There has been a great empirical progress in robust training of neural networks against noisy labels.

Our derivation of the update for IL (Eq. 3) is based on an expansion of log We examine the consequences of this bias formula for our specific model. Note that the update term in Eq. (S1) is However, we will show in Appendix C that these updates may have high variance. 'reparameterization trick,' in which a change of variables allows the use of stochastic gradient descent It is worth noting that this'reparameterization' will work only for additive Gaussian noise. As already mentioned, WS can be viewed as a special case of IL. Since WS is a special case of IL, the bias properties of its individual samples are identical.

Proving algorithm-dependent generalization error bounds for gradient-type optimization methods has attracted significant attention recently in learning theory. However, most existing trajectory-based analyses require either restrictive assumptions on the learning rate (e.g., fast decreasing learning rate), or continuous injected

Recent findings demonstrate that modern neural networks trained by full-batch gradient descent typically enter a regime called Edge of Stability (EOS).

This paper investigates the asymmetric low-rank matrix completion problem, which can be formulated as an unconstrained non-convex optimization problem with a nonlinear least-squares objective function, and is solved via gradient descent methods. Previous gradient descent approaches typically incorporate regularization terms into the objective function to guarantee convergence. However, numerical experiments and theoretical analysis of the gradient flow both demonstrate that the elimination of regularization terms in gradient descent algorithms does not adversely affect convergence performance. By introducing the leave-one-out technique, we inductively prove that the vanilla gradient descent with spectral initialization achieves a linear convergence rate with high probability. Besides, we demonstrate that the balancing regularization term exhibits a small norm during iterations, which reveals the implicit regularization property of gradient descent. Empirical results show that our algorithm has a lower computational cost while maintaining comparable completion performance compared to other gradient descent algorithms.

This paper introduces Domain Generalization Sharpness-Aware Minimization Model-Agnostic Meta-Learning (DGS-MAML), a novel meta-learning algorithm designed to generalize across tasks with limited training data. DGS-MAML combines gradient matching with sharpness-aware minimization in a bi-level optimization framework to enhance model adaptability and robustness. We support our method with theoretical analysis using PAC-Bayes and convergence guarantees. Experimental results on benchmark datasets show that DGS-MAML outperforms existing approaches in terms of accuracy and generalization. The proposed method is particularly useful for scenarios requiring few-shot learning and quick adaptation, and the source code is publicly available at GitHub.

Low rank matrix completion plays a fundamental role in collaborative filtering applications, the key idea being that the variables lie in a smaller subspace than the ambient space. Often, additional information about the variables is known, and it is reasonable to assume that incorporating this information will lead to better predictions. We tackle the problem of matrix completion when pairwise relationships among variables are known, via a graph. We formulate and derive a highly efficient, conjugate gradient based alternating minimization scheme that solves optimizations with over 55 million observations up to 2 orders of magnitude faster than state-of-the-art (stochastic) gradient-descent based methods. On the theoretical front, we show that such methods generalize weighted nuclear norm formulations, and derive statistical consistency guarantees.

We study optimization algorithms based on variance reduction for stochastic gradientdescent (SGD). Remarkable recent progress has been made in this directionthrough development of algorithms like SAG, SVRG, SAGA. These algorithmshave been shown to outperform SGD, both theoretically and empirically. However,asynchronous versions of these algorithms--a crucial requirement for modernlarge-scale applications--have not been studied. We bridge this gap by presentinga unifying framework that captures many variance reduction techniques.Subsequently, we propose an asynchronous algorithm grounded in our framework,with fast convergence rates. An important consequence of our general approachis that it yields asynchronous versions of variance reduction algorithms such asSVRG, SAGA as a byproduct. Our method achieves near linear speedup in sparsesettings common to machine learning. We demonstrate the empirical performanceof our method through a concrete realization of asynchronous SVRG.

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic simulations. However, such stochastic gradient MCMC samplers have lagged behind their full-data counterparts in terms of the complexity of dynamics considered since proving convergence in the presence of the stochastic gradient noise is non-trivial. Even with simple dynamics, significant physical intuition is often required to modify the dynamical system to account for the stochastic gradient noise. In this paper, we provide a general recipe for constructing MCMC samplers--including stochastic gradient versions--based on continuous Markov processes specified via two matrices.