reasoning-core/procedural-pile

Reasoning-Core : Procedural Pile (ProcPile) ◉

ProcPile is designed for formal/symbolic pre-training, mid-training and SFT.
The data is procedurally generated on cpu and can be scaled to trillion tokens, and the difficulty is also adjustable with a single knob.
Unlike LLM-generated synthetic data, the answers are correct by design.

Task Categories

📐 Formal Proof Assistants & Formal Math: lean_missing_proof_line_selection · lean_candidate_compilation · metamath_entailment · metamath_core_select
⚖️ Automated Logic & Formal Semantics: logic_nli · logic_formalization · logic_qa · defeasible_nli
📜 Multi-Step Evidence & Inference: multistep_nli · multistep_evidence_retrieval · multistep_abduction · qualitative_reasoning
📏 Geometry, Causality & Qualitative Models: planar_geometry_relations · qualitative_causal
🔢 Mathematical Computation: arithmetics · math_word_problem · equation_system · sequential_induction
🔁 Symbolic Binding, Unification & Rewriting: lambda_reduction · rewrite_system · mgu_implied_equality · string_transduction
💻 Code, Execution & Program Reasoning: code_runnability · code_execution · code_analysis · program_synthesis
🕸️ Graph & Dependency Reasoning: graph_pathfinding · graph_successors · graph_dependencies
🎲 Probabilistic Reasoning: most_probable_evidence · most_probable_outcome
📝 Regex & Formal Languages: regex_following · regex_reasoning · parsing_derivation
✍️ Constrained Generation & Error Localization: constrained_continuation · locate_error · analogical_case_retrieval
📋 Table Processing: table_qa · table_equivalence · table_statistics
🔎 Set Operations: set_missing_element · set_expression
🧭 Planning, Constraints & State Tracking: planning · constraint_satisfaction · navigation · reference_tracking · coreference · theory_of_mind
🎮 Games & Strategic Reasoning: game_best_move · game_forced_win

Task Modes

Most tasks are available in three SFT/pretraining-friendly formats:
➡️ Instruct mode: direct prompt/answer format.
🧩 Few-shot mode: few-shot prompt/answer format with in-context examples.
✅ Verification mode: candidate-verification format: given a prompt and a proposed answer, determine whether the candidate is valid. Used about 10% of the time to strengthen self-verification capabilities.

🧪 Paper: Reasoning Core: A Scalable RL Environment for LLM Symbolic Reasoning
📦 Code: GitHub Repository (An updated paper for pre-training results is coming.)

RLVR version

See rc1 for the post-training/RLVR version

Abstract

We introduce Reasoning Core, a new scalable environment for Reinforcement Learning with Verifiable Rewards (RLVR), designed to advance foundational symbolic reasoning in Large Language Models (LLMs). Unlike existing benchmarks that focus on games or isolated puzzles, Reasoning Core procedurally generates problems across core formal domains, including PDDL planning, first-order logic, context-free grammar parsing, causal reasoning, and system equation solving. The environment is built on key design principles of high-generality problem distributions, verification via external tools, and continuous difficulty control, which together provide a virtually infinite supply of novel training instances. Initial zero-shot evaluations with frontier LLMs confirm the difficulty of Reasoning Core's tasks, positioning it as a promising resource to improve the reasoning capabilities of future models.

Usage

ds = load_dataset("reasoning-core/procedural-pile")

Citation

@article{reasoningcore2026,
  title={Reasoning Core: A Scalable Procedural Data Generation Suite for Symbolic Pre-training and Post-Training},
  author={Lacombe, Valentin and Quesnel, Valentin and Sileo, Damien},
  journal={arXiv preprint arXiv:2603.02208},
  year={2026},
  url={https://arxiv.org/abs/2603.02208}
}