Convergence Theory for Iterative LLM-Based Neural Architecture Search: A Parametric Cross-Entropy Framework with Closed-Form Proxy Reliability
Large language models (LLMs) are increasingly used as generators in iterative neural architecture search (NAS), yet no formal convergence theory exists for this class of algorithms. We model iterative LLM-NAS as a parametric Cross-Entropy (CE) method over executable programs and prove six results: (1) iterative LLM fine-tuning on elite architectures is equivalent to the CE update restricted to the LLM parametric family; (2) expected architecture quality is monotonically non-decreasing across cycles; (3) elite-set probability converges to a fixed point at a geometric rate C_t >= 1-(1-rho_0)^t; (4) delta-based generation achieves a strictly higher valid-generation rate than full-code genera...
| Authors | Santosh Premi Adhikari, Radu Timofte, Dmitry Ignatov |
|---|---|
| Primary category | cs.LG |
| Published | 28 May 2026 |
| Last updated at source | 28 May 2026 |
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