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

arXiv:2607.29008 · stat.ML, cs.LG · Submitted 2026-07-31 · Read on arXiv

Tyler Ashoff, Jordan Rodu

stat.ML, cs.LG

Submitted: 2026-07-31

Comments: Code available at github.com/tylerashoff/persiscope (PyPI: persiscope)

Code: https://github.com/tylerashoff/persiscope

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Embeddings — 24× in this paper · explained in 2 episodes
• Accuracy — 9× in this paper · explained in 1 episode
• Wasserstein Distance — 7× in this paper · explained in 6 episodes
• Coherence — 6× in this paper · explained in 2 episodes
• AI Alignment — 5× in this paper · explained in 2 episodes
• Diffusion Model — 5× in this paper · explained in 10 episodes
• Diffusion Models — 5× in this paper · explained in 9 episodes
• Homogeneity — 4× in this paper · explained in 2 episodes
• Interpretability — 4× in this paper · explained in 15 episodes
• Adam — 3× in this paper · explained in 3 episodes
• Kernel Density Estimation — 3× in this paper
• Knowledge Graph — 3× in this paper · explained in 8 episodes
• Synthetic Data Generation — 3× in this paper · explained in 5 episodes
• Clustering — 2× in this paper · explained in 2 episodes
• Domain Shift — 2× in this paper · explained in 7 episodes
• Latent Space — 2× in this paper · explained in 7 episodes
• Persistent Homology — 2× in this paper · explained in 4 episodes
• Point Clouds — 2× in this paper · explained in 2 episodes
• Weight Decay — 2× in this paper · explained in 2 episodes
• Artificial Intelligence (AI) — 1× in this paper · explained in 2 episodes
• Bias-Variance Trade-off — 1× in this paper · explained in 4 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Decoder — 1× in this paper · explained in 2 episodes
• Evaluation Framework — 1× in this paper · explained in 3 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Formal Methods — 1× in this paper · explained in 3 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 3 episodes
• Knowledge graphs — 1× in this paper · explained in 2 episodes
• Mechanistic Interpretability — 1× in this paper · explained in 4 episodes
• Monotonicity — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 6 episodes
• Transformer — 1× in this paper · explained in 2 episodes

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