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

2026-03-02

AI Summary

Existing approaches to symbolic reasoning data generation rely on fixed templates, limiting diversity and scalability of training signals. This work proposes the first unified, multi-domain procedural data generation framework that encompasses core formal reasoning tasks—including PDDL planning, first-order logic, context-free grammars, causal reasoning, and systems of equations—while supporting controllable difficulty levels, solver-based verification, and complete reasoning trace generation. The framework enables early integration of supervised signals during pretraining and provides verifiable rewards for reinforcement learning. Experiments demonstrate that pretraining with a mixture of generated data substantially enhances downstream reasoning capabilities without compromising language modeling performance. Zero-shot evaluations further reveal that these tasks remain challenging even for state-of-the-art models such as GPT-5.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: Generation
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

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.

Problem

• symbolic reasoning
• procedural data generation
• language model pre-training
• scalable reasoning data
• verifiable symbolic data

Innovation

• procedural data generation
• symbolic reasoning
• verifiable training
• curriculum learning
• reasoning traces