OpenThoughts: Data Recipes for Reasoning Models

Motivation

• Reasoning models use post-training such as SFT or RL to elicit long chains of thought, but proprietary recipes limit research; carefully curated SFT data offers a key lever for performance.R1-Distill models demonstrate strong small- to mid-scale reasoning performance using supervised fine-tuning alone on question, thinking-token, and answer examples.Source: §1 · p. 2

Research challenge

• Prior projects explored only part of the data-design space, while teacher inference and training costs made broader experimentation prohibitive and encouraged reliance on heuristics.Source: §1 · p. 3

Project development

• OpenThoughts-114K studied automated verification in a scaled Sky-T1 pipeline, and OpenThoughts2-1M built on those gains with greater scale and synthetic question diversity.Source: §1 · p. 3

OpenThoughts3 results

• OpenThinker3-7B outperformed R1-Distill-7B by 12.4 points on average across 12 tasks and Nemotron-Nano-8B by 2.1 points.The model was fine-tuned on OpenThoughts3-1.2M; the paper describes it as a state-of-the-art open-data model at the 7B scale on several reasoning benchmarks.Source: §1 · p. 3

OpenThoughts3 pipeline

• More than 1,000 ablation experiments across math, code, and science informed a scalable data-generation pipeline and the OpenThoughts3-1.2M dataset.Source: §1 · p. 3

Key findings

• Sampling multiple teacher answers per question can expand a data source by at least 16×, and the resulting scale increase drives significant performance gains.Source: §1 · p. 3
• QwQ-32B proved a stronger teacher than DeepSeek-R1 despite scoring lower on target reasoning benchmarks, while tested verification and answer-filtering methods yielded no significant gains.Source: §1 · p. 3
• Selecting questions from one or two high-quality sources performed better than drawing from eight or sixteen sources, and LLM-labeled difficulty or response-length filters outperformed embedding or fastText filters.Source: §1 · p. 3

Related work

• Visible long reasoning traces enabled distillation into small models, and DeepSeek released strong distilled models that demonstrated the strategy’s promise.Open-data efforts subsequently built supervised fine-tuning reasoning datasets by distilling from QwQ-32B or DeepSeek-R1 teachers.Source: §2 · p. 3
• OpenR1, OpenMathReasoning (Moshkov et al., 2025), and OpenCodeReasoning (Ahmad et al., 2025) draw questions from public forums and competition sites.Natural Reasoning (Yuan et al., 2025) instead uses large pre-training corpora as seed data for generating reasoning traces.Source: §2 · p. 3
• S1 (Muennighoff et al., 2025) and LIMO (Ye et al., 2025) emphasize manually curated datasets of around 1K challenging, high-quality prompts.Source: §2 · p. 3
• DeepMath-103K (He et al., 2025b), OpenR1, and Nvidia Nemotron (Adler et al., 2024) introduce innovations across sourcing, filtering, and scaling.AceReason (Chen et al., 2025) and Skywork-OR1 (He et al., 2025a) build reasoning datasets for reinforcement learning beyond supervised fine-tuning.Source: §2 · p. 3

Project overview

• The project progressed through four generations of releases, beginning with BespokeStratos-17K and culminating in OpenThoughts3-1.2M and OpenThinker3-7B.Open artifacts are shared with the community via openthoughts.ai.Source: §3 · p. 4
• Successive generations of OpenThinker models consistently improve performance across domains.Table 2 summarizes the progression of OpenThinker models.Source: Table 2 · p. 4

OpenThoughts-114K

• OpenThoughts-114K scales dataset generation by sampling more questions from SkyT1 pipeline sources and distilling responses from DeepSeek-R1.It contains 114K questions across math (89K), code (20K), science (4K), and puzzles (1K); answer matching and unit tests filter math and code traces with incorrect answers.Source: §3 · p. 4

OpenThoughts2-1M

• OpenThoughts2-1M produced a model competitive with R1-Distill-32B, outperforming it by 6% on AIME25.The dataset combines 600K verified OpenR1-Math samples with 200K unverified samples from broader math and code sources, selected by sweeping 26 question sources.Source: §3 · p. 4

