What does this research mean for the field?

Orthogonal probing detects 4 to 5 times more failures than same-axis self-auditing in large-scale systems, demonstrating a structural limitation that prevents LLMs from effectively auditing their own compression manifolds from within. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research explores the limitations of self-auditing in large language models (LLMs) using analogical compression.

March 31, 2026Open Access

The Logos Made Code: Analogical Compression and the Limits of Self-Audit

Key Points

This research explores the limitations of self-auditing in large language models (LLMs) using analogical compression.
Utilized orthogonal probing to identify failures in a production system.
Compared failure discovery rates between orthogonal probing and same-axis self-audit.
Analyzed 58 documented failure classes using persistent homology to find topological structures.
Implemented a production reference with 85 deterministic validators and 524 end-to-end tests.
Orthogonal probing discovered approximately 80% of failures, while self-audit revealed only 20%.
Identified 20 significant topological loops in failure classes using persistent homology.
Demonstrated that LLMs struggle to audit their own compression mechanisms, indicating structural limits.

Abstract

Preprint. Orthogonal probing discovers roughly 4–5× more failures than same-axis self-audit (~80% vs ~20%) in a 350,000-line production system. We argue this asymmetry reflects a structural limit: LLMs trained via analogical compression cannot audit their own compression manifold from within. Formalized via Tarski undefinability and Rice's theorem. Persistent homology on 58 documented failure classes yields β₁ = 20 significant topological loops. Production reference implementation: 85 deterministic validators, 524 E2E tests, 8-axis probe framework.

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Martin Brodeur

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The Logos Made Code: Analogical Compression and the Limits of Self-Audit

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