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

arXiv: https://arxiv.org/abs/2607.29008 · HTML: https://mlsanity.com/paper/2607.29008/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 31 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Embedding Comparator: Visualizing Differences in Global Structure and Local Neighborhoods via Small Multiples](https://mlsanity.com/paper/1912.04853/) (2019)
- [Accurate Layerwise Interpretable Competence Estimation](https://mlsanity.com/paper/1910.11363/) (2019)
- [Statistical inference on black-box generative models in the data kernel perspective space](https://mlsanity.com/paper/2410.01106/) (2024)
- [Interpreting Embedding Spaces by Conceptualization](https://mlsanity.com/paper/2209.00445/) (2022)
- [Comparing multiple latent space embeddings using topological analysis](https://mlsanity.com/paper/2208.12435/) (2022)

## Built on by (most cited first, 1 of 1)

- [Semantic Alignment of AI Models: Concept Collapse, Checkpoint Dynamics, and Cross-Lingual Transfer](https://mlsanity.com/paper/2608.01585/) (2026)

## Abstract (arXiv)

Modern opaque AI models prize performance over interpretability, which makes testing difficult. However, formal statistical tests conducted on a model's embedding space can provide robust characterizations of semantic structure, concept separation, and knowledge graph alignment. Model developers would benefit from a model comparison technique that leverages human-curated knowledge structures to test alignment. The scale of the input space for even relatively simple tasks motivates the need for alignment checks that augment standard outcome reasoning. This work develops and demonstrates a topology-based multi-modal alignment test to make deployment, selection, and comparison of opaque models more interpretable. These methods also offer an intuitive connection to possibility theory and a unified decision theoretic framework from data to deployment.