# Norm-Hierarchy Transitions in Representation Learning: When and Why Neural Networks Abandon Shortcuts

arXiv: https://arxiv.org/abs/2603.07323 · HTML: https://mlsanity.com/paper/2603.07323/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 28 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 23 of 23)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [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)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (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)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [Learning from Failure: Training Debiased Classifier from Biased Classifier](https://mlsanity.com/paper/2007.02561/) (2020)
- [Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking](https://mlsanity.com/paper/2311.18817/) (2023)

## Built on by (most cited first, 2 of 2)

- [Spectral Entropy Collapse as a Phase Transition in Delayed Generalisation: An Interventional and Predictive Framework for Grokkin](https://mlsanity.com/paper/2604.13123/) (2026)
- [Phase Transitions in Driven Informational Systems: A Two-Field Perspective on Learning Theory and Non-Equilibrium Chemistry](https://mlsanity.com/paper/2605.16325/) (2026)

## Abstract (arXiv)

Neural networks often rely on spurious shortcuts for many epochs before discovering structured representations. However, the mechanism governing when this transition occurs and whether its timing can be predicted remains unclear. Prior work shows that gradient descent converges to low norm solutions and that neural networks exhibit simplicity bias, but neither explains the timescale of the transition from shortcut features to structured representations. We introduce the Norm-Hierarchy Transition (NHT) framework, which explains delayed representation learning as the slow traversal of a hierarchy of parameter norms during regularized optimization. When multiple interpolating solutions exist with different norms, weight decay gradually moves the model from high norm shortcut solutions toward lower norm structured representations. We derive a tight bound showing that the transition delay grows logarithmically with the ratio between shortcut and structured norms. Experiments on modular arithmetic, CIFAR-10 with spurious features, CelebA, and Waterbirds support the predictions of the framework. The results suggest that grokking, shortcut learning, and delayed feature discovery arise from a common mechanism based on norm hierarchy traversal during training.