验证两个神经网络在局部区域的逻辑蕴含关系，确保小模型决策始终优于大模型。
Formal Local Implication Between Two Neural Networks
- 构建形式化局部蕴含框架，证明一个网络的正确判断必然包含另一个。
- 在MNIST、CIFAR10和两个医学数据集上验证，结果稳定可靠。
- 适用于模型压缩后效果对比，适合关注模型可靠性与可解释性的研究者。
针对具有相同输入输出空间的两个神经网络分类器，本文提出在整体输入区域（如某个样本邻域内）比较二者之间形式化局部蕴含关系——即网络N2在区域D内每次正确决策时，网络N1也始终正确。为此，建立了一种可形式化验证（可证明正确）的局部蕴含判定方法。该方法在多个应用场景中具有价值，例如对比训练后的网络与其压缩版本（如剪枝、量化、蒸馏）之间的性能一致性。我们在MNIST、CIFAR10以及两个真实医学数据集上进行了评估，验证了该方法的有效性与实用性。
原文摘要 · Abstract (English)
Given two neural network classifiers with the same input and output domains, our goal is to compare the two networks in relation to each other over an entire input region (e.g., within a vicinity of an input sample). To this end, we establish the foundation of formal local implication between two networks, i.e., N2 implies N1, in an entire input region D. That is, network N1 consistently makes a correct decision every time network N2 does, and it does so in an entire input region D. We further propose a sound formulation for establishing such formally-verified (provably correct) local implications. The proposed formulation is relevant in the context of several application domains, e.g., for comparing a trained network and its corresponding compact (e.g., pruned, quantized, distilled) networks. We evaluate our formulation based on the MNIST, CIFAR10, and two real-world medical datasets, to show its relevance.
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