cs.LOMar 2, 2026
SaveBound Propagation meets Constraint Simplification: Improving Logic-based XAI for Neural Networks
Organizations: Department of Computer Science, Instituto Federal do Ceará (IFCE), Maracanaú, Brazil
Abstract
Logic-based methods for explaining neural network decisions offer formal guarantees of correctness and non-redundancy, but they often suffer from high computational costs, especially for large networks. In this work, we improve the efficiency of such methods by combining bound propagation with constraint simplification. These simplifications, derived from the propagation, tighten neuron bounds and eliminate unnecessary binary variables, making the explanation process more efficient. Our experiments suggest that combining these techniques reduces explanation time by up to 89.26%, particularly for larger neural networks.
Figures & tables
Fig. 1: Example of Neural Network
| Dataset | NN | Exp (s) | Exp (s) | Solver (s) | Solver (s) | % Bounds | % Bin Vars | % Bin Vars |
| INMS | Ours | INMS | Ours | tightened | Removed (Before) | Removed (Ours) | ||
| Iris (4) | 3L-3N | 0.92 | 1.15 | 0.24 | 0.05 | 92.83 | 0.00 | 31.61 |
| 6L-6N | 1.28 | 1.79 | 0.56 | 0.05 | 96.04 | 21.21 | 56.43 | |
| Wine (13) | 3L-4N | 1.71 | 2.72 | 0.86 | 0.06 | 100.00 | 0.00 | 46.90 |
| 6L-8N | 4.77 | 5.72 | 3.84 | 0.06 | 97.33 | 23.25 | 67.08 | |
| Sonar (60) | 3L-4N | 6.09 | 13.20 | 4.88 | 0.06 | 100.00 | 10.00 | 65.13 |
TABLE I: Comparison between INMS and our approach, highlighting total explanation times, solver execution times, and the impact of bound propagation and constraint simplification on neuron bounds and binary variable reduction.