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This research explores the limitations of self-audit in LLMs due to the nature of analogical compression.

March 31, 2026Open Access

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

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This research explores the limitations of self-audit in LLMs due to the nature of analogical compression.
Utilized orthogonal probing to identify failures in a production system.
Compared failure detection rates of orthogonal probing and same-axis self-audit.
Applied persistent homology to analyze failure classes and identify significant topological features.
Structural theories like Tarski undefinability and Rice's theorem were examined.
Orthogonal probing discovered approximately 4-5 times more failures (80%) compared to self-audit (20%).
Identified 20 significant topological loops from persistent homology analysis.
Implemented 85 deterministic validators and 524 end-to-end tests confirming findings.

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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