LLMCO4MR: LLMs-aided Neural Combinatorial Optimization for Ancient Manuscript Restoration from Fragments with Case Studies on Dunhuang

Restoring ancient manuscripts fragments, such as those from Dunhuang, is crucial for preserving human historical culture. However, their worldwide dispersal and the shifts in cultural and historical contexts pose significant restoration challenges. Traditional archaeological efforts primarily focus on manually piecing major fragments together, yet the vast majority of small, more intricate pieces remain largely unexplored, which is technically due to their irregular shapes, sparse textual content, and extensive combinatorial space for reassembly. In this paper, we formalize the task of restoring the ancient manuscript from fragments as a cardinality-constrained combinatorial optimization problem, and propose a general framework named LLMCO4MS: (Multimodal) Large Language Model-aided Combinatorial Optimization Neural Networks for Ancient Manuscript Restoration. Specifically, LLMCO4MS encapsulates a neural combinatorial solver equipped with a differentiable optimal transport (OT) layer, to efficiently predict the Top-K likely reassembly candidates. Innovatively, the Multimodal Large Language Model (MLLM) is then adopted and prompted to yield pairwise matching confidence and relative directions for final restoration. Extensive experiments on both synthetic data and real-world famous Dunhuang fragments demonstrate superior performance of our approach. In particular, LLMCO4MS has facilitated the discovery of previously unknown civilian economic documents from the 10-th century in real-world applications.