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MathFimer: Enhancing Mathematical Reasoning by Expanding Reasoning Steps through Fill-in-the-Middle Task

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
LLM ReasoningMathematical ReasoningData Augmentation
Abstract:

Mathematical reasoning represents a critical frontier in advancing large language models (LLMs). While step-by-step approaches have emerged as the dominant paradigm for mathematical problem-solving in LLMs, the quality of reasoning steps in training data fundamentally constrains model performance. Recent studies has demonstrated that more detailed intermediate steps can enhance model performance, yet existing methods for step expansion either require more powerful external models or incur substantial computational costs. In this paper, we introduce MathFimer, a novel framework for mathematical reasoning step expansion inspired by the "Fill-in-the-middle" from code completion. By decomposing solution chains into prefix-suffix pairs and training models to reconstruct missing intermediate steps, we develop a specialized model, MathFimer-7B, on our carefully curated NuminaMath-Fim dataset. We then apply these models to enhance existing mathematical reasoning datasets by inserting detailed intermediate steps into their solution chains, creating MathFimer-expanded versions. Through comprehensive experiments on multiple mathematical reasoning datasets, including MathInstruct and MetaMathQA, we demonstrate that models trained on MathFimer-expanded data consistently outperform their counterparts trained on original data across various benchmarks such as GSM8K and MATH. Our approach offers a practical, scalable solution for enhancing mathematical reasoning capabilities in LLMs without relying on more powerful external models or expensive inference procedures.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces MathFimer, a framework that applies fill-in-the-middle training to expand mathematical reasoning steps, producing a specialized 7B model and an enhanced dataset. Within the taxonomy, it resides in the 'Fill-in-the-Middle Based Step Expansion' leaf alongside one sibling paper (ClozeMath). This leaf is part of a broader 'Step Expansion and Intermediate Reasoning Generation' branch containing three leaves total, indicating a moderately active but not overcrowded research direction focused on generating missing intermediate steps.

The taxonomy reveals neighboring branches addressing reasoning correction and verification mechanisms, fill-in-the-middle training paradigms across domains, and backward reasoning approaches. MathFimer's leaf sits adjacent to 'Thought Leap Detection and Bridging' and 'Enriched Instruction Tuning for Multi-Step Reasoning', which tackle similar step-completion goals through different mechanisms (detecting omissions versus human-AI feedback synergy). The broader taxonomy includes 18 papers across diverse directions, suggesting the field balances step expansion with verification, tool use, and formal proof generation, positioning MathFimer within a specific niche of proactive infilling-based expansion.

Among 30 candidates examined, none clearly refute any of the three contributions. The MathFimer framework (10 candidates examined, 0 refutable), the NuminaMath-FIM dataset and model (10 candidates, 0 refutable), and the empirical performance demonstrations (10 candidates, 0 refutable) all appear novel within this limited search scope. The single sibling paper in the same taxonomy leaf suggests the specific application of fill-in-the-middle to mathematical step expansion remains relatively underexplored, though the broader step expansion category contains multiple alternative approaches that address overlapping goals through different technical means.

Based on the top-30 semantic matches and taxonomy structure, the work appears to occupy a distinct position within mathematical reasoning step expansion. The limited search scope and sparse sibling count suggest novelty, though the taxonomy shows active neighboring research in related verification and training paradigm directions. The analysis covers semantic proximity and structural taxonomy placement but does not exhaustively survey all mathematical reasoning literature or adjacent code-completion domains that inspired the approach.

Taxonomy

Core-task Taxonomy Papers
18
3
Claimed Contributions
30
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: expanding mathematical reasoning steps through fill-in-the-middle task. The field addresses how language models can generate, verify, and refine intermediate reasoning steps in mathematical problem-solving. The taxonomy reveals several complementary directions: some branches focus on step expansion and intermediate reasoning generation, exploring how models can produce missing derivations between problem statements and solutions; others examine reasoning correction and verification mechanisms that detect and fix errors in multi-step chains. Fill-in-the-middle training paradigms investigate architectural choices for infilling tasks, while backward reasoning explores inverse problem formulation. Additional branches address tool use and external knowledge grounding (such as Chain-of-Abstraction[5]), context utilization for long-form reasoning (Fully Utilize Context[3]), formal verification and proof generation (Informal to Formal[4]), and even tokenization strategies at the byte level. Educational perspectives consider pedagogical applications, reflecting the dual role of these methods in both advancing AI capabilities and supporting human learning. Particularly active lines of work contrast autoregressive step expansion with explicit infilling objectives, and explore whether models benefit more from forward generation or backward reasoning (Backward Reasoning[17]). Search-based correction methods (Search-Based Correction[2]) and system-level reasoning frameworks (System-2 Mathematical Reasoning[1]) highlight ongoing debates about how to balance generation fluency with verification rigor. MathFimer[0] sits within the fill-in-the-middle based step expansion cluster, closely aligned with ClozeMath[6], which similarly frames intermediate step generation as a cloze-style infilling problem. Compared to approaches that emphasize post-hoc verification or tool-augmented reasoning, MathFimer[0] and its neighbors prioritize training models to natively predict missing derivation steps, leveraging the fill-in-the-middle objective to encourage coherent bridging between given context and conclusions. This positions the work as part of a growing effort to make reasoning expansion an intrinsic model capability rather than an external search or correction process.

Claimed Contributions

MathFimer framework for mathematical reasoning step expansion

The authors introduce MathFimer, a framework that adapts the fill-in-the-middle paradigm from code reasoning to mathematical problem-solving. By decomposing solution chains into prefix-suffix pairs and training models to reconstruct missing intermediate steps, the framework enables targeted expansion of reasoning steps without generating entirely new solution chains.

10 retrieved papers
NuminaMath-FIM dataset and MathFimer-7B model

The authors construct NuminaMath-FIM by decomposing NuminaMath-CoT solutions into prefix-suffix pairs with missing intermediate steps, resulting in 2.5M training samples. They train MathFimer-7B on this dataset using Qwen2.5-Math-7B as the base model, creating a specialized model for step expansion that can be applied to enhance existing mathematical reasoning datasets.

10 retrieved papers
Empirical demonstration of consistent performance improvements

The authors conduct comprehensive experiments showing that models trained on MathFimer-expanded data consistently outperform those trained on original data across various benchmarks including GSM8K and MATH. The improvements are observed across both general-purpose and math-specialized models, demonstrating the practical effectiveness and scalability of the approach.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

MathFimer framework for mathematical reasoning step expansion

The authors introduce MathFimer, a framework that adapts the fill-in-the-middle paradigm from code reasoning to mathematical problem-solving. By decomposing solution chains into prefix-suffix pairs and training models to reconstruct missing intermediate steps, the framework enables targeted expansion of reasoning steps without generating entirely new solution chains.

Contribution

NuminaMath-FIM dataset and MathFimer-7B model

The authors construct NuminaMath-FIM by decomposing NuminaMath-CoT solutions into prefix-suffix pairs with missing intermediate steps, resulting in 2.5M training samples. They train MathFimer-7B on this dataset using Qwen2.5-Math-7B as the base model, creating a specialized model for step expansion that can be applied to enhance existing mathematical reasoning datasets.

Contribution

Empirical demonstration of consistent performance improvements

The authors conduct comprehensive experiments showing that models trained on MathFimer-expanded data consistently outperform those trained on original data across various benchmarks including GSM8K and MATH. The improvements are observed across both general-purpose and math-specialized models, demonstrating the practical effectiveness and scalability of the approach.

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