# Freeze then Train: Towards Provable Representation Learning under Spurious Correlations and Feature Noise

arXiv: https://arxiv.org/abs/2210.11075 · HTML: https://mlsanity.com/paper/2210.11075/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 76 references that are in the map.
- First posted on arXiv 20 Oct 2022.

## Builds on (most cited first, 30 of 52)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [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)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Understanding self-supervised Learning Dynamics without Contrastive Pairs](https://mlsanity.com/paper/2102.06810/) (2021)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Demographic Dialectal Variation in Social Media: A Case Study of African-American English](https://mlsanity.com/paper/1608.08868/) (2016)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced](https://mlsanity.com/paper/1806.00900/) (2018)
- [Correct-N-Contrast: A Contrastive Approach for Improving Robustness to Spurious Correlations](https://mlsanity.com/paper/2203.01517/) (2022)

## Built on by (most cited first, 22 of 22)

- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [Calibrated Self-Rewarding Vision Language Models](https://mlsanity.com/paper/2405.14622/) (2024)
- [Discover and Cure: Concept-aware Mitigation of Spurious Correlation](https://mlsanity.com/paper/2305.00650/) (2023)
- [Understanding Multimodal Contrastive Learning and Incorporating Unpaired Data](https://mlsanity.com/paper/2302.06232/) (2023)
- [Robust Learning with Progressive Data Expansion Against Spurious Correlation](https://mlsanity.com/paper/2306.04949/) (2023)
- [Understanding and Improving Feature Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2304.11327/) (2023)
- [Fine-Grained Verifiers: Preference Modeling as Next-token Prediction in Vision-Language Alignment](https://mlsanity.com/paper/2410.14148/) (2024)
- [HappyMap: A Generalized Multi-calibration Method](https://mlsanity.com/paper/2303.04379/) (2023)
- [Complexity Matters: Dynamics of Feature Learning in the Presence of Spurious Correlations](https://mlsanity.com/paper/2403.03375/) (2024)
- [Sharpness-Aware Minimization Enhances Feature Quality via Balanced Learning](https://mlsanity.com/paper/2405.20439/) (2024)
- [Constructing Concept-based Models to Mitigate Spurious Correlations with Minimal Human Effort](https://mlsanity.com/paper/2407.08947/) (2024)
- [Severing Spurious Correlations with Data Pruning](https://mlsanity.com/paper/2503.18258/) (2025)
- [Towards Formalizing Spuriousness of Biased Datasets Using Partial Information Decomposition](https://mlsanity.com/paper/2407.00482/) (2024)
- [BMFT: Achieving Fairness via Bias-based Weight Masking Fine-tuning](https://mlsanity.com/paper/2408.06890/) (2024)
- [Diffexplainer: Towards Cross-modal Global Explanations with Diffusion Models](https://mlsanity.com/paper/2404.02618/) (2024)
- [Sparse Model Inversion: Efficient Inversion of Vision Transformers for Data-Free Applications](https://mlsanity.com/paper/2510.27186/) (2025)
- [FedBug: A Bottom-Up Gradual Unfreezing Framework for Federated Learning](https://mlsanity.com/paper/2307.10317/) (2023)
- [On the Unreasonable Effectiveness of Last-layer Retraining](https://mlsanity.com/paper/2512.01766/) (2025)
- [NeuronTune: Towards Self-Guided Spurious Bias Mitigation](https://mlsanity.com/paper/2505.24048/) (2025)
- [Hierarchical Simplicity Bias of Neural Networks](https://mlsanity.com/paper/2311.02622/) (2023)
- [Whitening Improves Robustness to Spurious Correlations in Linear Probes](https://mlsanity.com/paper/2609.39177/) (2026)
- [The Conflict Between Logic and Memory: Training Conditions for Optimizer-Dependent Rule Acquisition](https://mlsanity.com/paper/2610.00403/) (2026)

## Abstract (arXiv)

The existence of spurious correlations such as image backgrounds in the training environment can make empirical risk minimization (ERM) perform badly in the test environment. To address this problem, Kirichenko et al. (2022) empirically found that the core features that are related to the outcome can still be learned well even with the presence of spurious correlations. This opens a promising strategy to first train a feature learner rather than a classifier, and then perform linear probing (last layer retraining) in the test environment. However, a theoretical understanding of when and why this approach works is lacking. In this paper, we find that core features are only learned well when their associated non-realizable noise is smaller than that of spurious features, which is not necessarily true in practice. We provide both theories and experiments to support this finding and to illustrate the importance of non-realizable noise. Moreover, we propose an algorithm called Freeze then Train (FTT), that first freezes certain salient features and then trains the rest of the features using ERM. We theoretically show that FTT preserves features that are more beneficial to test time probing. Across two commonly used spurious correlation datasets, FTT outperforms ERM, IRM, JTT and CVaR-DRO, with substantial improvement in accuracy (by 4.5%) when the feature noise is large. FTT also performs better on general distribution shift benchmarks.