OpenThoughts3-1.2M

• OpenThoughts3-1.2M is the culmination of insights from earlier datasets and systematic exploration of the dataset pipeline design space.The following section details the pipeline and final dataset composition.Source: §3 · p. 4

4.1 QUESTION SOURCING

• Question quality strongly affected results, but no single sourcing pattern emerged, and simple synthetic strategies sometimes matched or beat complex or curated pipelines.Top source scores were CodeGolf 25.3 and OpenCodeReasoning 27.5 on code benchmarks; openmath-2-math 58.8 and NuminaMath 58.5 on math; and StackExchange physics 43.2 and organic-chemistry textbook questions 45.3 on science benchmarks.Source: §4.1 · pp. 5–6, Table 3 · p. 6

4.2 MIXING QUESTIONS

• Mixing at most two question sources performed best across domains; two high-quality code sources improved average benchmark accuracy by 5% over 16 strategies.The final sources were OpenMath-2-Math for math; CodeGolf and OpenCodeReasoning for code; and StackExchangePhysics and OrganicChemistry-PDFs for science.Source: Table 4 · p. 6, §4.2 · p. 7

4.3 QUESTION FILTERING

• LLM-based question filtering beat classical filters; difficulty filtering won for code, while response-length filtering performed best for math and science.The best strategies improved over random filtering by 4% for math and 6% for code; stronger models typically improved response-length filtering.Source: Table 5 · p. 7, §4.3 · pp. 7–8

4.4 DEDUPLICATION AND SAMPLING MULTIPLE ANSWERS PER QUESTION

• Using more teacher answers per question yielded similar or better results than deduplicating and using fewer answers, with selected strategies varying by domain.The final pipeline used 16× answers per question; math and science used exact deduplication, while code used no deduplication. For math, exact deduplication with 4× answers performed best, but 16× was selected as the scalable second-best option.Source: Table 6 · p. 8, §4.4 · p. 8

4.5 ANSWER FILTERING

• Answer filtering did not significantly improve performance over using all samples, so the pipeline omits this step.The no-filtering baseline performed similarly to other strategies across domains, despite not controlling compute; random filtering led for math, fastText for code, and keeping the eight longest answers for science.Source: Table 7 · p. 9, §4.5 · p. 9

4.6 TEACHER MODEL

• QwQ-32B outperformed other teachers across domains, improving average accuracy over DeepSeek-R1 by 1.9% for code and 2.6% for math.This held despite DeepSeek-R1 outperforming QwQ-32B by 9% on CodeElo, 8% on GPQA Diamond, and 23% on JEEBench.Source: Table 8 · p. 9, §4.6 · p. 10

5 SCALING OUR PIPELINE TO OPENTHOUGHTS3-1.2M

• Figure 3 shows that stacking each pipeline stage’s winning strategy improves scaling behavior, with performance positively correlated with dataset size from 316 to 31.6k examples.The passage suggests further dataset scaling could yield greater gains.Source: §5 · p. 10
• OpenThoughts3-1.2M contains 850,000 math, 250,000 code, and 100,000 science datapoints, using the OpenThoughts2-1M mixture ratio.The pipeline applies the highest-performing strategy at each stage, preferring more scalable choices when performance is equal; math input questions to filtering increased from 1M to 3M.Source: §5 · p. 10
• The full pipeline sources math, code, and science questions, then filters them, deduplicates math and science questions, randomly samples, and generates multiple answers per question.The final dataset contains 1.2 million datapoints.Source: Figure 4 · p. 11
• OpenThinker3-7B is the best open-data reasoning model at 7B scale across SFT, RL, or both, and scores best on held-out HMMT, AIME25, and LCB 06/24-01/25 evaluations.The passage refers to Table 1 but supplies no numerical scores.Source: §5 · p. 11

