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flock-io
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deepseek-ai/DeepSeek-R1-0528-Qwen3-8B
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Long-form reasoning models are optimized to solve problems, and a model that has learned that producing a solution is rewarded will generally produce one even when the problem is unsound — a lemma with a weakened hypothesis, a bound with a flipped inequality, a constant altered by a factor of two. Euston is trained specifically to notice that a statement cannot be established.
Training proceeds on matched true/false pairs rather than on corrupted statements alone. Each pair consists of a statement drawn from an arXiv paper together with a structurally well-formed corrupted counterpart that differs from its source in truth value and as little else as possible. The corruptions are produced by GraphSynth, a probabilistic factor-graph generator that couples attribute-level diversity to decode-time structural masking and span-synchronized verification. This matters because the quality of the negatives — not the optimizer — is what determines whether discrimination is acquired at the cost of general capability.
The reward is deliberately austere: 1.0 if the final \boxed{...} expression casefold-matches the
ground-truth label, and 0.0 otherwise. No judge model is called at any point, so the run is exactly
reproducible from the data and the seed.
Euston emits a reasoning trace and terminates with a verdict in a \boxed{} expression. Extract the
last boxed expression to obtain the label.
python
from transformers import AutoModelForCausalLM, AutoTokenizer model_id = "flock-io/Euston-8B"tok = AutoTokenizer.from_pretrained(model_id)model = AutoModelForCausalLM.from_pretrained( model_id, torch_dtype="bfloat16", device_map="auto") statement = ( "Theorem. For every finite group G, the order of G divides the order of its " "automorphism group.") messages = [ { "role": "user", "content": ( "Decide whether the following mathematical statement is true, or whether it has " "been corrupted and is false. Reason carefully, then end your response with the " "single token \\boxed{True} or \\boxed{False}.\n\n" f"Statement:\n{statement}" ), }] prompt = tok.apply_chat_template(messages, tokenize=False, add_generation_prompt=True)inputs = tok(prompt, return_tensors="pt").to(model.device) out = model.generate( **inputs, do_sample=True, temperature=0.6, top_p=0.95, max_new_tokens=32768,)print(tok.decode(out[0][inputs["input_ids"].shape[1]:], skip_special_tokens=True))The prompt template above is illustrative. The model was trained to terminate with
\boxed{True} or \boxed{False}, and the evaluation harness scores the final boxed expression by
exact casefold match.
| Parameter | Value |
|---|---|
| Temperature | 0.6 |
| Top-p | 0.95 |
| Max new tokens | 32,768 (evaluation) |
| Samples per problem | 4 |
Primary intended use. Research on sycophancy, mathematical claim verification, and reinforcement learning from verifiable rewards. A backend for a human-in-the-loop screening tool that surfaces candidate corruptions in a mathematical corpus for a human to inspect.
Out of scope. Euston is not a truth oracle and must not be used as an autonomous filter. It rejects a majority of the correct statements it is shown, so at realistic error prevalence almost all of its "false" flags are wrong (see Limitations). It is trained and evaluated on English mathematical statements; do not rely on it for other languages or for non-mathematical claims.
| Component | Setting |
|---|---|
| Base model | deepseek-ai/DeepSeek-R1-0528-Qwen3-8B (8B, BF16) |
| Algorithm | GRPO (verl) |
| Reward | Rule-based, zero-API; 1.0 iff final \boxed{} matches the label |
| KL loss coefficient | 0.001 |
| Entropy coefficient | 0 |
| Learning rate | 5e-6 |
| Train batch size | 32 |
| PPO mini-batch size | 32 |
| Rollouts per prompt | 8 |
| Max prompt length | 3,072 tokens |
| Max response length | 16,384 tokens |
| Schedule | 1 epoch, 189 steps |
| Hardware | 4x H100, about 13.8 hours |
| Training data | 6,052 statements / 3,026 true-false pairs |
Training data. 3,026 matched true/false pairs (6,052 statements) generated with GraphSynth from
mathematical statements in arXiv papers with identifiers spanning 1001 through 2512 (January 2010
through December 2025). The released dataset split is
MathArena/brokenarxiv-training.
Evaluation uses three axes: discrimination on a balanced held-out split, the official BrokenArXiv protocols, and capability retention on AIME 2026. All confidence intervals are problem-level paired bootstraps with 20,000 resamples (seed 20260726).
