A Rate-Distortion Framework for Explaining Neural Network Decisions
This work addresses the challenge of explaining neural network decisions for researchers and practitioners, providing a theoretical foundation and practical improvements, though it is incremental in building on existing interpretability ideas.
The paper formalizes neural network interpretability as a rate-distortion optimization problem, where relevant features are identified by their impact on classifier scores, and proves the problem is computationally hard (NP^PP-complete) and NP-hard to approximate, while presenting a heuristic method that outperforms existing approaches in generating sparse explanations for image classification datasets.
We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected classifier score remains nearly constant when randomising the remaining features. We discuss the computational complexity of finding small sets of relevant features and show that the problem is complete for $\mathsf{NP}^\mathsf{PP}$, an important class of computational problems frequently arising in AI tasks. Furthermore, we show that it even remains $\mathsf{NP}$-hard to only approximate the optimal solution to within any non-trivial approximation factor. Finally, we consider a continuous problem relaxation and develop a heuristic solution strategy based on assumed density filtering for deep ReLU neural networks. We present numerical experiments for two image classification data sets where we outperform established methods in particular for sparse explanations of neural network decisions.