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:
We introduce geomstats, a Python package for Riemannian modelization and optimization over manifolds such as hyperspheres, hyperbolic spaces, SPD matrices or Lie groups of transformations. Our contribution is threefold. First, geomstats allows the flexible modeling of many a machine learning problem through an efficient and extensively unit-tested implementations of these manifolds, as well as the set of useful Riemannian metrics, exponential and logarithm maps that we provide. Moreover, the wide choice of loss functions and our implementation of the corresponding gradients allow fast and easy optimization over manifolds. Finally, geomstats is the only package to provide a unified framework for Riemannian geometry, as the operations implemented in geomstats are available with different computing backends (numpy,tensorflow and keras), as well as with a GPU-enabled mode–-thus considerably facilitating the application of Riemannian geometry in machine learning. In this paper, we present geomstats through a review of the utility and advantages of manifolds in machine learning, using the concrete examples that they span to show the efficiency and practicality of their implementation using our package

Ex Output:
We introduce geomstats, an efficient Python package for Riemannian modelization and optimization over manifolds compatible with both numpy and tensorflow .


Ex Input:
The Deep Image Prior (DIP, Ulyanov et al., 2017) is a fascinating recent approach for recovering images which appear natural, yet is not fully understood. This work aims at shedding some further light on this approach by investigating the properties of the early outputs of the DIP. First, we show that these early iterations demonstrate invariance to adversarial perturbations by classifying progressive DIP outputs and using a novel saliency map approach. Next we explore using DIP as a defence against adversaries, showing good potential. Finally, we examine the adversarial invariancy of the early DIP outputs, and hypothesize that these outputs may remove non-robust image features. By comparing classification confidence values we show some evidence confirming this hypothesis.

Ex Output:
We investigate properties of the recently introduced Deep Image Prior (Ulyanov et al, 2017)


Ex Input:
We address two challenges of probabilistic topic modelling in order to better estimate
 the probability of a word in a given context, i.e., P(wordjcontext) : (1) No
 Language Structure in Context: Probabilistic topic models ignore word order by
 summarizing a given context as a “bag-of-word” and consequently the semantics
 of words in the context is lost. In this work, we incorporate language structure
 by combining a neural autoregressive topic model (TM) with a LSTM based language
 model (LSTM-LM) in a single probabilistic framework. The LSTM-LM
 learns a vector-space representation of each word by accounting for word order
 in local collocation patterns, while the TM simultaneously learns a latent representation
 from the entire document. In addition, the LSTM-LM models complex
 characteristics of language (e.g., syntax and semantics), while the TM discovers
 the underlying thematic structure in a collection of documents. We unite two complementary
 paradigms of learning the meaning of word occurrences by combining
 a topic model and a language model in a unified probabilistic framework, named
 as ctx-DocNADE. (2) Limited Context and/or Smaller training corpus of documents:
 In settings with a small number of word occurrences (i.e., lack of context)
 in short text or data sparsity in a corpus of few documents, the application of TMs
 is challenging. We address this challenge by incorporating external knowledge
 into neural autoregressive topic models via a language modelling approach: we
 use word embeddings as input of a LSTM-LM with the aim to improve the wordtopic
 mapping on a smaller and/or short-text corpus. The proposed DocNADE
 extension is named as ctx-DocNADEe.

 We present novel neural autoregressive topic model variants coupled with neural
 language models and embeddings priors that consistently outperform state-of-theart
 generative topic models in terms of generalization (perplexity), interpretability
 (topic coherence) and applicability (retrieval and classification) over 6 long-text
 and 8 short-text datasets from diverse domains.

Ex Output:

Unified neural model of topic and language modeling to introduce language structure  in topic models for contextualized topic vectors