TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Knowledge Bases (KBs) are becoming increasingly large, sparse and probabilistic. These KBs are typically used to perform query inferences and rule mining. But their efficacy is only as high as their completeness. Efficiently utilizing incomplete KBs remains a major challenge as the current KB completion techniques either do not take into account the inherent uncertainty associated with each KB tuple or do not scale to large KBs.

 Probabilistic rule learning not only considers the probability of every KB tuple but also tackles the problem of KB completion in an explainable way. For any given probabilistic KB, it learns probabilistic first-order rules from its relations to identify interesting patterns. But, the current probabilistic rule learning techniques perform grounding to do probabilistic inference for evaluation of candidate rules. It does not scale well to large KBs as the time complexity of inference using grounding is exponential over the size of the KB. In this paper, we present SafeLearner -- a scalable solution to probabilistic KB completion that performs probabilistic rule learning using lifted probabilistic inference -- as faster approach instead of grounding. 

 We compared SafeLearner to the state-of-the-art probabilistic rule learner ProbFOIL+ and to its deterministic contemporary AMIE+ on standard probabilistic KBs of NELL (Never-Ending Language Learner) and Yago. Our results demonstrate that SafeLearner scales as good as AMIE+ when learning simple rules and is also significantly faster than ProbFOIL+.

SOLUTION: Probabilistic Rule Learning system using Lifted Inference

PROBLEM: Understanding how people represent categories is a core problem in cognitive science, with the flexibility of human learning remaining a gold standard to which modern artificial intelligence and machine learning aspire. Decades of psychological research have yielded a variety of formal theories of categories, yet validating these theories with naturalistic stimuli remains a challenge. The problem is that human category representations cannot be directly observed and running informative experiments with naturalistic stimuli such as images requires having a workable representation of these stimuli. Deep neural networks have recently been successful in a range of computer vision tasks and provide a way to represent the features of images. In this paper, we introduce a method for estimating the structure of human categories that draws on ideas from both cognitive science and machine learning, blending human-based algorithms with state-of-the-art deep representation learners. We provide qualitative and quantitative results as a proof of concept for the feasibility of the method. Samples drawn from human distributions rival the quality of current state-of-the-art generative models and outperform alternative methods for estimating the structure of human categories.

SOLUTION: using deep neural networks and clever algorithms to capture human mental visual concepts

PROBLEM: Capsule networks are constrained by the parameter-expensive nature of their layers, and the general lack of provable equivariance guarantees. We present a variation of capsule networks that aims to remedy this. We identify that learning all pair-wise part-whole relationships between capsules of successive layers is inefficient. Further, we also realise that the choice of prediction networks and the routing mechanism are both key to equivariance. Based on these, we propose an alternative framework for capsule networks that learns to projectively encode the manifold of pose-variations, termed the space-of-variation (SOV), for every capsule-type of each layer. This is done using a trainable, equivariant function defined over a grid of group-transformations. Thus, the prediction-phase of routing involves projection into the SOV of a deeper capsule using the corresponding function. As a specific instantiation of this idea, and also in order to reap the benefits of increased parameter-sharing, we use type-homogeneous group-equivariant convolutions of shallower capsules in this phase. We also introduce an equivariant routing mechanism based on degree-centrality. We show that this particular instance of our general model is equivariant, and hence preserves the compositional representation of an input under transformations. We conduct several experiments on standard object-classification datasets that showcase the increased transformation-robustness, as well as general performance, of our model to several capsule baselines.

SOLUTION:
A new scalable, group-equivariant model for capsule networks that preserves compositionality under transformations, and is empirically more transformation-robust to older capsule network models.