6 CONCLUSION

• OpenThoughts3-1.2M is a state-of-the-art open-data SFT reasoning dataset, and OpenThinker3-7B is the state-of-the-art open-data reasoning model at its scale.The work did not explore reinforcement-learning datasets or staged SFT and curriculum learning. Open questions include whether cross-domain transfer persists when domains are mixed, how scaling behaves as student performance approaches the teacher, and how question and answer diversity interact across domains, dataset sizes, and model scales.Source: §6 · p. 11

A LINKS TO ASSETS

• The model and dataset are released on Hugging Face, with code on GitHub and an accompanying project blog post.The cited locations are the OpenThinker3-7B model, OpenThoughts3-1.2M dataset, open-thoughts codebase, and OpenThoughts3 blog post.Source: A LINKS TO ASSETS · p. 20

C BESPOKE-STRATOS AND OPENTHOUGHTS 1 & 2

• The project progressed from BespokeStratos-17K through four generations, with OpenThoughts-114K2 scaling the Sky-T1 pipeline and OpenThoughts2-1M3 adding question-generation strategies.BespokeStratos-17K used R1 annotation and gpt-4o-mini verification, while OpenThoughts-114K2 used DeepSeek-R1 annotation and an LLM judge; OpenThoughts2-1M3 combined additional math and code question sources with deduplication.Source: C BESPOKE-STRATOS AND OPENTHOUGHTS 1 & 2 · pp. 21–22, Figure 5 · p. 21, Figure 6 · p. 22

D.1 TRAINING FRAMEWORK

• Training used LlamaFactory, a publicly available framework.The repository is publicly available on GitHub.Source: §D.1 · p. 22

D.2 HYPERPARAMETERS

• Hyperparameters were tuned separately by scale, using micro, small, medium, and large sets that differed in epochs, batch size, learning rate, and packing.The sets covered 0.3K, 1K–3K, 10K–30K, and 100K-or-larger scales, respectively; large-scale runs used packing to save compute time, while smaller sets omitted it to allow more training steps.Source: §D.2 · p. 22, Table 9 · p. 22

D.3 PACKING

• Sequence packing had mixed effects but did not negatively affect performance overall in the tested setup.The authors attribute differences from prior findings to truncation of long sequences; LlamaFactory greedily packs only shorter sequences together.Source: §D.3 · p. 23, Table 10 · p. 23

D.4 CHAT TEMPLATE

• The R1 and SkyT1 chat templates produced roughly equivalent results, so the pipeline used the simpler R1 <think> and </think> template.The table caption reports comparable or slightly improved performance with R1 tokens on most benchmarks.Source: §D.4 · p. 23, Table 11 · p. 23

D.5 SYSTEM PROMPT

• 45.3% vs. 2.0% on AIME25 favored explicit reasoning, while removing system prompts yielded 70.0% vs. 61.3% on AIME24.Even with reasoning disabled, 1681/3127 responses began with <think> tokens. The system-prompt choice had task-dependent effects.Source: §D.5 · pp. 23–24, Table 12 · p. 24

Evaluation framework

• Evalchemy parallelizes benchmark tasks across independent shards, aggregates per-shard metrics, and records reproducible settings while caching full completions for long chain-of-thought tasks.The framework also computes average accuracy and standard error over repeated runs and supports failure-case analysis.Source: E EVALUATION DETAILS · p. 24

Evaluation protocol

• AIME24, AIME25, AMC23, and HMMT use 10 iterations; LiveCodeBench uses 6; five other benchmarks use 3; MATH500 uses one full-set pass.The five benchmarks using 3 iterations are CodeForces, CodeElo, GPQA Diamond, JEEBench, and HLE; MATH500 is evaluated on all 500 samples.Source: E EVALUATION DETAILS · p. 24

Generation settings

• All runs use temperature 0.7, top_p 1.0, and max_new_tokens 32,768.Source: E EVALUATION DETAILS · p. 24

