One Mechanism for Many Mental Spaces

The setup

Told “in reality the flower is red, but in the painting it's purple,” a capable model has to keep two values for the same entity apart without mixing them up. The same problem recurs every time a sentence opens a context other than the actual: a character's belief, a hypothetical, a memory, a story someone is telling. Linguists have a name for each of these individually, and a competing claim about whether they're the same thing.

Formal semantics keeps them separate: belief, counterfactual, and fiction each get their own logic.¹ Fauconnier's mental-space theory says they're all instances of one general operation: opening a space, filling it with values, and later reading from the right one. This pair of papers asks which picture a transformer implements, mechanistically, not which theory sounds nicer, but whether the same causal machinery actually does the work in every case.

A shared router over a value slot

The answer splits into two pieces, each locatable at a different token position.

A value slot, at the token where a value gets attributed, stores whatever content is assigned (a color, a location, a fact) and is agnostic to which space that value belongs to. A router (the space index), at the query token, is a separate low-rank subspace that selects which space's value a later query reads out. Neither piece alone would explain the behavior: the slot has to hold more than one candidate value at once, and something else has to decide which one surfaces.

How shared, exactly

“Shared mechanism” is a testable causal claim, not just a metaphor. Train a small subspace (via Distributed Alignment Search) to control which space's value comes out, using only counterfactual-space examples. Apply that same, unmodified subspace to belief-space examples it never saw. If the router really is one shared object, the subspace should still work.

It does, well above the floor a random subspace of the same size reaches, on three unrelated model families.² Pick a model below to see the within-type control (train and test on the same space type: always near ceiling) against the cross-type transfer (train on one type, test on a type it never saw), and where that lands relative to the paper's pre-registered bar for calling the mechanism unified.

Falcon3, the family with the least sharing among its per-type directions to begin with,³ is also the one where cross-type transfer comes in lowest. Every family tested still clears the bar. The generality even extends to a builder type never trained on at all: a subspace trained only on past-tense contexts transfers to future-tense contexts at 0.81–0.90 across the three families, against the same random floor.

Report and reasoning come apart

A router that only ever fed the final answer wouldn't tell you much about what the model actually uses internally. The papers test this with a task that has both a reported value and a value the model must derive by applying a rule to it.

Training a subspace on the reported color fully controls what the model reports (1.00 → 0.00 flip on the rule-derived consequent it doesn't touch); training a separate subspace on the rule-derived consequent fully controls that instead, leaving the report largely alone.⁴ The two subspaces are nearly orthogonal. What a model says and what it infers from what it holds can be pried apart with two different levers, a mechanistic foothold for the broader worry that a model's stated reasoning needn't match what it actually computed with.

Building a space mints a new router

Compose two space-builders (a belief about the past, a painting inside a belief, a photograph of a painting) and the model reuses the same value slot (high transfer, near the random floor's ceiling) but mints a distinct, near-orthogonal router at the query position for the compound.⁵ Constructing a new context is itself a binding operation, not a byproduct of already having the pieces.

One further wrinkle: the router only partly distinguishes belief from the rest. A coarse taxonomy survives inside the shared subspace: attitude reports, modals, and temporal reference each cluster a little more with their own kind than across kinds. But belief gets no special boundary beyond that. That's the more surprising reading: it argues for Fauconnier's unification as the right frame at the level this mechanism operates on, not merely a failure to find where semantics says the line should be.

The two papers

The cross-type generality above is one paper's whole argument. Belief gets its own paper because of its special status in philosophy, psychology, and linguistics (theory of mind, propositional attitudes, epistemology), even though mechanistically it turns out not to need special-casing.

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