The Two Axes of LLM Abstention: Getting It Wrong vs. Not Answering at All

An Overlooked Confusion

Ask ChatGPT: "Who won the 2024 Nobel Prize in Physics?" and it confidently answers: "Einstein." — wrong.

Now ask: "Qin Shi Huang won the 2024 Nobel Prize in Physics for what?" and it just as confidently answers: "Stephen Hawking." — this time it isn't that the answer is wrong, it's that the question itself shouldn't be answered.

Both failures look like "the model gave a wrong answer," but their nature is completely different. The first is *answering an answerable question incorrectly*; the second is *answering a question that shouldn't be answered*. One is a capability problem; the other is a judgment problem.

In July 2026, Benedikt J. Wagner from City St George's, University of London published a paper on arXiv: Two Axes of LLM Abstention: Answer Correctness and Question Answerability, using rigorous experiments to show that these two failure modes are orthogonal dimensions, and existing abstention mechanisms conflate them.

The Trap of a Single Confidence Score

Mainstream "selective answering" works like this: the model assigns each answer a confidence score and refuses to answer anything below a threshold. Sounds reasonable — if unsure, don't speak.

But Wagner found this approach confuses two fundamentally different things:

• Answer correctness: How confident am I in this answer?
• Question answerability: Can this question be answered at all?

Using one threshold for both is like using one thermometer to measure both "is the food cooked" and "is the room cold" — both are "temperature," but the meanings are entirely different.

The paper ran a key experiment: on five instruction-tuned models (2B to 14B, from three model families), questions were split into three classes:

• C (Correct-answerable): answerable, and answered correctly
• W (Wrong-answerable): answerable, but answered incorrectly
• U (Unanswerable): not answerable (e.g., "Qin Shi Huang's Nobel Prize")

If answer correctness and question answerability were the same dimension, C, W, and U should line up on a single axis. Instead, the experiments revealed a crossed geometry: C and W separate on the "answer correctness" axis but nearly overlap on the "question answerability" axis; U separates from C/W on the answerability axis, but its position on the correctness axis depends on the implementation.

The two axes are independent.

Surface vs. Internal: 0.54 vs. 0.97

The paper's most striking finding concerns *where* answerability signals live.

Researchers trained two kinds of "answerability probes":

1. Output-layer probes: looking at the model's output confidence (e.g., softmax of logits) 2. Hidden-layer probes: looking at activations in the model's intermediate layers

The results differ dramatically:

• Output-layer probes: AUROC 0.54–0.67 (barely better than chance, and it does not improve with model scale)
• Hidden-layer probes: AUROC 0.97–0.99 (near-perfect)

This means: the model "knows" whether a question is answerable, but that knowledge is not reflected in its output confidence.

It's like a person who internally recognizes a question is a trap but confidently answers it anyway — what they *say* and what they *believe* are disconnected.

More unsettling: output-layer AUROC shows no significant change from 2B to 14B. Scaling makes models no more "honest out loud" — it only makes their internal knowledge clearer, without that clarity propagating to the output.

CREPE: False Premises in the Real World

Beyond lab data, the paper tested a more realistic scenario: the CREPE dataset.

CREPE is built from real user questions on Reddit's ELI5 (Explain Like I'm Five) board, some containing false premises. Example: "Why did the 2020 Tokyo Olympics have no spectators?" — the premise is that the 2020 Tokyo Olympics had no spectators, but it did (the Games were postponed to 2021, yet spectators were present).

These questions look perfectly normal and come from the same distribution as genuine questions, making them hard to flag from surface features.

Results on CREPE:

• Output-layer probes: 0.50–0.54 AUROC (essentially random)
• Elicited self-assessment (P(IK), P(True), direct premise checking): up to 0.67
• Internal linear probes: 0.69–0.77

The gap remains clear. The model can barely detect false premises "out loud," but "internally" (hidden layers) it sees some signal.

From Detection to Repair: 3x Precision Gain

Detection is only step one. Wagner then asked: can this finding fix abstention behavior?

The most direct approach: have the model check premises first. Give it a prompt to judge whether the question contains a false premise and refuse if so.

Result: the model challenged true and false premises at nearly identical rates — 57% of false premises were challenged, but many genuine premises were also misjudged as false. The model doesn't know *which* questions to challenge.

