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At high redshift, due to both observational limitations and the variety of galaxy morphologies in the early universe, measuring galaxy structure can be challenging. Non-parametric measurements such as the CAS system have thus become an…

Today, the human brain can be studied as a whole. Electroencephalography, magnetoencephalography, or functional magnetic resonance imaging techniques provide functional connectivity patterns between different brain areas, and during…

The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and…

We develop a biophysical model of neuro-sensory integration in the model organism Caenorhabditis elegans. Building on recent experimental findings of the neuron conductances and their resolved connectome, we posit the first full dynamic…

A fundamental bottleneck in utilising complex machine learning systems for critical applications has been not knowing why they do and what they do, thus preventing the development of any crucial safety protocols. To date, no method exist…

The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data, especially in topological deep learning (TDL), which designs…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

The study of the sub-structure of complex networks is of major importance to relate topology and functionality. Many efforts have been devoted to the analysis of the modular structure of networks using the quality function known as…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Network alignment task, which aims to identify corresponding nodes in different networks, is of great significance for many subsequent applications. Without the need for labeled anchor links, unsupervised alignment methods have been…

Current theoretical and empirical research in neural networks suggests that complex datasets require large network architectures for thorough classification, yet the precise nature of this relationship remains unclear. This paper tackles…

We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…

To achieve high accuracy, convolutional neural networks (CNNs) are increasingly growing in complexity and diversity in layer types and topologies. This makes it very challenging to efficiently deploy such networks on custom processor…

Non-Hermitian topological phases can produce some remarkable properties, compared with their Hermitian counterpart, such as the breakdown of conventional bulk-boundary correspondence and the non-Hermitian topological edge mode. Here, we…

Capsule Networks (CapsNets), recently proposed by the Google Brain team, have superior learning capabilities in machine learning tasks, like image classification, compared to the traditional CNNs. However, CapsNets require extremely intense…

The empirical results suggest that the learnability of a neural network is directly related to its size. To mathematically prove this, we borrow a tool in topological algebra: Betti numbers to measure the topological geometric complexity of…

Cancers are the leading cause of death in many countries. Early diagnosis plays a crucial role in having proper treatment for this debilitating disease. The automated classification of the type of cancer is a challenging task since…

Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy…

Due to the nonlinearity of artificial neural networks, designing topologies for deep convolutional neural networks (CNN) is a challenging task and often only heuristic approach, such as trial and error, can be applied. An evolutionary…

Classifying large scale networks into several categories and distinguishing them according to their fine structures is of great importance with several applications in real life. However, most studies of complex networks focus on properties…