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

arXiv:2607.18266v1 Announce Type: new 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.

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.

Artificial Intelligence (cs.AI)

arXiv:2607.18266 [cs.AI]

(or arXiv:2607.18266v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2607.18266 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

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

Subiecte conexe