# More Accurate or More Efficient? Evaluating Locally Deployed Compact Open-Weight Language Models for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2608.22048 · HTML: https://mlsanity.com/paper/2608.22048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 13 of 13)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [TokenPowerBench: Benchmarking the Power Consumption of LLM Inference](https://mlsanity.com/paper/2512.03024/) (2025)
- [ConsumerBench: Benchmarking Generative AI Applications on End-User Devices](https://mlsanity.com/paper/2506.17538/) (2025)

## Abstract (arXiv)

Large language models are increasingly deployed on local hardware for privacy, cost, and accessibility reasons. Yet many evaluations emphasize accuracy while fewer quantify local runtime and energy, characterize failure modes, or apply paired statistical comparisons under controlled conditions. This paper presents a controlled, documented procedure for evaluating locally hosted LLMs on mathematical reasoning. It combines fixed inference settings, hierarchical answer extraction and verification, explicit failure-mode classification, and per-question resource measurement, and reports accuracy with paired significance tests and effect sizes. We demonstrate it in a preliminary study of three compact open-weight models under five billion parameters, Gemma3:4b (Google), Phi3:3.8b (Microsoft), and Qwen3:4b (Alibaba), across datasets spanning Grade 8 Math, Calculus I, and Advanced Probability and Statistics. All models ran through the same local inference server on one workstation, using a shared prompt template, controlled settings, and a matched question set per dataset. No single model dominates. Qwen3:4b is most accurate on two datasets and Gemma3:4b on Calculus I, yet Gemma3:4b returns roughly three times more correct answers per watt-hour than Qwen3:4b on every dataset while generating far fewer output tokens; Qwen3:4b requires substantially more generation time, energy, and output per question. Phi3:3.8b is substantially less accurate on all three datasets; its low extraction-failure rate indicates incorrect answers rather than unparsed output, though we caveat possible prompt-format effects. These preliminary findings indicate that accuracy alone is an insufficient basis for selecting a local model.