Reasoning Core: Designing Broad Procedural Data for Completion-Supervised Reasoning Training

2026-08-05

AI Summary

This work addresses the lack of systematic design in procedurally generated data for supervised fine-tuning, which often fails to effectively enhance model reasoning capabilities. The authors propose a principled approach centered on compact objectives and calibrated difficulty, constructing 50 procedural generators spanning nine domains—including mathematics, logic, and planning—alongside a comprehensive auditing pipeline comprising semantic scoring, difficulty control, model-assisted validation, human adjudication, and regression testing to ensure training efficacy. Experimental results demonstrate that this method significantly outperforms baselines without procedural data and three alternative procedural datasets on a 3B-parameter model, achieving the highest average performance on DROP, LogiQA, and ARC-Challenge. The findings further reveal that semantic validity does not necessarily translate into training effectiveness.

Abstract

Procedural generators produce useful verifiable reasoning problems at scale, but have received less attention as data for completion-supervised fine-tuning. We introduce Reasoning Core, a collection of 50 generators spanning mathematics, logic, planning, state tracking, formal languages, structured data, games, causality, and code, with semantic scorers, difficulty controls, and task evaluators. Under a matched completion-supervised protocol, we compare Reasoning Core with Procedural Warmup, Reasoning Gym, and SynLogic across four base-model settings and multiple training durations. In the primary 3B comparison, Reasoning Core achieves the highest mean scores on DROP, LogiQA, and ARC-Challenge, exceeding both the baseline without procedural data and all three alternative procedural collections. Task-level analyses show that semantic validity alone does not ensure training utility, highlighting compact targets and calibrated difficulty as important design factors. We ran audits combining model-assisted review, human adjudication, and regression testing. Applied throughout Reasoning Core development and to the other collections, they reveal subtle mismatches among generation, rendering, targets, and scoring, a reminder that procedural generation alone does not guarantee correctness. The library, generated datasets, and audit material are publicly available.

Problem

• procedural generation
• reasoning training
• completion-supervised learning
• verifiable reasoning problems
• data quality

Innovation

• procedural generation
• completion-supervised training
• reasoning benchmarks
• semantic scoring
• difficulty calibration