# Context Is King: How In-Context Specification Shapes the Geometry of Concepts

arXiv: https://arxiv.org/abs/2607.24425 · HTML: https://mlsanity.com/paper/2607.24425/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)

## Builds on (most cited first, 18 of 18)

- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [Does Circuit Analysis Interpretability Scale? Evidence from Multiple Choice Capabilities in Chinchilla](https://mlsanity.com/paper/2307.09458/) (2023)
- [Improving Activation Steering in Language Models with Mean-Centring](https://mlsanity.com/paper/2312.03813/) (2023)
- [Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior](https://mlsanity.com/paper/2605.05115/) (2026)
- [The Topology and Geometry of Neural Representations](https://mlsanity.com/paper/2309.11028/) (2023)
- [Context Structure Reshapes the Representational Geometry of Language Models](https://mlsanity.com/paper/2601.22364/) (2026)
- [Language Models Struggle to Use Representations Learned In-Context](https://mlsanity.com/paper/2602.04212/) (2026)
- [Task Schema and Binding: A Double Dissociation Study of In-Context Learning](https://mlsanity.com/paper/2512.17325/) (2025)
- [Large language models reorganize representational geometry during in-context learning](https://mlsanity.com/paper/2605.28854/) (2026)

## Abstract (arXiv)

Large language models place structured concepts on geometrically faithful manifolds: weekdays lie on a circle, months on another, usually taken to be a fixed world-model the network stores and looks up. We show that context is king: the structure a model actually uses is set by the in-context specification. A declarative rule fixes not only which relations the geometry encodes but its topology type: the same tokens form a cycle or a branching tree on command, built even on arbitrary, meaning-free tokens with no prior to inherit, which a relabeled stored shape cannot do. When the specification conflicts with a strong pretrained prior, the context-set geometry dominates it in capable models, read from the same activations (representational similarity 0.6--0.9 to the imposed structure versus near-zero to the prior), across the priors we test and both families we study (Gemma, Qwen). Activation patching shows the map is causally used, not a probe correlate: swapping one entity's activation for another's makes the model answer with the other entity's successor under the imposed order. A rough map forms readily, present even in small and base models; what scale gates is using it cleanly: clean dominance and the causal crossover emerge only in the larger models (up to Gemma-31B and Qwen-27B) and weaken or reverse below, so a mechanism present in a large model can be absent in a smaller one of the same family. Whether the model builds this geometry anew or reconfigures a stored one we leave open; operationally, the geometry it uses is the one the context specifies.