Mathematical Programming Models for Exact and Interpretable Formulation of Neural Networks
This work addresses the need for exact and interpretable neural network formulations, bridging areas like explainable AI and formal verification, though it is incremental as it builds on existing optimization methods.
The paper tackles the problem of training neural networks that are sparse and interpretable by developing a unified mixed-integer programming framework, resulting in globally optimal solutions that balance prediction accuracy, weight sparsity, and architectural compactness.
This paper presents a unified mixed-integer programming framework for training sparse and interpretable neural networks. We develop exact formulations for both fully connected and convolutional architectures by modeling nonlinearities such as ReLU activations through binary variables and encoding structural sparsity via filter- and layer-level pruning constraints. The resulting models integrate parameter learning, architecture selection, and structural regularization within a single optimization problem, yielding globally optimal solutions with respect to a composite objective that balances prediction accuracy, weight sparsity, and architectural compactness. The mixed-integer programming formulation accommodates piecewise-linear operations, including max pooling and activation gating, and permits precise enforcement of logic-based or domain-specific constraints. By incorporating considerations of interpretability, sparsity, and verifiability directly into the training process, the proposed framework bridges a range of research areas including explainable artificial intelligence, symbolic reasoning, and formal verification.