# Sometimes I am a Tree: Data Drives Unstable Hierarchical Generalization

arXiv: https://arxiv.org/abs/2412.04619 · HTML: https://mlsanity.com/paper/2412.04619/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 54 references that are in the map.
- First posted on arXiv 5 Dec 2024.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [Assessing the Ability of LSTMs to Learn Syntax-Sensitive Dependencies](https://mlsanity.com/paper/1611.01368/) (2016)
- [Stress Test Evaluation for Natural Language Inference](https://mlsanity.com/paper/1806.00692/) (2018)
- [Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limit](https://mlsanity.com/paper/2207.08799/) (2022)
- [What shapes feature representations? Exploring datasets, architectures, and training](https://mlsanity.com/paper/2006.12433/) (2020)
- [Sudden Drops in the Loss: Syntax Acquisition, Phase Transitions, and Simplicity Bias in MLMs](https://mlsanity.com/paper/2309.07311/) (2023)
- [The MultiBERTs: BERT Reproductions for Robustness Analysis](https://mlsanity.com/paper/2106.16163/) (2021)
- [A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks](https://mlsanity.com/paper/2303.11873/) (2023)
- [Does syntax need to grow on trees? Sources of hierarchical inductive bias in sequence-to-sequence networks](https://mlsanity.com/paper/2001.03632/) (2020)
- [Competition Dynamics Shape Algorithmic Phases of In-Context Learning](https://mlsanity.com/paper/2412.01003/) (2024)
- [Grokking of Hierarchical Structure in Vanilla Transformers](https://mlsanity.com/paper/2305.18741/) (2023)
- [Characterizing Intrinsic Compositionality in Transformers with Tree Projections](https://mlsanity.com/paper/2211.01288/) (2022)
- [Injecting structural hints: Using language models to study inductive biases in language learning](https://mlsanity.com/paper/2304.13060/) (2023)
- [Revisiting the poverty of the stimulus: hierarchical generalization without a hierarchical bias in recurrent neural networks](https://mlsanity.com/paper/1802.09091/) (2018)
- [Coloring the Blank Slate: Pre-training Imparts a Hierarchical Inductive Bias to Sequence-to-sequence Models](https://mlsanity.com/paper/2203.09397/) (2022)
- [Revisiting Code Similarity Evaluation with Abstract Syntax Tree Edit Distance](https://mlsanity.com/paper/2404.08817/) (2024)
- [A Percolation Model of Emergence: Analyzing Transformers Trained on a Formal Language](https://mlsanity.com/paper/2408.12578/) (2024)
- [Critical Data Size of Language Models from a Grokking Perspective](https://mlsanity.com/paper/2401.10463/) (2024)
- [How to Plant Trees in Language Models: Data and Architectural Effects on the Emergence of Syntactic Inductive Biases](https://mlsanity.com/paper/2305.19905/) (2023)
- [Unified View of Grokking, Double Descent and Emergent Abilities: A Perspective from Circuits Competition](https://mlsanity.com/paper/2402.15175/) (2024)
- [The Curse of Performance Instability in Analysis Datasets: Consequences, Source, and Suggestions](https://mlsanity.com/paper/2004.13606/) (2020)
- [In-context Learning Generalizes, But Not Always Robustly: The Case of Syntax](https://mlsanity.com/paper/2311.07811/) (2023)

## Built on by (most cited first, 10 of 10)

- [ICLR: In-Context Learning of Representations](https://mlsanity.com/paper/2501.00070/) (2024)
- [From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit](https://mlsanity.com/paper/2506.03093/) (2025)
- [Hidden Breakthroughs in Language Model Training](https://mlsanity.com/paper/2506.15872/) (2025)
- [Can Interpretation Predict Behavior on Unseen Data?](https://mlsanity.com/paper/2507.06445/) (2025)
- [Random Scaling of Emergent Capabilities](https://mlsanity.com/paper/2502.17356/) (2025)
- [Position: Don't Just "Fix it in Post": A Science of AI Must Study Training Dynamics](https://mlsanity.com/paper/2606.06533/) (2026)
- [Structure Before Collapse: Transient semantic geometry in next-token prediction](https://mlsanity.com/paper/2606.26749/) (2026)
- [RL Excursions during Pre-Training: Re-examining Policy Optimization for LLM training](https://mlsanity.com/paper/2606.04272/) (2026)
- [Testing Transformer Learnability on the Arithmetic Sequence of Rooted Trees](https://mlsanity.com/paper/2512.01870/) (2025)
- [Structure and Scale in Simplicial Sequence Modelling](https://mlsanity.com/paper/2606.01302/) (2026)

## Abstract (arXiv)

Early in training, LMs can behave like n-gram models, but eventually they often learn tree-based syntactic rules and generalize hierarchically out of distribution (OOD). We study this shift using controlled grammar-learning tasks: question formation and tense inflection. We find that a model learns to generalize hierarchically if its training data is _complex_-in particular, if it includes center-embedded clauses, a special syntactic structure. Under this definition, complex data drives hierarchical rules, while less complex data encourages shortcut learning in the form of n-gram-like linear rules. Furthermore, we find that a model uses rules to generalize, whether hierarchical or linear, if its training data is _diverse_-in particular, if it includes many distinct syntax trees in the training set. Under this definition, diverse data promotes stable rule learning, whereas less diverse data promotes memorization of individual syntactic sequences. Finally, intermediate diversity and intermediate complexity form an *unstable regime*, which is characterized by oscillatory learning dynamics and inconsistent behaviors across random seeds. These results highlight the central role of training data in shaping generalization and explain why competing strategies can lead to unstable outcomes.