Research
& Publications
Pioneering higher-order neural connectivity analysis through topological data analysis, information theory, and deep learning on simplicial complexes.
Research
Domains
Our research spans six interconnected domains, united by the common goal of understanding brain connectivity beyond pairwise interactions.
Topological Data Analysis
Persistent homology and Betti number analysis of brain connectivity graphs across the lifespan.
Information Theory
O-information, partial information decomposition, and synergy/redundancy quantification in neural assemblies.
Geometric Deep Learning
Simplicial neural networks, hypergraph transformers, and directed higher-order message passing architectures.
Hypergraph Signal Processing
Spectral analysis on hypergraphs for multi-region co-fluctuation detection and brain state decoding.
Clinical Neuroscience
Translation of higher-order connectivity biomarkers into diagnostic tools for neurological disorders.
High-Performance Computing
GPU-accelerated toolkits for population-level higher-order interaction analysis in whole-brain connectomes.
Recent Papers
Click any paper to explore interactive figures, methodology, and citation data.
Topological Turning Points in Lifespan Brain Connectivity Reveal Five Critical Transition Stages
S. Chun, W. Choi, T. Han, M. Koilybay et al.
Synergistic Neural Assemblies in Frontoparietal Networks Encode Higher-Order Cognitive States
W. Choi, S. Chun, M. Koilybay
Directed Semi-Simplicial Neural Networks for Brain State Classification from EEG Signals
T. Han, M. Koilybay, S. Chun
Hypergraph Signal Processing Reveals Multi-Region Co-Fluctuation Patterns in Resting-State fMRI
M. Koilybay, T. Han, W. Choi, S. Chun
O-Information Quantification at Scale: GPU-Accelerated Higher-Order Interaction Detection in Whole-Brain Connectomes
S. Chun, W. Choi, T. Han
Global Constraints Oriented Multi-Resolution Learning of Brain Structure from Raw Neural Recordings
W. Choi, M. Koilybay, S. Chun
Research Impact
Research Timeline
Topological phase transitions in brain connectivity
Published in Nature Neuroscience, identifying 5 critical lifespan stages via persistent homology.
DSSNN achieves SOTA brain state classification
97.3% accuracy on 11-class EEG classification at NeurIPS 2025.
HINEC-OI open-source toolkit released
400x GPU speedup for population-level O-information analysis, published in Nature Methods.
Hypergraph signal processing framework
14 novel hyperedge communities discovered with clinical relevance in Cell Reports.
Lab founded at Yonsei University
HINEC established with focus on higher-order neural connectivity and computational neuroscience.
Research Analytics
Interactive visualizations of our research output and impact. Hover over data points for details.
Technical Deep Dive
The mathematical frameworks and computational methods behind our research.
Persistent Homology via Vietoris-Rips Filtration
We construct Vietoris-Rips complexes from functional connectivity matrices by thresholding at increasing filtration values. Birth-death pairs in dimensions 0, 1, and 2 track the creation and destruction of connected components, loops, and voids in the brain's topological landscape. Vectorization via persistence images enables machine learning on topological features.
O-Information & Partial Information Decomposition
O-information quantifies whether a set of variables is dominated by synergy (positive) or redundancy (negative). We compute Ω(X₁,...,Xₖ) for all subsets up to k=6 using k-nearest-neighbor entropy estimation. Partial information decomposition further separates unique, redundant, and synergistic information contributions.
Hypergraph Spectral Analysis
We generalize graph Fourier transforms to hypergraphs by constructing tensor-based hypergraph Laplacians. Spectral decomposition reveals frequency modes of co-fluctuation across multiple brain regions simultaneously, enabling detection of multi-region oscillatory coupling invisible to pairwise coherence.
Directed Semi-Simplicial Neural Networks
DSSNNs extend message passing to directed higher-order structures. Each k-simplex (edge, triangle, tetrahedron) has a direction inherited from the underlying directed graph. Attention-weighted messages flow along boundary and co-boundary maps, capturing both topological and directional information.
Open Datasets
All datasets are freely available for non-commercial research.
HINEC-HCP-HOI
CC-BY 4.0Higher-order interaction features computed from Human Connectome Project resting-state data. Includes O-information, persistent homology, and hyperedge weights.
HINEC-EEG-11Class
MITPre-processed EEG epochs with DSSNN-compatible simplicial features for 11-class brain state classification benchmarking.
HINEC-Lifespan-TDA
CC-BY-NC 4.0Topological features (persistence diagrams, Betti curves) from diffusion tensor imaging connectomes across ages 6-90.
HINEC-Neuropixels-847
CC0Multi-scale simplicial features from simultaneous Neuropixels recordings in mouse visual cortex during visual stimulation.
Collaborations
MIT Brain & Cognitive Sciences
Cambridge, MA, USA
Max Planck Institute for Brain Research
Frankfurt, Germany
Allen Institute for Brain Science
Seattle, WA
UCL Gatsby Computational Neuroscience
London, UK
Stanford Wu Tsai Neurosciences
Stanford, CA
RIKEN Center for Brain Science
Wako, Japan
Janelia Research Campus (HHMI)
Ashburn, VA
EPFL Blue Brain Project
Lausanne, Switzerland