相关论文: Memory Clustering using Persistent Homology for Mu…

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…

Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…

A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a…

We analyse a general class of bilevel problems, in which the upper-level problem consists in the minimization of a smooth objective function and the lower-level problem is to find the fixed point of a smooth contraction map. This type of…

Active learning selects the most informative samples from the unlabelled dataset to annotate in the context of a limited annotation budget. While numerous methods have been proposed for subsequent sample selection based on an initialized…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…

Engineers learn from every design they create, building intuition that helps them quickly identify promising solutions for new problems. Topology optimization (TO) - a well-established computational method for designing structures with…

This work explores the use of topological tools for achieving effective non-prehensile manipulation in cluttered, constrained workspaces. In particular, it proposes the use of persistent homology as a guiding principle in identifying the…

In Continual learning (CL) balancing effective adaptation while combating catastrophic forgetting is a central challenge. Many of the recent best-performing methods utilize various forms of prior task data, e.g. a replay buffer, to tackle…

We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. For linear and nonlinear systems, a learning…

The problem of (point) forecasting $ \textit{univariate} $ time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time…

We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…

Training models continually to detect and classify objects, from new classes and new domains, remains an open problem. In this work, we conduct a thorough analysis of why and how object detection models forget catastrophically. We focus on…

Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as…

In many real-world deployments of machine learning systems, data arrive piecemeal. These learning scenarios may be passive, where data arrive incrementally due to structural properties of the problem (e.g., daily financial data) or active,…

In multi-goal reinforcement learning with a sparse binary reward, training agents is particularly challenging, due to a lack of successful experiences. To solve this problem, hindsight experience replay (HER) generates successful…

Controlling structural complexity, particularly the number of holes, remains a fundamental challenge in topology optimization, with significant implications for both theoretical analysis and manufacturability. Most existing approaches rely…

We consider the problem of learning multiple tasks in a continual learning setting in which data from different tasks is presented to the learner in a streaming fashion. A key challenge in this setting is the so-called "catastrophic…

Multimodal learning (MML) is significantly constrained by modality imbalance, leading to suboptimal performance in practice. While existing approaches primarily focus on balancing the learning of different modalities to address this issue,…