NObSP reveals how deep networks split decisions by input features
NObSP: Functional Decomposition of Neural Networks via Oblique Subspace Projections
Machine Learning
Summary
It is often unclear how deep learning models decide what they do. The authors introduce NObSP, a method that breaks down a network’s prediction into parts linked to each input feature and residual interactions. This approach uses a clever math trick to avoid counting overlapping effects twice, allowing clearer explanations locally and globally. They tested it on image and tabular data, showing it works as well or better than popular methods while giving richer insight into feature roles. For convolutional networks, NObSP can create visual maps showing contributions without complex calculations after a quick setup.
What this means in practice
- •For machine learning engineers: Identify precise feature contributions in neural network predictions for better debugging and model transparency on tabular and image data.
- •For computer vision developers: Generate class activation maps for convolutional networks efficiently without backward passes to speed up visual explanation workflows after calibration.
Authors
Alexander Caicedo, Víctor De La Hoz, Santiago Alférez
Abstract
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.