How RL Unlocks the Aha Moment in Geometric Interleaved Reasoning

2026-03-01

AI Summary

This work addresses the limitations of multimodal large language models in geometric reasoning tasks, where supervised fine-tuning (SFT) merely imitates output formats without establishing causal dependencies between diagram generation and logical reasoning, thereby constraining performance. The authors propose Faire, a novel framework that, for the first time, elucidates the failure mechanism of SFT in such settings and introduces a reinforcement learning–based functional alignment paradigm. By enforcing three causality-inspired constraints, Faire shifts the model’s behavior from superficial imitation toward deep integration of drawing and reasoning processes. Extensive experiments demonstrate that this approach achieves state-of-the-art performance across multiple challenging geometric reasoning benchmarks, significantly enhancing the quality of model behavior and ensuring that generated diagrams genuinely support the reasoning process.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Solving complex geometric problems inherently requires interleaved reasoning: a tight alternation between constructing diagrams and performing logical deductions. Although recent Multimodal Large Language Models (MLLMs) have demonstrated strong capabilities in visual generation and plotting, we identify a counter-intuitive and underexplored phenomenon. Naively applying Supervised Fine-Tuning (SFT) on interleaved plot-solution data leads to a substantial degradation in reasoning performance compared to text-only baselines. We argue that this failure stems from a fundamental limitation of SFT, which primarily induces distributional alignment: the model learns to reproduce the surface format of interleaved plotting but fails to internalize the causal dependency between the generated plot and reasoning steps. To overcome this limitation, we propose Faire (Functional alignment for interleaved reasoning), a reinforcement learning framework that enforces three casual constraints to move beyond superficial imitation toward functional alignment. Extensive experiments show that Faire induces a qualitative shift in model behavior in which the plotting is effectively internalized, yielding competitive performance on challenging geometric reasoning benchmarks.

Problem

• interleaved reasoning
• geometric reasoning
• supervised fine-tuning
• multimodal large language models
• reinforcement learning

Innovation

• reinforcement learning
• interleaved reasoning
• functional alignment
• geometric reasoning
• multimodal LLMs