Motion prediction in soccer involves capturing complex dynamics from player
and ball interactions. We present FootBots, an encoder-decoder
transformer-based architecture addressing motion prediction and conditioned
motion prediction through equivariance properties. FootBots captures temporal
and social dynamics using set attention blocks and multi-attention block
decoder. Our evaluation utilizes two datasets: a real soccer dataset and a
tailored synthetic one. Insights from the synthetic dataset highlight the
effectiveness of FootBots' social attention mechanism and the significance of
conditioned motion prediction. Empirical results on real soccer data
demonstrate that FootBots outperforms baselines in motion prediction and excels
in conditioned tasks, such as predicting the players based on the ball
position, predicting the offensive (defensive) team based on the ball and the
defensive (offensive) team, and predicting the ball position based on all
players. Our evaluation connects quantitative and qualitative findings.
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足球中的运动预测通过捕捉球员和球的相互作用的复杂动力学。我们提出了 FootBots，一种基于编码器 - 解码器变压器结构的体系结构，通过等变性属性来解决运动预测和有条件的运动预测。FootBots 使用集合注意力块和多注意力块解码器来捕捉时间和社交动力学。我们的评估使用两个数据集：一个真实的足球数据集和一个定制的合成数据集。合成数据集的洞见突显了 FootBots 社交注意机制的有效性和有条件运动预测的重要性。对真实足球数据的实证结果表明，FootBots 在运动预测方面优于基准模型，并在有条件任务中表现出色，例如根据球的位置预测球员，根据球和防守（进攻）球队预测进攻（防守）球队，以及根据所有球员预测球的位置。我们的评估连接了定量和定性研究结果。

FootBots: 基于 Transformer 的足球运动预测架构

FootBots: A Transformer-based Architecture for Motion Prediction in  Soccer

The translational equivariant nature of Convolutional Neural Networks (CNNs)
is a reason for its great success in computer vision. However, networks do not
enjoy more general equivariance properties such as rotation or scaling,
ultimately limiting their generalization performance. To address this
limitation, we devise a method that endows CNNs with simultaneous equivariance
with respect to translation, rotation, and scaling. Our approach defines a
convolution-like operation and ensures equivariance based on our proposed
scalable Fourier-Argand representation. The method maintains similar efficiency
as a traditional network and hardly introduces any additional learnable
parameters, since it does not face the computational issue that often occurs in
group-convolution operators. We validate the efficacy of our approach in the
image classification task, demonstrating its robustness and the generalization
ability to both scaled and rotated inputs.

本文提出了一种方法，通过使用可缩放的傅里叶 - 阿甘德表示法和类似卷积的操作来实现卷积神经网络对于平移、旋转和缩放的同时等变性，并验证了该方法在图像分类任务方面的有效性和对缩放和旋转输入的泛化能力。