# How Do Transformers Learn to Associate Tokens: Gradient Leading Terms Bring Mechanistic Interpretability

arXiv: https://arxiv.org/abs/2601.19208 · HTML: https://mlsanity.com/paper/2601.19208/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge and representations inside LLMs, one of 13 directions in Mechanistic interpretability.
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Placed in

- Mechanistic interpretability / [Knowledge and representations inside LLMs](https://mlsanity.com/mechinterp/knowledge-and-representations-inside-llms/)

## Builds on (most cited first, 30 of 36)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation](https://mlsanity.com/paper/2205.01445/) (2022)
- [The Evolution of Statistical Induction Heads: In-Context Learning Markov Chains](https://mlsanity.com/paper/2402.11004/) (2024)
- [How Transformers Learn Causal Structure with Gradient Descent](https://mlsanity.com/paper/2402.14735/) (2024)
- [Scan and Snap: Understanding Training Dynamics and Token Composition in 1-layer Transformer](https://mlsanity.com/paper/2305.16380/) (2023)
- [Learning Single-Index Models with Shallow Neural Networks](https://mlsanity.com/paper/2210.15651/) (2022)
- [How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding](https://mlsanity.com/paper/2303.04245/) (2023)
- [On the Origins of Linear Representations in Large Language Models](https://mlsanity.com/paper/2403.03867/) (2024)
- [How Two-Layer Neural Networks Learn, One (Giant) Step at a Time](https://mlsanity.com/paper/2305.18270/) (2023)
- [Transformers Provably Solve Parity Efficiently with Chain of Thought](https://mlsanity.com/paper/2410.08633/) (2024)
- [Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape](https://mlsanity.com/paper/2402.01258/) (2024)
- [Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit](https://mlsanity.com/paper/2406.01581/) (2024)
- [Gradient-Based Feature Learning under Structured Data](https://mlsanity.com/paper/2309.03843/) (2023)
- [A phase transition between positional and semantic learning in a solvable model of dot-product attention](https://mlsanity.com/paper/2402.03902/) (2024)
- [Nonlinear spiked covariance matrices and signal propagation in deep neural networks](https://mlsanity.com/paper/2402.10127/) (2024)

## Built on by (most cited first, 3 of 3)

- [From Syntax to Semantics: Unveiling the Emergence of Chirality in SMILES Translation Models](https://mlsanity.com/paper/2605.09949/) (2026)
- [Tracing LLM Behavior to the Training Data with Empirical Next-Token Distributions](https://mlsanity.com/paper/2607.14306/) (2026)
- [Syntax vs. Semantics: How Transformers Learn Deep Dependencies](https://mlsanity.com/paper/2608.26139/) (2026)

## Abstract (arXiv)

Semantic associations such as the link between "bird" and "flew" are foundational for language modeling as they enable models to go beyond memorization and instead generalize and generate coherent text. Understanding how these associations are learned and represented in language models is essential for connecting deep learning with linguistic theory and developing a mechanistic foundation for large language models. In this work, we analyze how these associations emerge from natural language data in attention-based language models through the lens of training dynamics. By leveraging a leading-term approximation of the gradients, we develop closed-form expressions for the weights at early stages of training that explain how semantic associations first take shape. Through our analysis, we reveal that each set of weights of the transformer has closed-form expressions as simple compositions of three basis functions (bigram, token-interchangeability, and context mappings), reflecting the statistics of the text corpus and uncovering how each component of the transformer captures semantic associations based on these compositions. Experiments on real-world LLMs demonstrate that our theoretical weight characterizations closely match the learned weights, and qualitative analyses further show how our theorem shines light on interpreting the learned associations in transformers.