Related papers: Latent Space Topology Evolution in Multilayer Perc…
A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (in our case, a simplicial complex). Modern packages for persistent homology often construct Vietoris--Rips or other…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Spatial-temporal data modeling aims to mine the underlying spatial relationships and temporal dependencies of objects in a system. However, most existing methods focus on the modeling of spatial-temporal data in a single mode, lacking the…
Topological neural networks have emerged as powerful successors of graph neural networks. However, they typically involve higher-order message passing, which incurs significant computational expense. We circumvent this issue with a novel…
Given the large volume of side information from different modalities, multimodal recommender systems have become increasingly vital, as they exploit richer semantic information beyond user-item interactions. Recent works highlight that…
Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional…
A multilayer perceptron (MLP) is typically made of multiple fully connected layers with nonlinear activation functions. There have been several approaches to make them better (e.g. faster convergence, better convergence limit, etc.). But…
Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing implicit time-dependent…
Recent empirical evidence has demonstrated that the training dynamics of large-scale deep neural networks occur within low-dimensional subspaces. While this has inspired new research into low-rank training, compression, and adaptation,…
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…
Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
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…
Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems' elements. These networks have attracted a lot of attention recently…
Previous work has demonstrated that MLPs within ReLU Transformers exhibit high levels of sparsity, with many of their activations equal to zero for any given token. We build on that work to more deeply explore how token-level sparsity…
In this paper, we explore the role of network topology on maintaining the extensive property of entropy. We study analytically and numerically how the topology contributes to maintaining extensivity of entropy in multiplex networks, i.e.…
Spatial awareness in mammals is based on an internalized representation of the environment, encoded by large networks of spiking neurons. While such representations can last for a long time, the underlying neuronal network is transient:…