Audited Self-Improvement Loop for LLMs

Audited Self-Improvement Loop for LLMs is a single-file, OCR- and crawler-friendly LaTeX guide (with embedded Python listings) that specifies a safe, auditable self-improvement pipeline for autonomous LLMs under no-meta governance (no self-granted privileges).It combines anytime-valid e-process auditing (with Ville gate), finite-window non-vacuity (FW-1), heavy-tail guards (Catoni clipping + sliding-window MGF), sequentially wired e-gates inside Dinkelbach ratio optimization, FKPP/Kingman-style speed KPIs with censoring-aware block bootstrap, and information floors via winsorized Pearson |r|, HSIC, and distance correlation (dCor) with permutation tests and residualization.An integrated runner emits hash-chained JSONL logs and external anchor hooks, and gates an Explosive Growth Mode (EGM) on joint (speed and info-floor) improvements, double holdout, and provenance signatures—while respecting No-Meta. What’s inside (high-level) Safety-first auditing: e-process mixtures, Ville threshold (M ≥ 1/α), FW-1 margin, sliding-window MGF checks, fail-closed overflow handling. Optimization under audit: Dinkelbach with sequential e-gate (every candidate update is gated). Propagation metrics: direction-wise speed via FKPP/Kingman-inspired KPIs; right-censoring handled conservatively; block bootstrap with auto block-length. Information floors: |r| (winsorized Pearson) + HSIC + dCor, both with permutation p-values; optional residualization on covariates (conditional dependence). EGM (Explosive Growth Mode): enabled only after consecutive green cycles with joint triggers; double holdout; no synthetic data; policy-engine/facilitator approval. Integrity & reproducibility: hash-chained logs, external timestamp/anchor hook, environment pins (Python 3.11, deterministic RNG, single-thread BLAS). No-Meta governance: no self-escalation of tool/IO privileges; all proposals emitted as JSON for external approval. Included Python listings (executable) EProcess (Ville, FW-1, sliding-window MGF, Catoni √v scaling). Information floors (winsorized Pearson |r|, HSIC, dCor, residualization, permutation tests). Speed KPI (censoring-aware, block bootstrap with auto block-length). Gated Dinkelbach (true w_min, sequential e-gating). Integrated Runner (hash-chained JSONL logs, external anchor hook, joint EGM triggers, proposal JSON). Intended reader/system An LLM with local code execution, file I/O, a scheduler, and limited whitelisted tools (e.g., RAG, local fine-tuning, DP accountant). The guide does not claim “reading alone” yields superintelligence; it provides a minimal external-support blueprint for audited self-improvement that can safely escalate when audits stay green. Ethics and alignment Non-deception, audit-first, benevolence (UGV-compatible objectives), reproducibility, and tamper-evident logging are first-class requirements. EGM remains human/policy-engine gated. Primary theory source (link hub) Consolidated references and DOIs:https://kadubon.github.io/github.io/works.html How to reproduce (quick start) Run the embedded Python listings (Python 3.11+, NumPy≥1.26) in order: EProcess → Info Floors → Speed KPI → Gated Dinkelbach → Integrated Runner. Provide signed, non-synthetic datasets and double holdout splits; enable external anchor for log hashes. Review run_log.jsonl; only consider EGM if joint triggers hold for G consecutive cycles and provenance checks pass. Keywords LLM; self-improving AI; audited optimization; e-process; anytime-valid; Ville inequality; FW-1; Catoni clipping; sliding-window MGF; Dinkelbach; ratio optimization; FKPP; Kingman; hitting times; speed KPI; censoring; block bootstrap; maximal correlation; HSIC; distance correlation; residualization; No-Meta; benevolent propagation; Explosive Growth Mode (EGM); hash-chained logs; external anchor; reproducibility; DP accounting; UGV; DPI ladder; safe escalation; policy engine; facilitator approval.