标题： 使用组合神经网络和离散优化的精确CHY积分构造 显示英文标题

标题： Exact CHY Integrand Construction Using Combinatorial Neural Networks and Discrete Optimization

摘要： 我们提出了一种新颖的方法来解决逆CHY问题——通过建立CHY组合学与组合神经网络（CNNs）之间的对应关系，从所需的极点结构构造积分表达式。 我们的关键创新是广义极点次数$K(s_A)$，它在积分表达式相乘时具有可加性，并满足分层递归关系。 这些递归关系自然映射到CNN的信息传递架构，从而实现保留精确整数约束的离散自动微分。 与产生数值近似的传统机器学习方法不同，我们的方法利用了CHY形式主义的内在组合结构，以保证精确的代数解。 这项工作展示了专用神经架构如何解决需要严格数学约束的基本物理问题，为连接组合学、机器学习和散射振幅理论提供了一个初步的步骤。 显示英文摘要

摘要： We present a novel approach to the inverse CHY problem-constructing integrands from desired pole structures-by establishing a correspondence between CHY combinatorics and Combinatorial Neural Networks (CNNs). Our key innovation is the generalized pole degree $K(s_A)$, which is additive under integrand multiplication and satisfies hierarchical recursion relations. These recursions naturally map to CNN message-passing architectures, enabling discrete automatic differentiation that preserves exact integer constraints throughout the computation. Unlike conventional machine learning approaches that yield numerical approximations, our method leverages the intrinsic combinatorial structure of the CHY formalism to guarantee exact algebraic solutions. This work demonstrates how specialized neural architectures can solve fundamental physics problems requiring strict mathematical constraints, providing a modest step toward bridging combinatorics, machine learning, and scattering amplitude theory.