Related papers: Towards Scalable Persistence-Based Topological Opt…

High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…

We propose a simple, scalable algorithm for using stochastic interpolants to sample from unnormalized densities and for fine-tuning generative models. The approach, Tilt Matching, arises from a dynamical equation relating the flow matching…

Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…

Many computer vision systems require low-cost segmentation algorithms based on deep learning, either because of the enormous size of input images or limited computational budget. Common solutions uniformly downsample the input images to…

Despite topology optimization producing high-performance structures, late-stage localized revisions remain brittle: direct density-space edits (e.g., warping pixels, inserting holes, swapping infill) can sever load paths and sharply degrade…

This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…

Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as locally Lipschitz functions that are smooth on some regular…

This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of…

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we…

In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…

The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…

Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…