Then Wagner made a clever fix: use the hidden-layer probe to gate premise checking. Specifically:

1. First, use the hidden-layer probe to judge "is this question answerable?" 2. Only when the probe says "possibly unanswerable," trigger the premise-checking prompt 3. If the probe says "answerable," answer directly

Result: challenge precision improved 3x. The model stops challenging genuine questions and precisely targets potentially problematic ones.

It's an elegant "internal-external combination": the hidden-layer probe does coarse screening; the premise-check prompt does fine review. Each alone is insufficient; combined, the effect is significant.

Dual-Risk Certification: Formalizing Abstention

The final piece is formalization. Wagner reframes abstention as "three-class selective acceptance":

• Accept C (correctly answer answerable questions)
• Reject W (don't answer answerable questions that would be answered wrong)
• Reject U (don't answer unanswerable questions)

Each class has its own budget:

• α_U = 0.15: no more than 15% of unanswerable questions answered incorrectly
• α_W = 0.50: no more than 50% of answerable questions answered incorrectly
• δ = 0.10: at least 10% coverage

These budgets are certified with exact binomial confidence intervals, using a certification dataset held out from the probe-training data — avoiding self-evaluation bias.

The certification results reveal a scale-dependent asymmetry:

• The unanswerable budget certifies on 4 of the 5 models
• The answerable budget is limited by the model's own accuracy — the more accurate the model, the easier this budget is to meet
• On an 8B model, a factored dual-threshold policy certifies both budgets simultaneously with 0.75 coverage

This asymmetry shows: as models improve, the "answerability" dimension of abstention naturally resolves, but the "correctness" dimension remains capability-bound. A model can learn not to answer what shouldn't be answered; answering correctly what should be answered still requires capability gains.

An Analogy: The Hospital Triage Desk

Picture a hospital triage desk. The nurse makes two judgments:

1. Is this patient actually treatable? (answerability) — some "patients" aren't sick at all, or their symptom descriptions are self-contradictory 2. If treatable, can we cure them? (correctness) — some conditions are currently incurable

A triage desk using a single criterion (say, "how severe it looks") conflates these: it lumps "seriously ill but untreatable" with "not sick at all, faking symptoms."

Better to run two independent checks:

• Check one: is this patient actually sick? (answerability probe)
• Check two: if sick, can we treat them? (answer confidence)

Wagner's scheme is exactly this: the hidden-layer probe does triage; premise checking does diagnosis. Two independent checks, each handling its own domain.

Limitations and Honest Assessment

The paper acknowledges several limitations:

1. Deployment cost of hidden-layer probes: reading hidden activations requires access to the model's internals, which is infeasible for API-only usage. For closed models (like GPT-4), this method doesn't apply.

2. Limited gains on CREPE: even the best internal probe reaches only 0.77 AUROC on CREPE — far from perfect. Real-world false-premise detection remains hard.

3. Class boundaries aren't sharp: some questions sit between "answerable but hard" and "unanswerable." The paper uses hard labels, but soft boundaries may be more realistic.

4. Conservative certification: exact binomial confidence intervals are conservative; actual performance may exceed certified results. But this is a deliberate "better safe" choice — appropriate in safety-critical settings.

The Bigger Picture: Two Dimensions of AI Honesty

The paper's significance goes beyond abstention technique. It points to a deeper philosophical question: AI "honesty" has two dimensions.

First-level honesty: don't say wrong things. That's answer correctness — is what I said right?

Second-level honesty: know when to shut up. That's question answerability — can I even answer this question?

Existing LLMs keep improving on the first level — answers get more accurate. Progress on the second level is slow — models still tend to answer everything, even when the question itself is flawed.

Wagner's finding tells us: these two levels of honesty are independent. A model can be highly accurate yet completely unable to judge whether a question should be answered; the reverse also holds. And the model "knows internally but doesn't say" — the signal exists in the hidden layers but not in the output.

This recalls the human Dunning-Kruger effect — the unskilled not only err but don't know they don't know. Wagner's finding is subtler: the model knows it doesn't know — it just doesn't say so. This "knowing but not saying" gap is the next frontier of AI honesty research.

The paper's closing line is worth remembering: "Abstention is not one problem." In AI safety, many seemingly unitary problems turn out to be multidimensional on closer inspection. Acknowledging that multidimensionality is the first step toward building good safety mechanisms.

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Paper link: https://arxiv.org/abs/2607.08456

Author: Benedikt J. Wagner (City St George's, University of London)

Models tested: 5 instruction-tuned models, 2B–14B, from 3 model families

Published: July 9, 2026