# Dynamics Reveals Structure: Challenging the Linear Propagation Assumption

arXiv: https://arxiv.org/abs/2601.21601 · HTML: https://mlsanity.com/paper/2601.21601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 47 references that are in the map.
- First posted on arXiv 29 Jan 2026.

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

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Memory-Based Model Editing at Scale](https://mlsanity.com/paper/2206.06520/) (2022)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [MQuAKE: Assessing Knowledge Editing in Language Models via Multi-Hop Questions](https://mlsanity.com/paper/2305.14795/) (2023)
- [Negated and Misprimed Probes for Pretrained Language Models: Birds Can Talk, But Cannot Fly](https://mlsanity.com/paper/1911.03343/) (2019)
- [Evaluating the Ripple Effects of Knowledge Editing in Language Models](https://mlsanity.com/paper/2307.12976/) (2023)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [Editable Neural Networks](https://mlsanity.com/paper/2004.00345/) (2020)
- [Rewriting a Deep Generative Model](https://mlsanity.com/paper/2007.15646/) (2020)
- [How Do Large Language Models Acquire Factual Knowledge During Pretraining?](https://mlsanity.com/paper/2406.11813/) (2024)
- [Open Problems in Machine Unlearning for AI Safety](https://mlsanity.com/paper/2501.04952/) (2025)
- [Fundamental Problems With Model Editing: How Should Rational Belief Revision Work in LLMs?](https://mlsanity.com/paper/2406.19354/) (2024)
- [Is the Reversal Curse a Binding Problem? Uncovering Limitations of Transformers from a Basic Generalization Failure](https://mlsanity.com/paper/2504.01928/) (2025)

## Built on by (most cited first, 1 of 1)

- [What are the Right Symmetries for Formal Theorem Proving?](https://mlsanity.com/paper/2605.22257/) (2026)

## Abstract (arXiv)

Neural networks adapt through first-order parameter updates, yet it remains unclear whether such updates preserve logical coherence. We investigate the geometric limits of the Linear Propagation Assumption (LPA), the premise that local updates coherently propagate to logical consequences. To formalize this, we adopt relation algebra and study three core operations on relations: negation flips truth values, converse swaps argument order, and composition chains relations. For negation and converse, we prove that guaranteeing direction-agnostic first-order propagation necessitates a tensor factorization separating entity-pair context from relation content. However, for composition, we identify a fundamental obstruction. We show that composition reduces to conjunction, and prove that any conjunction well-defined on linear features must be bilinear. Since bilinearity is incompatible with negation, this forces the feature map to collapse. These results suggest that failures in knowledge editing, the reversal curse, and multi-hop reasoning may stem from common structural limitations inherent to the LPA.