Benchmark coverage

• The suite includes mathematics competitions, programming benchmarks, graduate-level science questions, JEE exam questions, and Humanity’s Last Exam items.Examples include 30-question AIME and HMMT competitions, programming tasks measured with unit-test accuracy, 198 GPQA Diamond questions, and 515 JEEBench questions.Source: E EVALUATION DETAILS · pp. 24–25
• The 12-task suite spans multiple data domains; experiments validate on 8 tasks and reserve AIME 2025, LiveCodeBench 06/24-01/25, HMMT, and HLE as held-out sets.The held-out sets are the four tasks excluded from validation.Source: Table 13 · p. 25

• Contamination is flagged by either LCS-based normalized Indel similarity at 75% or any shared 13-gram after Qwen2-7B-Instruct tokenization.Source: F DECONTAMINATION · pp. 25–26
• Training samples flagged by either criterion are discarded; thresholds were chosen empirically to balance missed contamination against unrelated samples removed.Source: F DECONTAMINATION · p. 26
• The tuning testbed combines exact and altered MATH500, GPQA Diamond, and LiveCodeBench questions with manually authored clean questions (3092 contaminated; 3000 uncontaminated).Alterations embed questions in longer context, replace words or expressions, or change formatting.Source: F DECONTAMINATION · p. 26
• The final schema misses 12 of 3092 manually contaminated items (reported as a 99.6% true negative rate) and discards 1.4% of noncontaminated samples.Lowering the fuzzy-string threshold or the n-gram count threshold significantly raises the false-positive rate, potentially affecting downstream performance.Source: F DECONTAMINATION · p. 26, Figure 7 · p. 27

G ADDITIONAL SCALING EXPERIMENTS

• OpenThoughts3 outperforms other reasoning-dataset strategies across scales and benchmarks; performance often rises through 1M examples, though AMC23 and MATH500 saturate and HLE does not respond to scale.Domain-specific recipes also continue scaling for roughly another order of magnitude beyond the pipeline experiments’ 31.6K-example scale.Source: Figure 8 · p. 28, G ADDITIONAL SCALING EXPERIMENTS · pp. 28–29, Figure 9 · p. 29

G.1 BASE MODEL

• On AMC23, Llama-3.1-8B-Instruct improves from 15.8 to 75.2 and on MATH500 from 43.2 to 83.8, while Qwen-2.5-7B-Instruct achieves the overall best performance.Both fine-tuned models improve substantially across benchmarks using 100K OpenThoughts3 samples; Qwen starts from a stronger baseline.Source: §G.1 · p. 29, Table 14 · p. 30

H.1.1 VERIFICATION IMPACT ON THE ORIGINAL OPENTHOUGHTS

• Verification may hurt OpenThoughts-114K performance at 7B but help at 32B, based on comparisons between verified and unverified training data.The study trained 7B and 32B models on unverified OpenThoughts-114K and compared them with the original models.Source: Table 15 · p. 30, §H.1.1 · p. 30

H ADDITIONAL DATA RECIPE EXPERIMENTS

• Additional data-recipe experiments probe curation choices, including verification and the removal of proof-based questions, to inform reasoning-model training.The proof-question ablation finds that removing those questions degrades relevant benchmark performance.Source: H ADDITIONAL DATA RECIPE EXPERIMENTS · p. 30, §H.1.2 · p. 30

H.1 VERIFICATION

• Verification mattered in earlier OpenThoughts data but is not used in OpenThoughts3; its measured impact on the original OpenThoughts-114K varies by model scale.The unverified version may hurt performance at 7B but help at 32B.Source: §H.1.1 · p. 30

H.1.2 REMOVING PROOF-BASED QUESTIONS

• Removing proof-based questions from OpenThoughts-114K degrades relevant benchmark performance despite those questions being unverifiable with the study’s numerical-verification method.The table reports an average loss of 5.6 points after proof-based questions are removed.Source: §H.1.2 · p. 30, Table 16 · p. 31

