Convergence Theory for Iterative LLM-Based Neural Architecture Search: A Parametric Cross-Entropy Framework with Closed-Form Proxy Reliability

2026-05-28 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new convergence theory for iterative Large Language Model (LLM)-based Neural Architecture Search (NAS) has been developed, modeling the process as a parametric Cross-Entropy (CE) method over executable programs. This theory establishes six key results, including the equivalence of iterative LLM fine-tuning on elite architectures to the CE update, and a monotonically non-decreasing expected architecture quality across cycles. It also proves that elite-set probability converges geometrically and that delta-based generation achieves a strictly higher valid-generation rate than full-code generation under a first-order Markov token-error model. Furthermore, the theory demonstrates that a MinHash-Jaccard novelty filter prevents mode collapse and provides a closed-form for proxy reliability: rho_S = (6/pi) arcsin(rho_P(SNR)/2), identifying sigma^2_arch >> sigma^2_noise as a necessary condition for trustworthy proxy-based rankings. Experimental validation across a 22-cycle, three-LLM, six-dataset setup involving 3,300 generated architectures confirmed these predictions.

Key takeaway

For Machine Learning Engineers designing iterative LLM-based Neural Architecture Search systems, this theory provides critical validation and practical guidance. You should implement delta-based generation to improve valid architecture rates and integrate MinHash-Jaccard novelty filters to prevent mode collapse. Additionally, ensure your proxy reliability diagnostics confirm sigma^2_arch >> sigma^2_noise for trustworthy architecture rankings.

Key insights

Formal convergence theory validates iterative LLM-NAS, ensuring quality improvement and providing reliability diagnostics.

Principles

• Iterative LLM fine-tuning aligns with CE updates.
• Architecture quality improves monotonically.
• MinHash-Jaccard filters prevent mode collapse.

Method

The paper models iterative LLM-NAS as a parametric Cross-Entropy method. It uses delta-based generation and a MinHash-Jaccard novelty filter to guide architecture search.

In practice

• Use delta-based generation for higher valid rates.
• Implement MinHash-Jaccard to avoid mode collapse.
• Check sigma^2_arch >> sigma^2_noise for proxy reliability.

Topics

• Large Language Models
• Neural Architecture Search
• Convergence Theory
• Cross-Entropy Method
• MinHash-Jaccard
• Proxy Reliability

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.