Notes · Reading list · verifiable science data

Verifiable science data and environments

Ten papers on scalable, verifiable science data and environments for the Apertus 2 STEM climb. Nine are from the last twelve months; only MegaScience (July 2025) is older. Grouped by where the verifiable signal comes from.

The four for the slide: one executable environment, one simulator, one mined corpus, and the held-out target. Each in plain words first, then the numbers.

Ohio State, Wisconsin, CiscoApril 2026arxiv 2604.27977

envs, workflow, trajectories, models

D3-GymExecutable science environment

In plain words: take a real scientific repo with its data, turn a step of its analysis into a task, and synthesise a script that checks the model's output. The model writes and runs code; the script grades.
565 tasks from 239 real repositories: bioinformatics, computational chemistry, GIS, psychology
Verifier scripts synthesised plan-then-code, 87.5% agreement with human pass/fail verdicts
Rejection-sampled trajectories lift Qwen3-32B by +7.8 on ScienceAgentBench
The coding-heavy core: the verifier-synthesis step is reusable on Apertus-clean repos

CMU, LambdaApril 2026arxiv 2604.11805

codemodels 3B to 30B

Sim2ReasonSimulator-generated physics

In plain words: sample random physics scenes (masses, inclines, springs, initial velocities) as text, build each one in the MuJoCo engine, run it, and read the answer off the trajectory. Nobody annotates anything; the model only ever sees the text problem.
Three question types per scene: numeric (predict a quantity), reverse (recover a parameter from the outcome), symbolic (give the expression)
Trained on simulated data only: IPhO mechanics +5.4 at 32B, +7.5 at 3B; up to +17.9 on JEEBench
The clearest sim-to-real transfer result; the pattern to copy for chemistry and circuits

UC Santa BarbaraJanuary 2026arxiv 2601.05567

data released

WildSciLiterature-mined QA

In plain words: feed peer-reviewed papers to an LLM, get multiple-choice questions out, filter them by refinement and model voting. Cheap and broad, no code involved.
56K MCQ from Nature Communications papers, 9 disciplines, 26 subdomains
GRPO with MCQ reward on Qwen 1.5B and 3B: +7.3 average on GPQA-Aug, SuperGPQA, MMLU-Pro
Template for mining Swiss and EU open-access corpora; the non-coding counterweight in the mix

ApodexAugust 2026arxiv 2608.24979

eval only97 of 300 released

FrontierChallengeHeld-out target

In plain words: a real lab workflow with fixed inputs and a bundle of required deliverables; the model has to complete the whole thing end to end.
300 workflows, 97 public: quantum chemistry, molecular dynamics, materials, analytical chemistry, life science, electrochemistry
Best configurations pass 20 of 97; 75.5% of failing Claude Code runs still claimed completion
What the coding-heavy climb is for, and a warning about self-reported success

Literature-mined QASimulators and proceduralExecutable environmentsTooling

Submission month on arXiv. April 2026 alone brought BioAlchemy, Sim2Reason and D3-Gym.

Literature-mined QA

Papers and textbooks become multiple-choice or short-answer questions. Cheap, broad, verifiable by string match; quality rests on the filtering.

UC Santa BarbaraJanuary 2026arxiv 2601.05567

data released

WildSciScientific reasoning from in-the-wild literature

56K MCQ from Nature Communications papers, 9 disciplines, 26 subdomains; LLM generation, refinement with expanded options, model voting as filter
GRPO on Qwen 1.5B and 3B with verifiable MCQ reward; +7.3 avg on GPQA-Aug, SuperGPQA, MMLU-Pro at 1.5B
Template for mining Swiss and EU open-access corpora into RL prompts

U Chicago, ArgonneApril 2026arxiv 2604.03506

model on the Hub

BioAlchemyBiological literature into RL training data

345K verifiable biology QA pairs mined from research text, aligned to current topic distributions
BioAlchemist-8B: +9.1% over its base on biology benchmarks
Same recipe as WildSci at domain depth; shows a single field can carry a climb

SJTU, GAIRJuly 2025arxiv 2507.16812

CC BY-NC-SA

MegaSciencePost-training datasets for science reasoning

1.25M instances; 651K from 12.8K university textbooks across 7 disciplines, plus ablated public sets
SFT on Llama 3.1, Qwen2.5, Qwen3 beats the official instruct models on 15 benchmarks
Licence blocks it for Apertus training; useful as the eval and ablation reference

Simulators and procedural generators

Answers are computed, not annotated. Unlimited supply and controllable difficulty; the question is transfer to real problems.

