One mechanism for many mental spaces: a shared router over a value slot in language models
Summary
This paper investigates how transformer language models implement multiple mental spaces (counterfactual, belief, fictional, etc.) using a shared router mechanism over a value slot, showing that a single low-rank subspace controls all space types and drives inference.
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# One mechanism for many mental spaces: a shared router over a value slot in language models Source: [https://arxiv.org/abs/2607.10248](https://arxiv.org/abs/2607.10248) [View PDF](https://arxiv.org/pdf/2607.10248) > Abstract: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 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 \(epistemology, theory of mind, and propositional attitude reports\)\. ## Submission history From: Oliver Steele \[[view email](https://arxiv.org/show-email/090b3254/2607.10248)\] **\[v1\]**Sat, 11 Jul 2026 10:30:36 UTC \(1,220 KB\)
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