# Can Circuit Alignment Predict OOD Generalization?

arXiv: https://arxiv.org/abs/2609.31996 · HTML: https://mlsanity.com/paper/2609.31996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 69 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [Adversarial Domain Adaptation with Domain Mixup](https://mlsanity.com/paper/1912.01805/) (2019)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [Open Problems in Mechanistic Interpretability](https://mlsanity.com/paper/2501.16496/) (2025)
- [Leveraging Unlabeled Data to Predict Out-of-Distribution Performance](https://mlsanity.com/paper/2201.04234/) (2022)
- [Predicting the Generalization Gap in Deep Networks with Margin Distributions](https://mlsanity.com/paper/1810.00113/) (2018)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift](https://mlsanity.com/paper/2206.13089/) (2022)
- [PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization](https://mlsanity.com/paper/2211.13609/) (2022)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Empirical or Invariant Risk Minimization? A Sample Complexity Perspective](https://mlsanity.com/paper/2010.16412/) (2020)
- [Towards Vision-Language Mechanistic Interpretability: A Causal Tracing Tool for BLIP](https://mlsanity.com/paper/2308.14179/) (2023)

## Abstract (arXiv)

Can out-of-distribution (OOD) generalization be predicted from a trained model's weights alone, without any target-domain data? Existing representational similarity metrics (CKA, SVCCA, RSA) compare activations rather than forecast generalization. We show they are provably insensitive to structural rerouting in the computational graph, the very change distribution shift induces. We close this gap with the Circuit Alignment Score (CAS), which compares class-specific circuits across domains via graph kernels, decomposed into same-class coherence and cross-class confusion. Casting CAS as a Lebesgue integral over the domain distribution, we prove its Monte Carlo estimate recovers the ground-truth ranking of learners by OOD accuracy, with pairwise inversion error vanishing at rate O(1/M), where M is the number of sampled domains. Across 48 learners on PACS, CAS attains 0.88 rank correlation with OOD accuracy, versus 0.58 (CKA), 0.23 (SVCCA), and 0.14 (RSA), with similar trends on other benchmarks and even against data-dependent methods, making it the first provably consistent predictor of distributional robustness requiring neither target-domain data nor labels. The code is available at: https://github.com/ayanban011/ACE