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.

[Q]: Since deep neural networks are over-parameterized, they can memorize noisy examples. We address such memorizing issue in the presence of annotation noise. From the fact that deep neural networks cannot generalize neighborhoods of the features acquired via memorization, we hypothesize that noisy examples do not consistently incur small losses on the network under a certain perturbation. Based on this, we propose a novel training method called Learning with Ensemble Consensus (LEC) that prevents overfitting noisy examples by eliminating them using the consensus of an ensemble of perturbed networks. One of the proposed LECs, LTEC outperforms the current state-of-the-art methods on noisy MNIST, CIFAR-10, and CIFAR-100 in an efficient manner.
[A]: This work presents a method of generating and using ensembles effectively to identify noisy examples in the presence of annotation noise. 


[Q]: 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+.
[A]: Probabilistic Rule Learning system using Lifted Inference


[Q]: Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average potential over the posterior distribution of weights along with an entropic regularization term. This potential is however not the original loss function in general. So SGD does perform variational inference, but for a different loss than the one used to compute the gradients. Even more surprisingly, SGD does not even converge in the classical sense: we show that the most likely trajectories of SGD for deep networks do not behave like Brownian motion around critical points. Instead, they resemble closed loops with deterministic components. We prove that such out-of-equilibrium behavior is a consequence of highly non-isotropic gradient noise in SGD; the covariance matrix of mini-batch gradients for deep networks has a rank as small as 1% of its dimension. We provide extensive empirical validation of these claims, proven in the appendix.
[A]:
SGD implicitly performs variational inference; gradient noise is highly non-isotropic, so SGD does not even converge to critical points of the original loss