In this paper, we develop a generic methodology to encode hierarchical causality structure among observed variables into a neural network in order to improve its predictive performance. The proposed methodology, called causality-informed neural network (CINN), leverages three coherent steps to systematically map the structural causal knowledge into the layer-to-layer design of neural network while strictly preserving the orientation of every causal relationship. In the first step, CINN discovers causal relationships from observational data via directed acyclic graph (DAG) learning, where causal discovery is recast as a continuous optimization problem to avoid the combinatorial nature. In the second step, the discovered hierarchical causality structure among observed variables is systematically encoded into neural network through a dedicated architecture and customized loss function. By categorizing variables in the causal DAG as root, intermediate, and leaf nodes, the hierarchical causal DAG is translated into CINN with a one-to-one correspondence between nodes in the causal DAG and units in the CINN while maintaining the relative order among these nodes. Regarding the loss function, both intermediate and leaf nodes in the DAG graph are treated as target outputs during CINN training so as to drive co-learning of causal relationships among different types of nodes. As multiple loss components emerge in CINN, we leverage the projection of conflicting gradients to mitigate gradient interference among the multiple learning tasks. Computational experiments across a broad spectrum of UCI data sets demonstrate substantial advantages of CINN in predictive performance over other state-of-the-art methods. In addition, an ablation study underscores the value of integrating structural and quantitative causal knowledge in enhancing the neural network's predictive performance incrementally.

翻译：本文提出一种通用方法，将观测变量间的层次化因果结构编码至神经网络中，以提升其预测性能。该框架名为因果信息神经网络（CINN），通过三个连贯步骤将结构因果知识系统性地映射至神经网络的层间设计，并严格保持每个因果关系的方向性。第一步，CINN通过有向无环图（DAG）学习从观测数据中挖掘因果关系，将因果发现转化为连续优化问题以规避组合爆炸。第二步，通过专用架构与定制损失函数，将观测变量间发现的层次因果结构系统编码至神经网络中：通过将因果DAG中的变量划分为根节点、中间节点与叶节点，构建因果DAG与CINN节点的一一对应关系并保持节点间相对顺序。在损失函数层面，将DAG中的中间节点与叶节点同时作为CINN训练的目标输出，驱动不同类型节点间因果关系的协同学习。针对CINN中多损失分量引发的梯度干扰问题，采用梯度投影机制缓解多任务学习的梯度冲突。基于UCI数据集的广泛实验表明，CINN在预测性能上显著优于其他先进方法。此外，消融研究进一步验证了融合结构性与定量因果知识对渐进式提升神经网络预测性能的关键价值。