# Canonical Face Embeddings

arXiv: https://arxiv.org/abs/2106.07822 · HTML: https://mlsanity.com/paper/2106.07822/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 58 references that are in the map.
- First posted on arXiv 15 Jun 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [MS-Celeb-1M: A Dataset and Benchmark for Large-Scale Face Recognition](https://mlsanity.com/paper/1607.08221/) (2016)
- [Learning Face Representation from Scratch](https://mlsanity.com/paper/1411.7923/) (2014)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Additive Margin Softmax for Face Verification](https://mlsanity.com/paper/1801.05599/) (2018)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Partial FC: Training 10 Million Identities on a Single Machine](https://mlsanity.com/paper/2010.05222/) (2020)
- [Learning Data Augmentation Strategies for Object Detection](https://mlsanity.com/paper/1906.11172/) (2019)
- [Understanding How Image Quality Affects Deep Neural Networks](https://mlsanity.com/paper/1604.04004/) (2016)
- [Robust Learning Through Cross-Task Consistency](https://mlsanity.com/paper/2006.04096/) (2020)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [On the Reconstruction of Face Images from Deep Face Templates](https://mlsanity.com/paper/1703.00832/) (2017)
- [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, 3 of 3)

- [Grounding and Distinguishing Conceptual Vocabulary Through Similarity Learning in Embodied Simulations](https://mlsanity.com/paper/2305.13668/) (2023)
- [Privacy-Preserving Face Recognition in Hybrid Frequency-Color Domain](https://mlsanity.com/paper/2401.13386/) (2024)
- [Model Pairing Using Embedding Translation for Backdoor Attack Detection on Open-Set Classification Tasks](https://mlsanity.com/paper/2402.18718/) (2024)

## Abstract (arXiv)

We present evidence that many common convolutional neural networks (CNNs) trained for face verification learn functions that are nearly equivalent under rotation. More specifically, we demonstrate that one face verification model's embeddings (i.e. last-layer activations) can be compared directly to another model's embeddings after only a rotation or linear transformation, with little performance penalty. This finding is demonstrated using IJB-C 1:1 verification across the combinations of ten modern off-the-shelf CNN-based face verification models which vary in training dataset, CNN architecture, method of angular loss calculation, or some combination of the 3. These networks achieve a mean true accept rate of 0.96 at a false accept rate of 0.01. When instead evaluating embeddings generated from two CNNs, where one CNN's embeddings are mapped with a linear transformation, the mean true accept rate drops to 0.95 using the same verification paradigm. Restricting these linear maps to only perform rotation produces a mean true accept rate of 0.91. These mappings' existence suggests that a common representation is learned by models despite variation in training or structure. We discuss the broad implications a result like this has, including an example regarding face template security.