Related papers: Graded damage solutions in one dimension
When using graphs and graph transformations to model systems, consistency is an important concern. While consistency has primarily been viewed as a binary property, i.e., a graph is consistent or inconsistent with respect to a set of…
In the development of first-order methods for smooth (resp., composite) convex optimization problems, where smooth functions with Lipschitz continuous gradients are minimized, the gradient (resp., gradient mapping) norm becomes a…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
One classical canon of statistics is that large models are prone to overfitting, and model selection procedures are necessary for high dimensional data. However, many overparameterized models, such as neural networks, perform very well in…
We study the problem of meta-learning through the lens of online convex optimization, developing a meta-algorithm bridging the gap between popular gradient-based meta-learning and classical regularization-based multi-task transfer methods.…
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
This paper develops a framework for creating damage accumulation models for engineered wood products by invoking the classical theory of non--dimensionalization. The result is a general class of such models. Both the US and Canadian damage…
Stochastic gradient descent is one of the most successful approaches for solving large-scale problems, especially in machine learning and statistics. At each iteration, it employs an unbiased estimator of the full gradient computed from one…
In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…
The quasistatic rate-independent damage combined with linearized plasticity with hardening at small strains is investigated. The fractional-step time discretisation is devised with the purpose to obtain a numerically efficient scheme…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
We present a general definition of damage spreading in a pair of models. Using this general framework, one can define damage spreading in an objective manner, that does not depend on the particular dynamic procedure that is being used. The…
Gradient-based adversarial attacks on deep neural networks pose a serious threat, since they can be deployed by adding imperceptible perturbations to the test data of any network, and the risk they introduce cannot be assessed through the…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
ReParameterization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. However, recent studies have revealed that, when applied to long-term reinforcement learning…
Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…