Convergence Theory for Iterative LLM-Based Neural Architecture Search: A Parametric Cross-Entropy Framework with Closed-Form Proxy Reliability
Authors: Santosh Premi Adhikari, Radu Timofte, Dmitry Ignatov
Organizations: Computer Vision Lab, CAIDAS & IFI, University of Würzburg, Germany
Abstract
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.
Neural Architecture Search (NAS) aims to automatically discover high-performing deep neural network (DNN) architectures. However, conventional algorithm-driven NAS relies on carefully hand-crafted search spaces to ensure executability, which restricts open-ended exploration. Recent coding-based agentic approaches using large language models (LLMs) reduce manual design, but current LLMs struggle to reliably generate complex, valid architectures, and their proposals are often biased toward a narrow set of patterns observed in their training data. To bridge reliable algorithmic search with powerful LLM assistance, we propose LLMasTool, a hierarchical tree-based NAS framework for stable and open-ended model evolution. Our method automatically extracts reusable modules from arbitrary source code and represents full architectures as hierarchical trees, enabling evolution through reliable tree transformations rather than code generation. At each evolution step, coarse-level planning is governed by a diversity-guided algorithm that leverages Bayesian modeling to improve exploration efficiency, while the LLM resolves the remaining degrees of freedom to ensure a meaningful evolutionary trajectory and an executable generated architecture. With this formulation, instead of fully agentic LLM approaches, our method explores diverse directions beyond the inherent biases in the LLM. Our method improves over existing NAS methods by 0.69, 1.83, and 2.68 points on CIFAR-10, CIFAR-100, and ImageNet16-120, demonstrating its effectiveness.
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.
Santosh Premi Adhikari, Radu Timofte, Dmitry Ignatov
This paper focuses on a key challenge in Neural Architecture Search (NAS): integrating established architectural knowledge while exploring new designs under expensive evaluations. Large language models (LLMs) are a promising assistant for NAS because they can translate rich architectural and coding priors into executable code edits. However, in practice, seemingly local revisions often propagate into non-local behavioral and performance shifts because a single edit can inadvertently couple multiple interacting functional factors, a phenomenon we refer to as functional entanglement. To make LLM knowledge usable under such entanglement, we propose Structured Progressive Knowledge Activation (SPARK), which activates relevant priors by explicitly selecting the functional factor to modify and conditioning the edit on that factor. This factor-conditioned editing reduces entangled side effects and yields more targeted, reliable architecture modifications. On CLRS-DFS, SPARK achieves a 28.1x sample-efficient architecture evolution speedup and yields a 22.9% relative improvement in OOD accuracy. Our code is available at https://github.com/AIM-ResearchLab/SPARK.