Link prediction is critical for the application of incomplete knowledge graph (KG) in the downstream tasks. As a family of effective approaches for link predictions, embedding methods try to learn low-rank representations for both entities and relations such that the bilinear form defined therein is a well-behaved scoring function. Despite of their successful performances, existing bilinear forms overlook the modeling of relation compositions, resulting in lacks of interpretability for reasoning on KG. To fulfill this gap, we propose a new model called DihEdral, named after dihedral symmetry group. This new model learns knowledge graph embeddings that can capture relation compositions by nature. Furthermore, our approach models the relation embeddings parametrized by discrete values, thereby decrease the solution space drastically. Our experiments show that DihEdral is able to capture all desired properties such as (skew-) symmetry, inversion and (non-) Abelian composition, and outperforms existing bilinear form based approach and is comparable to or better than deep learning models such as ConvE.

Kandinsky Figures and Kandinsky Patterns are mathematically describable, simple self-contained hence controllable test data sets for the development, validation and training of explainability in artificial intelligence. Whilst Kandinsky Patterns have these computationally manageable properties, they are at the same time easily distinguishable from human observers. Consequently, controlled patterns can be described by both humans and computers. We define a Kandinsky Pattern as a set of Kandinsky Figures, where for each figure an "infallible authority" defines that the figure belongs to the Kandinsky Pattern. With this simple principle we build training and validation data sets for automatic interpretability and context learning. In this paper we describe the basic idea and some underlying principles of Kandinsky Patterns and provide a Github repository to invite the international machine learning research community to a challenge to experiment with our Kandinsky Patterns to expand and thus make progress in the field of explainable AI and to contribute to the upcoming field of explainability and causability.

Dance is an art and when technology meets this kind of art, it's a novel attempt in itself. Several researchers have attempted to automate several aspects of dance, right from dance notation to choreography. Furthermore, we have encountered several applications of dance automation like e-learning, heritage preservation, etc. Despite several attempts by researchers for more than two decades in various styles of dance all round the world, we found a review paper that portrays the research status in this area dating to 1990 \cite{politis1990computers}. Hence, we decide to come up with a comprehensive review article that showcases several aspects of dance automation. This paper is an attempt to review research work reported in the literature, categorize and group all research work completed so far in the field of automating dance. We have explicitly identified six major categories corresponding to the use of computers in dance automation namely dance representation, dance capturing, dance semantics, dance generation, dance processing approaches and applications of dance automation systems. We classified several research papers under these categories according to their research approach and functionality. With the help of proposed categories and subcategories one can easily determine the state of research and the new avenues left for exploration in the field of dance automation.

Gaze correction aims to redirect the person's gaze into the camera by manipulating the eye region, and it can be considered as a specific image resynthesis problem. Gaze correction has a wide range of applications in real life, such as taking a picture with staring at the camera. In this paper, we propose a novel method that is based on the inpainting model to learn from the face image to fill in the missing eye regions with new contents representing corrected eye gaze. Moreover, our model does not require the training dataset labeled with the specific head pose and eye angle information, thus, the training data is easy to collect. To retain the identity information of the eye region in the original input, we propose a self-guided pretrained model to learn the angle-invariance feature. Experiments show our model achieves very compelling gaze-corrected results in the wild dataset which is collected from the website and will be introduced in details. Code is available at https://github.com/zhangqianhui/GazeCorrection.

Making high quality inference on large, feature rich datasets under a constrained computational budget is arguably the primary goal of the learning community. This, however, comes with significant challenges. On the one hand, the exact computation of linear algebraic quantities may be prohibitively expensive, such as that of the log determinant. On the other hand, an analytic expression for the quantity of interest may not exist at all, such as the case for the entropy of a Gaussian mixture model, and approximate methods are often both inefficient and inaccurate.

We present the first verification that a neural network produces a correct output within a specified tolerance for every input of interest. We define correctness relative to a specification which identifies 1) a state space consisting of all relevant states of the world and 2) an observation process that produces neural network inputs from the states of the world. Tiling the state and input spaces with a finite number of tiles, obtaining ground truth bounds from the state tiles and network output bounds from the input tiles, then comparing the ground truth and network output bounds delivers an upper bound on the network output error for any input of interest. Results from a case study highlight the ability of our technique to deliver tight error bounds for all inputs of interest and show how the error bounds vary over the state and input spaces.

In order to meet the diverse challenges in solving many real-world problems, an intelligent agent has to be able to dynamically construct a model of its environment. Objects facilitate the modular reuse of prior knowledge and the combinatorial construction of such models. In this work, we argue that dynamically bound features (objects) do not simply emerge in connectionist models of the world. We identify several requirements that need to be fulfilled in overcoming this limitation and highlight corresponding inductive biases.

Artificial neural networks suffer from catastrophic forgetting when they are sequentially trained on multiple tasks. To overcome this problem, we present a novel approach based on task-conditioned hypernetworks, i.e., networks that generate the weights of a target model based on task identity. Continual learning (CL) is less difficult for this class of models thanks to a simple key observation: instead of relying on recalling the input-output relations of all previously seen data, task-conditioned hypernetworks only require rehearsing previous weight realizations, which can be maintained in memory using a simple regularizer. Besides achieving good performance on standard CL benchmarks, additional experiments on long task sequences reveal that task-conditioned hypernetworks display an unprecedented capacity to retain previous memories. Notably, such long memory lifetimes are achieved in a compressive regime, when the number of trainable weights is comparable or smaller than target network size. We provide insight into the structure of low-dimensional task embedding spaces (the input space of the hypernetwork) and show that task-conditioned hypernetworks demonstrate transfer learning properties. Finally, forward information transfer is further supported by empirical results on a challenging CL benchmark based on the CIFAR-10/100 image datasets.

Class-conditional generative models are an increasingly popular approach to achieve robust classification. They are a natural choice to solve discriminative tasks in a robust manner as they jointly optimize for predictive performance and accurate modeling of the input distribution. In this work, we investigate robust classification with likelihood-based conditional generative models from a theoretical and practical perspective. Our theoretical result reveals that it is impossible to guarantee detectability of adversarial examples even for near-optimal generative classifiers. Experimentally, we show that naively trained conditional generative models have poor discriminative performance, making them unsuitable for classification. This is related to overlooked issues with training conditional generative models and we show methods to improve performance. Finally, we analyze the robustness of our proposed conditional generative models on MNIST and CIFAR10. While we are able to train robust models for MNIST, robustness completely breaks down on CIFAR10. This lack of robustness is related to various undesirable model properties maximum likelihood fails to penalize. Our results indicate that likelihood may fundamentally be at odds with robust classification on challenging problems.

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.