Puechmorel Stéphane
ENAC (École Nationale de l'Aviation Civile), Université de Toulouse, 7, Avenue Edouard Belin, 31055 Toulouse, France.
Entropy (Basel). 2023 Oct 15;25(10):1450. doi: 10.3390/e25101450.
Explainable Artificial Intelligence (XAI) and acceptable artificial intelligence are active topics of research in machine learning. For critical applications, being able to prove or at least to ensure with a high probability the correctness of algorithms is of utmost importance. In practice, however, few theoretical tools are known that can be used for this purpose. Using the Fisher Information Metric (FIM) on the output space yields interesting indicators in both the input and parameter spaces, but the underlying geometry is not yet fully understood. In this work, an approach based on the pullback bundle, a well-known trick for describing bundle morphisms, is introduced and applied to the encoder-decoder block. With constant rank hypothesis on the derivative of the network with respect to its inputs, a description of its behavior is obtained. Further generalization is gained through the introduction of the pullback generalized bundle that takes into account the sensitivity with respect to weights.
可解释人工智能（XAI）和可接受人工智能是机器学习领域的热门研究课题。对于关键应用而言，能够证明算法的正确性，或者至少以高概率确保其正确性至关重要。然而在实践中，几乎没有已知的理论工具可用于此目的。在输出空间上使用费希尔信息度量（FIM）会在输入空间和参数空间中产生有趣的指标，但底层几何结构尚未完全理解。在这项工作中，引入了一种基于拉回丛（一种描述丛态射的著名技巧）的方法，并将其应用于编码器 - 解码器模块。基于网络关于其输入的导数的恒定秩假设，获得了对其行为的描述。通过引入考虑权重敏感性的拉回广义丛，实现了进一步的推广。
