# Measuring Representational Robustness of Neural Networks Through Shared Invariances

arXiv: https://arxiv.org/abs/2206.11939 · HTML: https://mlsanity.com/paper/2206.11939/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 45 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Do Better ImageNet Models Transfer Better?](https://mlsanity.com/paper/1805.08974/) (2018)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [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)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (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)
- [Generalisation in humans and deep neural networks](https://mlsanity.com/paper/1808.08750/) (2018)
- [Generating Images with Perceptual Similarity Metrics based on Deep Networks](https://mlsanity.com/paper/1602.02644/) (2016)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Inverting Visual Representations with Convolutional Networks](https://mlsanity.com/paper/1506.02753/) (2015)
- [Towards Understanding Learning Representations: To What Extent Do Different Neural Networks Learn the Same Representation](https://mlsanity.com/paper/1810.11750/) (2018)

## Built on by (most cited first, 11 of 11)

- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Mechanistic Mode Connectivity](https://mlsanity.com/paper/2211.08422/) (2022)
- [Tracing Representation Progression: Analyzing and Enhancing Layer-Wise Similarity](https://mlsanity.com/paper/2406.14479/) (2024)
- [On Robustness of Finetuned Transformer-based NLP Models](https://mlsanity.com/paper/2305.14453/) (2023)
- [Diffused Redundancy in Pre-trained Representations](https://mlsanity.com/paper/2306.00183/) (2023)
- [What Happens During Finetuning of Vision Transformers: An Invariance Based Investigation](https://mlsanity.com/paper/2307.06006/) (2023)
- [Understanding the Role of Invariance in Transfer Learning](https://mlsanity.com/paper/2407.04325/) (2024)
- [Perturbed examples reveal invariances shared by language models](https://mlsanity.com/paper/2311.04166/) (2023)
- [Synthesizing Images on Perceptual Boundaries of ANNs for Uncovering Human Perceptual Variability on Facial Expressions](https://mlsanity.com/paper/2507.14549/) (2025)
- [TopoAlign: Topology-Aware Visual Representation Alignment](https://mlsanity.com/paper/2605.25541/) (2026)

## Abstract (arXiv)

A major challenge in studying robustness in deep learning is defining the set of ``meaningless'' perturbations to which a given Neural Network (NN) should be invariant. Most work on robustness implicitly uses a human as the reference model to define such perturbations. Our work offers a new view on robustness by using another reference NN to define the set of perturbations a given NN should be invariant to, thus generalizing the reliance on a reference ``human NN'' to any NN. This makes measuring robustness equivalent to measuring the extent to which two NNs share invariances, for which we propose a measure called STIR. STIR re-purposes existing representation similarity measures to make them suitable for measuring shared invariances. Using our measure, we are able to gain insights into how shared invariances vary with changes in weight initialization, architecture, loss functions, and training dataset. Our implementation is available at: urlhttps://github.com/nvedant07/STIR.