# Bilinear representation mitigates reversal curse and enables consistent model editing

arXiv: https://arxiv.org/abs/2509.21993 · HTML: https://mlsanity.com/paper/2509.21993/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 38 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 30 of 31)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Editing Large Language Models: Problems, Methods, and Opportunities](https://mlsanity.com/paper/2305.13172/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Modifying Memories in Transformer Models](https://mlsanity.com/paper/2012.00363/) (2020)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [Physics of Language Models: Part 3.2, Knowledge Manipulation](https://mlsanity.com/paper/2309.14402/) (2023)
- [Language Models Implement Simple Word2Vec-style Vector Arithmetic](https://mlsanity.com/paper/2305.16130/) (2023)
- [EasyEdit: An Easy-to-use Knowledge Editing Framework for Large Language Models](https://mlsanity.com/paper/2308.07269/) (2023)
- [Synthetic continued pretraining](https://mlsanity.com/paper/2409.07431/) (2024)
- [Reverse Training to Nurse the Reversal Curse](https://mlsanity.com/paper/2403.13799/) (2024)
- [On the generalization of language models from in-context learning and finetuning: a controlled study](https://mlsanity.com/paper/2505.00661/) (2025)
- [Do Large Language Models Perform Latent Multi-Hop Reasoning without Exploiting Shortcuts?](https://mlsanity.com/paper/2411.16679/) (2024)
- [Towards a Theoretical Understanding of the 'Reversal Curse' via Training Dynamics](https://mlsanity.com/paper/2405.04669/) (2024)
- [The Factorization Curse: Which Tokens You Predict Underlie the Reversal Curse and More](https://mlsanity.com/paper/2406.05183/) (2024)
- [Fundamental Problems With Model Editing: How Should Rational Belief Revision Work in LLMs?](https://mlsanity.com/paper/2406.19354/) (2024)
- [Representation Shattering in Transformers: A Synthetic Study with Knowledge Editing](https://mlsanity.com/paper/2410.17194/) (2024)
- [Precise Localization of Memories: A Fine-grained Neuron-level Knowledge Editing Technique for LLMs](https://mlsanity.com/paper/2503.01090/) (2025)
- [Lessons from Studying Two-Hop Latent Reasoning](https://mlsanity.com/paper/2411.16353/) (2024)
- [Inferring Functionality of Attention Heads from their Parameters](https://mlsanity.com/paper/2412.11965/) (2024)

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

- [How Training Data Shapes the Use of Parametric and In-Context Knowledge in Language Models](https://mlsanity.com/paper/2510.02370/) (2025)

## Abstract (arXiv)

The reversal curse--a language model's inability to infer an unseen fact "B is A" from a learned fact "A is B"--is widely considered a fundamental limitation. We show that this is not an inherent failure but an artifact of how models encode knowledge. Our results demonstrate that training from scratch on synthetic relational knowledge graphs leads to the emergence of a bilinear relational structure within the models' hidden representations. This structure alleviates the reversal curse and facilitates inference of unseen reverse facts. Crucially, this bilinear geometry is foundational for consistent model editing: updates to a single fact propagate correctly to its reverse and logically dependent relations. In contrast, models lacking this representation suffer from the reversal curse and fail to generalize model edits, leading to logical inconsistencies. Our results establish that training on a relational knowledge dataset induces the emergence of bilinear internal representations, which in turn support language models in behaving in a logically consistent manner after editing. This suggests that the efficacy of language model editing depends not only on the choice of algorithm but on the underlying representational geometry of the knowledge itself.