Hector Zenil

Researcher in algorithmic information theory and its application to machine learning. The v2 byline of zenil-2026-self-improvement-limits (arXiv:2601.05280) lists him alone, affiliated with the Algorithmic Dynamics Lab at King’s College London (King’s Institute for AI) and Oxford Immune Algorithmics. The v5 record adds Abicumaran Uthamacumaran and Luan Ozelim as coauthors, so authorship gets quoted against the version. He formalises recursive self-training as a dynamical system and proves entropy decay and variance amplification as external grounding vanishes, under the scope condition that collapse requires the exogenous fraction to go to zero. The escape he proposes, program synthesis weighted by algorithmic probability, is his own research programme: the collapse paper’s bibliography leans on his earlier texts, the 2018 decomposition method, the 2020 iScience algorithmic-information calculus, and the 2023 Cambridge book on Algorithmic Information Dynamics.

No journal version is verified: the DOI 10.70777/si.v2i6.17159 that an earlier revision cited returns 404 at doi.org and Crossref. arXiv is the record. See log.

Secondary blogs converted his conditional theorem into “recursive self-improvement is mathematically impossible,” a framing his own abstract and conclusion foreclose. See agi-impossibility-claims and model-collapse.

Sources

• arXiv:2601.05280v2 HTML (byline, affiliations, full text), read 2026-10-04.
• arXiv:2601.05280 abs page (title, authors, v5), fetched directly 2026-09 by the orchestrator; see outputs/llm-degradation-toward-the-mean.provenance.md.
• Drift note 2026-10-04 (tools/citecheck.rs first run): the paper is at v6, retitled “Large Language Models are Shannon Lossy Compressors Not Solomonoff Induction Estimators: Self-improvement and Singularity Are Not Near Without Symbolic Model Synthesis”. The v2 record the theorem claims were read against is unchanged in substance so far; re-read before quoting theorem statements.