# Transformer Block Coupling and its Correlation with Generalization in LLMs

arXiv: https://arxiv.org/abs/2407.07810 · HTML: https://mlsanity.com/paper/2407.07810/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 64 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [The emergence of clusters in self-attention dynamics](https://mlsanity.com/paper/2305.05465/) (2023)
- [Traces of Class/Cross-Class Structure Pervade Deep Learning Spectra](https://mlsanity.com/paper/2008.11865/) (2020)
- [A Theory of Emergent In-Context Learning as Implicit Structure Induction](https://mlsanity.com/paper/2303.07971/) (2023)
- [Residual Connections Encourage Iterative Inference](https://mlsanity.com/paper/1710.04773/) (2017)
- [How Does BERT Answer Questions? A Layer-Wise Analysis of Transformer Representations](https://mlsanity.com/paper/1909.04925/) (2019)
- [Convolutional Neural Networks Analyzed via Convolutional Sparse Coding](https://mlsanity.com/paper/1607.08194/) (2016)
- [Highway and Residual Networks learn Unrolled Iterative Estimation](https://mlsanity.com/paper/1612.07771/) (2016)
- [Deep Neural Collapse Is Provably Optimal for the Deep Unconstrained Features Model](https://mlsanity.com/paper/2305.13165/) (2023)
- [Linguistic Collapse: Neural Collapse in (Large) Language Models](https://mlsanity.com/paper/2405.17767/) (2024)
- [VISIT: Visualizing and Interpreting the Semantic Information Flow of Transformers](https://mlsanity.com/paper/2305.13417/) (2023)
- [Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination](https://mlsanity.com/paper/2311.02960/) (2023)
- [Separation and Concentration in Deep Networks](https://mlsanity.com/paper/2012.10424/) (2020)

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

- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)
- [Short-LVLM: Compressing and Accelerating Large Vision-Language Models by Pruning Redundant Layers](https://mlsanity.com/paper/2507.23362/) (2025)
- [Lines of Thought in Large Language Models](https://mlsanity.com/paper/2410.01545/) (2024)
- [Dynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology](https://mlsanity.com/paper/2605.14258/) (2026)
- [Attribution-Guided Continual Learning for Large Language Models](https://mlsanity.com/paper/2605.05285/) (2026)
- [Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction](https://mlsanity.com/paper/2606.05863/) (2026)
- [Feature Dynamics as Implicit Data Augmentation: A Depth-Decomposed View on Deep Neural Network Generalization](https://mlsanity.com/paper/2509.20334/) (2025)
- [Dynamic Mode Decomposition along Depth in Vision Transformers](https://mlsanity.com/paper/2605.07556/) (2026)
- [Gradient Smoothing: Coupling Layer-wise Updates for Improved Optimization](https://mlsanity.com/paper/2606.30813/) (2026)
- [Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models](https://mlsanity.com/paper/2610.19042/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have made significant strides in natural language processing, and a precise understanding of the internal mechanisms driving their success is essential. In this work, we analyze the trajectories of token embeddings as they pass through transformer blocks, linearizing the system along these trajectories through their Jacobian matrices. By examining the relationships between these block Jacobians, we uncover the phenomenon of transformer block coupling in a multitude of LLMs, characterized by the coupling of their top singular vectors across tokens and depth. Our findings reveal that coupling textitpositively correlates with model performance, and that this relationship is stronger than with other hyperparameters such as parameter count, model depth, and embedding dimension. We further investigate how these properties emerge during training, observing a progressive development of coupling, increased linearity, and layer-wise exponential growth in token trajectories. Additionally, experiments with Vision Transformers (ViTs) corroborate the emergence of coupling and its relationship with generalization, reinforcing our findings in LLMs. Collectively, these insights offer a novel perspective on token interactions in transformers, opening new directions for studying their mechanisms as well as improving training and generalization.