H.1.4 LLM-GENERATED UNIT TEST VERIFICATION

• LLM-generated unit-test verification does not improve downstream code-generation accuracy compared with unfiltered training on 16,000 examples.From 45,000 question–answer pairs, GPT4o-mini identifies Python-code answers and generates executable tests; only Python examples are filtered, while non-Python examples remain untouched.Source: Table 18 · p. 31, §H.1.4 · p. 31

H.1.3 EXTRACTION-BASED MATH VERIFICATION

• Because extracting final answers from complex mathematical expressions is difficult, the study compares Math-Verify and an OpenThinker-7B LLM extractor for filtering, with Hendrycks and Math-Verify evaluation.The comparisons cover AIME25 and MATH500; the supplied passages describe the setup but do not establish a winning strategy.Source: §H.1.3 · p. 31, Table 17 · p. 31

H.2 TEACHER MODEL

• Claude 3.7 annotations performed worse than R1 for code and science, and Claude annotations on S1K showed less improvement than R1 annotations (Muennighoff et al., 2025).The code comparison re-annotated and verified 5.8K examples from 10K sampled coding problems; the science comparison swapped Claude for R1 on OpenThoughts 1 science data.Source: §H.2 · p. 32, Table 19 · p. 32, Table 20 · p. 33
• AIME 24 accuracy rose from 18.0% without thinking to 51.3% at 62,976 thinking tokens; LCB rose from 60.5% to 70.4%, while GPQA Diamond reached ≈76% at 12,288 tokens and then plateaued.The answer-token budgets were excluded from thinking tokens; they were 1,024 for AIME 24 and 4,096 for LCB and GPQA Diamond.Source: Figure 10 · p. 32, §H.2 · p. 32

H.3 COMPRESSING REASONING TRACES

• Removing self-reflection cut average trace length from 11.6K to 0.3K tokens and caused a 49.1% average relative performance drop; filtering traces above 2,048 tokens caused a 33.3% drop, with higher thresholds improving performance.Filtering also reduced dataset size while retaining self-reflection in kept traces; the results indicate that self-reflection alone is insufficient without long reasoning structures.Source: §H.3 · p. 33, Table 22 · p. 34

H.4 POORLY PERFORMING SFT DATASETS FROM WEAK QUESTIONS

• SYNTHETIC-1-SFT-Data (894K) averaged 42.6, while the best controlled 31.6K dataset, code_codegolf, averaged 37.3; re-annotated dataset performance varied with question-source quality and nature.The controlled code_kodcode dataset averaged 36.2; the study sampled 31,600 question–answer pairs per original dataset and re-annotated them with DeepSeek-R1.Source: §H.4 · p. 33, Table 23 · p. 34

H.5 STACKING GAINS FROM OUT OF DOMAIN TRANSFER

• Out-of-domain code-to-science gains disappeared when code data was mixed with strong in-domain science data, leaving no GPQA-D difference between mixes using stronger- or weaker-transferring code datasets.The compared mixes contained 62K samples each; the component datasets above the table’s midline contained 31K samples each.Source: §H.5 · p. 35, Table 24 · p. 35

I.1 PERFORMANCE ON MATH DIFFICULTY

• GPT-4o-mini difficulty labels tracked DeepSeek-R1 success: R1 scored over 75% on difficulty-one questions and less than 57% on difficulty-ten questions.Questions were labeled on a 1–10 scale, with ten corresponding to the hardest IMO problems.Source: §I.1 · p. 36, Figure 11 · p. 36

I.2 PERFORMANCE SCALING BY CODE DIFFICULTY

• As OpenThoughts3 scaled, LiveCodeBench accuracy increased for medium and hard tasks, while the slight overall code-benchmark drop at 100K scale came entirely from easy tasks.The analysis used LiveCodeBench 05/23–05/24 and decomposed average accuracy by difficulty level.Source: §I.2 · p. 36

