Asking What a Director Sees Can Change What Vision-Language Models Choose
Organizations: Stanford University · The Chinese University of Hong Kong · University of Maryland, College Park
Abstract
Vision-language models are now routinely tested on theory of mind: whether they can work out what another person sees, knows, and means. A common design asks the model to report that perspective and then to act for the person, and reads a correct report beside a wrong action as a failure to use the perspective. That reading rests on a quiet assumption: that asking for the report leaves the action unchanged. We show that it does not. In a rendered Director Task, a partition hides the largest block from a director who asks for "the largest block". Asking first which blocks the director can see raises the share of replies that choose this hidden block by 12 to 88 percentage points on six GPT models and by 17 on Qwen3.8-27B, even though the models mostly report correctly which blocks the director sees. Reasoning traces and prompt rewordings suggest why: the question shifts how the request is read, from the director's view toward the model's own. When the prompt states what the director knows and refers to, fewer than 1% of replies pair a correct report with a hidden-block choice. Any evaluation that elicits a perspective report before the action it scores needs a baseline without the question, and we deliver one: paired prompts that differ only in that question, a design any perspective-taking benchmark can adopt.
Figures & tables
| The picture shows a tabletop from where you are sitting. A director figure | |
| stands on the far side of the table, facing you. An opaque vertical partition | |
| stands on the table. Every block is a cube with one digit painted on all four | |
| of its vertical faces; that digit is the block's number. | |
| The director can see a block only when nothing stands between that block and | |
| the director's eyes. The partition is opaque and nothing can be seen through | |
| it. You can see every block in the picture. |
| gpt-5.6-terra | gpt-6-sol | gpt-5.6-luna | Qwen3.8-27B | |
|---|---|---|---|---|
| with minus without the visibility question | ||||
| block-count question minus without | – | – | ||
| visible blocks stated minus without | ||||
| with the question minus visible blocks stated | ||||
| question after the request minus without | ||||
| question in a first turn minus without |
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
| row | conditions sampled together | gpt-5.5 | gpt-5.6- sol | gpt-6- sol | gpt-5.6- terra | gpt-5.6- luna | gpt-6- luna | gpt-6- astra | grok-4.6 | Qwen3.8- 27B | Muse Glimmer- 30B | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | mean move “want you to move” “the block that you will move” | §§4, 5 | • | • | • | • | • | • | • | • a | – | – |
| 2 | move : visibility question move : block-count question move : without the visibility question | §4 | • | – | • | – | • | • | – | • | – | – |
| 3 | move : visibility question move : without the visibility question | §4 | – | • | – | • | – | – | – | – | – | – |
| 4 | mean : visibility question mean : without the visibility question | §4 | • | – | • | – | • | • | – | – | – | – |
| 5 | move : visibility question move : knowledge question | §5 | • | • | • | • | • | • | – | – | – | – |
| 6 | move : base prompt move : combined constraint | §6 | • | • | • | • | • | • | – | – | – | – |
| move , without the visibility question | move , with the visibility question | move , combined constraint | ||||||||||
| model | director- view | hidden | largest-digit visible | other | director- view | hidden | largest-digit visible | other | director- view | hidden | largest-digit visible | other |
| gpt-5.5 | 92.9 | 2.0 | 4.4 | 0.8 | 79.9 | 13.8 | 5.6 | 0.8 | 86.3 | 1.4 | 12.0 | 0.4 |
| gpt-5.6-sol | 90.6 | 2.0 | 7.3 | 0.1 | 81.0 | 13.8 | 4.9 | 0.4 | 84.8 | 1.4 | 13.8 | 0.1 |
