Related papers: Topological Signal Processing Over Cell MultiCompl…

Surgical Scene Graphs abstract the complexity of surgical operating rooms (OR) into a structure of entities and their relations, but existing paradigms suffer from strictly dyadic structural limitations. Frameworks that predominantly rely…

In order to cope with the rapidly increasing service demand in cellular networks, more cells are needed with better resource usage efficiency. This poses challenges for the network planning since service demand in practical networks is not…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

Spatial transcriptomics has the potential to transform our understanding of RNA expression in tissues. Classical array-based technologies produce multiple-cell-scale measurements requiring deconvolution to recover single cell information.…

Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the…

Molecular communication (MC) engineering is inspired by the use of chemical signals as information carriers in cell biology. The biological nature of chemical signaling makes MC a promising methodology for interdisciplinary applications…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…

This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…

The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…

Topological spaces, represented by simplicial complexes, capture richer relationships than graphs by modeling interactions not only between nodes but also among higher-order entities, such as edges or triangles. This motivates the…

Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures…

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…

Graph convolution networks (GCNs) have been enormously successful in learning representations over several graph-based machine learning tasks. Specific to learning rich node representations, most of the methods have solely relied on the…

In this article, we show how the recent statistical techniques developed in Topological Data Analysis for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological…

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by…

In-context learning (ICL) enables large language models (LLMs) to adapt to new tasks without weight updates by learning from demonstration sequences. While ICL shows strong empirical performance, its internal representational mechanisms are…

Cross-lingual transfer learning is an important property of multilingual large language models (LLMs). But how do LLMs represent relationships between languages? Every language model has an input layer that maps tokens to vectors. This…