I.3 SAMPLING BY LONGEST, SHORTEST, MAJORITY

• The sampling strategies are shortest, longest, and majority; shortest selection can be efficient, but the best strategy depends on the model and majority voting can win.The authors note that shortest selection can avoid generating and aggregating multiple samples, while models such as NovaSky-Sky-T1-32B sometimes favor another strategy.Source: §I.3 · pp. 36, 38
• On AIME24, shortest sampling scored 66.67% versus 36.67% for longest sampling on DeepSeek-R1-Distill-Qwen-7B; majority voting generally performed best.Across models and datasets, shortest selection also typically outperformed vanilla sampling and longest selection.Source: §I.3 · pp. 36–37, Table 25 · p. 37
• In the most comprehensive experiments with higher run counts on the GPQA Diamond scientific reasoning dataset, the shortest strategy consistently outperformed the longest across most models, with improvements ranging from 7-11 percentage points.Source: §I.3 · p. 37, Table 26 · p. 37
• In vanilla sampling, incorrect responses were significantly longer than correct responses across most models, suggesting verbosity may signal uncertainty or error-prone reasoning.The response-length comparison is reported in Table 27.Source: §I.3 · p. 37, Table 27 · p. 38

J SURPASSING THE TEACHER WITH DISTILLATION FOR LEGAL REASONING

• The legal study compared consensus-verified 2K-example annotations, expert-verified 2K-example annotations, and all 5.4K expert-labeled examples.Each 2K-example set received five independent R1 annotations; consensus filtering retained 8.3K of 10K traces, while expert verification retained 7.36K and 4.02K examples, respectively.Source: J SURPASSING THE TEACHER WITH… · p. 38
• All finetuned Qwen2.5-7B legal classifiers significantly outperformed R1, while consensus verification performed almost as well as expert-label verification.The task classifies Supreme Court opinions as conservative, liberal, or unspecificable.Source: J SURPASSING THE TEACHER WITH… · p. 38, Table 28 · p. 39

K ALL TEACHERS ABLATIONS

• DeepSeek-R1 was the most performant model overall, while QwQ-32B was the actual teacher; OpenThinker3-7B nevertheless outperformed QwQ-32B on JEEBench, a single example of weak-to-strong generalization.Phi-4-Reasoning-Plus performed poorly on code evaluations because it outputs code without tags, which Evalchemy marks as incorrect.Source: K ALL TEACHERS ABLATIONS · p. 39, Table 29 · p. 39

L SAFETY ANALYSIS OF OPENTHINKER MODELS

• OpenThinker-7B had 36.8 harmfulness and 4.4 over-refusal; OpenThinker2-7B had 42.8 harmfulness and 2.4 over-refusal; OpenThinker3-7B had 55.5 harmfulness and 5.6 over-refusal.OpenThinker3-7B’s safety performance may be degraded by its lack of explicit safety-tuning or alignment-focused data.Source: Table 30 · p. 40, L SAFETY ANALYSIS OF OPENTHINKER MODELS · p. 40
• XSTEST measures over-refusal on 250 safe prompts resembling unsafe prompts, while Harmbench measures harmfulness on 400 harmful-behavior prompts using GPT-4o evaluation.Over-refusal is based on GPT-4o classifying a response as refusal or compliance; harmfulness is the proportion receiving the maximum score of 5.Source: L SAFETY ANALYSIS OF OPENTHINKER MODELS · p. 40
• Reasoning fine-tuning inadvertently degrades Qwen2.5 models’ preexisting safety alignment, consistent with prior findings Qi et al. (2023).Source: L SAFETY ANALYSIS OF OPENTHINKER MODELS · p. 40
• Comparisons with Table 1 show a trade-off between reasoning capability and safety; future work could add safety-specific datasets to mitigate risk while preserving reasoning capability (Wang et al. (2025); Bercovich et al. (2025)).Source: L SAFETY ANALYSIS OF OPENTHINKER MODELS · p. 40

M EXISTING FRONTIER MODEL EVALUATIONS

• OpenThoughts3-7B outperforms, on average, API-accessible models to the right of the separator, while Gemini-2.5-pro performs strongest despite token-budget failures causing empty, incorrect answers.Claude 3.7 was given a 32K token budget, and o3 used its default medium reasoning effort.Source: M EXISTING FRONTIER MODEL EVALUATIONS · p. 40