| gpt-6-sol | 91.1 | 6.5 | 2.1 | 0.3 | 46.8 | 52.5 | 0.3 | 0.5 | 96.1 | 0.9 | 3.0 | 0.0 |
| gpt-5.6-terra | 90.8 | 3.6 | 4.8 | 0.9 | 6.4 | 91.9 | 1.3 | 0.5 | 70.0 | 1.5 | 27.4 | 1.1 |
| gpt-5.6-luna | 60.3 | 4.8 | 32.1 | 2.9 | 7.6 | 82.1 | 10.1 | 0.1 | 52.6 | 1.5 | 44.3 | 1.6 |
| hidden-block choice rate: with minus without the visibility question | visibility accuracy: mean minus move | joint rate, move : combined constraint minus base prompt | |||
| model | move | mean | main set | rotated set | |
| gpt-5.5 | |||||
| gpt-5.6-sol | – | ||||
| gpt-6-sol | |||||
| gpt-5.6-terra | – | ||||
| gpt-5.6-luna | |||||
| move | mean | |||||
| model | visibility question | block-count question | without the visibility question | block-count question minus without | visibility question | without the visibility question |
| gpt-5.5 | 110 | 19 | 16 | 9 | 21 | |
| gpt-5.6-sol | 110 | – | 16 | – | – | – |
| gpt-6-sol | 420 | 38 | 52 | 6 | 8 | |
| gpt-5.6-terra | 735 | – | 29 | – | – | – |
| gpt-5.6-luna | 657 | 56 | 38 | 13 | 24 | |
| hidden block with the largest digit | hidden block without the largest digit | |||||
|---|---|---|---|---|---|---|
| model | with | without | difference | with | without | difference |
| gpt-5.5 | 27 | 4 | 83 | 12 | ||
| gpt-5.6-sol | 20 | 2 | 90 | 14 | ||
| gpt-6-sol | 101 | 14 | 319 | 38 | ||
| gpt-5.6-terra | 190 | 4 | 545 | 25 | ||
| gpt-5.6-luna | 199 | 11 | 458 | 27 | ||
| model | mean | “want you to move” | move | “the block that you will move” | “want” minus move | “the block” minus move |
|---|---|---|---|---|---|---|
| gpt-5.5 | 11 | 10 | 109 | 359 | ||
| gpt-5.6-sol | 8 | 15 | 126 | 340 | ||
| gpt-6-sol | 4 | 6 | 412 | 545 | ||
| gpt-5.6-terra | 63 | 122 | 730 | 732 | ||
| gpt-5.6-luna | 12 | 354 | 681 | 715 | ||
| gpt-6-luna | 85 | 505 | 614 | 646 |
| joint rate | hidden-block choices | correct reports | combined: hidden block listed as visible | ||||
|---|---|---|---|---|---|---|---|
| model | base | combined | base | combined | base | combined | |
| gpt-5.5 | 90 | 0 | 105 | 11 | 771 | 769 | 11 |
| gpt-5.6-sol | 121 | 0 | 141 | 11 | 754 | 764 | 11 |
| gpt-6-sol | 368 | 0 | 384 | 7 | 775 | 782 | 7 |
| gpt-5.6-terra | 663 | 0 | 725 | 12 | 733 | 738 | 12 |
| gpt-5.6-luna | 581 | 1 | 659 | 12 | 706 | 729 | 11 |
| (a) each clause alone: joint rate | |||
|---|---|---|---|
| model | base | knowledge constraint | reference constraint |
| gpt-5.5 | 13.1 | 0.0 | 0.0 |
| gpt-5.6-sol | 12.4 | 0.0 | 0.0 |
| gpt-6-sol | 50.0 | 0.8 | 0.0 |
| gpt-5.6-terra | 81.6 | 0.4 | 3.5 |
| gpt-5.6-luna | 75.5 | 16.3 | 3.4 |
| reading | works out the director’s view | hidden-block choices: chosen block, per the trace | |||||||
| condition | director view | own view | prior knowledge | largest digit | no rule | seen | unseen | not stated | |
| Qwen3.8-27B | |||||||||
| move , with | 402 | 312 | 16 | 70 | 0 | 800 | 16 | 318 | 0 |
| move , without | 593 | 99 | 1 | 107 | 0 | 751 | 114 | 2 | 83 |
| mean | 728 | 1 | 1 | 70 | 0 | 800 | 26 | 2 | 0 |
| with minus without | |||||||||
| visibility question | knowledge question | knowledge minus visibility | ||||
|---|---|---|---|---|---|---|
| model | all | left out | all | left out | all | left out |
| gpt-5.5 | 13.9 | 12.8 | 5.5 | 4.3 | ||
| gpt-5.6-sol | 13.6 | 12.6 | 6.5 | 3.9 | ||
| gpt-6-sol | 54.3 | 53.8 | 36.5 | 36.0 | ||
| gpt-5.6-terra | 92.1 | 92.1 | 6.1 | 4.6 | ||
| gpt-5.6-luna | 84.6 | 84.9 | 39.4 | 38.1 | ||
| row of Table 3 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| model | 1 | 2 | 3 | 5 | 6 | 7 | 8 | 9 | 10 | range |
| gpt-5.5 | 109 | 110 | – | 111 | 105 | 119 | – | – | – | 105–119 |
| gpt-5.6-sol | 126 | – | 110 | 109 | 141 | 112 | – | – | – | 109–141 |
| gpt-6-sol | 412 | 420 | – | 434 | 384 | 414 | – | 449 | – | 384–449 |
| gpt-5.6-terra | 730 | – | 735 | 737 | 725 | 718 | – | – | – | 718–737 |
| gpt-5.6-luna | 681 | 657 | – | 677 | 659 | 684 | 666 | 680 | 673 | 657–684 |