Reinforcement Learning Goes Topological: Learning of Cellular Complexes

Can reinforcement learning learn the shape of data? This project explores how RL can recover and exploit the topology of data when it is represented as a cellular complex. You will work with reinforcement learning algorithms, implement it, and run and analyze experiments. Different learning models, such as kernel methods, linear models, and neural networks, will be compared. We are looking for students with solid skills in mathematics (linear algebra, probability) and programming (Python, scientific computing) who are motivated to work on reproducible, research-oriented problems. Strong experimental and analytical contributions may lead to co-authorship on a publication with Simula researchers.

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This project aims to implement and experimentally evaluate a reinforcement learning algorithm that learns the topology of data when represented as a cellular complex. Cellular complexes generalize graphs and simplicial complexes, allowing the modeling of multi-way relationships between data points [1]. The algorithm will leverage the neighborhoods of the cellular complex to capture complex dependencies and recover the underlying topological structure. The student will build a modular experimental framework that works with different model classes, including kernel methods, linear models, and neural network-based approaches such as CC-VAR, CWN, and RFNL-TIRSO. The expected outcome is a prototype that reconstructs the topology from data, evaluates its quality using performance metrics, and compares results against baselines, including synthetic ablation studies. Students will focus on reproducible coding and experimental design, including coding experiments, analyzing results, and running model comparisons. Strong contributions will be recognized through co-authorship on a scientific publication with Simula researchers. For curious students, see reference [1] below for a primer on cellular complexes and their use in modeling multi-way relationships.

Goal

The goal of this thesis is to implement and experimentally evaluate a reinforcement learning algorithm that learns the topological structure of data represented by a cellular complex. The algorithm will exploit the neighborhood structure of the complex to capture multi-way relationships and support different model classes (kernel models, linear models, neural networks). The student's main focus will be building a working prototype, running experiments against baselines (including synthetic ablation), and evaluating the quality of the reconstructed topology using suitable performance metrics.

Learning outcome

Knowledge:

Understand cellular complex machine learning and how reinforcement learning can be used to learn topological structure.

Skills:

Implement and run experiments for a reinforcement learning algorithm on cellular complex data.
Compare different model classes (kernel models, linear models, neural networks) and evaluate performance using suitable metrics.
Apply reproducible research practices, including experiment design and ablation studies.

General competence:

Analyze and interpret experimental results in a research setting and report findings in a scientific format.

Qualifications

Linear algebra, probability, and signal processing background
Experience with Python and scientific computing
Familiarity with graph signal processing or graph machine learning methods
Familiarity with algebraic topology is a plus

Supervisors

Abdullah Canbolat
Rohan Money

References