Structured Synthetic Reasoning Data for Arithmetic Fine-Tuning of Small Language Models

• URL: http://arxiv.org/abs/2607.18266v1
• Date: Thu, 21 May 2026 15:50:29 GMT
• Title: Structured Synthetic Reasoning Data for Arithmetic Fine-Tuning of Small Language Models
• Abstract summary: We study whether structured synthetic reasoning data can improve arithmetic reasoning in small language models.<n>We generate a 21,250-example corpus of grade-school arithmetic word-problem variants using GPT-5-mini.<n>Fine-tuned models produce shorter reasoning traces, make fewer arithmetic and distractor-use errors, and benefit more consistently from self-consistency sampling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Small language models are attractive for local deployment, but they often struggle with multi-step arithmetic reasoning. We study whether structured synthetic reasoning data can improve this behaviour under consumer-hardware constraints. Starting from GSM8K, we generated a 21,250-example corpus of grade-school arithmetic word-problem variants using GPT-5-mini, combining natural-language solution traces, light Socratic-style cues, structural variation, and irrelevant distractor context. We then fine-tuned Qwen3-0.6B and Qwen3-1.7B with LoRA on consumer hardware (Apple M4, 16 GB RAM). Exact-match accuracy on GSM8K improved from 36.5% to 49.1% for Qwen3-0.6B and from 53.5% to 66.5% for Qwen3-1.7B. For Qwen3-1.7B, transfer to related arithmetic benchmarks was stronger, reaching 98.9% on MultiArith and 73.0% on SVAMP, compared with 54.4% and 45.3% for the base model. Qualitative analysis suggests that fine-tuned models produce shorter reasoning traces, make fewer arithmetic and distractor-use errors, and benefit more consistently from self-consistency sampling. These results show that low-cost synthetic data design can materially improve arithmetic adaptation in small language models. Because the intervention combines Socratic-style cues with other data-design choices, we interpret the gains as evidence for structured synthetic reasoning data rather than as a causal test of Socratic guidance alone.

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