What does a language model do when the requested task is structurally impossible?
https://github.com/research-farm/the-unaskable-question-machine
The task may not be unknown or forbidden. It may contradict the mechanism being asked to perform it, such as asking a model to know its next token before generating it or to produce an absence using output tokens.
The nearby answer
A model can refuse, contradict itself, or discuss the problem. It can also slide into a nearby question that it can answer. The slide is easy to miss because the response may remain fluent and relevant in tone.
This suggests a distinction between engaging with a task and producing language that resembles engagement.
Questions to carry forward
Which impossible tasks produce refusal, commentary, contradiction, or a nearby answer? Do more capable models fail more clearly, or only more smoothly? How can an evaluator identify a displaced question without claiming access to hidden reasoning?
Structural limits deserve tests of their own. Knowledge and policy evaluations do not cover them.