TWO AXES OF LLM ABSTENTION: ANSWER CORRECTNESS AND QUESTION ANSWERABILITY

Standard approaches to making language models safer rely on thresholding a single confidence score—such as token log-probabilities or semantic entropy—to decide when a model should abstain from answering. This paper demonstrates that this approach is fundamentally flawed because it conflates two distinct failure modes: providing a wrong answer to a valid question (correctness) and attempting to answer a question that is inherently unanswerable or based on a false premise (answerability).

Through an analysis of five instruction-tuned models ranging from 2B to 14B parameters, the author shows that these two failure modes form a crossed geometry. Standard confidence scores are relatively effective at identifying when an answer is likely to be wrong, but they are nearly blind to whether a question is answerable. Conversely, linear probes applied to the model's hidden states can accurately identify unanswerable questions but are less effective at gauging the correctness of an answer.

This research is critical for building reliable AI systems that know when to remain silent. When models are prompted to check for false premises, they often fail because they cannot distinguish between sound and false premises, leading to indiscriminate refusals. By decomposing the problem into two axes, the author develops a factorized abstention policy that uses separate thresholds for answerability and correctness. This policy allows developers to set specific risk budgets for each type of failure, providing a measurable and controllable way to ensure model safety that scales effectively with model size.

• Answerability: The property of a question being logically valid and answerable, as opposed to being unanswerable or resting on a false premise.
• Correct-Answerable (C): A state where a question is answerable and the model provides a correct response.
• Wrong-Answerable (W): A state where a question is answerable but the model provides an incorrect response.
• Unanswerable (U): A state where a question cannot be answered correctly because it is nonsensical, lacks sufficient information, or contains a false presupposition.
• CREPE: A benchmark consisting of naturally occurring questions from Reddit that contain false presuppositions, used to test a model's ability to detect unanswerable queries in real-world data.
• Factorized Abstention: A policy that uses two distinct signals—one for answerability and one for correctness—to decide whether to answer a question, rather than relying on a single confidence score.