# Demystifying the Neural Tangent Kernel from a Practical Perspective: Can it be trusted for Neural Architecture Search without training?

arXiv: https://arxiv.org/abs/2203.14577 · HTML: https://mlsanity.com/paper/2203.14577/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 70 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 30 of 60)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [Large-Scale Evolution of Image Classifiers](https://mlsanity.com/paper/1703.01041/) (2017)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [Designing Neural Network Architectures using Reinforcement Learning](https://mlsanity.com/paper/1611.02167/) (2016)
- [PC-DARTS: Partial Channel Connections for Memory-Efficient Architecture Search](https://mlsanity.com/paper/1907.05737/) (2019)
- [Searching for A Robust Neural Architecture in Four GPU Hours](https://mlsanity.com/paper/1910.04465/) (2019)
- [Random Search and Reproducibility for Neural Architecture Search](https://mlsanity.com/paper/1902.07638/) (2019)
- [Neural Architecture Search without Training](https://mlsanity.com/paper/2006.04647/) (2020)
- [Progressive Differentiable Architecture Search: Bridging the Depth Gap between Search and Evaluation](https://mlsanity.com/paper/1904.12760/) (2019)
- [SMASH: One-Shot Model Architecture Search through HyperNetworks](https://mlsanity.com/paper/1708.05344/) (2017)
- [Zero-Cost Proxies for Lightweight NAS](https://mlsanity.com/paper/2101.08134/) (2021)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)
- [Understanding and Robustifying Differentiable Architecture Search](https://mlsanity.com/paper/1909.09656/) (2019)
- [On the Inductive Bias of Neural Tangent Kernels](https://mlsanity.com/paper/1905.12173/) (2019)

## Built on by (most cited first, 18 of 18)

- [SWAP-NAS: Sample-Wise Activation Patterns for Ultra-fast NAS](https://mlsanity.com/paper/2403.04161/) (2024)
- [Neural Lineage](https://mlsanity.com/paper/2406.11129/) (2024)
- [Robust NAS under adversarial training: benchmark, theory, and beyond](https://mlsanity.com/paper/2403.13134/) (2024)
- [Scalable Reinforcement Learning-based Neural Architecture Search](https://mlsanity.com/paper/2410.01431/) (2024)
- [L-SWAG: Layer-Sample Wise Activation with Gradients information for Zero-Shot NAS on Vision Transformers](https://mlsanity.com/paper/2505.07300/) (2025)
- [Equivariant Neural Tangent Kernels](https://mlsanity.com/paper/2406.06504/) (2024)
- [Finite-Width Neural Tangent Kernels from Feynman Diagrams](https://mlsanity.com/paper/2508.11522/) (2025)
- [Revisiting Training-free NAS Metrics: An Efficient Training-based Method](https://mlsanity.com/paper/2211.08666/) (2022)
- [Boosting Residual Networks with Group Knowledge](https://mlsanity.com/paper/2308.13772/) (2023)
- [Analyzing Tree Architectures in Ensembles via Neural Tangent Kernel](https://mlsanity.com/paper/2205.12904/) (2022)
- [NEAR: A Training-Free Pre-Estimator of Machine Learning Model Performance](https://mlsanity.com/paper/2408.08776/) (2024)
- [Variation Matters: from Mitigating to Embracing Zero-Shot NAS Ranking Function Variation](https://mlsanity.com/paper/2502.19657/) (2025)
- [Half Search Space is All You Need](https://mlsanity.com/paper/2505.13586/) (2025)
- [Generalization Bound of Gradient Flow through Training Trajectory and Data-dependent Kernel](https://mlsanity.com/paper/2506.11357/) (2025)
- [Compact Vision Transformer by Reduction of Kernel Complexity](https://mlsanity.com/paper/2507.12780/) (2025)
- [Zero-Shot Neural Network Evaluation with Sample-Wise Activation Patterns](https://mlsanity.com/paper/2605.07378/) (2026)
- [Kernel Reboot: Breaking the Boundaries of Neural Tangent Kernels for Neural Fields](https://mlsanity.com/paper/2609.03117/) (2026)
- [Rank-Reliable Teacher-Guided Fitness Approximation for Expensive Evolutionary Optimization: A TinyML Architecture Search Study](https://mlsanity.com/paper/2609.30553/) (2026)

## Abstract (arXiv)

In Neural Architecture Search (NAS), reducing the cost of architecture evaluation remains one of the most crucial challenges. Among a plethora of efforts to bypass training of each candidate architecture to convergence for evaluation, the Neural Tangent Kernel (NTK) is emerging as a promising theoretical framework that can be utilized to estimate the performance of a neural architecture at initialization. In this work, we revisit several at-initialization metrics that can be derived from the NTK and reveal their key shortcomings. Then, through the empirical analysis of the time evolution of NTK, we deduce that modern neural architectures exhibit highly non-linear characteristics, making the NTK-based metrics incapable of reliably estimating the performance of an architecture without some amount of training. To take such non-linear characteristics into account, we introduce Label-Gradient Alignment (LGA), a novel NTK-based metric whose inherent formulation allows it to capture the large amount of non-linear advantage present in modern neural architectures. With minimal amount of training, LGA obtains a meaningful level of rank correlation with the post-training test accuracy of an architecture. Lastly, we demonstrate that LGA, complemented with few epochs of training, successfully guides existing search algorithms to achieve competitive search performances with significantly less search cost. The code is available at: https://github.com/nutellamok/DemystifyingNTK.