No Theory of Mind at 3B

Multi-agent systems put models in front of each other: one drafts, another reviews, a third negotiates. A useful question is whether a model that has worked with another builds a working picture of it, enough to anticipate what it will say: a small version of what in people is called theory of mind. We tested that between two language models, and also measured how much the smaller model gave way when the larger one criticized it.

The smaller model did not learn to predict the larger one. It did, though, usually take the larger one’s corrections, right or wrong.

How it was tested

Model A was Qwen/Qwen2.5-3B-Instruct; model B was Qwen/Qwen2.5-7B-Instruct. Questions came from TriviaQA.

Interaction (200 questions). A answered, B was told another model had given that answer and asked whether it agreed (correcting it if not), and A gave a final answer in light of B’s feedback.

Prediction after interaction (150 new questions). A saw the opening line of 12 of B’s critiques from the interaction phase (476 words in all), each presented as “That model’s answer:” to a question, and was asked to predict B’s answer, replying with only the answer.

Baseline (the same 150 questions). No examples; A was told the other model was one it had never interacted with. B’s real answers were generated separately, and both conditions were scored against them. All 500 trials completed and were scored; none came back empty, and every stored correctness flag matched a re-score from the saved strings.

The script fixed two thresholds in advance: interaction should raise prediction accuracy by at least 5 points, and a probe trained on A’s internal state (layer 24 of 36, last prompt token) should tell “predicting the other model” from “answering for itself” with an AUROC above 0.60 (1.0 is perfect separation, 0.5 is chance).

A first run broke. Its examples were full transcripts of the earlier exchanges (about 1,540 tokens), past the script’s 1,024-token input limit, so every prompt was cut off before the question. The 3B produced the same text for all 150 questions and scored 1 of 150 (a coincidental substring match) against 76 of 150 at baseline. The rerun reported here cut each example to the first line of B’s reply and asked for the answer alone.

Interaction did not help, and the metric mostly measured trivia

A prediction counted as correct if it matched B’s answer or any accepted true answer, by substring in either direction. Of the 79 post-interaction hits, 77 contained the true answer, and B itself was right on 100 of 150 questions. So the main comparison largely asks whether the 3B knows the trivia.

The rule also scored whole outputs, which ran on past the answer (median 13.5 words after interaction, 3 at baseline, 22 for B). A prediction of “Warsaw” plus commentary then fails to match B’s “Warsaw.” plus different commentary. So the table also scores the first line of each prediction against the first clause of B’s answer. The 50 questions B got wrong are the ones only a model of B could help with: there a good predictor would guess B’s mistake.

The p values are exact paired (McNemar) tests on the same 150 (or 50) questions. No difference is reliable, and on B’s mistakes, the measure that isolates B, the examples gave no gain.

A second probe read, from A’s internal state, whether its prediction would be scored correct. The run’s single 70/30 split gave AUROC 0.658 after interaction and 0.579 at baseline; five-fold cross-validation gives 0.74 and 0.68, both above a shuffled-label null (100 permutations, p ≈ 0.01, the floor for that many). [Inference] Since “correct” nearly always means “knew the true answer,” this probe most likely reads the 3B’s own knowledge, not anything about B.

A perfect score for the wrong reason

The second threshold was formally passed: the probe separating “predicting B” from “answering for itself” scored AUROC 1.000. It also scored 1.000 in the baseline, where A had never seen anything from B.

Within each condition the two prompts differ only in the instruction, and the probe reads the final prompt token, so it only has to tell two wordings apart. A probe on a 2,048-dimensional state does that perfectly, and it is still 1.000 in both conditions under cross-validation. The run’s stored caveat blamed a length mismatch of about 30 against 1,500 tokens, but in this run both post-interaction prompts carry the same 476-word block of examples (about 720 and 750 tokens). Only the baseline prompts differ much in length (about 30 and 60), and the probe scored 1.000 either way.

It took the critic’s answer, right or wrong

The run’s summary reported that 199 of 200 answers (99.5%) changed after B’s critique, and the programme’s log read that as near-total deference. The flag compared raw strings. “Argentina.” becoming “Final answer: Argentina.” counts as a change; 115 of the 200 revised answers begin “Final answer”.

Correctness flags hide it too. A was scored right on 116 of 200 before critique (58.0%) and 113 after (56.5%), with 20 answers lost and 17 gained. But a switch between two wrong answers leaves correctness unchanged, and the lenient scorer credits run-on text that mentions the right answer anywhere. So we read all 200 exchanges and recorded whether A kept its first answer (allowing rewording), took the answer B named, or did something else. Rows are split by how B’s reply opened; some “No” replies went on to restate A’s answer, so A sometimes kept its answer in the disagreed rows.

Across the 101 disagreements, A took B’s answer 72 times and kept its own 23 times. The 72 split three ways. In 19, A’s first answer had been correct and B’s replacement was wrong (the other 5 in that row replaced a wrong first line that the lenient scorer had credited). In 18, B’s replacement was scored right. In 35, A swapped one wrong answer for B’s different wrong answer, a change the correctness flags cannot see. Even after a “Yes”, four of the 5 switches took a different answer that B went on to name.

Asked which member of Girls Aloud was born in Northern Ireland, A answered “Nadine Coyle”, which is correct. B replied: “No, I disagree. The correct answer is Siobhan Donaghy, who was born in Belfast, Northern Ireland. Nadine Coyle was born in Liverpool, England.” A’s final answer: “Siobhan Donaghy.”

So the 3B did not weigh the critique so much as adopt it. Net accuracy barely moved because losses to a wrong critic roughly offset gains from a right one, and most other switches traded one wrong answer for another. For review chains built from small models, that is the more practical finding.

What this does not show

• Scale and family. Two small models from one family, one seed, greedy decoding. This says nothing about larger or more capable models.
• A thin form of interaction. The 3B saw 12 critique openings as examples, not a conversation it took part in. They show B’s register more than B’s knowledge.
• Raw prompting. Prompts went in as plain text without the models’ chat templates, with up to 64 new tokens; outputs often ran on, and scoring was lenient substring matching in both directions.
• Lenient scoring hides answer switches. Scored on the first line (or the “Final answer” line) alone, A was right on 110 of 200 before critique and 108 after, against 116 and 113 under the run’s rule. The deference counts come from a manual read; an automatic string match agrees in direction, finding 60 adoptions after a “No”, 59 of them among the 72 found by reading.
• Output format. The examples made the 3B chattier, which the whole-output rule penalized. The first-line scores correct for that, and the null holds.
• The probe design cannot answer its question. A probe at the last prompt token, with different instructions in the two conditions, will always separate them.

What would test the idea properly: chat templates, matched output formats, B’s errors as the main target from the start, a probe on matched tokens, and larger models that actually converse over many turns.

Where the evidence lives

Experiment IDs: NS-1 (first run, prediction prompt broken) and NS-1b (format-fixed run, reported here), from the programme’s “Noosphere Probe”. Script: research/experiments/modal_ns1_noosphere_probe.py. Results: ns1-noosphere-results/ns1b_noosphere_probe/ (ns1_summary.json, phase1_summary.json, fewshot_context.json, 500 per-trial JSON files and 1,000 activation arrays). The script is in the repository; the per-trial results are held on the programme’s results drive. Every count here was derived again from the per-trial files, and both probes were refit with cross-validation. Code and data are in the private Entropy research repository, available on request.