Research

The AIDOS lab is dedicated to establishing foundational principles in machine learning. Leveraging our experience in computational geometry and topology, we focus on shaping well-principled methods to address holes in rapidly evolving AI landscape. We see ourselves as toolsmiths, crafting both observational and interventional frameworks using concepts such as the Euler characteristic, metric space magnitude, curvature, persistent homology, etc. Whether working with graphs, images, or natural language, our goal is to build tools that shed light on the most difficult questions, prioritizing simplicity, elegance, and interpretability over mere performance. We hope our work can give back to the community, empowering new research directions and application developments grounded in principled methods. Although our core research targets method development in machine learning, we are also passionate about impacting change with the help of our wonderful collaborators in biomedical, healthcare, and environmental applications.

Toolbox

Here is a collection of tools that have been developed by the AIDOS Lab, in order from most to least recent.

SCOTT

SCOTT is a Python package for computing curvature filtrations for graphs and graph distributions. Our method introduces a novel way to compare graph distributions by combining discrete curvature on graphs with persistent homology, providing descriptors of graph sets that are: robust, stable, expressive, and compatible with statistical testing.

magnipy

The magnitude of a metric space is a powerful invariant that provides a measure of the ’effective size’ of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We provide a toolbox for computing and comparing the magnitude of metric spaces.

PRESTO

The world of machine learning research is riddled with small decisions, from data collection, cleaning, into model selection and parameter tuning 🎶. Each choice leads to a potential universe where we can analyze and interpret results. PRESTO offers topological tools to efficiently measure the structural variation between representations that arise from different choices in a machine learning workflow.

DECT

The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. With the Differentiable Euler Characteristic Transform (DECT), we provide a fast and computationally efficient implementation of a differentiable, end-to-end-trainable ECT, which can be integrated into deep neural networks.

TARDIS

The manifold hypothesis is a staple of modern machine learning research. However, real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. We provide a topological framework that quantifies the local intrinsic dimension, and yields a Euclidicity score for assessing the ‘manifoldness’ of a point along multiple scales.

Orchid

Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalisation to the emerging domain of hypergraphs has remained largely unexplored. Our toolbox aims to fill this gap and presents a new framework for hypergraph curvature.

Publications

Here are all publications of lab members, sorted by year. Publications appear in the order in which they are accepted.