Bi-EZP: LLM-Guided Bilevel Program Evolution for Ensemble Zero-Cost Proxy Discovery

Neural Architecture Search (NAS) automates network design, but evaluating a single candidate requires training it to convergence, making exhaustive search intractable. Zero-cost proxies estimate architecture quality at initialization in seconds, yet a single proxy is noisy, and combining several does not straightforwardly help: proxies are strongly correlated, so naive aggregation compounds their shared errors instead of averaging them out. Existing methods exploit either proxy signals or architectural topology - never both within a single active-learning framework. We introduce ZAPS (Zero-cost Active Proxy Search), a four-stage pipeline that closes this gap. ZAPS (i) selects a compact, non-redundant proxy subset offline via ProxyFit, a greedy anti-redundancy criterion; (ii) seeds the search with a hybrid K-means strategy that balances exploitation and exploration; (iii) re-selects proxies at every iteration by a bootstrapped vote as the labeled set grows; and (iv) ranks candidates with an XGBoost ensemble trained jointly on proxy ranks and one-hot topological encodings, queried through an Upper Confidence Bound (UCB) acquisition function. On NAS-Bench-201 under a budget of B=200 evaluations, ZAPS recovers 52.3% of the true top-100 architectures on CIFAR-10 and 65.8% on CIFAR-100, ahead of every baseline we consider - Random Search, Local Search, REA, BANANAS and TPE - and, on CIFAR-10, with less than half the run-to-run standard deviation of the strongest of them. The advantage is largest where evaluations are scarce: on NAS-Bench-201 it narrows as the budget grows, whereas on the harder NAS-Bench-101, which no method comes close to saturating, it widens instead. All methods are scored by a single criterion: how much of the true top-100 lies among the architectures they actually evaluated.

Efficient neural architecture search (NAS) requires accurate performance estimation under limited evaluation budgets. Existing zero-cost proxies (ZCPs) provide fast training-free signals, but each proxy usually captures only a partial property of an architecture, leading to unstable rankings across datasets and search spaces. In contrast, GNN-based predictors can improve accuracy, but often depend on labeled architectures, graph encoders, and costly representation learning, which makes them less suitable for extreme few-shot settings. We propose FENAS, a topology-agnostic few-shot prediction framework that turns complementary initialization priors into robust ranking signals. Its core component, CAST, is a feature pipeline that combines copula alignment and synergy transformation. CAST maps heterogeneous ZCPs into a compact feature manifold, enabling lightweight meta-learners to produce reliable rankings from scarce supervision. On NAS-Bench-201, with only 0.5% labeled samples, FENAS achieves a Kendall's Tau ($τ$) of 0.70, outperforming representative topology-based few-shot predictors in this low-label regime. In closed-domain search, FENAS evaluates the NAS-Bench-201 space in approximately 1138 seconds and achieves competitive test accuracy. By providing a fast, reliable, and structurally simple evaluation mechanism, FENAS supports the design of automated neural architectures under limited evaluation budgets.

Training-free neural architecture search promises efficient discovery of high-performance networks without costly training. However, existing zero-cost proxies rely on fragmented heuristics that fail to capture the fundamental question: what makes an architecture trainable? This paper introduces Intrinsic Trainability (InTrain), a unified theoretical proxy that formalizes trainability as an architectural invariant emerging from two synergistic components: geometric capacity and optimization resilience. We operationalize intrinsic trainability through analysis of neural information processing. Geometric capacity is quantified via the participation ratio of activation covariance eigenspectrum, capturing the effective dimensionality of representation manifolds. Optimization resilience is measured through cumulative gradient health, assessing the robustness of backpropagation across network depth. InTrain synthesizes these dimensions through a scale-invariant multiplicative coupling, which we hypothesize is essential for capturing their synergistic, non-additive relationship. Extensive experiments on standard NAS benchmarks and search spaces demonstrate that InTrain achieves ranking correlations on par with state-of-the-art ensemble-based proxies and outperforms other single-metric methods.