SGD Provably Prioritizes a Shortcut Spurious Feature in the XOR Model

arXiv:2606.30444 · stat.ML, cs.LG · Submitted 2026-06-29 · Read on arXiv

Tyler LaBonte, Vidya Muthukumar

stat.ML, cs.LG

Submitted: 2026-06-29

Comments: v2: Fixed typos

Code: https://github.com/tmlabonte/xor

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Sample Complexity — 13× in this paper · explained in 20 episodes
• Robustness — 12× in this paper · explained in 5 episodes
• Accuracy — 10× in this paper · explained in 1 episode
• Generalization — 10× in this paper · explained in 13 episodes
• International Conference on Learning Representations — 8× in this paper
• International Conference on Machine Learning — 8× in this paper
• Phase Transition — 8× in this paper · explained in 2 episodes
• Phase Transitions — 8× in this paper · explained in 2 episodes
• Conference on Learning Theory — 3× in this paper
• Loss Function — 3× in this paper · explained in 2 episodes
• Shortcut Learning — 3× in this paper · explained in 3 episodes
• Transactions on Machine Learning Research — 3× in this paper
• Association for Computational Linguistics — 2× in this paper
• Conference on Computer Vision and Pattern Recognition — 2× in this paper
• Fixed Point — 2× in this paper · explained in 2 episodes
• Monotonicity — 2× in this paper · explained in 2 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Accountability — 1× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Adaptivity — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Distribution Shift — 1× in this paper · explained in 9 episodes
• Distribution Shifts — 1× in this paper · explained in 2 episodes
• EMMA — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Feature Selection — 1× in this paper · explained in 4 episodes
• Hierarchical Structure — 1× in this paper · explained in 3 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Hyperparameters — 1× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 8 episodes
• Multi-objective Optimization — 1× in this paper · explained in 4 episodes
• ReLU Network — 1× in this paper · explained in 2 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Transferability — 1× in this paper · explained in 5 episodes

Sources

• Invariant Risk Minimization
• The Elephant in the Room

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• Efficient quadratic entropy with distance sketches
• Embedding-Bias in Conditional Independence Testing
• From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier