Bachelor/Master Thesis: Applications of Modified Stiefel Manifold Restricted Neural Networks

Background

Imposing orthonormality constraints on parameter matrices within various computational models has demonstrated considerable benefits, contributing to enhanced stability and performance of these models. Despite the observed advantages, there remains substantial potential for further enhancing the effectiveness of these constraints. This could be achieved through refined modification and optimization of the constraints themselves, ensuring they are more aptly suited to the unique characteristics of different models and data types. Additionally, there is a compelling avenue for research in the application of orthonormality constraints across a broader spectrum of model types and data sets. Exploring this domain could unveil new insights into how these constraints impact model performance in diverse contexts, potentially leading to more robust and better performing computational models.

Tasks

1. Implement/Adapt a modified Stiefel manifold restricted neural network
2. Implement learning strategies
3. Evaluate for specific data sets

Skillset

• We will need to use advanced mathematical concepts to restrict neural networks to manifolds. If you try to stay away from math, these thesis topics are probably not for you. Some knowledge in differential geometry would be very good, but this can also be acquired during thesis.
• Strong programming skills (Python)
• At least basic knowledge in machine learning

I have several ideas related to this topic. If you are interested in this topic or just want to hear more details about this topic, please reach out to Alexander Studt (studt@teco.edu) and I can give a more detailed overview of the thesis topics.