Persistent Convolution: A Topological Framework for AI Alignment Testing and Semantic Space Characterization

Flexible multi-modal alignment tests between human-curated knowledge structures (formal ontologies or low-dimensional concept encodings) and model embeddings under a single rigorous statistical framework to track model manipulation even while test sets saturate.

Implementation: persiscope GitHub · PyPI

Open-source implementation of the Persistent Convolution framework: a model-agnostic topological comparison library covering graph construction, filtration, aggregated persistence representations, and formal similarity scoring, with visualization utilities.

Semantic Alignment of AI Models: Concept Collapse, Checkpoint Dynamics, and Cross-Lingual Transfer

Ashoff, Rodu · arXiv:2608.01585

Applies the Persistent Convolution framework to LLMs in three regimes: detection of concept collapse under increasingly aggressive LoRA adaptation, characterization of semantic structure across training checkpoints and layer depth, and two-sample testing of cross-lingual representational alignment on translation pairs.

Identifiable Persistence: Rotational Stability and Cylindrical Representations for Topological Data Analysis

Ashoff, Brown · in preparation

The theoretical foundation for the companion papers: a tightened Lipschitz stability bound for rotated H₀ persistence landscapes and a cylindrical representation recovering the point identity discarded by standard persistence diagrams.

Persistent Convolution: A Topological Approach to Formal AI Alignment Testing

Ph.D. dissertation · University of Virginia, 2026 · DOI: 10.18130/8k9j-9k42