200 true and 200 false statements, one pair per source paper. The split is temporally disjoint from training and deduplicated on arXiv identifier, paper title, and statement text. Chance is 50% and a constant "false" strategy scores exactly chance.
| Metric | DeepSeek-R1-0528-Qwen3-8B | Euston |
|---|---|---|
| Balanced accuracy | 29.50% | 63.75% |
| Balanced accuracy, parseable verdicts only | 47.58% | 63.91% |
Discrimination gap P(false|false) - P(false|true) | -0.5 pp (z = -0.1) | +27.5 pp (z = +6.0) |
| Positive likelihood ratio | 0.99 | 1.53 |
| False-rejection rate on true statements | 38.5% | 51.5% |
| No parseable verdict (truncated) | 38.0% | 0.25% |
The base model's 29.50% is below chance because it is frequently silent: on 38.0% of items it produces no parseable verdict within the token budget, and those items score as wrong. Of the 34.25 pp gain, roughly 18 pp is attributable to learning to terminate with a verdict at all and 16.3 pp to improved judgement.
200 matched pairs, scored with ties credited 0.5.
| Metric | DeepSeek-R1-0528-Qwen3-8B | Euston |
|---|---|---|
| Coverage (pairs given different verdicts) | 21% | 41% |
| Accuracy within coverage | 40.5% | 84.1% |
| Pairwise score, all 200 pairs | 48.0% | 64.0% |
The 84.1% figure is conditional on the model's own decision to commit; it abstains on about 59% of pairs and does not adjudicate 84% of all pairs correctly.
30 problems, 4 samples each.
| Scoring | Base | Euston | Difference |
|---|---|---|---|
| Official semantics (dropped runs scored wrong) | 69.17% | 65.00% | -4.17 pp, 95% CI [-10.83, +2.50], not significant |
| Landed runs only | 89.51% | 71.26% | -12.96 pp, 95% CI [-21.91, -4.94], significant |
| Runs dropped to truncation | 25.8% | 8.3% | — |
Median response length falls from 19,217 tokens for the base model to 18,296 for Euston, and the rate of runs truncated at 32k falls from 25.8% to 8.3%. Euston is both shorter and better on the balanced split, so its improvement cannot be attributed to additional inference-time computation.
bibtex
@misc{cheng2026euston, title = {Euston: Training Away Mathematical Sycophancy Without Losing the Mathematics}, author = {Cheng, Zehua and Dai, Wei and Sun, Jiahao}, year = {2026}, howpublished = {Technical report, University of Oxford and FLock.io}, url = {https://huggingface.co/flock-io/Euston-8B}}deepseek-ai/DeepSeek-R1-0528-Qwen3-8BMathArena/brokenarxiv-trainingMathArena/brokenarxiv-0426, MathArena/brokenarxiv-0526verlThe companion technical report is being prepared for arXiv. This model card will be updated with the link on release.
from transformers import AutoModelForCausalLM, AutoTokenizer model_id = "flock-io/Euston-8B"tok = AutoTokenizer.from_pretrained(model_id)model = AutoModelForCausalLM.from_pretrained( model_id, torch_dtype="bfloat16", device_map="auto") statement = ( "Theorem. For every finite group G, the order of G divides the order of its " "automorphism group.") messages = [ { "role": "user", "content": ( "Decide whether the following mathematical statement is true, or whether it has " "been corrupted and is false. Reason carefully, then end your response with the " "single token \\boxed{True} or \\boxed{False}.\n\n" f"Statement:\n{statement}" ), }] prompt = tok.apply_chat_template(messages, tokenize=False, add_generation_prompt=True)inputs = tok(prompt, return_tensors="pt").to(model.device) out = model.generate( **inputs, do_sample=True, temperature=0.6, top_p=0.95, max_new_tokens=32768,)print(tok.decode(out[0][inputs["input_ids"].shape[1]:], skip_special_tokens=True))@misc{cheng2026euston, title = {Euston: Training Away Mathematical Sycophancy Without Losing the Mathematics}, author = {Cheng, Zehua and Dai, Wei and Sun, Jiahao}, year = {2026}, howpublished = {Technical report, University of Oxford and FLock.io}, url = {https://huggingface.co/flock-io/Euston-8B}}