论文标题
深度学习功能从图像中学习的特征空间中的决策边界和凸壳
Decision boundaries and convex hulls in the feature space that deep learning functions learn from images
论文作者
论文摘要
深度神经网络在图像分类和学习中的成功可以部分归因于它们从图像中提取的功能。通常，人们推测出模型提取和从图像中学习的低维流形的性质。但是，基于理论或经验证据，对这个低维空间没有足够的了解。对于图像分类模型，它们的最后一个隐藏层是每个类的图像与其他类别分开的图像，并且它的功能数量最少。在这里，我们开发了研究任何模型的特征空间的方法和公式。我们研究特征空间中域的分区，确定保证具有某些分类的区域，并研究其对像素空间的影响。我们观察到，与像素空间相比，特征空间中决策边界的几何布置有显着不同，从而提供了有关对抗性脆弱性，图像变形，外推，分类中的歧义以及对图像分类模型的数学理解的见解。
The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and learn from images. However, there is not sufficient understanding about this low-dimensional space based on theory or empirical evidence. For image classification models, their last hidden layer is the one where images of each class is separated from other classes and it also has the least number of features. Here, we develop methods and formulations to study that feature space for any model. We study the partitioning of the domain in feature space, identify regions guaranteed to have certain classifications, and investigate its implications for the pixel space. We observe that geometric arrangements of decision boundaries in feature space is significantly different compared to pixel space, providing insights about adversarial vulnerabilities, image morphing, extrapolation, ambiguity in classification, and the mathematical understanding of image classification models.
