# Memorization, Emergence, and Explaining Reversal Failures: A Controlled Study of Relational Semantics in LLMs

arXiv: https://arxiv.org/abs/2601.02931 · HTML: https://mlsanity.com/paper/2601.02931/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [From f(x) and g(x) to f(g(x)): LLMs Learn New Skills in RL by Composing Old Ones](https://mlsanity.com/paper/2509.25123/) (2025)
- [Towards a Theoretical Understanding of the 'Reversal Curse' via Training Dynamics](https://mlsanity.com/paper/2405.04669/) (2024)
- [An Analysis and Mitigation of the Reversal Curse](https://mlsanity.com/paper/2311.07468/) (2023)
- [Delving into the Reversal Curse: How Far Can Large Language Models Generalize?](https://mlsanity.com/paper/2410.18808/) (2024)
- [Rote Learning Considered Useful: Generalizing over Memorized Data in LLMs](https://mlsanity.com/paper/2507.21914/) (2025)
- [3D Rotation and Translation for Hyperbolic Knowledge Graph Embedding](https://mlsanity.com/paper/2305.13015/) (2023)

## Abstract (arXiv)

Autoregressive LLMs perform well on relational tasks that require linking entities via relational words (e.g., father/son, friend), but it is unclear whether they learn the logical semantics of such relations (e.g., symmetry and inversion logic) and, if so, whether reversal-type failures arise from missing relational semantics or left-to-right order bias. We propose a controlled Knowledge Graph-based synthetic framework that generates text from symmetric/inverse triples, train GPT-style autoregressive models from scratch, and evaluate memorization, logical inference, and in-context generalization to unseen entities to address these questions. We find a sharp phase transition in which relational semantics emerge with sufficient logic-bearing supervision, even in shallow (2-3 layer) models, and that successful generalization aligns with stable intermediate-layer signals. Finally, order-matched forward/reverse tests and a diffusion baseline indicate that reversal failures are primarily driven by autoregressive order bias rather than deficient inversion semantics.