Robust representation learning under imperfect supervision

Deep neural networks are evaluated under assumptions that fail in deployment: training labels may be wrong, test data may not follow the training distribution, a model may be found after training to contain corruption, and inputs with identical meaning may be processed inconsistently. This thesis studies robustness under such imperfect supervision. Its central claim is that these failures are best diagnosed inside the model, through the geometry of its learned representations, their spectral structure, and the weight-space directions it occupies, rather than through output accuracy alone. For image classification with wrong labels, we introduce Noisy Centroids Outlier Discounting (NCOD), a loss that weighs each sample by its similarity to the centre of its labelled class and learns a per-sample discount for likely-mislabelled examples, with no noise rate or clean data in its objective. For graph classification, we show that the Dirichlet energy, a measure of how sharply node features vary across a graph's edges, rises when a network memorises wrong graph labels; we prove a conditional lower bound explaining the rise and introduce three interventions that suppress it, including Graph Centroid Outlier Discounting (GCOD). A public competition we organised at the International Joint Conference on Neural Networks 2025 made this problem a controlled community benchmark. For vision-language models, we show that unchanged answers can conceal large representation drift, that model scale does not reduce this sensitivity, and that attention from text tokens to image tokens behaves as a frequency filter whose overlap with a perturbation's spectrum correlates with the drift. Corrective Unlearning in Task Space (CUTS) removes corruption discovered after training without the original training data, and Prioritized Invariant Subgraph Aggregation (PISA) improves generalisation to shifted graph distributions. Two co-authored works address audio deepfake detection. Across all settings, looking inside the model reveals failures that output accuracy alone misses.