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Complexity Matters: Feature Learning in the Presence of Spurious Correlations
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Proposes a boolean-function-based synthetic spurious-correlation dataset (parity and staircase features) to study how spurious feature complexity and correlation strength affect feature learning dynamics in two-layer ReLU networks, with theory for XOR/parity features.
Problem
How the relative simplicity of spurious features and their correlation strength with the label affect the learning dynamics of core features under spurious correlations, which prior benchmarks cannot control precisely.
Approach
Builds a controllable spurious dataset where core and spurious features are boolean functions (parity or threshold staircase) of disjoint coordinates, with confounder strength lambda, so feature complexity (degree) and correlation can be varied independently; it uses Fourier analysis to derive gradient gaps explaining slowed core learning and persistence of spurious features.
Key results
- Stronger spurious correlation or simpler spurious features slow core feature learning, with a threshold-like jump in convergence time as confounder strength increases (model still fits core perfectly even at lambda=0.99).
- Jaccard scores of JTT and SpareMix for identifying minority groups stay below 0.5 on staircase and Domino datasets, while they succeed on parity cases with an early spurious spike.
- Last layer retraining improves worst group accuracy mainly by reducing second-layer weights connected to spurious neurons.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use simpler spurious features | Neural network on Boolean spurious-feature data · Boolean spurious-feature dataset | epochs to reach 0.95 core correlation | Hurt |
| Increase spurious-feature correlation strength | Neural network on Boolean spurious-feature data · Boolean spurious-feature dataset | epochs to reach 0.95 core correlation | Hurt |
| Learn a spurious feature before the core feature | Neural network on Boolean spurious-feature data · Boolean spurious-feature dataset | core-feature gradient: 4λ(1-λ) smaller | Hurt |
| Use high confounder strength | Neural network on Boolean spurious-feature data · Boolean spurious-feature dataset | decoded spurious correlation | Helped |
| Use low confounder strength (around 0.6) | Neural network on Boolean spurious-feature data · Boolean spurious-feature dataset | decoded spurious correlation: around 0.6 | Hurt |
| Retrain the last layer with balanced data | Neural network trained on spurious data · Boolean and semi-synthetic spurious-correlation datasets | worst group accuracy / core function correlation | Helped |
| Use a small amount of group-balanced data for last-layer retraining | Last Layer Retraining · Spurious-correlation datasets | worst group accuracy | Helped |
| Apply JTT or Spare using an early-stopped model | JTT and Spare · Parity, staircase, and Domino datasets | minority-group inference (Jaccard score): below 0.5 | Mixed |
| Upsample using the minority group inferred by debiasing methods | JTT and Spare · Challenging staircase and Domino datasets | worst group accuracy | No clear effect |
| Use spurious and core features of similar complexity | Early-stop-based debiasing algorithms · Staircase and Domino datasets | minority-group inference (Jaccard score): below 0.5 | Hurt |
| Train on limited-size data while spurious features delay core learning | Neural network on Boolean spurious-feature data · Limited-size Boolean datasets | robustness | Hurt |
| Train with a high spurious correlation after the spurious feature is learned | Neural network on Boolean spurious-feature data · Parity, deg(fs)=4, deg(fc)=10 | decoded spurious correlation | Helped |
Surprising findings
- Spurious features of complexity similar to or only slightly lower than the core feature still substantially slow core feature learning.
- Spurious features are retained in the representation after the core feature is fully learned when the correlation strength is high.
Limitations
- Theory covers only parity features in a one-hidden-layer ReLU network and does not provide an end-to-end analysis.
- Spurious and core features are assumed to be completely separate in coordinates, unlike real datasets.
- Staircase/threshold analysis is empirical rather than fully proven.
Experimental setup
Datasets: Boolean spurious dataset (parity and staircase) Waterbirds Colorful-MNIST Domino Image CIFAR-MNIST
Benchmarks: Boolean spurious dataset (parity, staircase) Waterbirds Colorful-MNIST Domino Image
Metrics: core correlation spurious correlation decoded correlation worst group accuracy Jaccard score containment score epochs to 0.95 core correlation
Baselines: Just Train Twice SpareMix Last Layer Retraining
Builds on: simplicity bias Just Train Twice Last Layer Retraining Hidden progress in sparse parity learning
Closest papers by meaning
- Let Samples Speak: Mitigating Spurious Correlation by Exploiting the Clusterness of Samples (CVPR 2025 · similarity 0.89)
- How Spurious Features are Memorized: Precise Analysis for Random and NTK Features (ICML 2024 · similarity 0.88)
- Severing Spurious Correlations with Data Pruning (ICLR 2025 · similarity 0.88)
- Spurious Correlations in High Dimensional Regression: The Roles of Regularization, Simplicity Bias and Over-Parameterization (ICML 2025 · similarity 0.87)
- From Kernels to Features: A Multi-Scale Adaptive Theory of Feature Learning (ICML 2025 · similarity 0.87)
- Understanding Visual Feature Reliance through the Lens of Complexity (NeurIPS 2024 · similarity 0.86)
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