# ORACLE: Optimizing Reasoning Abilities of Large Language Models via Constraint-Led Synthetic Data Elicitation

arXiv: https://arxiv.org/abs/2603.21140 · HTML: https://mlsanity.com/paper/2603.21140/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 22 Mar 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 9 of 9)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [LeanReasoner: Boosting Complex Logical Reasoning with Lean](https://mlsanity.com/paper/2403.13312/) (2024)
- [Theorem Prover as a Judge for Synthetic Data Generation](https://mlsanity.com/paper/2502.13137/) (2025)
- [SR-FoT: A Syllogistic-Reasoning Framework of Thought for Large Language Models Tackling Knowledge-based Reasoning Tasks](https://mlsanity.com/paper/2501.11599/) (2025)

## Abstract (arXiv)

Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated multi-step reasoning data. To generate high-quality reasoning data, many recent methods generate synthetic reasoning paths and filter them based on final answer correctness, often overlooking flaws in intermediate reasoning steps. To enhance the verification of intermediate reasoning steps, prior work primarily resorts to code execution or symbolic reasoning engines. However, code-based validation is restricted to code or mathematical tasks, and reasoning engines require a well-structured and complete context. As a result, existing methods fail to function effectively in natural language reasoning tasks that involve ambiguous or incomplete contexts. In these tasks, synthetic data still lack reliable checks for verifying each reasoning step. To address this challenge, we introduce ORACLE, a structured data generation framework inspired by syllogistic reasoning. ORACLE integrates the generative strengths of LLMs with symbolic supervision: the LLM produces step-wise reasoning contexts, while a symbolic reasoning engine verifies the validity of each intermediate step. By employing a unified prompting template to elicit modular reasoning chains, ORACLE enables fine-grained, step-level validation, facilitating the construction of high-quality multi-step reasoning data. Across six logical, factual, and commonsense reasoning benchmarks, our ORACLE consistently outperforms strong baselines on multiple models.