G-ICSO-NAS: Shifting Gears between Gradient and Swarm for Robust Neural Architecture Search

Neural Architecture Search (NAS) aims to automate neural network architecture design, reducing reliance on human expertise. Among the various NAS methods, differentiable NAS has gained prominence due to its efficiency and accuracy compared to conventional NAS approaches. Since differentiable NAS relaxes the architecture search space into a continuous domain, it is possible to apply principles from continuous optimization to NAS. In this paper, we propose Linear Programming-based NAS (LP-NAS), a mathematical programming-based framework for differentiable NAS that is applicable to a wide range of continuous search spaces. LP-NAS formulates a linear program (LP) using the validation-loss gradient and the training-loss Hessian to compute an architecture update direction that improves generalization while preserving the optimality of the model parameters. By following this LP-derived descent direction, LP-NAS efficiently navigates the architecture search space, leading to faster and more effective architecture optimization. We introduce two computationally efficient variants of LP-NAS, namely S-LP-NAS and R-LP-NAS. Applying LP-NAS to the Differentiable Architecture Search (DARTS) search space results in two algorithmic variants, S-LP-DARTS and R-LP-DARTS. Both variants achieve faster convergence and significantly higher validation performance during the early search iterations than the standard DARTS algorithm. Extensive experiments on CIFAR-10 and CIFAR-100 show that LP-DARTS outperforms standard DARTS in both the architecture search and evaluation phases. Additionally, we compare our approach with several DARTS variants (P-DARTS, PC-DARTS, and STO-DARTS) on the CIFAR-10 dataset and demonstrate its effectiveness. Furthermore, we validate the transferability of the discovered architectures through experiments on the ImageNet dataset.

Neural Architecture Search (NAS) is naturally formulated as a bilevel optimization problem, where the upper-level optimizes the architecture using validation performance and the lower-level trains network parameters using training loss. However, NAS is computationally expensive due to discrete architectural decisions, exponentially growing search spaces, and the high cost of training candidate architectures. This work develops a general bilevel optimization framework for NAS across diverse architectures, including MLPs, CNNs, RNNs, and Transformers, to identify compact architectures with strong predictive performance. We propose three scalable formulations that replace discrete neuron- and activation-level decisions with continuous relaxations, enabling differentiable optimization over otherwise combinatorial architecture spaces. These formulations give rise to three NAS methods: NAS based on Neuron Gating (NAS-NG), NAS based on Mixed Activation (NAS-MA), and NAS based on Neuron Gating and Mixed Activation (NAS-NGMA). Experiments on MLPs and CNNs using MNIST and CIFAR-10 show that the proposed methods consistently identify compact architectures with competitive or improved predictive performance. On MNIST, NAS-NGMA achieves 98.68% test accuracy with 7.69M MLP parameters, while NAS-NG achieves 99.63% accuracy with only 0.26M CNN parameters. On CIFAR-10, the proposed methods consistently outperform vanilla DARTS. Further experiments demonstrate that NAS-NG can optimize substantially over-parameterized and literature-optimal architectures, improving accuracy while reducing parameters. These results establish relaxed bilevel optimization as a scalable alternative to discrete NAS and provide a general framework for efficient neuron- and activation-level architecture optimization.

Low-cost NAS must both explore high-performing architectures and identify them reliably, yet reducing evaluation cost often weakens the fidelity of candidate comparisons. Training-free methods reduce evaluation cost by replacing learned task feedback with proxy signals measured at initialization. We introduce LESS (Lightweight Evolutionary Supernet Search), a data-driven method that combines a brief fair hard-path warm-up with discrete search under a single CMA-ES distribution. Each proposal is evaluated as its decoded hard genotype after six candidate-conditioned supernet updates. On NAS-Bench-201, LESS achieves $93.189\pm0.467\%$ CIFAR-10 test accuracy in 409.1 seconds, coming within 0.04 percentage points of FairNAS using approximately $1/24$ of its source-reported search time. Matched controls show that calibration improves selected validation accuracy by $0.577$ percentage points while changing best-visited accuracy by only $0.054$ points, indicating that its primary effect is to reduce selection regret. The frozen configuration transfers without tuning to CIFAR-100 and ImageNet16-120 with $69.615\pm1.139\%$ and $43.720\pm1.697\%$ accuracy. Applied without tuning to the larger DARTS space, LESS achieves $96.95\pm0.14\%$ on CIFAR-10 and $82.43\pm0.80\%$ on CIFAR-100, with each search completing in approximately 43.5 minutes on a single GPU. Together, these results show that short, balanced, data-dependent updates enable competitive neural architecture search across datasets and search spaces within minutes.