In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

We present a graph neural network assisted Monte Carlo Tree Search approach for the classical traveling salesman problem (TSP). We adopt a greedy algorithm framework to construct the optimal solution to TSP by adding the nodes successively. A graph neural network (GNN) is trained to capture the local and global graph structure and give the prior probability of selecting each vertex every step. The prior probability provides a heuristics for MCTS, and the MCTS output is an improved probability for selecting the successive vertex, as it is the feedback information by fusing the prior with the scouting procedure. Experimental results on TSP up to 100 nodes demonstrate that the proposed method obtains shorter tours than other learning-based methods.
A Graph Neural Network Assisted Monte Carlo Tree Search Approach to Traveling Salesman Problem

The Convolutional Neural Network (CNN) has been successfully applied in many fields during recent decades; however it lacks the ability to utilize prior domain knowledge when dealing with many realistic problems. We present a framework called Geometric Operator Convolutional Neural Network (GO-CNN) that uses domain knowledge, wherein the kernel of the first convolutional layer is replaced with a kernel generated by a geometric operator function. This framework integrates many conventional geometric operators, which allows it to adapt to a diverse range of problems. Under certain conditions, we theoretically analyze the convergence and the bound of the generalization errors between GO-CNNs and common CNNs. Although the geometric operator convolution kernels have fewer trainable parameters than common convolution kernels, the experimental results indicate that GO-CNN performs more accurately than common CNN on CIFAR-10/100. Furthermore, GO-CNN reduces dependence on the amount of training examples and enhances adversarial stability.
Traditional image processing algorithms are combined with Convolutional Neural Networks，a new neural network.

This paper proposes a new approach for step size adaptation in gradient methods. The proposed method called step size optimization (SSO) formulates the step size adaptation as an optimization problem which minimizes the loss function with respect to the step size for the given model parameters and gradients. Then, the step size is optimized based on alternating direction method of multipliers (ADMM). SSO does not require the second-order information or any probabilistic models for adapting the step size, so it is efficient and easy to implement. Furthermore, we also introduce stochastic SSO for stochastic learning environments. In the experiments, we integrated SSO to vanilla SGD and Adam, and they outperformed state-of-the-art adaptive gradient methods including RMSProp, Adam, L4-Adam, and AdaBound on extensive benchmark datasets.

We propose an efficient and effective step size adaptation method for the gradient methods.