Persistent Convolution: A Topological Approach to Formal AI Alignment Testing 25 views

This work compares topological representations of AI models’ embeddings to formally test the alignment of their semantic spaces against interpretable baselines. Persistence landscapes and silhouettes offer a way to characterize global and local structure that focuses on connectivity and shape rather than scale. Since these representations are agnostic to the embedding dimensionality, different model architectures can be compared consistently. This also allows for intuitive low-dimensional relationships between concepts or formal knowledge structures like ontologies to be used as baselines for alignment tests. The results show that these methods can effectively be used for model selection and training by tracking semantic structure as it is induced, optimized, or degraded.

PHD (Doctor of Philosophy)

AI Alignment; Topological Data Analysis; Semantic Structure; Mechanistic Interpretability; Persistent Homology

English

2026-05-01