Related papers: Understanding Gradient Regularization in Deep Lear…
Matrix factorization is a simple and natural test-bed to investigate the implicit regularization of gradient descent. Gunasekar et al. (2017) conjectured that Gradient Flow with infinitesimal initialization converges to the solution that…
Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to…
Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…
With the growing attention on learning-to-learn new tasks using only a few examples, meta-learning has been widely used in numerous problems such as few-shot classification, reinforcement learning, and domain generalization. However,…
Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a…
Sharpness-aware minimization (SAM) is known to improve the generalization performance of neural networks. However, it is not widely used in real-world applications yet due to its expensive model perturbation cost. A few variants of SAM have…
Reinforcement learning with verifiable rewards (RLVR) typically optimizes for outcome rewards without imposing constraints on intermediate reasoning. This leaves training susceptible to reward hacking, where models exploit loopholes (e.g.,…
Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine the role of GD in inducing implicit regularization for tensor…
We study the implicit regularization of gradient descent towards structured sparsity via a novel neural reparameterization, which we call a diagonally grouped linear neural network. We show the following intriguing property of our…
Despite overparameterization, deep networks trained via supervised learning are easy to optimize and exhibit excellent generalization. One hypothesis to explain this is that overparameterized deep networks enjoy the benefits of implicit…
This work considers the problem of decentralized online learning, where the goal is to track the optimum of the sum of time-varying functions, distributed across several nodes in a network. The local availability of the functions and their…
Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic…
Deep neural networks (DNN) are typically optimized using stochastic gradient descent (SGD). However, the estimation of the gradient using stochastic samples tends to be noisy and unreliable, resulting in large gradient variance and bad…
Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in…
We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…
Despite their overwhelming capacity to overfit, deep neural networks trained by specific optimization algorithms tend to generalize well to unseen data. Recently, researchers explained it by investigating the implicit regularization effect…
We present and analyze a novel regularized form of the gradient clipping algorithm, proving that it converges to global minima of the loss surface of deep neural networks under the squared loss, provided that the layers are of sufficient…
Many theoretical studies on neural networks attribute their excellent empirical performance to the implicit bias or regularization induced by first-order optimization algorithms when training networks under certain initialization…
Federated reinforcement learning (FRL) enables distributed learning of optimal policies while preserving local data privacy through gradient sharing.However, FRL faces the risk of data privacy leaks, where attackers exploit shared gradients…
We study the conjectured relationship between the implicit regularization in neural networks, trained with gradient-based methods, and rank minimization of their weight matrices. Previously, it was proved that for linear networks (of depth…