# One mechanism for many mental spaces: a shared router over a value slot in language models

arXiv: https://arxiv.org/abs/2607.10248 · HTML: https://mlsanity.com/paper/2607.10248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Causal Mediation Analysis for Interpreting Neural NLP: The Case of Gender Bias](https://mlsanity.com/paper/2004.12265/) (2020)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [Emergent World Models and Latent Variable Estimation in Chess-Playing Language Models](https://mlsanity.com/paper/2403.15498/) (2024)
- [Language Models use Lookbacks to Track Beliefs](https://mlsanity.com/paper/2505.14685/) (2025)
- [The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?](https://mlsanity.com/paper/2507.08802/) (2025)
- [Representational Analysis of Binding in Language Models](https://mlsanity.com/paper/2409.05448/) (2024)
- [Counterfactual reasoning: Testing language models' understanding of hypothetical scenarios](https://mlsanity.com/paper/2305.16572/) (2023)
- [How Do Transformers Learn Variable Binding in Symbolic Programs?](https://mlsanity.com/paper/2505.20896/) (2025)
- [Just-in-time and distributed task representations in language models](https://mlsanity.com/paper/2509.04466/) (2025)
- [Counterfactual reasoning: an analysis of in-context emergence](https://mlsanity.com/paper/2506.05188/) (2025)

## Abstract (arXiv)

Language builds discourse contexts other than the actual: a painting, a belief, a memory, a hypothetical. Each is a mental space in which the same entity can take a different value, as when a flower is red in reality but purple in a portrait. Formal semantics keeps these contexts apart because their logics differ (modal, temporal, doxastic, depictive). Fauconnier's mental-space theory, by contrast, treats them as one space-building operation. We ask which of these a transformer language model implements, and find a mechanistic version of Fauconnier's unification. The model uses one router/slot format across the inventory: a reusable value slot stores attributed content, and a causally manipulable router (the space index) selects which space is read. A subspace trained with Distributed Alignment Search to control one space type, counterfactual, belief, fictional, or temporal, also controls the others, well above a random floor, on three model families. Belief, which formal semantics marks as a distinct case, is not specially separated. The router is low-rank, composes additively with entity identity, and acts through a few late-layer heads. Two further results show the mechanism drives inference and composes: a subspace trained on a rule-derived conclusion flips what the model infers while dissociating from what it reports, and composing space-builders mints a fresh router over the shared slot. This paper establishes the cross-type generality. A companion paper develops belief in depth, because of its special status in philosophy, psychology, and linguistics (epistemology, theory of mind, and propositional attitude reports).