On behalf of Prof. Omer Bobrowski and Prof Primoz Skraba.

An exciting PhD opportunity at the intersection of Machine Learning, Mathematics and model interpretability is offered at the Centre for Probability, Statistics and Data Science at Queen Mary University of London.

Project description This PhD position is part of the “Erlangen Programme for AI,” a prestigious multi-university initiative focused on developing a rigorous mathematical foundation for Artificial Intelligence. The project emphasizes the integration of concepts from topology, geometry, and probability, with the overarching goal of enhancing the interpretability, robustness, and generalization of AI models. Understanding Deep Neural Networks DNNs represent a cutting-edge approach in machine learning and AI, but there remains a significant gap in understanding the intrinsic mechanisms behind their powerful performance. This research aims to combine topological and geometric tools with probabilistic analysis to unveil hidden structures in neural networks. By investigating how these structures arise during training, how information flows through layers, and what vulnerabilities exist, we expect to gain insights that will drive future advancements in model design, optimization, and resilience. Understanding Large Language Models LLMs have shown to capture (encode) both the semantics and structure (grammar) of language within their learned parameters. However, the methods used to access this knowledge (decoding) remain basic, typically involving the representation of textual objects (e.g., words, sentences) as continuous vectors in Euclidean space. This project aims to leverage geometry and topology to explore the internal representations and latent spaces within the LLMs parameters that go beyond simple vectors analysis. We will develop advanced methods for decoding meaning and structure from LLMs, enabling richer and more diverse access to the linguistic knowledge they encode, and test it in a range of linguistic tasks (polysemy, cross-lingual transfer, among others). This approach holds the potential for breakthroughs in both AI theory and practical applications. Deadline is Wednesday, January 29, 2025

Further details can be found here: https://www.findaphd.com/phds/project/mathematical-foundations-for-ai/?p1777...