Belief–Reality Separation Lives in Routing over a Shared Value Slot in Language Models
Told “Anna believes the cup is blue; in reality it's red,” a model answers blue about Anna and red about the world. That separation lives in the routing at the query position, not in the value itself.
Background: False-belief tasks, The lookback mechanism, Interchange interventions & DAS
The setup
“Anna believes the cup is blue; in reality it is red” asks a model to keep two answers about one object ready at once, and give back the right one depending on which question is asked. Two things could explain that: a single tagged value (“blue, and it's Anna's belief”), or a value that's neutral about whose it is, paired with something else that decides which value a given question wants.
The paper finds the second picture, at two different token positions.1 A generic value slot binds the attributed value, wherever it comes from. A router, at the query position, picks which frame, belief or reality, a given question reads out. Belief is special only in how the value gets into the slot in the first place, not in how the slot works.
Two ways to fill the slot
A belief can be handed to the model directly (“Anna believes the cup is blue”) or it can be left implicit, inferable only from what Anna could see (“Anna saw Ben paint the cup blue”). The asserted route binds straight into the slot. The derived route has to look back at what the character actually observed.
Schematic: a drawing of the two routes, not a readout of the model's internals. The derived route's dependence on visibility is behaviorally established by an input intervention (swap who saw the painter: the derived belief flips ~99% of the time, the asserted belief ~0%); it is not localized to a specific attention head or QK path. The measured transfer and flip rates are in the text and notes below.
An input-level test makes the two routes' difference stark: swap which character actually saw the paint job, and the derived belief flips in ~99% of cases, while the asserted belief, given an identical extra visibility clause, barely moves at all.2 Yet both routes converge on the same slot: a subspace (a handful of directions in the model's hidden state) trained to control one substantially steers the other (0.74–1.00 across three architectures), sharing a ~3-dimensional core.3
The slot doesn't know; the router does
The central causal test: does belief-vs-reality live in the value, or in something that decides which value to read?
Both loci sit on the residual stream. The two clauses bind their colors into a shared value slot; a router at the query position selects which frame the answer reads. Route and the packet enters the router (the answer switches frame; the slot's values are untouched). Patch the slot and the packet enters the slot (the value itself is overwritten, whichever frame is routed).
Real: the cross-frame transfer (0.87–0.95, floor 0.03) and router cross-leg leakage (≤0.16, bar 0.30) in the table are the paper's fig-dissection numbers. Schematic: the residual-stream layout, token boxes, and the traveling slice are a drawing of the mechanism, not a readout of activations. The belief paper localizes the two loci to a depth band (0.25–0.75 of depth), not to specific layer indices or attention heads.
Interchange a belief-trained subspace into the reality readout (or the reverse) and it moves the readout 87–95% of the way, as if the slot never tagged which frame the value belonged to.4 A separate splice test at the query position tells the opposite story: a router trained to flip belief queries barely moves reality queries, and vice versa, on two of the three architectures not at all.5
Put the two halves together and the paper's title is the finding: belief–reality separation lives in routing, at the query position, over a value slot that itself carries no such tag.
When the behavior shows up at all
Everything above is studied at 7B and up because that's where the underlying behavior, correctly attributing a belief from described visibility, first becomes reliable and order-independent. Three architectures fail this at 3B (via recency sensitivity or plain unreliability); the same three solve it cleanly at 7B.
Second-order false belief needs both scale and instruction-tuning
The recursive case reuses the same machinery in a suggestive way: a subspace trained on first-order belief steers second-order belief at 0.90 of its own range, and vice versa at 1.00. But the router for the nested belief is, once again, distinct from the first-order router (zero cross-transfer both directions). Recursion looks like a flat re-application of the same slot-and-router format, not a new mechanism, though this specific result is single-model and the paper flags it as the least-replicated finding here.
The cross-type companion
The same router/value-slot format this paper works out in depth for belief is, per the companion paper, one shared object reused across counterfactual, fictional, and temporal reference too; belief needs no special-casing at the level this mechanism operates on.