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Bilinear relational structure fixes reversal curse and enables consistent model editing

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
model editingreversal curselanguage modelrelational knowledgeknowledge editing
Abstract:

The reversal curse---a language model's (LM) inability to infer an unseen fact ``B is A'' from a learned factA 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. By training LMs from scratch on a synthetic dataset of relational knowledge graphs, we demonstrate that bilinear relational structure emerges in their hidden representations. This structure is associated with alleviating the reversal curse, facilitating the inference of unseen reverse facts. Crucially, we also find that this bilinear structure plays a key role in consistent model editing. When a fact is updated in a LM with this structure, the edit correctly propagates to its reverse and other logically dependent facts. In contrast, models lacking this representation not only suffer from the reversal curse but also fail to generalize edits, further introducing logical inconsistencies. Our results establish that training on a relational knowledge dataset induces the emergence of bilinear internal representations, which in turn support LMs in behaving in a logically consistent manner after editing. This implies that the success of model editing may be tied not just to editing algorithms but to the underlying representational geometry of the knowledge being modified.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

This paper investigates how bilinear relational structure in language model representations can alleviate the reversal curse and enable consistent model editing. It sits within the 'Bilinear Model Training Dynamics' leaf of the taxonomy, which contains only two papers total. This is a notably sparse research direction, suggesting the specific focus on bilinear structure emergence during training represents a relatively unexplored angle within the broader reversal curse literature. The work bridges theoretical analysis of training dynamics with practical implications for model editing consistency.

The taxonomy reveals two main branches: theoretical analysis and intervention methods. This paper occupies the theoretical branch but uniquely connects to intervention concerns through its model editing findings. The sibling paper in the same leaf examines reversal curse dynamics, while neighboring leaves address causal coherence and logical consistency from different angles. The intervention branch contains bidirectional editing techniques and pretraining methods, which represent alternative approaches to the same fundamental problem but operate at different stages of the model lifecycle.

Among seven candidates examined across three contributions, none were found to clearly refute the paper's claims. The first contribution (bilinear structure alleviating reversal curse) examined one candidate with no refutation. The second contribution (enabling consistent editing) examined two candidates, again with no refutation. The synthetic dataset contribution examined four candidates without finding overlapping prior work. This limited search scope suggests the specific combination of bilinear structure analysis, reversal curse mitigation, and editing consistency may be relatively novel, though the small candidate pool prevents definitive conclusions about the broader literature.

Based on the top-seven semantic matches examined, the work appears to occupy a distinct position connecting training dynamics, representational structure, and editing behavior. However, the sparse taxonomy (only four total papers) and limited search scope mean this assessment reflects only a narrow slice of potentially relevant work. The analysis cannot rule out related investigations in adjacent areas like knowledge graph embeddings or relational learning that might not surface through reversal-curse-focused queries.

Taxonomy

Core-task Taxonomy Papers
4
3
Claimed Contributions
7
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Overcoming the reversal curse through bilinear relational structure in language models. The reversal curse refers to the phenomenon where language models trained on facts in one direction (e.g., 'A is B') fail to infer the reverse relation ('B is A'), revealing fundamental limitations in how these models encode relational knowledge. The field has organized around two complementary perspectives. The first branch, Theoretical Analysis of Reversal Curse Mechanisms, investigates the underlying causes of this asymmetry, examining training dynamics, representational structure, and the mathematical properties that lead models to learn directional rather than bidirectional associations. Works like Reversal Curse Dynamics[2] and Causal Incoherence Dilemma[3] explore how gradient flow and architectural constraints shape this behavior. The second branch, Intervention Methods for Reversal Curse Mitigation, focuses on practical techniques to correct or prevent the curse, ranging from data augmentation strategies to architectural modifications and post-hoc editing approaches such as Bidirectional Reversal Editing[1]. Recent theoretical work has begun to unpack the precise mechanisms by which standard training fails to produce symmetric relational representations. Bilinear Reversal Cure[0] sits squarely within the theoretical analysis branch, specifically examining training dynamics through the lens of bilinear relational structure. It shares common ground with Reversal Curse Dynamics[2], which also investigates how models evolve during training, but emphasizes the role of bilinear factorization in enabling or blocking bidirectional inference. Meanwhile, Forward Reverse Relations[4] and Causal Incoherence Dilemma[3] highlight broader issues of logical consistency and causal reasoning that intersect with reversal phenomena. The central open question across these lines is whether the curse stems primarily from optimization pathologies, representational bottlenecks, or inherent limitations of autoregressive objectives—a debate that continues to shape both theoretical insights and intervention design.

Claimed Contributions

Bilinear relational structure alleviates reversal curse

The authors show that language models trained with appropriate regularization on relational knowledge graphs develop a bilinear structure in their internal representations. This emergent structure enables models to overcome the reversal curse by correctly inferring reverse facts that were not explicitly seen during training.

1 retrieved paper
Bilinear structure enables consistent model editing

The authors demonstrate that the presence of bilinear relational structure is crucial for logically consistent model editing. When models possess this structure, edits to factual knowledge automatically propagate to inverse relations and other logically entailed facts, whereas models lacking this structure fail to generalize edits.

2 retrieved papers
Synthetic relational knowledge dataset and training framework

The authors create a controlled synthetic family knowledge graph dataset with eight relations exhibiting inverse and compositional properties. They train transformer models from scratch on this dataset to systematically investigate how relational structure emerges and supports logical reasoning.

4 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Bilinear relational structure alleviates reversal curse

The authors show that language models trained with appropriate regularization on relational knowledge graphs develop a bilinear structure in their internal representations. This emergent structure enables models to overcome the reversal curse by correctly inferring reverse facts that were not explicitly seen during training.

Contribution

Bilinear structure enables consistent model editing

The authors demonstrate that the presence of bilinear relational structure is crucial for logically consistent model editing. When models possess this structure, edits to factual knowledge automatically propagate to inverse relations and other logically entailed facts, whereas models lacking this structure fail to generalize edits.

Contribution

Synthetic relational knowledge dataset and training framework

The authors create a controlled synthetic family knowledge graph dataset with eight relations exhibiting inverse and compositional properties. They train transformer models from scratch on this dataset to systematically investigate how relational structure emerges and supports logical reasoning.

Table of Contents

Bilinear relational structure fixes reversal curse and enables consistent model editing | Novelty Validation