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 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.

Delta-Based Neural Architecture Search: LLM Fine-Tuning via Code Diffs

Large language models (LLMs) show strong potential for neural architecture generation, yet existing approaches produce complete model implementations from scratch -- computationally expensive and yielding verbose code. We propose Delta-Code Generation, where fine-tuned LLMs generate compact unified diffs (deltas) to refine baseline architectures rather than synthesizing entire models. Our pipeline iteratively fine-tunes the LLM via LoRA on curated architectures from the LEMUR dataset, with MinHash-Jaccard novelty filtering for structural diversity. We evaluate three 7B-class LLMs -- DeepSeek-Coder-7B, Qwen2.5-Coder-7B, and Mistral-7B -- across six datasets (CIFAR-10, CIFAR-100, MNIST, SVHN, ImageNette, CelebA) using a 22-cycle protocol (1,100 candidates per LLM). All three substantially surpass the full-generation baseline (50.6% valid rate, 42.3% mean first-epoch accuracy): DeepSeek-Coder reaches 75.3% valid rate and 65.8% mean accuracy; Qwen2.5-Coder 72.1%/64.6%; Mistral 66.6%/66.1%. On CIFAR-10, best first-epoch accuracies reach 85.5% (Mistral), 85.2% (DeepSeek), 80.6% (Qwen) -- well above 63.98% full generation and 71.5% for the concurrent approach of Gu et al. Output lengths are 30-50 lines versus 200+ for full generation (75-85% reduction). A 50-epoch study confirms the 1-epoch proxy preserves rankings (Mistral: Spearman $ρ$ = 0.926). Delta-based generation is a token-efficient, multi-domain, LLM-agnostic alternative to full-model synthesis for LLM-driven NAS.