Neuron Activation-based Computation of Logical Explanations for Deep Neural Networks
Authors: Tomáš Kolárik, Faezeh Labbaf, Fabrizio Leopardi, Grigory Fedyukovich, Michael Wand, Natasha Sharygina
Organizations: University of Lugano (USI), Lugano, Switzerland · Florida State University, United States of America · SUPSI, IDSIA, Lugano, Switzerland
Formal explainability of classifying neural networks (NNs) is an active area of research, providing explanations with provable guarantees of the classification within continuous regions of the input feature space. However, the existing techniques are either limited to individual input features without guarantees on their relations or the provided solutions fail to scale to deep architectures. This paper addresses these issues by introducing a flexible symbolic framework for an efficient, guided computation of explanations of the NN behavior, parametrized by the activations of internal neurons, and using logical engines such as SMT solvers. Unlike prior methods that rely on specialized NN verifiers, our method yields explanations that are not restricted in shape. Our algorithm is implementable on top of a general-purpose logical solver, isolating the NN-specific encoding from the algorithmic framework. We experimented with a wide range of benchmarks from the domains of image recognition and medicine, illustrating the advantages of the new method, particularly in computational efficiency. Notably, our approach enables logical explanation of deep networks not amenable to prior logic-based methods.
Figures & tables
Figure 1: Neuron activation-based framework for automated computation of logical explanations, which takes as input a sample point, NN, the classification, and configurations of internal neurons, and outputs a logical explanation.
Figure 2: Performance comparison of our methods and interpolation algorithms. In medical datasets, it shows PAR-2 only up to 40 to make methods other than Direct visible.
Figure 4: Visual comparison of selected 2D snapshots of explanation spaces of the heart-attack dataset (with two classes: high and low risk) produced by different methods.
Figure 6: Performance of an enumerative invariant discovery with/without fixing.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 7: A simple neural network example
Figure 8: Performance comparison with VeriX on networks with 200 neurons per layer.