Related papers: ATOL: Measure Vectorization for Automatic Topologi…

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…

Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…

Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing…

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…

Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased…

Weakly supervised object localization (WSOL) aims at predicting object locations in an image using only image-level category labels. Common challenges that image classification models encounter when localizing objects are, (a) they tend to…

Active Learning (AL) is a learning task that requires learners interactively query the labels of the sampled unlabeled instances to minimize the training outputs with human supervisions. In theoretical study, learners approximate the…

Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…

Test-Time Optimization enables models to adapt to new data during inference by updating parameters on-the-fly. Recent advances in Vision-Language Models (VLMs) have explored learning prompts at test time to improve performance in downstream…

Out-of-distribution (OOD) generalization is a challenging machine learning problem yet highly desirable in many high-stake applications. Existing methods suffer from overly pessimistic modeling with low generalization confidence. As…

Active learning (AL) is a promising ML paradigm that has the potential to parse through large unlabeled data and help reduce annotation cost in domains where labeling data can be prohibitive. Recently proposed neural network based AL…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

Vision-language models (VLMs) such as CLIP exhibit strong Out-of-distribution (OOD) detection capabilities by aligning visual and textual representations. Recent CLIP-based test-time adaptation methods further improve detection performance…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

The reliability of segmentation models in the medical domain depends on the model's robustness to perturbations in the input space. Robustness is a particular challenge in medical imaging exhibiting various sources of image noise,…

Many real-world datasets are labeled with natural orders, i.e., ordinal labels. Ordinal regression is a method to predict ordinal labels that finds a wide range of applications in data-rich domains, such as natural, health and social…

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

Robustness in AI systems refers to their ability to maintain reliable and accurate performance under various conditions, including out-of-distribution (OOD) samples, adversarial attacks, and environmental changes. This is crucial in…