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The analysis of nonlinear dynamics is an important issue in numerous fields of science. In this study, we propose a new method to analyze the time series data using persistent homology (PH). The key idea is the application of PH to the…

Data Analysis, Statistics and Probability · Physics 2023-04-04 Takashi Ichinomiya

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…

Machine Learning · Computer Science 2026-05-29 Junru Zhang , Lang Feng , Jinbo Wang , Xu Guo , Yucheng Wang , Han Yu , Min Wu , Yabo Dong , Duanqing Xu

Diffusion models, celebrated for their generative capabilities, have recently demonstrated surprising effectiveness in image classification tasks by using Bayes' theorem. Yet, current diffusion classifiers must evaluate every label…

Computer Vision and Pattern Recognition · Computer Science 2025-03-11 Arundhati S. Shanbhag , Brian B. Moser , Tobias C. Nauen , Stanislav Frolov , Federico Raue , Andreas Dengel

Few-shot learning and parameter-efficient fine-tuning (PEFT) are crucial to overcome the challenges of data scarcity and ever growing language model sizes. This applies in particular to specialized scientific domains, where researchers…

Computation and Language · Computer Science 2025-09-18 Jonas Rieger , Mattes Ruckdeschel , Gregor Wiedemann

In long-term multivariate time series forecasting, effectively capturing both periodic patterns and residual dynamics is essential. To address this within standard deep learning benchmark settings, we propose the Hierarchical Patching Mixer…

Machine Learning · Computer Science 2026-02-20 Jung Min Choi , Vijaya Krishna Yalavarthi , Lars Schmidt-Thieme

Feature extraction from persistence diagrams, as a tool to enrich machine learning techniques, has received increasing attention in recent years. In this paper we explore an adaptive methodology to localize features in persistent diagrams,…

Machine Learning · Computer Science 2019-10-16 Luis Polanco , Jose A. Perea

Multivariate time series have many applications, from healthcare and meteorology to life science. Although deep learning models have shown excellent predictive performance for time series, they have been criticised for being "black-boxes"…

Machine Learning · Computer Science 2024-05-06 Qiqi Su , Christos Kloukinas , Artur d'Avila Garcez

Deep homography estimation has broad applications in computer vision and robotics. Remarkable progresses have been achieved while the existing methods typically treat it as a direct regression or iterative refinement problem and often…

Computer Vision and Pattern Recognition · Computer Science 2026-01-27 Mengfan He , Liangzheng Sun , Chunyu Li , Ziyang Meng

The classification of time-series data is pivotal for streaming data and comes with many challenges. Although the amount of publicly available datasets increases rapidly, deep neural models are only exploited in a few areas. Traditional…

Machine Learning · Computer Science 2021-09-27 Dominique Mercier , Andreas Dengel , Sheraz Ahmed

Deep neural networks often rely on spurious features to make predictions, which makes them brittle under distribution shift and on samples where the spurious correlation does not hold (e.g., minority-group examples). Recent studies have…

Computer Vision and Pattern Recognition · Computer Science 2026-04-01 Aryan Yazdan Parast , Khawar Islam , Soyoun Won , Basim Azam , Naveed Akhtar

To analyze the topological properties of the given discrete data, one needs to consider a continuous transform called filtration. Persistent homology serves as a tool to track changes of homology in the filtration. The outcome of the…

Optimization and Control · Mathematics 2024-10-08 Keunsu Kim , Jae-Hun Jung

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known…

Algebraic Topology · Mathematics 2023-01-18 Renata Turkeš , Guido Montúfar , Nina Otter

In the rapidly advancing field of Large Language Models (LLMs), effectively leveraging existing datasets during fine-tuning to maximize the model's potential is of paramount importance. This paper introduces P3, an adaptive framework aimed…

Computation and Language · Computer Science 2024-10-21 Yingxuan Yang , Huayi Wang , Muning Wen , Xiaoyun Mo , Qiuying Peng , Jun Wang , Weinan Zhang

Periodicity is a fundamental characteristic of time series data and has long played a central role in forecasting. Recent deep learning methods strengthen the exploitation of periodicity by treating patches as basic tokens, thereby…

Machine Learning · Computer Science 2025-10-07 Yiming Niu , Jinliang Deng , Yongxin Tong

A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…

Algebraic Topology · Mathematics 2019-06-19 Heather A. Harrington , Nina Otter , Hal Schenck , Ulrike Tillmann

Survival analysis plays a vital role in making clinical decisions. However, the models currently in use are often difficult to interpret, which reduces their usefulness in clinical settings. Prototype learning presents a potential solution,…

Computer Vision and Pattern Recognition · Computer Science 2025-10-08 Shuo Jiang , Zhuwen Chen , Liaoman Xu , Yanming Zhu , Changmiao Wang , Jiong Zhang , Feiwei Qin , Yifei Chen , Zhu Zhu

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade…

Machine Learning · Computer Science 2026-05-11 Arjun Roy , Prajna G. Malettira , Manish Nagaraj , Kaushik Roy

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine…

Machine Learning · Statistics 2019-06-11 Bartosz Zieliński , Michał Lipiński , Mateusz Juda , Matthias Zeppelzauer , Paweł Dłotko

Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained…

Quantum Physics · Physics 2024-02-28 Bernardo Ameneyro , George Siopsis , Vasileios Maroulas

Neural Network pruning is an increasingly popular way for producing compact and efficient models, suitable for resource-limited environments, while preserving high performance. While the pruning can be performed using a multi-cycle training…

Machine Learning · Computer Science 2025-01-22 Athanasios Glentis Georgoulakis , George Retsinas , Petros Maragos