相关论文: TopoMap: A Feature-based Semantic Discriminator of…

With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based…

Deep learning (DL) has achieved unprecedented success in a variety of tasks. However, DL systems are notoriously difficult to test and debug due to the lack of explainability of DL models and the huge test input space to cover. Generally…

This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation,…

Topological structures in image data, such as connected components and loops, play a crucial role in understanding image content (e.g., biomedical objects). % Despite remarkable successes of numerous image processing methods that rely on…

Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…

Deep Learning (DL) has been successfully applied to a wide range of application domains, including safety-critical ones. Several DL testing approaches have been recently proposed in the literature but none of them aims to assess how…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Deep Learning (DL) applications are being used to solve problems in critical domains (e.g., autonomous driving or medical diagnosis systems). Thus, developers need to debug their systems to ensure that the expected behavior is delivered.…

Evaluating the behavioral boundaries of deep learning (DL) systems is crucial for understanding their reliability across diverse, unseen inputs. Existing solutions fall short as they rely on untargeted random, model- or latent-based…

We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…

Deep neural networks (DNNs) offer a means of addressing the challenging task of clustering high-dimensional data. DNNs can extract useful features, and so produce a lower dimensional representation, which is more amenable to clustering…

Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…

Deep learning (DL) defines a new data-driven programming paradigm where the internal system logic is largely shaped by the training data. The standard way of evaluating DL models is to examine their performance on a test dataset. The…

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…

There has been a lot of interest in developing algorithms to extract clusters or communities from networks. This work proposes a method, based on blockmodelling, for leveraging communities and other topological features for use in a…

Deep neural networks often consist of a great number of trainable parameters for extracting powerful features from given datasets. On one hand, massive trainable parameters significantly enhance the performance of these deep networks. On…

The human visual system excels at detecting local blur of visual images, but the underlying mechanism is not well understood. Traditional views of blur such as reduction in energy at high frequencies and loss of phase coherence at localized…

Deep learning (DL) systems are increasingly deployed in safety- and security-critical domains including self-driving cars and malware detection, where the correctness and predictability of a system's behavior for corner case inputs are of…