Stephan Chalup

Khalil Mathieu Hannouch, Stephan Chalup

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks (CNNs), impractical due to computational constraints. This study aims to estimate the topology type of 4D image-type data cubes that exhibit topological intricateness and size above our current processing capacity. The experiments using synthesised 4D data and a real-world 3D data set demonstrate that it is possible to circumvent computational complexity issues by applying downscaling methods to the data before training a CNN. This is achievable even when persistent homology software indicates that downscaling can significantly alter the homology of the training data. When provided with downscaled test data, the CNN can still estimate the Betti numbers of the original sample cubes with over 80\% accuracy, which outperforms the persistent homology approach, whose accuracy deteriorates under the same conditions. The accuracy of the CNNs can be further increased by moving from a mathematically-guided approach to a more vision-based approach where cavity types replace the Betti numbers as training targets.

Dylan Peek, Matthew P. Skerritt, Siddharth Pritam et al.

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural network-based estimators capable of reducing computational overhead and inference time. A key barrier to advancing these methods is the lack of labeled 3D data with class distributions and diversity tailored specifically for supervised learning in TDA tasks. To address this, we introduce a novel approach for systematically generating labeled 3D datasets using the Repulsive Surface algorithm, allowing control over topological invariants, such as hole count. The resulting dataset offers varied geometry with topological labeling, making it suitable for training and benchmarking neural network estimators. This paper uses a synthetic 3D dataset to train a genus estimator network, created using a 3D convolutional transformer architecture. An observed decrease in accuracy as deformations increase highlights the role of not just topological complexity, but also geometric complexity, when training generalized estimators. This dataset fills a gap in labeled 3D datasets and generation for training and evaluating models and techniques for TDA.

Dylan Peek, Matt P. Skerritt, Stephan Chalup

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the genus of these manifolds. This data used random homeomorphic deformations to provoke the learning of visual topological features. We demonstrate that deep learning models could extract these features and discuss some advantages over existing topological data analysis tools that are based on persistent homology. Semantic segmentation was used to provide additional geometric information in conjunction with topological labels. Common point cloud multi-layer perceptron and transformer networks were both used to compare the viability of these methods. The experimental results of this pilot study support the hypothesis that, with the aid of sophisticated synthetic data generation, neural networks can perform segmentation-based topological data analysis. While our study focused on simulated data, the accuracy achieved suggests a potential for future applications using real data.

Khalil Mathieu Hannouch, Stephan Chalup

Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological features in these data. These models also appear to tolerate the use of image preprocessing techniques where existing topological data analysis techniques such as persistent homology do not. This paper investigates how methods from algebraic topology, combined with image processing techniques such as morphology, can be used to generate topologically sophisticated and diverse-looking 2-, 3-, and 4D image-type data with topological labels in simulation. These approaches are illustrated in 2D and 3D with the aim of providing a roadmap towards achieving this in 4D.

Dylan Peek, Matthew P. Skerritt, Stephan Chalup

Persistent Homology (PH) and Artificial Neural Networks (ANNs) offer contrasting approaches to inferring topological structure from data. In this study, we examine the noise robustness of a supervised neural network trained to predict Betti numbers in 2D binary images. We compare an ANN approach against a PH pipeline based on cubical complexes and the Signed Euclidean Distance Transform (SEDT), which is a widely adopted strategy for noise-robust topological analysis. Using one synthetic and two real-world datasets, we show that ANNs can outperform this PH approach under noise, likely due to their capacity to learn contextual and geometric priors from training data. Though still emerging, the use of ANNs for topology estimation offers a compelling alternative to PH under structural noise.

Dylan Peek, Siddharth Pritam, Matthew P. Skerritt et al.

We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence between neurons, producing weighted, directed graphs that reflect dynamic interactions. These graphs are then analyzed using PH, enabling assessment of topological complexity across multiple structural scales and dimensions. We apply this TE+PH pipeline to synthetic spiking networks trained on logic gate tasks, image-classification networks exposed to structured and perturbed inputs, and mouse cortical recordings annotated with behavioral events. Across all settings, the resulting topological signatures reveal distinctions in task complexity, stimulus structure, and behavioral regime. Higher-dimensional features become more prominent in complex or noisy conditions, reflecting interaction patterns that extend beyond pairwise connectivity. Our findings offer a principled approach to mapping directed information flow onto global organizational patterns in both artificial and biological neural systems. The framework is generalizable and interpretable, making it well suited for neural systems with time-resolved and binary spiking data.

Ysobel Sims, Alexandre Mendes, Stephan Chalup

Zero-shot learning enables models to generalise to unseen classes by leveraging semantic information, bridging the gap between training and testing sets with non-overlapping classes. While much research has focused on zero-shot learning in computer vision, the application of these methods to environmental audio remains underexplored, with poor performance in existing studies. Generative methods, which have demonstrated success in computer vision, are notably absent from zero-shot environmental sound classification studies. To address this gap, this work investigates generative methods for zero-shot learning in environmental audio. Two successful generative models from computer vision are adapted: a cross-aligned and distribution-aligned variational autoencoder (CADA-VAE) and a leveraging invariant side generative adversarial network (LisGAN). Additionally, we introduced a novel diffusion model conditioned on class auxiliary data. Synthetic embeddings generated by the diffusion model are combined with seen class embeddings to train a classifier. Experiments are conducted on five environmental audio datasets, ESC-50, ARCA23K-FSD, FSC22, UrbanSound8k and TAU Urban Acoustics 2019, and one music classification dataset, GTZAN. Results show that the diffusion model outperforms all baseline methods on average across six audio datasets. This work establishes the diffusion model as a promising approach for zero-shot learning and introduces the first benchmark of generative methods for zero-shot environmental sound classification, providing a foundation for future research.