# Complexity Matters: Dynamics of Feature Learning in the Presence of Spurious Correlations

arXiv: https://arxiv.org/abs/2403.03375 · HTML: https://mlsanity.com/paper/2403.03375/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 62 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Builds on (most cited first, 30 of 50)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [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)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Noise or Signal: The Role of Image Backgrounds in Object Recognition](https://mlsanity.com/paper/2006.09994/) (2020)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limit](https://mlsanity.com/paper/2207.08799/) (2022)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Simple data balancing achieves competitive worst-group-accuracy](https://mlsanity.com/paper/2110.14503/) (2021)
- [Correct-N-Contrast: A Contrastive Approach for Improving Robustness to Spurious Correlations](https://mlsanity.com/paper/2203.01517/) (2022)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)
- [On Feature Learning in the Presence of Spurious Correlations](https://mlsanity.com/paper/2210.11369/) (2022)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics](https://mlsanity.com/paper/2302.11055/) (2023)
- [The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networks](https://mlsanity.com/paper/2202.08658/) (2022)
- [Deep Learning Through the Lens of Example Difficulty](https://mlsanity.com/paper/2106.09647/) (2021)

## Built on by (most cited first, 12 of 12)

- [Learned feature representations are biased by complexity, learning order, position, and more](https://mlsanity.com/paper/2405.05847/) (2024)
- [Accuracy on the wrong line: On the pitfalls of noisy data for out-of-distribution generalisation](https://mlsanity.com/paper/2406.19049/) (2024)
- [Spurious Correlations in High Dimensional Regression: The Roles of Regularization, Simplicity Bias and Over-Parameterization](https://mlsanity.com/paper/2502.01347/) (2025)
- [Identifying Backdoored Graphs in Graph Neural Network Training: An Explanation-Based Approach with Novel Metrics](https://mlsanity.com/paper/2403.18136/) (2024)
- [Spurious Correlation Learning in Preference Optimization: Mechanisms, Consequences, and Mitigation via Tie Training](https://mlsanity.com/paper/2605.11134/) (2026)
- [OOD-Chameleon: Is Algorithm Selection for OOD Generalization Learnable?](https://mlsanity.com/paper/2410.02735/) (2024)
- [Hypernym Bias: Unraveling Deep Classifier Training Dynamics through the Lens of Class Hierarchy](https://mlsanity.com/paper/2502.12125/) (2025)
- [Large Learning Rates Simultaneously Achieve Robustness to Spurious Correlations and Compressibility](https://mlsanity.com/paper/2507.17748/) (2025)
- [Early Period of Training Impacts Adaptation for Out-of-Distribution Generalization: An Empirical Study](https://mlsanity.com/paper/2403.15210/) (2024)
- [Mitigating Spurious Correlations with Memorization-Guided Dataset De-Biasing](https://mlsanity.com/paper/2606.02830/) (2026)
- [Whitening Improves Robustness to Spurious Correlations in Linear Probes](https://mlsanity.com/paper/2609.39177/) (2026)
- [Prospective Prediction of OOD Degradation from Source-Side Training Dynamics](https://mlsanity.com/paper/2610.12397/) (2026)

## Abstract (arXiv)

Existing research often posits spurious features as easier to learn than core features in neural network optimization, but the impact of their relative simplicity remains under-explored. Moreover, studies mainly focus on end performance rather than the learning dynamics of feature learning. In this paper, we propose a theoretical framework and an associated synthetic dataset grounded in boolean function analysis. This setup allows for fine-grained control over the relative complexity (compared to core features) and correlation strength (with respect to the label) of spurious features to study the dynamics of feature learning under spurious correlations. Our findings uncover several interesting phenomena: (1) stronger spurious correlations or simpler spurious features slow down the learning rate of the core features, (2) two distinct subnetworks are formed to learn core and spurious features separately, (3) learning phases of spurious and core features are not always separable, (4) spurious features are not forgotten even after core features are fully learned. We demonstrate that our findings justify the success of retraining the last layer to remove spurious correlation and also identifies limitations of popular debiasing algorithms that exploit early learning of spurious features. We support our empirical findings with theoretical analyses for the case of learning XOR features with a one-hidden-layer ReLU network.