# Hierarchical Simplicity Bias of Neural Networks

arXiv: https://arxiv.org/abs/2311.02622 · HTML: https://mlsanity.com/paper/2311.02622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 47 references that are in the map.
- First posted on arXiv 5 Nov 2023.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)
- [Implicit Bias of Gradient Descent on Linear Convolutional Networks](https://mlsanity.com/paper/1806.00468/) (2018)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Towards Understanding the Spectral Bias of Deep Learning](https://mlsanity.com/paper/1912.01198/) (2019)
- [Correct-N-Contrast: A Contrastive Approach for Improving Robustness to Spurious Correlations](https://mlsanity.com/paper/2203.01517/) (2022)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [Strike (with) a Pose: Neural Networks Are Easily Fooled by Strange Poses of Familiar Objects](https://mlsanity.com/paper/1811.11553/) (2018)
- [What shapes feature representations? Exploring datasets, architectures, and training](https://mlsanity.com/paper/2006.12433/) (2020)
- [Salient ImageNet: How to discover spurious features in Deep Learning?](https://mlsanity.com/paper/2110.04301/) (2021)

## Abstract (arXiv)

Neural networks often exhibit simplicity bias, favoring simpler features over more complex ones, even when both are equally predictive. We introduce a novel method called imbalanced label coupling to explore and extend this simplicity bias across multiple hierarchical levels. Our approach demonstrates that trained networks sequentially consider features of increasing complexity based on their correlation with labels in the training set, regardless of their actual predictive power. For example, in CIFAR-10, simple spurious features can cause misclassifications where most cats are predicted as dogs and most trucks as automobiles. We empirically show that last-layer retraining with target data distribution citepkirichenko2022last is insufficient to fully recover core features when spurious features perfectly correlate with target labels in our synthetic datasets. Our findings deepen the understanding of the implicit biases inherent in neural networks.