# Representation Alignment in Neural Networks

arXiv: https://arxiv.org/abs/2112.07806 · HTML: https://mlsanity.com/paper/2112.07806/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 58 references that are in the map.
- First posted on arXiv 15 Dec 2021.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Do Better ImageNet Models Transfer Better?](https://mlsanity.com/paper/1805.08974/) (2018)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [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)
- [Characterizing and Avoiding Negative Transfer](https://mlsanity.com/paper/1811.09751/) (2018)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Fine-grained Analysis of Sentence Embeddings Using Auxiliary Prediction Tasks](https://mlsanity.com/paper/1608.04207/) (2016)
- [Object Detectors Emerge in Deep Scene CNNs](https://mlsanity.com/paper/1412.6856/) (2014)
- [What do Neural Machine Translation Models Learn about Morphology?](https://mlsanity.com/paper/1704.03471/) (2017)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)

## Built on by (most cited first, 6 of 6)

- [Training the Untrainable: Introducing Inductive Bias via Representational Alignment](https://mlsanity.com/paper/2410.20035/) (2024)
- [Enabling Multi-Robot Collaboration from Single-Human Guidance](https://mlsanity.com/paper/2409.19831/) (2024)
- [Spectral Alignment as Predictor of Loss Explosion in Neural Network Training](https://mlsanity.com/paper/2510.04202/) (2025)
- [Label Alignment Regularization for Distribution Shift](https://mlsanity.com/paper/2211.14960/) (2022)
- [Model alignment using inter-modal bridges](https://mlsanity.com/paper/2505.12322/) (2025)
- [Value Bonuses using Ensemble Errors for Exploration in Reinforcement Learning](https://mlsanity.com/paper/2602.12375/) (2026)

## Abstract (arXiv)

It is now a standard for neural network representations to be trained on large, publicly available datasets, and used for new problems. The reasons for why neural network representations have been so successful for transfer, however, are still not fully understood. In this paper we show that, after training, neural network representations align their top singular vectors to the targets. We investigate this representation alignment phenomenon in a variety of neural network architectures and find that (a) alignment emerges across a variety of different architectures and optimizers, with more alignment arising from depth (b) alignment increases for layers closer to the output and (c) existing high-performance deep CNNs exhibit high levels of alignment. We then highlight why alignment between the top singular vectors and the targets can speed up learning and show in a classic synthetic transfer problem that representation alignment correlates with positive and negative transfer to similar and dissimilar tasks.