Neural Networks Are Implicit Decision Trees: The Hierarchical Simplicity Bias

Neural networks exhibit simplicity bias; they rely on simpler features while ignoring equally predictive but more complex features. In this work, we introduce a novel approach termed imbalanced label coupling to investigate scenarios where simple and complex features exhibit different levels of predictive power. In these cases, complex features still contribute to predictions. The trained networks make predictions in alignment with the ascending complexity of input features according to how they correlate with the label in the training set, irrespective of the underlying predictive power. For instance, even when simple spurious features distort predictions in CIFAR-10, most cats are predicted to be dogs, and most trucks are predicted to be automobiles! This observation provides direct evidence that the neural network learns core features in the presence of spurious features. We empirically show that last-layer retraining with target data distribution is effective, yet insufficient to fully recover core features when spurious features are perfectly correlated with the target labels in our synthetic dataset. We hope our research contributes to a deeper understanding of the implicit bias of neural networks.