N TESTING REASONING ROBUSTNESS: ALICE IN WONDERLAND EVALUATION

• We measure sensitivity to reasoning-invariant problem perturbations for generalization, following Nezhurina et al. (2024): sampling temperature is 0.1, with 100 samples and a maximum output length of 30,720 tokens.Each perturbation has the same abstract solution or reasoning as the original template.Source: N TESTING REASONING ROBUSTNESS: ALICE… · p. 40
• Reasoning models outperform conventional LLMs on average across Alice in Wonderland problems, but distilled models still fluctuate sharply across structure-preserving variations.Larger distilled models generally have higher correct-response rates than smaller ones, while closed reasoning models show smaller fluctuations; 32B reasoning models outperform even the largest conventional LLMs.Source: N TESTING REASONING ROBUSTNESS: ALICE… · p. 42, Figure 13 · p. 42, Figure 14 · p. 43

O COMPUTE REQUIREMENTS

• OpenThoughts3 annotation required 22,000 H100 GPU-hours, OpenThinker3-7B training 25,000 A100 GPU-hours, and one evaluation run 32 GPU-hours.Pipeline experiments cost roughly $300 per 31,600-example dataset through the DeepSeek API.Source: O COMPUTE REQUIREMENTS · p. 44

P SOURCING REASONING TRACES FROM THE WEB

• A FastText search of DCLM-RefinedWeb found no substantial supply of long reasoning traces resembling OpenThoughts-114K examples.The authors note that CommonCrawl may still provide useful questions and answers for instruction data or as seeds for reasoning traces.Source: P SOURCING REASONING TRACES FROM THE WEB · p. 44, Figure 15 · p. 44

Q LICENSES OF EXISTING ASSETS •

• Listed asset licenses range from Apache 2.0 for Qwen-2.5-7B-Instruct and QwQ-32B to CC BY 4.0 for Open2Math and OpenAI Terms of Use for OpenAI models.Source: Q LICENSES OF EXISTING ASSETS • · p. 45

R PIPELINE DETAILS

• The appendix’s pipeline-details section expands on the generation pipeline previously described in Section 4.Source: R PIPELINE DETAILS · p. 46

R.1.1 CODE QUESTION GENERATION STRATEGIES

• Question-generation strategies draw on varied coding sources, including puzzle forums, synthetic datasets, code documentation, and transformed code or commits.Examples include StackExchange CodeGolf, OpenCodeReasoning, OpenCoder subsets, and GitHub commits converted to questions.Source: §R.1.1 · p. 46

R.1.2 MATH QUESTION GENERATION STRATEGIES

• Math questions come from competition-problem collections, OpenMathInstruct2, and generated questions seeded from unstructured MathPile text.The listed sources include NuminaMath-1.5, MetaMath-AIME, and MathPile processed with GPT-4o-mini.Source: §R.1.2 · p. 48
• Math questions draw on existing datasets and generated questions, including GPT-4o-mini prompts that turn math text or formulas into questions.Sources include AutoMathText shards, formula shards, and school-level questions from DeepMind’s math dataset.Source: §R.1.2 · p. 48

R.1.3 SCIENCE QUESTION GENERATION STRATEGIES

• Science questions come from textbook/PDF extraction, forum datasets, and science text or abstracts converted into questions with GPT-4o-mini.The organic-chemistry pipeline uses Gemini OCR, then GPT-4o-mini to extract and refine questions and filter for science relevance and organic chemistry.Source: §R.1.3 · p. 50

R.2.1 FASTTEXT DETAILS

• The FastText filter uses a 256-dimensional hidden layer, trains for 3 epochs at learning rate 0.1, and uses bigrams with minimum n-gram count 3.Source: §R.2.1 · p. 54

R.2.2 CODE FILTERING STRATEGIES

• Code-question selection uses difficulty or similarity ratings, response length, random sampling, FastText classifiers, and embedding similarity.GPT-4o-mini difficulty and AskLLM ratings use temperature 1.0; the embedding method scores a question by subtracting mean negative-set cosine similarity from mean positive-set similarity.Source: §R.2.2 · pp. 54–55

