用乘积单元显式建模特征交互，提升模型可解释性与鲁棒性。
Modeling Nonlinear Feature Interactions with Product-Unit Residual Networks
- 引入乘积单元与残差连接，显式捕捉特征间非线性交互。
- 在低数据场景下表现更优，对噪声更鲁棒，准确率不降反升。
- 适合需要高可解释性的工业应用与小样本学习任务。
理解非线性特征交互在科学与工程中至关重要，但标准多层感知机（MLP）仅隐式捕捉此类交互，导致表示纠缠，影响模型鲁棒性与可解释性。本文提出乘积单元残差网络（PURe），将乘法型产品单元与残差连接结合，显式建模跨特征耦合，同时稳定优化过程。我们在一个交互驱动的合成基准和两个真实数据集上系统评估了性能，涵盖预测准确率、高斯特征噪声下的鲁棒性及小样本条件下的表现，并在参数量匹配条件下比较了实值与复值变体。除准确率外，基于SHAP的交互分析显示，PURe学习到的交互模式更集中且结构更清晰。整体上，PURe实现竞争力或更优性能，在低数据场景下具备更强鲁棒性与样本效率，且在交互层面具有更高可解释性。
原文摘要 · Abstract (English)
Understanding nonlinear feature interactions is crucial in science and engineering, yet standard multilayer perceptrons (MLPs) often capture such interactions only implicitly, leading to entangled representations that can impair robustness and interpretability. We investigate product-unit residual networks (PURe) that integrate multiplicative product units with residual connections to explicitly model cross-feature couplings while stabilizing optimization. We conduct a systematic evaluation on an interaction-driven synthetic benchmark and two real-world datasets, assessing predictive accuracy, robustness to Gaussian feature noise, and performance under limited training data, and we compare real- and complex-valued variants under a matched parameter budget. Beyond accuracy, SHapley Additive exPlanations (SHAP)-based interaction analyses show that PURe learns more concentrated and structurally coherent interaction patterns than MLP baselines. Overall, PURe achieves competitive or improved performance, better robustness and sample efficiency in low-data regimes, and enhanced interaction-level interpretability.
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