PhD
Theoretical Foundations of Artificial Intelligence
Technical University of Munich
Faculty of Informatics – I7
Boltzmannstr. 3
85748 Garching bei München
Biosketch
Nil obtained her Bachelor’s degree in Electrical and Computer Engineering and her Master’s degree in Robotics, Cognition, and Intelligence (RCI), both from the Technical University of Munich (TUM). She was a part of the first cohort of relAI master’s students, and is now pursuing her PhD in the Theoretical Foundations of Artificial Intelligence group at TUM, under the supervision of Prof. Debarghya Ghoshdastidar. Her research centers on Statistical Learning Theory, Machine Learning for Graphs, and Semi-Supervised Learning.
relAI Research
Statistical Foundations of Semi-supervised Learning with Graph Neural Networks
My research focuses on statistical foundations for graph neural networks. In recent work, I derived the first exact generalisation error expressions for a broad class of linear GNNs, including convolutional and PageRank-based models, through a signal-processing perspective. This analysis shows how graph structure and feature alignment shape learning performance and reveals biases in common benchmark datasets. While exact risk analysis provides a precise characterisation, it cannot directly capture the role of non-linear attention mechanisms. To address this, I studied the limits of infinite-width graph transformers under the Neural Network Gaussian Process framework, deriving node- and edge-level kernels that explain how attention preserves community structure and discriminative representations in deep layers. Together, these works provide a unified theoretical framework for understanding generalisation and representation learning in graph-based models.
Publications
https://arxiv.org/abs/2509.10337 (will submit to Electronic Journal of Statistics)
https://arxiv.org/abs/2603.17569 (submitted to UAI 2026)