# Deconfounded Representation Similarity for Comparison of Neural Networks

arXiv: https://arxiv.org/abs/2202.00095 · HTML: https://mlsanity.com/paper/2202.00095/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 54 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Unsupervised Cross-lingual Representation Learning at Scale](https://mlsanity.com/paper/1911.02116/) (2019)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Why Do Better Loss Functions Lead to Less Transferable Features?](https://mlsanity.com/paper/2010.16402/) (2020)
- [Unraveling Meta-Learning: Understanding Feature Representations for Few-Shot Tasks](https://mlsanity.com/paper/2002.06753/) (2020)
- [Grounding Representation Similarity with Statistical Testing](https://mlsanity.com/paper/2108.01661/) (2021)
- [An analysis of the transfer learning of convolutional neural networks for artistic images](https://mlsanity.com/paper/2011.02727/) (2020)
- [Transferred Discrepancy: Quantifying the Difference Between Representations](https://mlsanity.com/paper/2007.12446/) (2020)
- [Disentangling Transfer and Interference in Multi-Domain Learning](https://mlsanity.com/paper/2107.05445/) (2021)

## Built on by (most cited first, 19 of 19)

- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networks](https://mlsanity.com/paper/2207.13243/) (2022)
- [Revisiting the Platonic Representation Hypothesis: An Aristotelian View](https://mlsanity.com/paper/2602.14486/) (2026)
- [ModelDiff: A Framework for Comparing Learning Algorithms](https://mlsanity.com/paper/2211.12491/) (2022)
- [ReSi: A Comprehensive Benchmark for Representational Similarity Measures](https://mlsanity.com/paper/2408.00531/) (2024)
- [Objective drives the consistency of representational similarity across datasets](https://mlsanity.com/paper/2411.05561/) (2024)
- [GULP: a prediction-based metric between representations](https://mlsanity.com/paper/2210.06545/) (2022)
- [Deep RL Needs Deep Behavior Analysis: Exploring Implicit Planning by Model-Free Agents in Open-Ended Environments](https://mlsanity.com/paper/2506.06981/) (2025)
- [Measuring Domain Shifts using Deep Learning Remote Photoplethysmography Model Similarity](https://mlsanity.com/paper/2404.08184/) (2024)
- [Refining Remote Photoplethysmography Architectures using CKA and Empirical Methods](https://mlsanity.com/paper/2401.04801/) (2024)
- [Reconciling Privacy and Explainability in High-Stakes: A Systematic Inquiry](https://mlsanity.com/paper/2412.20798/) (2024)
- [Layer-wise Representation Dynamics: An Empirical Investigation Across Embedders and Base LLMs](https://mlsanity.com/paper/2605.12714/) (2026)
- [Stimulus symmetries can confound representational similarity analyses](https://mlsanity.com/paper/2605.21324/) (2026)
- [Has Your Pretrained Model Improved? A Multi-head Posterior Based Approach](https://mlsanity.com/paper/2401.02987/) (2024)
- [Revealing Vulnerabilities of Neural Networks in Parameter Learning and Defense Against Explanation-Aware Backdoors](https://mlsanity.com/paper/2403.16569/) (2024)
- [ReStNet: A Reusable & Stitchable Network for Dynamic Adaptation on IoT Devices](https://mlsanity.com/paper/2506.09066/) (2025)
- [Revisiting the Relation Between Robustness and Universality](https://mlsanity.com/paper/2510.19427/) (2025)
- [Tracing distinguishability through transformer processing with stochastic LayerNorm](https://mlsanity.com/paper/2608.30720/) (2026)
- [Hidden Activations are not Enough I: Knowledge Matrices as Higher Representations](https://mlsanity.com/paper/2609.34166/) (2026)

## Abstract (arXiv)

Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population structure of data items in the input space, leading to spuriously high similarity for even completely random neural networks and inconsistent domain relations in transfer learning. We introduce a simple and generally applicable fix to adjust for the confounder with covariate adjustment regression, which retains the intuitive invariance properties of the original similarity measures. We show that deconfounding the similarity metrics increases the resolution of detecting semantically similar neural networks. Moreover, in real-world applications, deconfounding improves the consistency of representation similarities with domain similarities in transfer learning, and increases correlation with out-of-distribution accuracy.