ReLU networks in nonparametric regression.
problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLUk neural networks, using variation norms and deep learning theory. result Optimal approximation rates for shallow ReLU networks in nonparametric regression.
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 iterations, which can be neatly described in a matrix form. When the network is suffic…
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…
CNNs trained by gradient descent can learn intrinsic image rank robustly to background noises.
problem Understanding the intrinsic dimension of data in over-parameterized CNNs.
method Theoretical analysis and experiments on synthetic and real datasets.
result CNNs trained by gradient descent can learn the intrinsic dimension of clean images robustly to background noises.
Ensembles of neural networks improve training dynamics and performance.
problem Improving neural network performance through model size increase.
method Defining collegial ensembles (CE) as multiple independent models trained as a single model, and using theoretical results on NTK to optimize architecture search.
result CE dynamics simplify and scale favorably, resembling wide models, and can be efficiently implemented using group convolutions and block diagonal layers.
Paper analyzes how neural networks learn from a teacher in a specific setting.
problem Understanding how two-layer ReLU neural networks learn from a teacher in a regression model.
method Used gradient descent with specific regularization and over-parameterization, combined with measure representation and sparse estimation.
result Student network can identify teacher network parameters with high probability via gradient descent.
Improves adaptivity in sequence models by over-parameterizing.
problem Adaptivity and generalization in sequence models.
method Over-parameterized gradient descent using eigenfunctions.
result Over-parameterization enhances model adaptivity and generalization.
State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties. A recent line of work has shown that in a certain over-parameterized regime, the learning dynamics of gradient descent are governed …
Geometric Occam's Razor shapes deep learning solutions.
problem Understanding the regularization in over-parameterized neural networks.
method Analyzing the geometric model complexity and Dirichlet energy in neural networks.
result Over-parameterized neural networks are implicitly regularized by geometric model complexity.
We study the training and generalization of deep neural networks (DNNs) in the over-parameterized regime, where the network width (i.e., number of hidden nodes per layer) is much larger than the number of training data points. We show that, the expected 0-1 loss of a wide enough ReLU network trained with stochastic…
New insights into bias and variance in over-parameterized models.
problem Understanding bias and variance in over-parameterized models.
method Analytic expressions derived from statistical physics for two minimal models.
result Over-parameterized models can overfit even in noiseless conditions.