# LARNet: Lie Algebra Residual Network for Face Recognition

arXiv: https://arxiv.org/abs/2103.08147 · HTML: https://mlsanity.com/paper/2103.08147/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 75 references that are in the map.
- First posted on arXiv 15 Mar 2021.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [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)
- [Joint Face Detection and Alignment using Multi-task Cascaded Convolutional Networks](https://mlsanity.com/paper/1604.02878/) (2016)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [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)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [The Shattered Gradients Problem: If resnets are the answer, then what is the question?](https://mlsanity.com/paper/1702.08591/) (2017)
- [Range Loss for Deep Face Recognition with Long-tail](https://mlsanity.com/paper/1611.08976/) (2016)
- [Towards Universal Representation Learning for Deep Face Recognition](https://mlsanity.com/paper/2002.11841/) (2020)
- [Occlusion Robust Face Recognition Based on Mask Learning with PairwiseDifferential Siamese Network](https://mlsanity.com/paper/1908.06290/) (2019)
- [Towards Large-Pose Face Frontalization in the Wild](https://mlsanity.com/paper/1704.06244/) (2017)
- [Neural Aggregation Network for Video Face Recognition](https://mlsanity.com/paper/1603.05474/) (2016)
- [Rotate-and-Render: Unsupervised Photorealistic Face Rotation from Single-View Images](https://mlsanity.com/paper/2003.08124/) (2020)
- [Pose-Robust Face Recognition via Deep Residual Equivariant Mapping](https://mlsanity.com/paper/1803.00839/) (2018)
- [Multi-Task Convolutional Neural Network for Pose-Invariant Face Recognition](https://mlsanity.com/paper/1702.04710/) (2017)
- [Decorrelated Adversarial Learning for Age-Invariant Face Recognition](https://mlsanity.com/paper/1904.04972/) (2019)
- [Orthogonal Deep Features Decomposition for Age-Invariant Face Recognition](https://mlsanity.com/paper/1810.07599/) (2018)
- [Targeting Ultimate Accuracy: Face Recognition via Deep Embedding](https://mlsanity.com/paper/1506.07310/) (2015)
- [Do We Really Need to Collect Millions of Faces for Effective Face Recognition?](https://mlsanity.com/paper/1603.07057/) (2016)
- [Triplet Probabilistic Embedding for Face Verification and Clustering](https://mlsanity.com/paper/1604.05417/) (2016)
- [Unconstrained Face Verification using Deep CNN Features](https://mlsanity.com/paper/1508.01722/) (2015)
- [Template Adaptation for Face Verification and Identification](https://mlsanity.com/paper/1603.03958/) (2016)

## Built on by (most cited first, 14 of 14)

- [SynFace: Face Recognition with Synthetic Data](https://mlsanity.com/paper/2108.07960/) (2021)
- [Improving Vision Transformers by Revisiting High-frequency Components](https://mlsanity.com/paper/2204.00993/) (2022)
- [Triangle Attack: A Query-efficient Decision-based Adversarial Attack](https://mlsanity.com/paper/2112.06569/) (2021)
- [Diversifying the High-level Features for better Adversarial Transferability](https://mlsanity.com/paper/2304.10136/) (2023)
- [Hardly Perceptible Trojan Attack against Neural Networks with Bit Flips](https://mlsanity.com/paper/2207.13417/) (2022)
- [Backdoor Secrets Unveiled: Identifying Backdoor Data with Optimized Scaled Prediction Consistency](https://mlsanity.com/paper/2403.10717/) (2024)
- [BATT: Backdoor Attack with Transformation-based Triggers](https://mlsanity.com/paper/2211.01806/) (2022)
- [Backdoor Defense via Suppressing Model Shortcuts](https://mlsanity.com/paper/2211.05631/) (2022)
- [Local Multi-Head Channel Self-Attention for Facial Expression Recognition](https://mlsanity.com/paper/2111.07224/) (2021)
- [Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebras](https://mlsanity.com/paper/2310.04521/) (2023)
- [Unconstrained Face Sketch Synthesis via Perception-Adaptive Network and A New Benchmark](https://mlsanity.com/paper/2112.01019/) (2021)
- [Cert-SSBD: Certified Backdoor Defense with Sample-Specific Smoothing Noises](https://mlsanity.com/paper/2504.21730/) (2025)
- [Attributes Shape the Embedding Space of Face Recognition Models](https://mlsanity.com/paper/2507.11372/) (2025)
- [RPP: A Certified Poisoned-Sample Detection Framework for Backdoor Attacks under Dataset Imbalance](https://mlsanity.com/paper/2602.00183/) (2026)

## Abstract (arXiv)

Face recognition is an important yet challenging problem in computer vision. A major challenge in practical face recognition applications lies in significant variations between profile and frontal faces. Traditional techniques address this challenge either by synthesizing frontal faces or by pose invariant learning. In this paper, we propose a novel method with Lie algebra theory to explore how face rotation in the 3D space affects the deep feature generation process of convolutional neural networks (CNNs). We prove that face rotation in the image space is equivalent to an additive residual component in the feature space of CNNs, which is determined solely by the rotation. Based on this theoretical finding, we further design a Lie Algebraic Residual Network (LARNet) for tackling pose robust face recognition. Our LARNet consists of a residual subnet for decoding rotation information from input face images, and a gating subnet to learn rotation magnitude for controlling the strength of the residual component contributing to the feature learning process. Comprehensive experimental evaluations on both frontal-profile face datasets and general face recognition datasets convincingly demonstrate that our method consistently outperforms the state-of-the-art ones.