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

arXiv: https://arxiv.org/abs/2605.30103 · HTML: https://mlsanity.com/paper/2605.30103/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 13 of 13)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Single Path One-Shot Neural Architecture Search with Uniform Sampling](https://mlsanity.com/paper/1904.00420/) (2019)
- [Neural Architecture Search: Insights from 1000 Papers](https://mlsanity.com/paper/2301.08727/) (2023)
- [LEMUR Neural Network Dataset: Towards Seamless AutoML](https://mlsanity.com/paper/2504.10552/) (2025)
- [From Memorization to Creativity: LLM as a Designer of Novel Neural Architectures](https://mlsanity.com/paper/2601.02997/) (2026)
- [Resource-Efficient Iterative LLM-Based NAS with Feedback Memory](https://mlsanity.com/paper/2603.12091/) (2026)
- [Delta-Based Neural Architecture Search: LLM Fine-Tuning via Code Diffs](https://mlsanity.com/paper/2605.04903/) (2026)

## Built on by (most cited first, 1 of 1)

- [Systematic Exploration of 4-Expert Heterogeneous Mixture-of-Experts via Automated Pipeline Search](https://mlsanity.com/paper/2606.23739/) (2026)

## Abstract (arXiv)

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 generation under a first-order Markov token-error model; (5) the MinHash-Jaccard novelty filter prevents mode collapse; (6) proxy reliability admits the closed-form rho_S = (6/pi) arcsin(rho_P(SNR)/2), yielding the practical diagnostic sigma^2_arch >> sigma^2_noise as a necessary condition for trustworthy proxy-based rankings. Testing against a 22-cycle, three-LLM, six-dataset experiment with 3,300 generated architectures confirms two predictions quantitatively, two at direction-of-effect level, and explains the proxy-reliability ceiling effect previously reported empirically but left unexplained.