CMU, LambdaApril 2026arxiv 2604.11805

codemodels 3B to 30B

Sim2ReasonPhysics Olympiad via RL on physics simulators

Random MuJoCo scenes through a DSL; numeric, reverse and symbolic questions with answers from running the simulation
Trained only on simulated data: IPhO mechanics +5.4 at 32B, +7.5 at 3B; up to +17.9 on JEEBench
The clearest sim-to-real result; the pattern to copy for chemistry and circuits

Inria, Univ. LilleMarch 2026arxiv 2603.02208

MIT5B + 2B tokens

Reasoning CoreProcedural data for symbolic pre- and post-training

Generators for PDDL planning, first-order logic, CFG parsing, causal reasoning over Bayesian nets, symbolic equations; external solvers verify, difficulty is continuous
Small-model pretraining mixes improve PlatinumBench without hurting LM loss
Follow-up (2608.05148): semantic validity alone does not guarantee training utility
European Reasoning Gym; licence-clean filler for the climb prompt pool

Executable environments

Agentic science: the model writes and runs code against real data, a hidden verifier grades. Closer to the tools/SWE climb than to a reasoning climb; the transferable idea is verifier synthesis.

Ohio State, Wisconsin, CiscoApril 2026arxiv 2604.27977

envs, workflow, trajectories, models

D3-GymVerifiable environments for data-driven discovery

565 tasks from 239 real scientific repositories: bioinformatics, computational chemistry, GIS, psychology
Evaluation scripts synthesised plan-then-code, 87.5% agreement with human pass/fail
Rejection-sampled trajectories lift Qwen3-32B by +7.8 on ScienceAgentBench
The anchor of the environment family; the verifier-synthesis step is reusable on its own

Shanghai AI LabJuly 2026arxiv 2607.28990

release not stated

SciDisco / SciThèqueScaling discovery environments for turn-level agentic RL

1,686 environments plus 504 stress variants over licence-tracked public data (UCI, OpenML, FRED, UniProt, CDC, USGS); tabular 61%, time series 17%, spatial 12%
Each environment carries a hypothesis, the data, a hidden evidence DAG and a verifier; DiscoPO gives turn-level credit
SciDisco-14B from Qwen3-14B: DiscoveryBench 35.2 vs Claude Sonnet 4 at 23.2
D3-Gym at 3× scale with licence tracking built in; nothing to download yet

Snowflake, UNCFebruary 2026, ICML 2026arxiv 2602.10090

code and environments

Agent World ModelSynthetic environments for agentic RL

LLM pipeline synthesises executable tool-use environments: scenario, tasks, database schema, interface, verification code
1,000 environments, 35K tools, 10K tasks; GRPO on 526 of them takes Qwen3-8B from 53.8 to 65.9 on BFCLv3, gains on τ²-bench and MCP-Universe
Not science-specific; the environment-synthesis recipe the science gyms could borrow to scale past hand-built repos

ApodexAugust 2026arxiv 2608.24979

eval only97 of 300 released

FrontierChallengeEvaluating scientific workflow completion

300 end-to-end lab workflows: quantum chemistry, molecular dynamics, materials, analytical chemistry, life science, electrochemistry; fixed inputs, required deliverables
Best configurations pass 20 of 97; 75.5% of failing Claude Code runs still claimed completion
The held-out target for the environment family, and a warning about self-reported success

Tooling

Generation infrastructure rather than a dataset.

NVIDIA15 September 2026arxiv 2609.17699

open source

NeMo Data DesignerExtensible framework for synthetic data generation

Declarative config: each field is a column with a generation strategy; samplers control diversity before any model call; LLM steps, validators and judges as stages
Behind recent Nemotron datasets; worked example is 96.5K validated text-to-SQL rows from 300K candidates, BIRD 26.8 to 41.8
The pipeline Nemotron-SFT-Science-v2 style sets come from; rebuild the science recipe on Apertus-clean sources

Caveat for any GPQA claim above: HLE-Physics moved from 47 to 79 after expert regrading (arxiv 2609.13009), closed-ended physics evals are noisy.

How the frontier reports scope the reasoning, STEM or math expert. Only MAI-Thinking-1 publishes the recipe; the rest give a scope line and the evals. Read for the Apertus 2 STEM climb (no issue yet), where the plan is copied from MAI.

