Hyperbolic Neural Architectures for Hierarchical Language Modeling and Brain Network Representation

ABSTRACT

Most deep learning models are typically built on Euclidean representations, which are often poorly suited for capturing the hierarchical structure and relational organization that inherent in real-world data such as language, electronic health record, and brain connectivity. This talk presents a unified line of work introducing hyperbolic geometry as an inductive bias for structured representation learning in sequence modeling and neuroimaging data analytics.

I will first present an overview of hyperbolic large language models, where linguistic hierarchies and compositional dependencies are embedded in negatively curved space to improve representational efficiency and long-context reasoning. I then describe hierarchy-aware sequence modeling in hyperbolic geometry, integrating state-space architectures with geometric structure to produce scalable language embeddings. Finally, I discuss fully hyperbolic neural networks for brain network modeling, where functional brain connectivity is embedded in hyperbolic space to better capture hierarchical organization and inter-regional relationships in neuroimaging data for aging trajectory detection and subjective cognitive decline detection.

Together, these works highlight hyperbolic neural architectures as a geometric foundation for hierarchical reasoning in LLMs and relational data modeling. I conclude by outlining key challenges and emerging opportunities toward geometry-aware, interpretable, and long-context intelligent systems.

BIOGRAPHY

Dr. Mengjia Xu is an Assistant Professor in the Department of Data Science at the Ying Wu College of Computing, New Jersey Institute of Technology (NJIT). Her research focuses on machine learning, geometric deep learning, and multimodal large language models, with emphasis on graph representation learning and hierarchical reasoning for graph-structured, temporal, and language data. She develops principled learning frameworks for applications, including neurodegenerative disease and brain aging, electronic health records and genomics for cancer detection, and scientific discovery in solar physics. Prior to joining NJIT, she held a joint postdoctoral position at the McGovern Institute for Brain Research at MIT and the Division of Applied Mathematics at Brown University, mentored by Prof. Tomaso Poggio and Prof. George Em Karniadakis. She received her Ph.D. in Computer Science from Northeastern University (China), including  a two-year joint PhD training at Brown University.