论文标题
恢复Hadamard矩阵的模棱两可的神经网络
Equivariant neural networks for recovery of Hadamard matrices
论文作者
论文摘要
我们提出了一条传递神经网络体系结构的消息，旨在与矩阵的列和行排列相等。我们在恢复Hadamard Matrix的一组已删除条目的组合优化任务上，说明了它比传统体系结构（MLPS），卷积神经网络（CNN）甚至变形金刚等传统体系结构的优势。我们认为，这是几何深度学习原理对基本数学的强大应用，也是使用机器学习技术对Hadamard猜想的更多见解的潜在垫脚石。
We propose a message passing neural network architecture designed to be equivariant to column and row permutations of a matrix. We illustrate its advantages over traditional architectures like multi-layer perceptrons (MLPs), convolutional neural networks (CNNs) and even Transformers, on the combinatorial optimization task of recovering a set of deleted entries of a Hadamard matrix. We argue that this is a powerful application of the principles of Geometric Deep Learning to fundamental mathematics, and a potential stepping stone toward more insights on the Hadamard conjecture using Machine Learning techniques.
