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. Our goal is to combine the rich multistep inference of symbolic logical reasoning with the generalization capabilities of neural networks. We are particularly interested in complex reasoning about entities and relations in text and large-scale knowledge bases (KBs). (2015) use RNNs to compose the distributed semantics of multi-hop paths in KBs; however for multiple reasons, the approach lacks accuracy and practicality. This paper proposes three significant modeling advances: (1) we learn to jointly reason about relations, entities, and entity-types; (2) we use neural attention modeling to incorporate multiple paths; (3) we learn to share strength in a single RNN that represents logical composition across all relations. On a largescale Freebase+ClueWeb prediction task, we achieve 25 error reduction, and a 53 error reduction on sparse relations due to shared strength. On chains of reasoning in WordNet we reduce error in mean quantile by 84 versus previous state-of-the-art. The code and data are available at this https URL We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules. Relational reasoning is a central component of generally intelligent behavior, but has proven difficult for neural networks to learn. In this paper we describe how to use Relation Networks (RNs) as a simple plug-and-play module to solve problems that fundamentally hinge on relational reasoning. We tested RN-augmented networks on three tasks: visual question answering using a challenging dataset called CLEVR, on which we achieve state-of-the-art, super-human performance; text-based question answering using the bAbI suite of tasks; and complex reasoning about dynamic physical systems. Then, using a curated dataset called Sort-of-CLEVR we show that powerful convolutional networks do not have a general capacity to solve relational questions, but can gain this capacity when augmented with RNs. Our work shows how a deep learning architecture equipped with an RN module can implicitly discover and learn to reason about entities and their relations.