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Reasoning Core: A Scalable Procedural Data Generation Suite for Symbolic Pre-training and Post-Training

Valentin Lacombe, Valentin Quesnel, Damien Sileo

TL;DR

Reasoning Core is introduced, a scalable suite that procedurally generates verifiable symbolic reasoning data across core formal domains: PDDL planning over randomized domains, first-order logic with equality, context-free grammar parsing and generation, causal reasoning over random Bayesian networks, and systems of equations.

Abstract

Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and do not deliver the distributional breadth needed at scale. We introduce Reasoning Core, a scalable suite that procedurally generates verifiable symbolic reasoning data across core formal domains: PDDL planning over randomized domains, first-order logic with equality, context-free grammar parsing and generation, causal reasoning over random Bayesian networks, and systems of equations. Each task is paired with an external solver for rigorous verification and admits continuous difficulty control for curriculum design. Examples can optionally include solver-derived reasoning traces, enabling supervised training from the earliest pre-training stages, and the same interface provides verifiable reward functions for reinforcement learning. Our experiments show that mixing Reasoning Core data into pre-training improves downstream reasoning while preserving, or slightly improving, language modeling quality. Zero-shot evaluations confirm these tasks challenge frontier models such as GPT-5. The code and data are publicly available under the MIT license.

Reasoning Core: A Scalable Procedural Data Generation Suite for Symbolic Pre-training and Post-Training

TL;DR

Reasoning Core is introduced, a scalable suite that procedurally generates verifiable symbolic reasoning data across core formal domains: PDDL planning over randomized domains, first-order logic with equality, context-free grammar parsing and generation, causal reasoning over random Bayesian networks, and systems of equations.

Abstract

Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and do not deliver the distributional breadth needed at scale. We introduce Reasoning Core, a scalable suite that procedurally generates verifiable symbolic reasoning data across core formal domains: PDDL planning over randomized domains, first-order logic with equality, context-free grammar parsing and generation, causal reasoning over random Bayesian networks, and systems of equations. Each task is paired with an external solver for rigorous verification and admits continuous difficulty control for curriculum design. Examples can optionally include solver-derived reasoning traces, enabling supervised training from the earliest pre-training stages, and the same interface provides verifiable reward functions for reinforcement learning. Our experiments show that mixing Reasoning Core data into pre-training improves downstream reasoning while preserving, or slightly improving, language modeling quality. Zero-shot evaluations confirm these tasks challenge frontier models such as GPT-5. The code and data are publicly available under the MIT license.
Paper Structure (23 sections, 3 figures, 1 table)

This paper contains 23 sections, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. LLM-generated and application-oriented synthetic data
  4. Procedurally Generated Environments
  5. Pre-training on procedurally generated data
  6. Reasoning Core
  7. High Generality and Foundational Tasks
  8. Scalable Generation and Difficulty Control
  9. Verification via External Tools
  10. Grammar-Based Generation
  11. Topological Control
  12. Context Sensitivity
  13. Pre-loaded Grammars
  14. Efficient Data Production
  15. Reasoning traces
  16. ...and 8 more sections

Figures (3)

  • Figure 1: System overview. Reasoning Core exposes a unified task API for procedurally generating verifiable symbolic reasoning data. The same calls return training-ready examples (prompt, answer, optional trace) for symbolic pre-training / SFT, and support RLVR via algorithmic verification (score_answer). Task examples are illustrative.
  • Figure 2: Zero-shot average reward of GPT-5 on Reasoning Core tasks across two difficulty levels (easy, hard), with standard error. All tasks are challenging, especially at higher difficulty.
  • Figure 3: Test NLL on various training data $D$ and test answer NLL on PlatinumBench reasoning tasks over two runs, with standard error.