Synergizing Difficulty Alignment and Inference Decision Optimization for Enhancing Mathematical Reasoning in LLMs

Synergizing Difficulty Alignment and Inference Decision Optimization for Enhancing Mathematical Reasoning in LLMs | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 22 January 2026 V1 Latest version Share on Synergizing Difficulty Alignment and Inference Decision Optimization for Enhancing Mathematical Reasoning in LLMs Authors : Zi-Han Jia and Xin-Hui Shao 0000-0002-4120-8428 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176909243.31152790/v1 83 views 31 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Mathematical reasoning is a critical metric for evaluating Large Language Models, yet large-scale synthetic datasets often suffer from logical redundancy and noise. This paper proposes a comprehensive framework integrating fine-grained filtering, difficulty-alignment evaluation, and reasoning decision optimization. Using Llama-3.1-8B and REASONEVAL, we established difficulty-alignment benchmarks and filtered the MMIQC dataset into validity and redundancy-based subsets. Mistral-7B was then fine-tuned using LoRA. To address tie-breaking in multi-round sampling, we introduced a position-based indexing strategy and a confidence-based ranking strategy for inference. Logical stability was assessed using the Average Consistency Score ( AC S ) and its differential ( ∆ AC S ). Results demonstrate that the validity-filtered model, using only 76.98% of the data, outperformed the baseline by 0.98% in accuracy. Furthermore, combining both validity and redundancy filtering (58.28% of data) with the confidence-based strategy achieved a 3.34% accuracy gain over the full-dataset baseline, with ∆ AC S increasing from 2.39 to 2.63. These findings suggest that synergizing difficulty alignment with optimized inference decisions effectively stimulates mathematical reasoning and logical stability using smaller, high-quality datasets. Supplementary Material File (synergizing difficulty alignment.docx) Download 893.75 KB Information & Authors Information Version history V1 Version 1 22 January 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords data filtering inference tie-breaking strategy llms mathematical reason Authors Affiliations Zi-Han Jia Northeastern University Department of Mathematics View all articles by this author Xin-Hui Shao 0000-0002-4120-8428 [email protected] Northeastern University Department of Mathematics View all articles by this author Metrics & Citations Metrics Article Usage 83 views 31 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Zi-Han Jia, Xin-Hui Shao. Synergizing Difficulty Alignment and Inference Decision Optimization for Enhancing Mathematical Reasoning in LLMs. Authorea . 22 January 2026. DOI: https://doi.org/10.22541/au.176909243.31152790/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.176909243.31152790/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9fe017b049f552ad',t:'MTc3OTE2MjE1NQ=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();