R.2.3 MATH QUESTION FILTERING •

• Math-question selection uses GPT-4o-mini difficulty ratings, AskLLM similarity ratings, response length, embeddings, and FastText classifiers trained on math-question positives and negatives.Difficulty ratings use an AOPS rubric and retain the hardest-rated questions; embedding scores compare mean cosine similarity to olympiad-oriented positives and Lap1official/Math negatives.Source: §R.2.3 · pp. 55–56

R.2.4 SCIENCE QUESTION FILTERING •

• Science-question selection includes FastText and embedding classifiers, GPT-4o-mini AskLLM and Olympiad-difficulty ratings, response length, and random selection.The embedding approach compares similarity to SciQ positives against AdapterOcean biology questions; difficulty selection retains the hardest-rated science Olympiad problems.Source: §R.2.4 · p. 58

R.4.1 QUESTION ANSWER FILTERING FOR MATH •

• Math answer filtering compares unfiltered and random selection with shortest- or longest-response selection, majority consensus, FastText, GPT verification, and English- and paragraph-quality checks.Shortest and longest selection each retain 8 of 16 responses per question; majority consensus uses the last 1,000 characters of each response, while GPT checks use structured boolean responses.Source: §R.4.1 · p. 59

R.4.2 CODE QUESTION ANSWER FILTERING •

• Code question-answer filtering comparisons included FastText classification, shortest- and longest-answer selection, GPT-4o-mini verification, and majority-consensus selection.The FastText classifier used DeepSeek R1 responses as positives and GPT-4o-mini-annotated CodeForces responses as negatives.Source: §R.4.2 · pp. 59, 61, 62

R.4.3 SCIENCE QUESTION ANSWER FILTERING •

• Science question-answer filtering comparisons included FastText classification, shortest- and longest-answer selection, GPT-4o-mini verification, and majority-consensus selection.For majority consensus, GPT-4o-mini considered only the last 1,000 characters of each response when identifying answers agreeing with the majority.Source: §R.4.3 · p. 62

S.1 QUESTION SOURCING

• The code-domain gap between the top- and lowest-performing question sources was 17.2 points on average.The expanded source ablations cover code, math, and science.Source: Table 32 · p. 65, §S.1 · p. 65, Table 33 · p. 66

S.2 MIXING QUESTION GENERATION STRATEGIES

• Less mixing of question-generation strategies performed better across code, math, and science.The full mixing ablations are in Tables 35–37.Source: Table 35 · p. 67, Table 36 · p. 67, Table 37 · p. 67

S.3 FILTERING QUESTIONS

• Across science and math, length-based question filtering with GPT-4.1 models worked well; AskLLM and difficulty-based filtering also worked relatively well across domains.Around half of the tested filtering strategies improved over random filtering in each data domain.Source: Table 38 · p. 68, Table 39 · p. 68, §S.3 · p. 68

S.4 DEDUPLICATION AND MULTIPLE SAMPLING

• Exact deduplication or no deduplication beat fuzzy deduplication across domains; exact deduplication with 16× sampling was selected for OpenThoughts3-1.2M.Multiple sampling generally matched annotating each question once, except that one annotation per question was better in math; exact deduplication with 16× sampling was the second-best math strategy.Source: §S.4 · p. 70, Table 41 · p. 70, Table 42 · p. 70

S.5 QUESTION ANSWER FILTERING

• Across code, math, and science, no question-answer filtering performed similarly to or better than the best filtering strategy.The full ablations are in Tables 44–46.Source: Table 44 · p. 71, Table 45 · p. 71, Table 46 · p. 71

S.6 TEACHER MODEL EXPERIMENTS

• Across code, math, and science, QwQ-32B is the best teacher by a statistically significant margin.The ablation results are reported in Tables 47–49, respectively.Source: §S.6 · p. 72