mlsanityData to 7 Oct 2026

Understanding image representations by measuring their equivariance and equivalence

arXiv 1411.5908 ↗First posted 21 Nov 2014cs.CV cs.LG cs.NEcited by 240

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Abstract (arXiv)

Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three key mathematical properties of representations: equivariance, invariance, and equivalence. Equivariance studies how transformations of the input image are encoded by the representation, invariance being a special case where a transformation has no effect. Equivalence studies whether two representations, for example two different parametrisations of a CNN, capture the same visual information or not. A number of methods to establish these properties empirically are proposed, including introducing transformation and stitching layers in CNNs. These methods are then applied to popular representations to reveal insightful aspects of their structure, including clarifying at which layers in a CNN certain geometric invariances are achieved. While the focus of the paper is theoretical, direct applications to structured-output regression are demonstrated too.

Key facts. Cited by 240 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Nov 2014.

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Citing papers per year: 2021: 36; 2022: 32; 2023: 48; 2024: 40; 2025: 33; 2026: 51.

240 papers.

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  1. 2023Eliciting Latent Predictions from Transformers with the Tuned Lenscited by 579
  2. 2024The Platonic Representation Hypothesiscited by 362
  3. 2024Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Modelscited by 225
  4. 2021Revisiting Model Stitching to Compare Neural Representationscited by 203
  5. 2022Relative representations enable zero-shot latent space communicationcited by 175
  6. 2022Linearly Mapping from Image to Text Spacecited by 139
  7. 2022Analyzing Transformers in Embedding Spacecited by 131
  8. 2023Similarity of Neural Network Models: A Survey of Functional and Representational Measurescited by 128
  9. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  10. 2021Equivariant Imaging: Learning Beyond the Range Spacecited by 83
  11. 2022Reliability of CKA as a Similarity Measure in Deep Learningcited by 82
  12. 2022Deep Model Reassemblycited by 78
38 more
  1. 2021Similarity and Matching of Neural Network Representationscited by 77
  2. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  3. 2021Equivariant Contrastive Learningcited by 65
  4. 2022On the Symmetries of Deep Learning Models and their Internal Representationscited by 63
  5. 2023Text-To-Concept (and Back) via Cross-Model Alignmentcited by 63
  6. 2023Self-Supervised Multimodal Learning: A Surveycited by 58
  7. 2021Adversarial Robustness Comparison of Vision Transformer and MLP-Mixer to CNNscited by 57
  8. 2022The Lie Derivative for Measuring Learned Equivariancecited by 51
  9. 2023Going Beyond Linear Mode Connectivity: The Layerwise Linear Feature Connectivitycited by 50
  10. 2021Learning Disentangled Representations in the Imaging Domaincited by 46
  11. 2023Latent Space Translation via Semantic Alignmentcited by 46
  12. 2021Time-Equivariant Contrastive Video Representation Learningcited by 44
  13. 2022Accurate 3-DoF Camera Geo-Localization via Ground-to-Satellite Image Matchingcited by 44
  14. 2024Do Vision and Language Encoders Represent the World Similarly?cited by 44
  15. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  16. 20233D molecule generation by denoising voxel gridscited by 38
  17. 2022Imaging with Equivariant Deep Learningcited by 35
  18. 2025Shared Global and Local Geometry of Language Model Embeddingscited by 34
  19. 2021Robust Representation Learning with Feedback for Single Image Derainingcited by 32
  20. 2022Robust (Controlled) Table-to-Text Generation with Structure-Aware Equivariance Learningcited by 32
  21. 2024T-Stitch: Accelerating Sampling in Pre-Trained Diffusion Models with Trajectory Stitchingcited by 32
  22. 2024Training-Free Pretrained Model Mergingcited by 32
  23. 2023PUG: Photorealistic and Semantically Controllable Synthetic Data for Representation Learningcited by 31
  24. 2021Grounding Representation Similarity with Statistical Testingcited by 28
  25. 2022LieGG: Studying Learned Lie Group Generatorscited by 28
  26. 2025Understanding the Emergence of Multimodal Representation Alignmentcited by 28
  27. 2023Stitchable Neural Networkscited by 26
  28. 2021Grounding inductive biases in natural images:invariance stems from variations in datacited by 25
  29. 2024On the Emergence of Cross-Task Linearity in the Pretraining-Finetuning Paradigmcited by 25
  30. 2023Image Data Augmentation Approaches: A Comprehensive Survey and Future directionscited by 23
  31. 2021Long Short View Feature Decomposition via Contrastive Video Representation Learningcited by 21
  32. 2023Steerers: A framework for rotation equivariant keypoint descriptorscited by 21
  33. 2025Franca: Nested Matryoshka Clustering for Scalable Visual Representation Learningcited by 21
  34. 2026There Will Be a Scientific Theory of Deep Learningcited by 21
  35. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  36. 2022EquiMod: An Equivariance Module to Improve Self-Supervised Learningcited by 20
  37. 2021Convolutional Neural Networks Are Not Invariant to Translation, but They Can Learn to Becited by 19
  38. 2024Decomposing and Interpreting Image Representations via Text in ViTs Beyond CLIPcited by 19

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