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.

Ex Input:
Neural network training depends on the structure of the underlying loss landscape, i.e. local minima, saddle points, flat plateaus, and loss barriers. In relation to the structure of the landscape, we study the permutation symmetry of neurons in each layer of a deep neural network, which gives rise not only to multiple equivalent global minima of the loss function but also to critical points in between partner minima. In a network of $d-1$ hidden layers with $n_k$ neurons in layers $k = 1, \ldots, d$, we construct continuous paths between equivalent global minima that lead through a 'permutation point' where the input and output weight vectors of two neurons in the same hidden layer $k$ collide and interchange. We show that such permutation points are critical points which lie inside high-dimensional subspaces of equal loss, contributing to the global flatness of the landscape. We also find that a permutation point for the exchange of neurons $i$ and $j$ transits into a flat high-dimensional plateau that enables all $n_k!$ permutations of neurons in a given layer $k$ at the same loss value. Moreover , we introduce higher-order permutation points by exploiting the hierarchical structure in the loss landscapes of neural networks, and find that the number of $K$-th order permutation points is much larger than the (already huge) number of equivalent global minima -- at least by a polynomial factor of order $K$. In two tasks, we demonstrate numerically with our path finding method that continuous paths between partner minima exist: first, in a toy network with a single hidden layer on a function approximation task and, second, in a multilayer network on the MNIST task. Our geometric approach yields a lower bound on the number of critical points generated by weight-space symmetries and provides a simple intuitive link between previous theoretical results and numerical observations.

Ex Output:
Weight-space symmetry in neural network landscapes gives rise to numerous number of saddles and flat high-dimensional subspaces.

Ex Input:
The reproducibility of reinforcement-learning research has been highlighted as a key challenge area in the field. In this paper, we present a case study in reproducing the results of one groundbreaking algorithm, AlphaZero, a reinforcement learning system that learns how to play Go at a superhuman level given only the rules of the game. We describe Minigo, a reproduction of the AlphaZero system using publicly available Google Cloud Platform infrastructure and Google Cloud TPUs. The Minigo system includes both the central reinforcement learning loop as well as auxiliary monitoring and evaluation infrastructure. With ten days of training from scratch on 800 Cloud TPUs, Minigo can play evenly against LeelaZero and ELF OpenGo, two of the strongest publicly available Go AIs. We discuss the difficulties of scaling a reinforcement learning system and the monitoring systems required to understand the complex interplay of hyperparameter configurations.

Ex Output:
We reproduced AlphaZero on Google Cloud Platform

Ex Input:
Creating a knowledge base that is accurate, up-to-date and complete remains a significant challenge despite substantial efforts in automated knowledge base construction. In this paper, we present Alexandria -- a system for unsupervised, high-precision knowledge base construction. Alexandria uses a probabilistic program to define a process of converting knowledge base facts into unstructured text. Using probabilistic inference, we can invert this program and so retrieve facts, schemas and entities from web text. The use of a probabilistic program allows uncertainty in the text to be propagated through to the retrieved facts, which increases accuracy and helps merge facts from multiple sources. Because Alexandria does not require labelled training data, knowledge bases can be constructed with the minimum of manual input. We demonstrate this by constructing a high precision (typically 97\%+) knowledge base for people from a single seed fact.

Ex Output:
This paper presents a system for unsupervised, high-precision knowledge base construction using a probabilistic program to define a process of converting knowledge base facts into unstructured text.