Conventional application of convolutional neural networks (CNNs) for image classification and recognition is based on the assumption that all target classes are equal(i.e., no hierarchy) and exclusive of one another (i.e., no overlap). CNN-based image classifiers built on this assumption, therefore, cannot take into account an innate hierarchy among target classes (e.g., cats and dogs in animal image classification) or additional information that can be easily derived from the data (e.g.,numbers larger than five in the recognition of handwritten digits), thereby resulting in scalability issues when the number of target classes is large. Combining two related but slightly different ideas of hierarchical classification and logical learning by auxiliary inputs, we propose a new learning framework called hierarchical auxiliary learning, which not only address the scalability issues with a large number of classes but also could further reduce the classification recognition errors with a reasonable number of classes. In the hierarchical auxiliary learning, target classes are semantically or non-semantically grouped into superclasses, which turns the original problem of mapping between an image and its target class into a new problem of mapping between a pair of an image and its superclass and the target class. To take the advantage of superclasses, we introduce an auxiliary block into a neural network, which generates auxiliary scores used as additional information for final classification recognition; in this paper, we add the auxiliary block between the last residual block and the fully-connected output layer of the ResNet. Experimental results demonstrate that the proposed hierarchical auxiliary learning can reduce classification errors up to 0.56, 1.6 and 3.56 percent with MNIST, SVHN and CIFAR-10 datasets, respectively.
Furthermore, auxiliary inputs are used to check logical reasoning in @cite_20 . Auxiliary inputs based on human knowledge are provided to the network to let the network learn logical reasoning. The network verifies the logical information with the auxiliary inputs first and proceeds to the next stage.
@cite_20
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This paper describes a neural network design using auxiliary inputs, namely the indicators, that act as the hints to explain the predicted outcome through logical reasoning, mimicking the human behavior of deductive reasoning. Besides the original network input and output, we add an auxiliary input that reflects the specific logic of the data to formulate a reasoning process for cross-validation. We found that one can design either meaningful indicators, or even meaningless ones, when using such auxiliary inputs, upon which one can use as the basis of reasoning to explain the predicted outputs. As a result, one can formulate different reasonings to explain the predicted results by designing different sets of auxiliary inputs without the loss of trustworthiness of the outcome. This is similar to human explanation process where one can explain the same observation from different perspectives with reasons. We demonstrate our network concept by using the MNIST data with different sets of auxiliary inputs, where a series of design guidelines are concluded. Later, we validated our results by using a set of images taken from a robotic grasping platform. We found that our network enhanced the last 1-2 of the prediction accuracy while eliminating questionable predictions with self-conflicting logics. Future application of our network with auxiliary inputs can be applied to robotic detection problems such as autonomous object grasping, where the logical reasoning can be introduced to optimize robotic learning.