发表机构
Pontificia Universidad Javeriana; Universitat Politècnica de Catalunya（哈维里亚纳主教大学; 加泰罗尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
NObSP通过斜子空间投影将神经网络预测分解为特征贡献函数和交互残差，支持局部与全局解释，在合成基准上函数复现分数达0.989，优于现有方法，并在TinyImageNet上提升了嵌入质量。
AI 中文摘要
理解深度神经网络如何做出决策仍然是一个根本性的挑战。我们提出了NObSP（非线性斜子空间投影），这是一个将预测分解为显式的每个特征贡献函数和交互残差的框架。NObSP利用训练好的网络的线性最终层，并在样本空间中使用斜投影，以减少当学习到的特征子空间重叠时的重复计算，从而同时支持局部解释和全局功能分析。我们建立了与函数方差分析（functional ANOVA）和Kolmogorov-Arnold表示定理的联系，并推导出一种用于样本外评估的高效偏回归算法。对于卷积网络，NObSP-CAM在一次校准后无需反向传播即可生成类激活图。在表格和视觉基准上的实验表明，其保真度与既有的归因方法相当。在一个具有已知分量函数的合成基准上，NObSP获得了0.989的函数复现分数，而KernelSHAP为0.966，积分梯度（Integrated Gradients）为0.922。在TinyImageNet上，贡献向量嵌入将平均最近邻类别纯度从原始激活的0.654提高到0.713，并将平均邻居距离减少了一半以上。这些结果表明，NObSP通过恢复具有可分离的正负证据的功能贡献分布，补充了标量归因方法。
英文摘要
Understanding how deep neural networks make decisions remains a fundamental challenge. We present NObSP (Nonlinear Oblique Subspace Projections), a framework that decomposes predictions into explicit per feature contribution functions and an interaction residual. NObSP exploits the linear final layer of a trained network and uses oblique projections in sample space to reduce double counting when learned feature subspaces overlap, thereby supporting both local explanations and global functional analysis. We establish connections to functional ANOVA and the Kolmogorov-Arnold representation theorem and derive an efficient partial regression algorithm for out of sample evaluation. For convolutional networks, NObSP-CAM produces class activation maps without backward passes after a one time calibration. Experiments on tabular and vision benchmarks show faithfulness comparable to established attribution methods. On a synthetic benchmark with known component functions, NObSP obtains a Function Reproduction Score of 0.989, compared with 0.966 for KernelSHAP and 0.922 for Integrated Gradients. On TinyImageNet, contribution vector embeddings improve mean nearest neighbor class purity from 0.654 for raw activations to 0.713 and reduce mean neighbor distance by more than half. These results indicate that NObSP complements scalar attribution methods by recovering functional contribution profiles with separable positive and negative evidence.
Comments24 pages, including 6 pages of supplementary material. Code available at https://github.com/santialferez/nobsp_lib
