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.
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Question: Reasoning over text and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. Transducing text to logical forms which can be operated on is a brittle and error-prone process . Operating directly on text by jointly learning representations and transformations thereof by means of neural architectures that lack the ability to learn and exploit general rules can be very data-inefficient and not generalise correctly . These issues are addressed by Neural Theorem Provers (NTPs) (Rocktaschel & Riedel, 2017), neuro-symbolic systems based on a continuous relaxation of Prolog's backward chaining algorithm, where symbolic unification between atoms is replaced by a differentiable operator computing the similarity between their embedding representations . In this paper, we first propose Neighbourhood-approximated Neural Theorem Provers (NaNTPs) consisting of two extensions toNTPs, namely a) a method for drastically reducing the previously prohibitive time and space complexity during inference and learning, and b) an attention mechanism for improving the rule learning process, deeming them usable on real-world datasets. Then, we propose a novel approach for jointly reasoning over KB facts and textual mentions, by jointly embedding them in a shared embedding space. The proposed method is able to extract rules and provide explanationsinvolving both textual patterns and KB relationsfrom large KBs and text corpora. We show that NaNTPs perform on par with NTPs at a fraction of a cost, and can achieve competitive link prediction results on challenging large-scale datasets, including WN18, WN18RR, and FB15k-237 (with and without textual mentions) while being able to provide explanations for each prediction and extract interpretable rules.

Answer: We scale Neural Theorem Provers to large datasets, improve the rule learning process, and extend it to jointly reason over text and Knowledge Bases.

Question: Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by transforming Gaussian noise through a deep neural network whose output are the parameters of a spline. Unlike Gaussian processes, Deep Random Splines allow us to readily enforce shape constraints while inheriting the richness and tractability of deep generative models. We also present an observational model for point process data which uses Deep Random Splines to model the intensity function of each point process and apply it to neuroscience data to obtain a low-dimensional representation of spiking activity. Inference is performed via a variational autoencoder that uses a novel recurrent encoder architecture that can handle multiple point processes as input.

Answer: We combine splines with neural networks to obtain a novel distribution over functions and use it to model intensity functions of point processes.

Question: We study two types of preconditioners and preconditioned stochastic gradient descent (SGD) methods in a unified framework. We call the first one the Newton type due to its close relationship to the Newton method, and the second one the Fisher type as its preconditioner is closely related to the inverse of Fisher information matrix. Both preconditioners can be derived from one framework, and efficiently estimated on any matrix Lie groups designated by the user using natural or relative gradient descent minimizing certain preconditioner estimation criteria. Many existing preconditioners and methods, e.g., RMSProp, Adam, KFAC, equilibrated SGD, batch normalization, etc., are special cases of or closely related to either the Newton type or the Fisher type ones. Experimental results on relatively large scale machine learning problems are reported for performance study.

Answer:
We propose a new framework for preconditioner learning, derive new forms of preconditioners and learning methods, and reveal the relationship to methods like RMSProp, Adam, Adagrad, ESGD, KFAC, batch normalization, etc.