The objective is to predict potential energy and forces.

Nevertheless, it remains elusive that whether the Transformer-based architecture can do molecular modeling as good as equivariant GNNs.

The widespread adoption of Transformer architectures in various data modalities has opened new avenues for the applications in molecular modeling. Nevertheless, it remains elusive that whether the Transformer-based architecture can do molecular modeling as good as equivariant GNNs. In this paper, by designing Interatomic Positional Encoding (IPE) thatparameterizes atomic environments as Transformer's positional encodings,we propose Geoformer, a novel geometric Transformer to effectively model molecular structures for various molecular property prediction. We evaluate Geoformer on several benchmarks, including the QM9 dataset and the recently proposed Molecule3D dataset.

The widespread adoption of Transformer architectures in various data modalities has opened new avenues for the applications in molecular modeling. Nevertheless, it remains elusive that whether the Transformer-based architecture can do molecular modeling as good as equivariant GNNs. In this paper, by designing Interatomic Positional Encoding (IPE) thatparameterizes atomic environments as Transformer's positional encodings,we propose Geoformer, a novel geometric Transformer to effectively model molecular structures for various molecular property prediction. We evaluate Geoformer on several benchmarks, including the QM9 dataset and the recently proposed Molecule3D dataset.

Air pollution represents a pivotal environmental challenge globally, playing a major role in climate change via greenhouse gas emissions and negatively affecting the health of billions. However predicting the spatial and temporal patterns of pollutants remains challenging. The scarcity of ground-based monitoring facilities and the dependency of air pollution modeling on comprehensive datasets, often inaccessible for numerous areas, complicate this issue. In this work, we introduce GeoFormer, a compact model that combines a vision transformer module with a highly efficient time-series transformer module to predict surface-level nitrogen dioxide (NO2) concentrations from Sentinel-5P satellite imagery. We train the proposed model to predict surface-level NO2 measurements using a dataset we constructed with Sentinel-5P images of ground-level monitoring stations, and their corresponding NO2 concentration readings. The proposed model attains high accuracy (MAE 5.65), demonstrating the efficacy of combining vision and time-series transformer architectures to harness satellite-derived data for enhanced GHG emission insights, proving instrumental in advancing climate change monitoring and emission regulation efforts globally.

Predicting human mobility holds significant practical value, with applications ranging from enhancing disaster risk planning to simulating epidemic spread. In this paper, we present the GeoFormer, a decoder-only transformer model adapted from the GPT architecture to forecast human mobility. Our proposed model is rigorously tested in the context of the HuMob Challenge 2023 -- a competition designed to evaluate the performance of prediction models on standardized datasets to predict human mobility. The challenge leverages two datasets encompassing urban-scale data of 25,000 and 100,000 individuals over a longitudinal period of 75 days. GeoFormer stands out as a top performer in the competition, securing a place in the top-3 ranking. Its success is underscored by performing well on both performance metrics chosen for the competition -- the GEO-BLEU and the Dynamic Time Warping (DTW) measures. The performance of the GeoFormer on the HuMob Challenge 2023 underscores its potential to make substantial contributions to the field of human mobility prediction, with far-reaching implications for disaster preparedness, epidemic control, and beyond.

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.