Related papers: Adapted Topologies and Higher Rank Signatures

This paper addresses the distributed consensus design problem for linear multi-agent systems with directed communication graphs and external disturbances. Both the cases with strongly connected communication graphs and leader-follower…

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as…

We draw upon a previously largely untapped literature on human collective intelligence as a source of inspiration for improving deep learning. Implicit in many algorithms that attempt to solve Deep Reinforcement Learning (DRL) tasks is the…

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…

This paper considers online optimization for a system that performs a sequence of back-to-back tasks. Each task can be processed in one of multiple processing modes that affect the duration of the task, the reward earned, and an additional…

This short note investigates convergence of adaptive MCMC algorithms, i.e.\ algorithms which modify the Markov chain update probabilities on the fly. We focus on the Containment condition introduced in \cite{roberts2007coupling}. We show…

Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…

We introduce a novel topology, called Kernel Mean Embedding Topology, for stochastic kernels, in a weak and strong form. This topology, defined on the spaces of Bochner integrable functions from a signal space to a space of probability…

Adapted or causal transport theory aims to extend classical optimal transport from probability measures to stochastic processes. On a technical level, the novelty is to restrict to couplings which are bicausal, i.e. satisfy a property which…

Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…

We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…

The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…

An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…

This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain…