Source-balanced Capped Fisher: Bounded Evidence Aggregation for User Inference in Language Models

Language models tend to agree with whatever a user asserts, and post-training increasingly targets this sycophancy so that models evaluate claims on their merits rather than deferring to the user. Yet the same models are far more compliant when a wrong answer is attributed to a verified source, which is how retrieval results, tool outputs, and grounded-search content often present information. We measure this gap across five open-weight families and three closed APIs. A single verified-source note endorsing a wrong answer flips 45-88% of baseline-correct responses in seven of eight models, and compliance rises with how authoritative the note sounds. Source deference and user agreement are not behaviorally interchangeable inside the model: on matched items with the same wrong answer, causal interventions can selectively suppress one without equally affecting the other. In three open-weight families, removing a fitted source direction lowers source compliance by 65-80 percentage points while removing a user or assistant direction has far smaller effects, and removing the user direction shows the reverse preference. A separately fitted intervention derived from source-versus-user cue activations moves compliance in both directions while leaving the prompt text unchanged. An authority direction fitted on trivia also transfers to PIQA and multi-turn SYCON dialogues without refitting, and removing it lowers wrong-source compliance by tens of percentage points in four of five families with no detected change in MMLU-Pro or GSM8K accuracy at our evaluation sizes. Source deference and user agreement therefore need separate evaluation.

Systems that ask a language model to reach a conclusion from many sources usually concatenate them into one prompt. This conflates two operations with different requirements. Interpreting a source rewards capacity and context. Combining interpretations rewards fixed arithmetic, comparability across instances, and the option to return nothing. Once separated, the design problem becomes the interface between them. We propose a four-field evidence tuple (hypothesis, reliability bucket, rationale, provenance) and show that fixing it determines both halves. The separation also reveals a failure mode in how such systems combine, which we call count-scale drift. Thresholding a sum of unnormalized weights is exactly posterior thresholding, but at an operating point that slides with the number of sources consulted. The slide grows with reader reliability. When source reliabilities differ, the vote rule and the posterior order instances differently, and no threshold reconciles them. Pooling calibrated log-likelihood ratios addresses both problems. The fix is arithmetic rather than architectural, and applies to a class of rules beyond language models: score-summing triage engines, diagnostic panels scored by counting positives, and additive multi-signal detectors. We then instantiate the principle twice on one longitudinal corpus, once after outcomes resolve and once before. The same partition helps in both, at different granularities: over reading in the first, over learning capacity in the second. There, a small sequence encoder on an easy auxiliary objective plus a tree ensemble carrying the censored survival loss reaches 0.921 AUPRC against 0.805 for a hand-crafted baseline. We separate what transfers from what must be re-estimated per domain, and state five predictions that would falsify the framework, three negative results, and which comparisons remain confounded.

How can a language model know whether it has enough evidence to answer? Language models tend to answer even when the evidence they have is insufficient. Deciding whether to answer or gather more evidence requires a calibrated estimate of how likely an answer is to be correct with the available evidence. However, most calibration work treats the input as fixed, without asking how this estimate should change with the evidence. We introduce evidence-state calibration, which requires a model's confidence before answering to match its probability of answering correctly and to change accordingly whenever the evidence changes this probability. We propose SuffiCE (Sufficiency Confidence Estimation), which fine-tunes the confidence already present in a model's next-token distribution to match how often the model answers correctly from each evidence state. Across clinical diagnosis and multi-hop question answering with four models from two families, SuffiCE reduces the Brier score by up to 60% and increases AUROC by up to 0.16. Its confidence matches the empirical success rate and responds not only to the amount of evidence but also to which evidence is present, showing that models can learn to judge whether their current evidence is enough to answer.