Although tremendous success has been achieved in spatial and network representation separately in recent years, there exist very little works on the representation of spatial networks. Extracting powerful representations from spatial networks requires the development of appropriate tools to uncover the pairing of both spatial and network information in the appearance of node permutation invariant, and rotation and translation invariant. Hence it can not be modeled merely with either spatial or network models individually. To address these challenges, this paper proposes a generic framework for spatial network representation learning. Specifically, a provably information-lossless and rotation-translation invariant representation of spatial information on networks is presented. Then a higher-order spatial network convolution operation that adapts to our proposed representation is introduced. To ensure efficiency, we also propose a new approach that relied on sampling random spanning trees to reduce the time and space complexity fromO(N3) to O(N).

Inpractice,wealso need to consider the lower numerical precision of GPU implementation in model training, which further deteriorates the stability.

The vast majority of time-series forecasting approaches require a substantial training dataset. However, many real-life forecasting applications have very little initial observations, sometimes just 40 or fewer. Thus, the applicability of most forecasting methods is restricted in data-sparse commercial applications.

Deceptive agents are a challenge for the safety, trustworthiness, and cooperation of AI systems.

Let B be the maximum difference betweenU1t and U2t, and let (π,θ1,θ2) be a Nash Equilibrium forG. Let π1 be the best response to the first teacher (with utilityU1t) and let π1+2 be the best response policy to the joint teacher. This result shows that as we reduce the number of random episodes, the approximation to aminimax regret strategy improves. Let G be the dual curriculum game in which the first teacher maximizes regret, so U1t = URt, and the second teacher plays randomly, soU2t = UUt . Finally,we need to show thatπ2+3 isoptimal for the student.

We investigate neural network representations from a probabilistic perspective.