Businesses need to query visually rich documents (VRDs) like receipts, medical records, and insurance forms to make decisions. Existing techniques for extracting entities from VRDs struggle with new layouts or require extensive pre-training data. We introduce VRDSynth, a program synthesis method to automatically extract entity relations from multilingual VRDs without pre-training data. To capture the complexity of VRD domain, we design a domain-specific language (DSL) to capture spatial and textual relations to describe the synthesized programs. Along with this, we also derive a new synthesis algorithm utilizing frequent spatial relations, search space pruning, and a combination of positive, negative, and exclusive programs to improve coverage. We evaluate VRDSynth on the FUNSD and XFUND benchmarks for semantic entity linking, consisting of 1,592 forms in 8 languages. VRDSynth outperforms state-of-the-art pre-trained models (LayoutXLM, InfoXLMBase, and XLMRobertaBase) in 5, 6, and 7 out of 8 languages, respectively, improving the F1 score by 42% over LayoutXLM in English. To test the extensibility of the model, we further improve VRDSynth with automated table recognition, creating VRDSynth(Table), and compare it with extended versions of the pre-trained models, InfoXLM(Large) and XLMRoberta(Large). VRDSynth(Table) outperforms these baselines in 4 out of 8 languages and in average F1 score. VRDSynth also significantly reduces memory footprint (1M and 380MB vs. 1.48GB and 3GB for LayoutXLM) while maintaining similar time efficiency.

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