Report	Expert	Scope	Data and reward	Tools	Evals
MAI-Thinking-1 §3.2	STEM climb, 1 of 3 specialists	single-turn problem solving: math, physics, chemistry, biology, CS, engineering, plus competitive code	STEM Mix, 5M (q, a) pairs mined from textbooks, PDFs, forums, contests, vendors; 550K hard; SymPy or judge, test cases for code	no	AIME, HMMT, GPQA-D, LCB v6
Nemotron 3 Ultra §3.3.2	STEM / general-reasoning teacher, 1 of 11	math, code, natural sciences, humanities, sociology	SFT 40B tokens (science 59%, math 24%, code 10%, general 7%), traces from DeepSeek-V4-Pro judged by gpt-oss-120b; then RL on non-STEM prompts, 128 per batch	"for these domains"	HLE, GPQA, MMLU-Pro, LCB v6, IMOAnswerBench, Apex Shortlist
Nemotron 3 Super	none, one joint RLVR policy	21 environments: math with and without Python, formal proofs, competition code, STEM, IF, safety, long context, agentic	prompts the SFT model always solves are dropped; joint training, single-environment runs regress	Python tool for math	AIME, GPQA-D, LCB, plus agentic
Nemotron-Cascade 2	math teacher = the SFT checkpoint	competition math and proofs	SFT: 2.6M math samples, 1.8M with tool calls, 816K proofs; MOPD from math, RLHF and multi-domain teachers	yes in SFT	AIME 25/26, HMMT, IMOAnswerBench, IMO-ProofBench
Kimi K3 §4.1.2	none: a "general" expert	general experience, vision, reasoning, faithfulness, search, knowledge work	verifiable problems in agentic environments plus an agentic generative reward model; 3 domains × 3 effort levels	yes	knowledge and reasoning suites, HLE
DeepSeek-V4 §5.1	a mathematics expert, 1 of 10+	not described	SFT then GRPO on "domain-specific prompts and reward signals"; rule-based verifiers, generative RM for the rest; 3 effort modes per expert	Lean 4 agentic for formal math	HMMT, IMOAnswerBench, Apex, HLE, GPQA-D, Putnam
Qwen3 §4	none: Reasoning RL stage of one model	math and code	3,995 query-verifier pairs, unseen in cold start, learnable, hard; GRPO 170 steps	no	AIME'24 70.1 to 85.1 (235B)
AceReason-Nemotron 1.1	none: math-only then code-only RL	math, code	prompt diversity beats responses per prompt; SFT gap 6.6 to 1.6 AIME after RL	no	AIME 24/25, LCB v5/v6
GLM-5	none: Reasoning RL stage, then agentic, general, cross-stage OPD	not described	not described
Apertus 1.5	none: one RLVR stage	math and code	349,300 prompts, async verl, then DPO and SDPO	no
Apertus 2 plan	"STEM math and general reasoning", 1 of 7 climbs	undefined; AIME-level target, grade-school math as prerequisite; Lean and code under #1027	TBD	open question	Artificial Analysis Index

Microsoft AI2026report PDF

full recipe

MAI-Thinking-1the one published STEM-expert recipe

Three specialists: STEM and competitive code, agentic coding and tool use, helpfulness and safety. Same RL recipe, different prompts and rewards. Consolidated by SFT on their traces, then a final RL stage.
STEM climb is "the longest of our three domain-specific RL training runs", single-turn, no tools. Every instance is (q, a) verified by SymPy or a judge, or (q, tests) for code.
Pipeline is the work: OCR and hierarchical parsing of PDFs, Q-A pairing across chapters and answer keys, taxonomy, PII and answer-leakage filters, MCQ and proofs rewritten to open-ended (MCQ can be guessed, proofs need a judge), 3× consensus, difficulty bins from pass rates of four solver tiers, blind grading to drop faulty ground truths.
Competitive code is a separate 160K-problem pipeline with tests, 17 languages. Dedup and decontamination in three stages against all reported benchmarks.
This is what "STEM expert" means in the Apertus plan. Scope it as this, minus code, and the deliverable is the verified prompt set with difficulty bins.

NVIDIAJune 2026arxiv 2606.15007

recipe + numbers

Nemotron 3 Ultrathe broadest definition

"General reasoning capabilities on a wide range of subjects including math, code, natural sciences, humanities, sociology, and tool use for these domains." Competitive coding is a separate teacher on top of it.
SFT seeds: Nemotron-Science-v1, a chemistry set, Multi-subject-RLVR, an internal set; easiest removed; 4 traces each (16 for hard) from DeepSeek-V4-Pro, judged by gpt-oss-120b. Held-out 3,000 prompts at pass rate 0.25 to 0.80.
After SFT, math, code and science were saturated, so RL ran on humanities and sociology prompts and "generalizes well, leading to significant improvements on all domains".
Teacher vs student: HLE 25.6 to 32.1, GPQA 85.0 to 88.5, IMOAnswerBench 84.5 to 92.5, Apex Shortlist 68.9 to 85.4. After MOPD the merged model kept only 17% of the HLE gain.
Two lessons: humanities prompts count as reasoning data, and the knowledge part of the gain does not survive the merge.

Moonshot, DeepSeek, NVIDIA2026

scope line only

The restwhat the other reports actually say

Kimi K3: no STEM expert. Three experts, general, general agents, coding agents, each at three effort levels; STEM appears only as verifiable visual reasoning inside agentic environments.
DeepSeek-V4: "for each target domain, such as mathematics, coding, agent, and instruction following, a separate expert model is trained": SFT then GRPO, nothing on data or rewards; the math expert is named once more as the OPD teacher for math prompts. Formal math is a separate Lean 4 agentic setting.
Nemotron 3 Super: no experts at all, one policy over 21 environments; the finding is that joint training is stable and single-environment training regresses elsewhere.
Nemotron-Cascade 2: the "math teacher" in its MOPD is the SFT checkpoint itself, trained on 2.6M competition-math samples and 816K proofs; no math RL stage.
Qwen3, AceReason: single models with a math-and-code RL stage; Qwen3's 3,995-pair prompt set is the smallest published climb.
Consensus: math and the sciences, single-turn, verifiable, no tools; code and proofs are their own thing everywhere.