TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems

Learning complex multi-agent system dynamics from data is crucial across many domains, such as in physical simulations and material modeling. Extended from purely data-driven approaches, existing physics-informed approaches such as Hamiltonian Neural Network strictly follow energy conservation law to introduce inductive bias, making their learning more sample efficiently. However, many real-world systems do not strictly conserve energy, such as spring systems with frictions. Recognizing this, we turn our attention to a broader physical principle: Time-Reversal Symmetry, which depicts that the dynamics of a system shall remain invariant when traversed back over time. It still helps to preserve energies for conservative systems and in the meanwhile, serves as a strong inductive bias for non-conservative, reversible systems. To inject such inductive bias, in this paper, we propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE). It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics. In addition, we further provide theoretical analysis to show that our regularization essentially minimizes higher-order Taylor expansion terms during the ODE integration steps, which enables our model to be more noise-tolerant and even applicable to irreversible systems. Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method. Particularly, it achieves an MSE improvement of 11.5 % on a challenging chaotic triple-pendulum systems.

Benign Overfitting for Two-layer ReLU Networks

Modern deep learning models with great expressive power can be trained to overfit the training data but still generalize well. This phenomenon is referred to as benign overfitting. Recently, a few studies have attempted to theoretically understand benign overfitting in neural networks. However, these works are either limited to neural networks with smooth activation functions or to the neural tangent kernel regime. How and when benign overfitting can occur in ReLU neural networks remains an open problem. In this work, we seek to answer this question by establishing algorithm-dependent risk bounds for learning two-layer ReLU convolutional neural networks with label-flipping noise. We show that, under mild conditions, the neural network trained by gradient descent can achieve near-zero training loss and Bayes optimal test risk. Our result also reveals a sharp transition between benign and harmful overfitting under different conditions on data distribution in terms of test risk. Experiments on synthetic data back up our theory.

Monocular Visual Analysis for Electronic Line Calling of Tennis Games

Electronic Line Calling is an auxiliary referee system used for tennis matches based on binocular vision technology. While ELC has been widely used, there are still many problems, such as complex installation and maintenance, high cost and etc. We propose a monocular vision technology based ELC method. The method has the following steps. First, locate the tennis ball's trajectory. We propose a multistage tennis ball positioning approach combining background subtraction and color area filtering. Then we propose a bouncing point prediction method by minimizing the fitting loss of the uncertain point. Finally, we find out whether the bouncing point of the ball is out of bounds or not according to the relative position between the bouncing point and the court side line in the two dimensional image. We collected and tagged 394 samples with an accuracy rate of 99.4%, and 81.8% of the 11 samples with bouncing points.The experimental results show that our method is feasible to judge if a ball is out of the court with monocular vision and significantly reduce complex installation and costs of ELC system with binocular vision.