# Learnable Adaptive Cosine Estimator (LACE) for Image Classification

arXiv: https://arxiv.org/abs/2110.05324 · HTML: https://mlsanity.com/paper/2110.05324/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 67 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 30 of 36)

- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [In Defense of the Triplet Loss for Person Re-Identification](https://mlsanity.com/paper/1703.07737/) (2017)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)
- [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019)
- [Fixing the train-test resolution discrepancy](https://mlsanity.com/paper/1906.06423/) (2019)
- [Whitening Sentence Representations for Better Semantics and Faster Retrieval](https://mlsanity.com/paper/2103.15316/) (2021)
- [Learning Fine-grained Image Similarity with Deep Ranking](https://mlsanity.com/paper/1404.4661/) (2014)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [Iterative Normalization: Beyond Standardization towards Efficient Whitening](https://mlsanity.com/paper/1904.03441/) (2019)
- [Decorrelated Batch Normalization](https://mlsanity.com/paper/1804.08450/) (2018)
- [AdaCos: Adaptively Scaling Cosine Logits for Effectively Learning Deep Face Representations](https://mlsanity.com/paper/1905.00292/) (2019)
- [ArcFace: Additive Angular Margin Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.07698/) (2018)
- [A survey on Semi-, Self- and Unsupervised Learning for Image Classification](https://mlsanity.com/paper/2002.08721/) (2020)
- [Natural Neural Networks](https://mlsanity.com/paper/1507.00210/) (2015)
- [Deep Texture Manifold for Ground Terrain Recognition](https://mlsanity.com/paper/1803.10896/) (2018)
- [Fixing the train-test resolution discrepancy: FixEfficientNet](https://mlsanity.com/paper/2003.08237/) (2020)
- [Contrastive-center loss for deep neural networks](https://mlsanity.com/paper/1707.07391/) (2017)

## Built on by (most cited first, 2 of 2)

- [Multi-Dimensional Refinement Graph Convolutional Network with Robust Decouple Loss for Fine-Grained Skeleton-Based Action Recognition](https://mlsanity.com/paper/2306.15321/) (2023)
- [Patch distribution modeling framework adaptive cosine estimator (PaDiM-ACE) for anomaly detection and localization in synthetic aperture radar imagery](https://mlsanity.com/paper/2504.08049/) (2025)

## Abstract (arXiv)

In this work, we propose a new loss to improve feature discriminability and classification performance. Motivated by the adaptive cosine/coherence estimator (ACE), our proposed method incorporates angular information that is inherently learned by artificial neural networks. Our learnable ACE (LACE) transforms the data into a new "whitened" space that improves the inter-class separability and intra-class compactness. We compare our LACE to alternative state-of-the art softmax-based and feature regularization approaches. Our results show that the proposed method can serve as a viable alternative to cross entropy and angular softmax approaches. Our code is publicly available: https://github.com/GatorSense/LACE.