Learning effective high-order feature interactions is very crucial in the CTR prediction task. However, it is very time-consuming to calculate high-order feature interactions with massive features in online e-commerce platforms. Most existing methods manually design a maximal order and further filter out the useless interactions from them. Although they reduce the high computational costs caused by the exponential growth of high-order feature combinations, they still suffer from the degradation of model capability due to the suboptimal learning of the restricted feature orders. The solution to maintain the model capability and meanwhile keep it efficient is a technical challenge, which has not been adequately addressed. To address this issue, we propose an adaptive feature interaction learning model, named as EulerNet, in which the feature interactions are learned in a complex vector space by conducting space mapping according to Euler's formula. EulerNet converts the exponential powers of feature interactions into simple linear combinations of the modulus and phase of the complex features, making it possible to adaptively learn the high-order feature interactions in an efficient way. Furthermore, EulerNet incorporates the implicit and explicit feature interactions into a unified architecture, which achieves the mutual enhancement and largely boosts the model capabilities. Such a network can be fully learned from data, with no need of pre-designed form or order for feature interactions. Extensive experiments conducted on three public datasets have demonstrated the effectiveness and efficiency of our approach. Our code is available at: https://github.com/RUCAIBox/EulerNet.

翻译：学习有效的高阶特征交互在点击率预测任务中至关重要。然而，在在线电商平台中，面对海量特征计算高阶特征交互极为耗时。现有方法大多手动设计最大阶数，并从中进一步筛选出无用的交互。尽管这些方法降低了因高阶特征组合指数级增长导致的高计算成本，但仍因受限特征阶数的次优学习而面临模型能力下降的问题。如何在保持模型能力的同时兼顾效率，是一个尚未充分解决的技术挑战。为此，我们提出一种名为EulerNet的自适应特征交互学习模型，该模型通过欧拉公式进行空间映射，在复数向量空间中学习特征交互。EulerNet将特征交互的指数幂转化为复数特征模长与相位的简单线性组合，从而能够以高效方式自适应学习高阶特征交互。此外，EulerNet将隐式和显式特征交互融入统一架构，实现了两者的相互增强并大幅提升模型能力。该网络完全从数据中学习，无需预先设计特征交互的形式或阶数。在三个公共数据集上进行的大量实验证明了我们方法的有效性和高效性。我们的代码开源在：https://github.com/RUCAIBox/EulerNet。