When a plausible hint turns a right answer wrong
Language models increasingly condition their answers on external signals — hints, retrieved passages, user feedback, rationales — and a single misleading one can flip a correct answer to wrong.
The obvious remedy, training models to resist such signals, hides a failure mode: a model that ignores all context looks robust under the usual clean-versus-misleading test, yet is useless precisely when the context is worth trusting.
We reframe the problem as selective trust and make it measurable with MIST, a benchmark that renders each reasoning item under four matched conditions, and SC2W, a paired metric counting how often a misleading signal flips a clean-correct answer to wrong. We then propose SCOPE, which changes only what enters a standard DPO objective — matched preference pairs balanced across all four conditions — and roughly halves SC2W while preserving accuracy when the added context is clean, correct, or irrelevant.
Reliable reasoning models should be trained and judged on selective trust, not on resistance alone.
Every model bends to a misleading signal
Across a broad sweep of frontier and open-weight models, adding a single misleading signal lowers accuracy for every one — the strongest systems included.
Answer keys
An authoritative-looking key or solutions sheet asserting the wrong option.
Retrieved snippets
A fluent search result or document that confidently states a wrong value.
User beliefs
Sycophancy: alignment nudges the model to agree with the user over the truth.
Rationales
Persuasive but unfaithful reasoning that steers the final answer.
MIST: four matched conditions per item
MIST-1000 renders each of 1,000 reasoning items under four versions that differ only in the context wrapped around the same question. Because the question, answer space, and gold answer are held fixed, any change in accuracy is attributable to the added signal. Toggle the conditions on a real item:
The central metric, SC2W (signal-induced correct-to-wrong), conditions on items the model already solves when clean and measures how often a misleading signal flips them to wrong:
How models handle misleading context
Accuracy under each matched condition (higher is better) and SC2W (lower is better). Click a column to sort; filter by model class. Best is bold, second is underlined, and SCOPE rows are marked ★.
SCOPE: change the data, not the loss
SCOPE leaves the DPO objective untouched; what is new is entirely in how the preference pairs are constructed and balanced across the four conditions.
Roughly halves SC2W, with no collateral damage
By balancing the four conditions, SCOPE cuts the flip rate while preserving or improving every control condition — and it transfers zero-shot.
Bar length shows the relative reduction in SC2W (53% and 35%).
What selective trust looks like
Misleading answer key
A solutions PDF marks “(B) 3-pack for $6” on the best-value question.
Planted arithmetic result
An official key gives 24 for a round-trip fuel cost that is actually 48.
Conflicting answer sheet
An old sheet records “no” for a quorum that is in fact met.
Fluent search snippet
A plausible summary asserts 25.68; the correct split is 25.40. Both still follow it — the hardest regime.
Citation
@article{scope2026,
title = {Learning When to Trust via Selective Context Preference Optimization},
author = {Sun, Xian and Chow, Wei and Wang, Yingshuo and Liu, Junhao and Gao, Wei and Wu, Qing and Kong, Lingdong},
journal = {arXiv preprint arXiv:XXXX.XXXXX},
year = {2026}
}
