Deep Neural Networks (DNNs) have revolutionized computer vision. We now have
DNNs that achieve top (performance) results in many problems, including object
recognition, facial expression analysis, and semantic segmentation, to name but
a few. The design of the DNNs that achieve top results is, however, non-trivial
and mostly done by trail-and-error. That is, typically, researchers will derive
many DNN architectures (i.e., topologies) and then test them on multiple
datasets. However, there are no guarantees that the selected DNN will perform
well in the real world. One can use a testing set to estimate the performance
gap between the training and testing sets, but avoiding
overfitting-to-the-testing-data is almost impossible. Using a sequestered
testing dataset may address this problem, but this requires a constant update
of the dataset, a very expensive venture. Here, we derive an algorithm to
estimate the performance gap between training and testing that does not require
any testing dataset. Specifically, we derive a number of persistent topology
measures that identify when a DNN is learning to generalize to unseen samples.
This allows us to compute the DNN's testing error on unseen samples, even when
we do not have access to them. We provide extensive experimental validation on
multiple networks and datasets to demonstrate the feasibility of the proposed
approach.

提出了一种算法来估计深度神经网络的训练误差和测试误差之间的差距，该算法不需要测试数据集，使用拓扑学指标来识别网络的泛化能力并计算其对未见样本的测试误差。

不使用测试集计算测试误差

Computing the Testing Error without a Testing Set

Zero-shot learning (ZSL) has received increasing attention in recent years
especially in areas of fine-grained object recognition, retrieval, and image
captioning. The key to ZSL is to transfer knowledge from the seen to the unseen
classes via auxiliary class attribute vectors. However, the popularly learned
projection functions in previous works cannot generalize well since they assume
the distribution consistency between seen and unseen domains at
sample-level.Besides, the provided non-visual and unique class attributes can
significantly degrade the recognition performance in semantic space. In this
paper, we propose a simple yet effective convolutional prototype learning (CPL)
framework for zero-shot recognition. By assuming distribution consistency at
task-level, our CPL is capable of transferring knowledge smoothly to recognize
unseen samples.Furthermore, inside each task, discriminative visual prototypes
are learned via a distance based training mechanism. Consequently, we can
perform recognition in visual space, instead of semantic space. An extensive
group of experiments are then carefully designed and presented, demonstrating
that CPL obtains more favorable effectiveness, over currently available
alternatives under various settings.

本文提出了一种卷积原型学习（CPL）框架，用于零样本识别。通过在任务级别假设分布一致性，CPL 能够平稳地转移知识以识别未见样本。在每个任务内部，通过基于距离的训练机制学习区分性视觉原型。因此，我们可以在视觉空间而不是语义空间中进行识别。