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Euclid-Omni: A Unified Neuro-Symbolic Framework for Geometry Problem Solving

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.5Download Report PDF
Geometry Problem SolvingNeuro-SymbolicLLMVLMSynthetic Data Generation
Abstract:

Euclidean geometry presents a compelling testbed for AI reasoning capabilities, requiring seamless integration of diagram understanding, logical deduction, and algebraic computation. Existing systems have either been narrowly scoped or struggled with challenging problems. We introduce Euclid-Omni, a unified neuro-symbolic framework that combines a formal geometry system with Large (Vision)–Language Models (LLMs and VLMs) to address both calculation- and proving-style problems across formal and natural languages, up to Olympiad-level difficulty. At its core, we develop Euclidea, a versatile geometry symbolic solver that automatically generates human-readable reasoning steps through logical deduction and algebraic solving. On top of this, we implement a comprehensive data generation pipeline that synthesizes symbolic problems, renders diagrams, and translates problems into natural language, yielding large-scale, diverse datasets for training LLMs and VLMs in different reasoning settings. Experiments on multiple benchmarks demonstrate that Euclidea can tackle a broader range of problems than prior symbolic systems. Our trained VLMs achieve superior results on calculation tasks, while combining LLMs with Euclidea remains competitive with state-of-the-art systems on Olympiad-level theorem proving problems, despite using orders of magnitude less compute and data.

Disclaimer
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.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

Euclid-Omni introduces a unified neuro-symbolic framework combining a formal geometry solver (Euclidea) with large vision-language models to address calculation and proving problems up to Olympiad difficulty. The paper resides in the 'Unified Neuro-Symbolic Frameworks' leaf, which contains only three papers total, indicating a relatively sparse but emerging research direction. This leaf sits within the broader 'Neuro-Symbolic and Hybrid Reasoning Systems' branch, suggesting the work targets a specialized intersection of symbolic logic and neural learning rather than a crowded subfield.

The taxonomy reveals neighboring leaves focused on 'Formal Language and Symbolic Reasoning' (four papers emphasizing theorem provers and logical deduction) and 'Guided Search and Automated Theorem Discovery' (three papers on tree-search methods). Euclid-Omni diverges from pure symbolic approaches by integrating VLMs for diagram understanding and natural language processing, while differing from search-based methods by emphasizing end-to-end neuro-symbolic orchestration. The broader 'Neural and Multimodal Learning Approaches' branch (nine papers across three leaves) represents an alternative paradigm relying primarily on pretrained models without explicit symbolic reasoning.

Among thirty candidates examined, the symbolic solver contribution (Euclidea) shows overlap with two prior works out of ten examined, while the data generation pipeline faces three potential refutations among ten candidates. The unified framework contribution (Euclid-Omni) appears more distinctive, with zero clear refutations across ten examined papers. These statistics suggest that while individual components (symbolic solving, data synthesis) have precedents in the limited search scope, the integrated architecture combining formal reasoning with VLMs for diverse problem types may represent a less-explored configuration within the examined literature.

Based on top-thirty semantic matches and citation expansion, the analysis indicates moderate novelty in system integration despite component-level overlap. The sparse taxonomy leaf (three papers) and absence of refutations for the unified framework suggest potential distinctiveness, though the limited search scope precludes definitive claims about exhaustive prior work coverage. The contribution-level statistics reflect what was examined, not the entire field landscape.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
5
Refutable Paper

Research Landscape Overview

Core task: Automated geometry problem solving. The field encompasses a diverse set of approaches ranging from classical computational geometry foundations to modern neural and multimodal learning methods. At the top level, the taxonomy organizes work into neuro-symbolic and hybrid reasoning systems that combine symbolic logic with learning, neural and multimodal learning approaches that leverage deep models and vision-language integration, data generation and formalization efforts that produce training corpora and formal representations, software systems and architectures for practical deployment, computational geometry foundations rooted in algorithmic theory, and domain-specific applications addressing specialized geometric challenges. Representative works such as FormalGeo[45] illustrate formalization efforts, while G-LLaVA[28] exemplifies multimodal learning directions, and classical references like Computational Geometry Survey[27] anchor foundational algorithmic methods. Within the neuro-symbolic branch, a particularly active line of work explores unified frameworks that integrate symbolic reasoning engines with neural components to tackle challenging Olympiad-level problems. Euclid-Omni[0] sits squarely in this unified neuro-symbolic cluster, emphasizing the orchestration of multiple reasoning modalities to handle diverse geometric tasks. It shares this emphasis with AlphaGeometry2[18], which similarly combines symbolic deduction with learned heuristics, and contrasts slightly with Olympiad Geometry[1], which may focus more narrowly on competition-level benchmarks. Across these efforts, key trade-offs revolve around balancing the interpretability and rigor of symbolic methods against the flexibility and generalization of neural learning, with open questions remaining about how best to scale such hybrid systems to broader problem classes and how to generate sufficient high-quality training data without manual annotation.

Claimed Contributions

Euclidea: A versatile geometry symbolic solver

The authors introduce Euclidea, a Python-based formal plane geometry system that unifies representation and reasoning for both proving and calculation tasks. It integrates a deductive database of inference rules with an advanced algebraic engine to automatically solve problems up to IMO level while producing human-readable solution steps.

10 retrieved papers
Can Refute
Comprehensive data generation pipeline for training LLMs and VLMs

The authors develop a configurable pipeline that generates training data by synthesizing symbolic geometry problems from scratch, rendering corresponding visual diagrams, and translating both problems and solutions into natural language. This enables creation of datasets tailored to different reasoning settings and difficulty levels.

10 retrieved papers
Can Refute
Euclid-Omni: A unified neuro-symbolic framework

The authors present Euclid-Omni, a unified framework that integrates the Euclidea symbolic solver with LLMs and VLMs to handle diverse geometry problem types (calculation and proving) across both formal and natural language modalities, achieving performance up to Olympiad level.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Euclidea: A versatile geometry symbolic solver

The authors introduce Euclidea, a Python-based formal plane geometry system that unifies representation and reasoning for both proving and calculation tasks. It integrates a deductive database of inference rules with an advanced algebraic engine to automatically solve problems up to IMO level while producing human-readable solution steps.

Contribution

Comprehensive data generation pipeline for training LLMs and VLMs

The authors develop a configurable pipeline that generates training data by synthesizing symbolic geometry problems from scratch, rendering corresponding visual diagrams, and translating both problems and solutions into natural language. This enables creation of datasets tailored to different reasoning settings and difficulty levels.

Contribution

Euclid-Omni: A unified neuro-symbolic framework

The authors present Euclid-Omni, a unified framework that integrates the Euclidea symbolic solver with LLMs and VLMs to handle diverse geometry problem types (calculation and proving) across both formal and natural language modalities, achieving performance up to Olympiad level.

Table of Contents