# How Do the Architecture and Optimizer Affect Representation Learning? On the Training Dynamics of Representations in Deep Neural Networks

arXiv: https://arxiv.org/abs/2405.17377 · HTML: https://mlsanity.com/paper/2405.17377/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [What shapes feature representations? Exploring datasets, architectures, and training](https://mlsanity.com/paper/2006.12433/) (2020)
- [Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be](https://mlsanity.com/paper/2304.13960/) (2023)
- [A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation](https://mlsanity.com/paper/1810.13243/) (2018)
- [When Do Curricula Work?](https://mlsanity.com/paper/2012.03107/) (2020)
- [Can Neural Network Memorization Be Localized?](https://mlsanity.com/paper/2307.09542/) (2023)
- [Can Neural Nets Learn the Same Model Twice? Investigating Reproducibility and Double Descent from the Decision Boundary Perspective](https://mlsanity.com/paper/2203.08124/) (2022)
- [AutoFreeze: Automatically Freezing Model Blocks to Accelerate Fine-tuning](https://mlsanity.com/paper/2102.01386/) (2021)
- [On the Implicit Bias of Adam](https://mlsanity.com/paper/2309.00079/) (2023)
- [What do CNNs Learn in the First Layer and Why? A Linear Systems Perspective](https://mlsanity.com/paper/2206.02454/) (2022)

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

- [Similarity of Processing Steps in Vision Model Representations](https://mlsanity.com/paper/2601.21621/) (2026)
- [On the dynamic evolution of CLIP texture-shape bias and its relationship to human alignment and model robustness](https://mlsanity.com/paper/2508.09814/) (2025)

## Abstract (arXiv)

In this paper, we elucidate how representations in deep neural networks (DNNs) evolve during training. Our focus is on overparameterized learning settings where the training continues much after the trained DNN starts to perfectly fit its training data. We examine the evolution of learned representations along the entire training process. We explore the representational similarity of DNN layers, each layer with respect to its own representations throughout the training process. For this, we use two similarity metrics: (1) The centered kernel alignment (CKA) similarity; (2) Similarity of decision regions of linear classifier probes that we train for the DNN layers. We visualize and analyze the decision regions of the DNN output and the layer probes during the DNN training to show how they geometrically evolve. Our extensive experiments discover training dynamics patterns that can emerge in layers depending on the relative layer-depth, architecture and optimizer. Among our findings: (i) The training phases, including those related to memorization, are more distinguishable in SGD training than in Adam training, and for Vision Transformer (ViT) than for ResNet; (ii) Unlike ResNet, the ViT layers have synchronized dynamics of representation learning.