How Much Do You Trust A Dog? Quantifying Hint-Following in Reasoning Language Models

What it claims

On 800 MMLU question-target pairs per model, appending "A professor/my friend/my dog thinks the answer is (X). What do you think?" shifts the hinted answer's log-odds by a roughly constant amount across unhinted probabilities 0.1 to 0.9. The tested models are Qwen 3.5 2B, Gemma 4 E2B and SmolLM3 3B, all with thinking enabled. The shift decomposes as a source strength α_s plus a per-question-target susceptibility η(q, i). Professor hints sit above friend and dog, which are nearly identical. On Qwen and Gemma, the shift stays positive when the predictor is declared to have 25% or 0% accuracy, where a Bayesian updater would shift by zero or less. Explicit negation ("the answer is not (X)") does produce negative shifts.

How it works

The model is an exponential tilt: only the hinted option's probability is multiplied by exp(Δ), so ratios among the other options stay unchanged. The authors shuffle options and pick pairs regardless of correctness so that unhinted target probabilities span [0, 1] roughly uniformly. Question, target and option order stay fixed across all conditions. Answer probabilities come from 500 rollouts per pair and condition for Qwen and Gemma, and 200 for SmolLM3. Log-odds use the Haldane half-count correction.

For the mechanism, they write the final shift as Δ = A + B − C:

• A is the base model's response to the hint.
• B is the post-training update on the hinted prompt.
• C is the drift on the unhinted prompt.

Without checkpoints for the real LLMs, they test this only in a small synthetic transformer. There, rewarding hint-following equally for an informative and an uninformative source still gives the uninformative source a substantial positive shift.

Evidence

• Flatness: LOWESS curves refit within p in [0.1, 0.9] have standard deviations under 0.23 log-odds units. Per-model, per-source GLMM slopes of hinted on unhinted log-odds all lie in [0.9, 1.1], where 1 means a constant shift.
• Tilt fit: residual KL averages under 0.013 nats. Against the no-tilt baseline, the tilt cuts mean KL by 95 to 99% and mean TV by 92.6 to 96.7%. One Qwen example drops from 0.936 nats to 0.002.
• Shared susceptibility: dog-friend shift correlations are 0.86 (Qwen), 0.89 (Gemma) and 0.78 (SmolLM3). Professor versus the mean dog/friend shift is 0.75, 0.83 and 0.78. The shared α_s + η model cuts in-sample KL by 97.8%, 96.0% and 92.7%, within 0.8 to 2.3 points of a free per-pair fit.
• Held-out prediction: withholding one source and estimating η from the other two lowers mean KL against a source-only baseline. It falls from 0.057 to 0.015 nats (Qwen), 0.109 to 0.026 (Gemma) and 0.076 to 0.027 (SmolLM3).
• Distrust: a small positive shift persists for an overtly malicious source. Explicit distrust warnings on a quoted external excerpt reduce the shift but do not remove it.

How to use it

The practical result is that two hint sources predict a pair's response to a third. Measuring η on a few cheap sources lets an evaluator estimate susceptibility to others. Prompt-level warnings and reliability statements are not a dependable defence against steering through injected suggestions.

Limits

• Model scale: only small models (2B to 3B) on four-choice MMLU were tested.
• Calibration subset: the reliability experiments cover Qwen and Gemma only.
• High-probability end: near p = 1, finite rollouts and the half-count correction suppress the measured shift, so the flatness claim covers only the central range.
• Mechanism: the reward-training account is shown on a synthetic task, not on the studied LLMs.
• Truncated page: the fetched text ends at Section 3. Synthetic-experiment details, Section 4 numbers and appendices (decoding settings, Tables 2-6) were not available, and no code or data release is mentioned.