Cech Closure Spaces: A Unified Framework for Discrete Homotopy

Motivated by constructions in topological data analysis and algebraic combinatorics, we study homotopy theory on the category of Cech closure spaces $\mathbf{Cl}$, the category whose objects are sets endowed with a Cech closure operator and whose morphisms are the continuous maps between them. We introduce new classes of Cech closure structures on metric spaces, graphs, and simplicial complexes, and we show how each of these cases gives rise to an interesting homotopy theory. In particular, we show that there exists a natural family of Cech closure structures on metric spaces which produces a non-trivial homotopy theory for finite metric spaces, i.e. point clouds, the spaces of interest in topological data analysis. We then give a Cech closure structure to graphs and simplicial complexes which may be used to construct a new combinatorial (as opposed to topological) homotopy theory for each skeleton of those spaces. We further show that there is a Seifert-van Kampen theorem for closure spaces, a well-defined notion of persistent homotopy, and an associated interleaving distance. As an illustration of the difference with the topological setting, we calculate the fundamental group for the circle, `circular graphs', and the wedge of circles endowed with different closure structures. Finally, we produce a continuous map from the topological circle to `circular graphs' which, given the appropriate closure structures, induces an isomorphism on the fundamental groups.Comment: Incorporated referee comments, 41 page

A Topological Approach to Spectral Clustering

We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a topological model for the connected components of $X$. Both algorithms work by selecting a graph on the samples from a natural one-parameter family of graphs, using a geometric criterion in the first case and an information theoretic criterion in the second. The estimated connected components of $X$ are identified with the kernel of the associated graph Laplacian, which allows the algorithm to work without requiring the number of expected clusters or other auxiliary data as input.Comment: 21 Page

Coisotropic Hofer-Zehnder capacities and non-squeezing for relative embeddings

We introduce the notion of a symplectic capacity relative to a coisotropic submanifold of a symplectic manifold, and we construct two examples of such capacities through modifications of the Hofer-Zehnder capacity. As a consequence, we obtain a non-squeezing theorem for symplectic embeddings relative to coisotropic constraints and existence results for leafwise chords on energy surfaces.Comment: 33 pages, 4 figures; further corrections thanks to comments from the referee; accepted for publication in Journal of Symplectic Geometr

Referenceless Quality Estimation for Natural Language Generation

Traditional automatic evaluation measures for natural language generation (NLG) use costly human-authored references to estimate the quality of a system output. In this paper, we propose a referenceless quality estimation (QE) approach based on recurrent neural networks, which predicts a quality score for a NLG system output by comparing it to the source meaning representation only. Our method outperforms traditional metrics and a constant baseline in most respects; we also show that synthetic data helps to increase correlation results by 21% compared to the base system. Our results are comparable to results obtained in similar QE tasks despite the more challenging setting.Comment: Accepted as a regular paper to 1st Workshop on Learning to Generate Natural Language (LGNL), Sydney, 10 August 201

Natural Language Generation enhances human decision-making with uncertain information

Decision-making is often dependent on uncertain data, e.g. data associated with confidence scores or probabilities. We present a comparison of different information presentations for uncertain data and, for the first time, measure their effects on human decision-making. We show that the use of Natural Language Generation (NLG) improves decision-making under uncertainty, compared to state-of-the-art graphical-based representation methods. In a task-based study with 442 adults, we found that presentations using NLG lead to 24% better decision-making on average than the graphical presentations, and to 44% better decision-making when NLG is combined with graphics. We also show that women achieve significantly better results when presented with NLG output (an 87% increase on average compared to graphical presentations).Comment: 54th annual meeting of the Association for Computational Linguistics (ACL), Berlin 201

RankME: Reliable Human Ratings for Natural Language Generation

Human evaluation for natural language generation (NLG) often suffers from inconsistent user ratings. While previous research tends to attribute this problem to individual user preferences, we show that the quality of human judgements can also be improved by experimental design. We present a novel rank-based magnitude estimation method (RankME), which combines the use of continuous scales and relative assessments. We show that RankME significantly improves the reliability and consistency of human ratings compared to traditional evaluation methods. In addition, we show that it is possible to evaluate NLG systems according to multiple, distinct criteria, which is important for error analysis. Finally, we demonstrate that RankME, in combination with Bayesian estimation of system quality, is a cost-effective alternative for ranking multiple NLG systems.Comment: Accepted to NAACL 2018 (The 2018 Conference of the North American Chapter of the Association for Computational Linguistics

Crowd-sourcing NLG Data: Pictures Elicit Better Data

Recent advances in corpus-based Natural Language Generation (NLG) hold the promise of being easily portable across domains, but require costly training data, consisting of meaning representations (MRs) paired with Natural Language (NL) utterances. In this work, we propose a novel framework for crowdsourcing high quality NLG training data, using automatic quality control measures and evaluating different MRs with which to elicit data. We show that pictorial MRs result in better NL data being collected than logic-based MRs: utterances elicited by pictorial MRs are judged as significantly more natural, more informative, and better phrased, with a significant increase in average quality ratings (around 0.5 points on a 6-point scale), compared to using the logical MRs. As the MR becomes more complex, the benefits of pictorial stimuli increase. The collected data will be released as part of this submission.Comment: The 9th International Natural Language Generation conference INLG, 2016. 10 pages, 2 figures, 3 table

Findings of the E2E NLG Challenge

This paper summarises the experimental setup and results of the first shared task on end-to-end (E2E) natural language generation (NLG) in spoken dialogue systems. Recent end-to-end generation systems are promising since they reduce the need for data annotation. However, they are currently limited to small, delexicalised datasets. The E2E NLG shared task aims to assess whether these novel approaches can generate better-quality output by learning from a dataset containing higher lexical richness, syntactic complexity and diverse discourse phenomena. We compare 62 systems submitted by 17 institutions, covering a wide range of approaches, including machine learning architectures -- with the majority implementing sequence-to-sequence models (seq2seq) -- as well as systems based on grammatical rules and templates.Comment: Accepted to INLG 201