用数学规划精确训练可解释的稀疏神经网络。
Mathematical Programming Models for Exact and Interpretable Formulation of Neural Networks
- 通过二元变量建模ReLU等非线性，实现网络结构的精确优化。
- 同时优化精度、稀疏性和紧凑性，获得全局最优解。
- 适合需要可解释性与形式验证的高可信场景。
本文提出一种统一的混合整数规划框架，用于训练稀疏且可解释的神经网络。通过二元变量建模ReLU等非线性激活函数，并利用滤波器级和层级剪枝约束编码结构稀疏性，精确构建全连接与卷积架构的公式。该框架将参数学习、架构选择与结构正则化整合到单一优化问题中，针对预测精度、权重稀疏性和架构紧凑性组成的复合目标，获得全局最优解。模型支持分段线性操作（如最大池化、激活门控），并能精确施加逻辑或领域特定约束。通过在训练过程中直接融入可解释性、稀疏性和可验证性考量，该框架连接了可解释人工智能、符号推理与形式验证等多个研究方向。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。