A.1 Additional experimental results We further introduce our additional experiments in this section. In our main article, we compared our model FREED with baseline models REINVENT and MORLD. For fairer comparison of quality scores, we also performed multi-objective optimization of REINVENT and MORLD on both quality score (pharmacochemical filter score) and docking score as follows. Table 1 in the main text shows that such an implicit method is not enough to achieve nearly perfect filter scores as our model did. Also, as shown in Table 1 REINVENT showed deteriorated performance when jointly trained with filter scores, in terms of hit ratio and top 5% scores, implying that multiobjective optimization is more difficult than explicitly constrained optimization. Such a result was consistent for all three targets. The two baseline models REINVENT and MORLD that are jointly trained to maximize filter scores are noted as REINVENT w/ filter and MORLD w/ filter.

The vocabulary Vconstructed by Algorithm 1 exhibits the following advantageous properties. Prior to the proof, we first present a clear observation of the created vocabulary V: Proposition A.2. Given any F,F V, for any their instances arising on an arbitrary molecule during the extraction process, either they are not spatially intersected F F =, or they contain each other: F F or F F. Now we prove each claim in the above theorem. We prove it by contradiction. If it is the former case, then Fi1 should be firstly extracted and then merged with other fragments to yield Fi2 which means i1 < i2, conflicting with the assumption.

This paper proposes the RePAIR dataset that represents a challenging benchmark to test modern computational and data driven methods for puzzle-solving and reassembly tasks. Our dataset has unique properties that are uncommon to current benchmarks for 2D and 3D puzzle solving. The fragments and fractures are realistic, caused by a collapse of a fresco during a World War II bombing at the Pompeii archaeological park. The fragments are also eroded and have missing pieces with irregular shapes and different dimensions, challenging further the reassembly algorithms. The dataset is multi-modal providing high resolution images with characteristic pictorial elements, detailed 3D scans of the fragments and meta-data annotated by the archaeologists. Ground truth has been generated through several years of unceasing fieldwork, including the excavation and cleaning of each fragment, followed by manual puzzle solving by archaeologists of a subset of approx.

Program synthesis of general-purpose source code from natural language specifi-cations is challenging due to the need to reason about high-level patterns in thetarget program and low-level implementation details at the same time.

Property prediction on molecular graphs is an important application of Graph Neural Networks (GNNs).

This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces.