Minho Lee

Han-Jun Choi, Hyunsung Kim, Minho Lee et al.

Multi-agent trajectory data collected from domains such as team sports often suffer from missing values due to various factors. While many imputation methods have been proposed for spatiotemporal data, they are not well-suited for multi-agent sports scenarios where player movements are highly dynamic and inter-agent interactions continuously evolve. To address these challenges, we propose MIDAS (Multi-agent Imputer with Derivative-Accumulating Self-ensemble), a framework that imputes multi-agent trajectories with high accuracy and physical plausibility. It jointly predicts positions, velocities, and accelerations through a Set Transformer-based neural network and generates alternative estimates by recursively accumulating predicted velocity and acceleration values. These predictions are then combined using a learnable weighted ensemble to produce final imputed trajectories. Experiments on three sports datasets demonstrate that MIDAS significantly outperforms existing baselines in both positional accuracy and physical plausibility. Lastly, we showcase use cases of MIDAS, such as approximating total distance and pass success probability, to highlight its applicability to practical downstream tasks that require complete tracking data.

Yun Young Choi, Sun Woo Park, Minho Lee et al.

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.

Taewon Park, Hyun-Chul Kim, Minho Lee

Neuro-symbolic neural networks have been extensively studied to integrate symbolic operations with neural networks, thereby improving systematic generalization. Specifically, Tensor Product Representation (TPR) framework enables neural networks to perform differentiable symbolic operations by encoding the symbolic structure of data within vector spaces. However, TPR-based neural networks often struggle to decompose unseen data into structured TPR representations, undermining their symbolic operations. To address this decomposition problem, we propose a Discrete Dictionary-based Decomposition (D3) layer designed to enhance the decomposition capabilities of TPR-based models. D3 employs discrete, learnable key-value dictionaries trained to capture symbolic features essential for decomposition operations. It leverages the prior knowledge acquired during training to generate structured TPR representations by mapping input data to pre-learned symbolic features within these dictionaries. D3 is a straightforward drop-in layer that can be seamlessly integrated into any TPR-based model without modifications. Our experimental results demonstrate that D3 significantly improves the systematic generalization of various TPR-based models while requiring fewer additional parameters. Notably, D3 outperforms baseline models on the synthetic task that demands the systematic decomposition of unseen combinatorial data.