# InTrain: Intrinsic Trainability for Zero-Cost Neural Architecture Search

arXiv: https://arxiv.org/abs/2606.18676 · HTML: https://mlsanity.com/paper/2606.18676/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 48 of its 55 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 30 of 48)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [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)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [Single Path One-Shot Neural Architecture Search with Uniform Sampling](https://mlsanity.com/paper/1904.00420/) (2019)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [SNAS: Stochastic Neural Architecture Search](https://mlsanity.com/paper/1812.09926/) (2018)
- [PC-DARTS: Partial Channel Connections for Memory-Efficient Architecture Search](https://mlsanity.com/paper/1907.05737/) (2019)
- [Neural Architecture Search without Training](https://mlsanity.com/paper/2006.04647/) (2020)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [Zero-Cost Proxies for Lightweight NAS](https://mlsanity.com/paper/2101.08134/) (2021)
- [BigNAS: Scaling Up Neural Architecture Search with Big Single-Stage Models](https://mlsanity.com/paper/2003.11142/) (2020)
- [Understanding and Robustifying Differentiable Architecture Search](https://mlsanity.com/paper/1909.09656/) (2019)
- [Neural Architecture Search on ImageNet in Four GPU Hours: A Theoretically Inspired Perspective](https://mlsanity.com/paper/2102.11535/) (2021)
- [A Survey on Evolutionary Neural Architecture Search](https://mlsanity.com/paper/2008.10937/) (2020)
- [Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice](https://mlsanity.com/paper/1711.04735/) (2017)
- [Group Fisher Pruning for Practical Network Compression](https://mlsanity.com/paper/2108.00708/) (2021)

## Abstract (arXiv)

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.