Related papers: Latent geometry emerging from network-driven proce…

While large language models (LLMs) are trained purely on textual data, prior work has shown that their internal representations can exhibit rich geometric structure in embedding space. Building on this line of work, we investigate whether…

We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to…

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection based approaches (e.g. the…

A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

Much of contemporary systems biology owes its success to the abstraction of a network, the idea that diverse kinds of molecular, cellular, and organismal species and interactions can be modeled as relational nodes and edges in a graph of…

Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

The latent space of many generative models are rich in unexplored valleys and mountains. The majority of tools used for exploring them are so far limited to Graphical User Interfaces (GUIs). While specialized hardware can be used for this…

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…

Neural networks can accurately forecast complex dynamical systems, yet how they internally represent underlying latent geometry remains poorly understood. We study neural forecasters through the lens of representational alignment,…

Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure. Recently, a significant amount of progresses have been made toward this emerging network analysis paradigm. In…

In studying resilience in temporal human networks, relying solely on global network measures would be inadequate; latent sub-structural network mechanisms need to be examined to determine the extent of impact and recovery of these networks…

Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…

This article proposes a method for mathematical modeling of human movements related to patient exercise episodes performed during physical therapy sessions by using artificial neural networks. The generative adversarial network structure is…

Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information…

Generative Adversarial Networks (GANs) have emerged as a significant player in generative modeling by mapping lower-dimensional random noise to higher-dimensional spaces. These networks have been used to generate high-resolution images and…

Embedding dyadic data into a latent space has long been a popular approach to modeling networks of all kinds. While clustering has been done using this approach for static networks, this paper gives two methods of community detection within…