COMPOSE: Composing Future Theorems from Citations and Formal Structure

2026-05-28 · Source: Computation and Language · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

COMPOSE is a novel dual-graph framework designed for grounded future mathematical generation, aiming to predict plausible theorem-like claims for anchor papers. It addresses the challenge of generating future mathematical claims that are both grounded in prior work and respect formal dependencies, a limitation of existing methods. COMPOSE conditions a language model using two complementary sources: an anchor paper's scientific citation graph and its aligned formal theorem dependency graph. To support this, the authors constructed a dataset of 108K paired scientific-formal graph examples from arXiv and Mathlib, along with a benchmark of 47K future papers from 2024-2025. Experiments demonstrate that COMPOSE surpasses strong baselines in retrieving real future papers and achieves superior overall performance in LLM-judge evaluations, yielding more grounded and mathematically richer outputs. This highlights the benefit of combining scientific context with formal structure for future mathematical generation.

Key takeaway

For AI Scientists and Research Scientists focused on automated theorem proving or mathematical discovery, COMPOSE offers a robust framework for generating more plausible and grounded future mathematical claims. You should consider integrating both scientific citation context and formal structural dependencies into your generative models to enhance output quality. This approach can lead to richer, more relevant conjectures, accelerating research in formal mathematics and automated reasoning.

Key insights

Combining scientific citation graphs with formal theorem structures significantly improves future mathematical claim generation.

Principles

• Plausible future claims require both scientific and formal grounding.
• Dual-graph conditioning enhances language model generation.

Method

COMPOSE conditions a language model on an anchor paper's scientific citation graph and its formal theorem dependency graph to generate future mathematical claims.

In practice

• Use dual-graph context for generating novel mathematical conjectures.
• Apply similar dual-context modeling to other scientific prediction tasks.

Topics

• COMPOSE Framework
• Mathematical Generation
• Citation Graph Analysis
• Formal Theorem Proving
• Language Models
• Scientific Context Modeling

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Computation and Language.