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

2026-07-11

AI Summary

This study investigates how language models uniformly represent the values of a single entity across distinct mental spaces—such as belief, fiction, counterfactuals, and tense—and proposes a mechanism combining shared value slots with a low-rank router. For the first time at the mechanistic level, this approach empirically validates the unifying principle of Fauconnier’s mental space theory, revealing that a single, reusable routing mechanism operates consistently across diverse mental spaces and that belief space is not specially isolated. Through integrated analyses—including distributed alignment search, causal interventions, subspace decomposition, and attention head localization—the work demonstrates the mechanism’s generalizability across three major model families, showing it not only supports compositional reasoning but also disentangles internal model reasoning from surface-level output behavior.

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).

Problem

• mental spaces
• language models
• context representation
• belief
• counterfactual

Innovation

• mental spaces
• shared router
• value slot
• Distributed Alignment Search
• cross-type generality