wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this \frechet paper we study the complexity of CPS under the discrete Fr\'echet \frechet distance (CPS-3F) . While\frechet CPS-3F was posed in 2008, its complexity has remained unknown . However, it was believed to be NP-complete since CPS based on \npc the Hausdorff distance (CPS-2H) was shown to be NP-complete \npc .
Revised:  In this \frechet paper we study the complexity of CPS under the discrete Fr\'echet \frechet distance (CPS-3F) . While\frechet CPS-3F was posed in 2008, its complexity has remained unknown . However, it was believed to be NP-complete since CPS based on \npc the Hausdorff distance (CPS-2H) was shown to be \npc .
Edit intent: fluency
Original:  We first prove that a more general version of CPS-3F , which allows arbitrary weights, is weakly NP-complete even in a single dimension\npc based on a reduction from the set partition problem.
Revised:  We first prove that a more general version of CPS-3F is indeed weakly\npc based on a reduction from the set partition problem.
Edit intent: clarity
Original:  We then prove that unweighted CPS-3F is polynomial by presenting an O(m ^4n^4 \min\{m,n\}) time algorithm for the corresponding minimization problem , which as an immediate consequence, solves CPS-3F (which is formulated as a decision problem ).
Revised:  Then, we prove that CPS-3F is polynomial by presenting an O(m ^4n^4 \min\{m,n\}) time algorithm for the corresponding minimization problem , which as an immediate consequence, solves CPS-3F (which is formulated as a decision problem ).
Edit intent: clarity
Original:  In model-based methods, we can easily express our problem domain knowledge in the constraints of the model  at the expense of difficulties during inference.
Revised:  In model-based methods, problem domain knowledge in the constraints of the model at the expense of difficulties during inference.
Edit intent: clarity
Original:  In model-based methods, we can easily express our problem domain knowledge in the constraints of the model  at the expense of difficulties during inference.
Revised:  In model-based methods, we can easily express our problem domain knowledge in the constraints of the model , typically at the expense of difficulties during inference.
Edit intent: clarity
Original:  Deterministic deep neural networks are constructed in such a way that inference is straightforward, but we sacrifice the ability to easily incorporate problem domain knowledge.
Revised:  In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but we sacrifice the ability to easily incorporate problem domain knowledge.
Edit intent: coherence
Original:  The goal of this paper is to provide a general strategy to obtain the advantages of both approaches while avoiding many of their disadvantages.
Revised:  This work aims to obtain the advantages of both approaches while avoiding many of their disadvantages.
Edit intent: clarity
Original:  The general idea can be summarized as follows: given a model-based approach that requires an iterative inference method, we unfold the iterations into a layer-wise structure analogous to a neural network .
Revised:  The general idea can be summarized as follows: given a model-based approach and unfold the iterations into a layer-wise structure analogous to a neural network .
Edit intent: clarity
Original:  The general idea can be summarized as follows: given a model-based approach that requires an iterative inference method, we unfold the iterations into a layer-wise structure analogous to a neural network .
Revised:  The general idea can be summarized as follows: given a model-based approach that requires an iterative inference method, we unfold the iterations of its inference method to form a layer-wise structure analogous to a neural network .
Edit intent: clarity
Original:  The general idea can be summarized as follows: given a model-based approach that requires an iterative inference method, we unfold the iterations into a layer-wise structure analogous to a neural network .
Revised:  The general idea can be summarized as follows: given a model-based approach that requires an iterative inference method, we unfold the iterations into a layer-wise structure .
Edit intent: clarity
Original:  We then de-couple the model parameters across layers to obtain novel neural-network-like architectures that can easily be trained discriminatively using gradient-based methods.
Revised:  We then untie the model parameters across layers to obtain novel neural-network-like architectures that can easily be trained discriminatively using gradient-based methods.
Edit intent: clarity
Original:  We show how this framework can be applied to the non-negative matrix factorization  to obtain a novel non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Revised:  We show how this framework can be applied to a non-negative matrix factorization to obtain a novel non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Edit intent: fluency
Original:  We show how this framework can be applied to the non-negative matrix factorization  to obtain a novel non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Revised:  We show how this framework can be applied to the non-negative matrix factorization model to obtain a novel non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Edit intent: clarity
Original:  We show how this framework can be applied to the non-negative matrix factorization  to obtain a novel non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Revised:  We show how this framework can be applied to the non-negative matrix factorization to obtain a new kind of non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Edit intent: clarity
Original:  We show how this framework can be applied to the non-negative matrix factorization  to obtain a novel non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Revised:  We show how this framework can be applied to the non-negative matrix factorization to obtain a novel non-negative deep neural network , that can be trained with a multiplicative back-propagation-style update algorithm.
Edit intent: clarity
Original:  We show how this framework can be applied to the non-negative matrix factorization  to obtain a novel non-negative deep neural network architecture , that can be trained with a multiplicative back-propagation-style update algorithm.
Revised:  We show how this framework can be applied to the non-negative matrix factorization to obtain a novel non-negative deep neural network architecture , that can be trained using a multiplicative backpropagation-style update algorithm.
Edit intent: fluency
Original:  This results in novel neural-network-like architectures that incorporate our model-based constraints, but can be trained discriminatively to perform fast and accurate inference .
Revised:  This results in novel neural-network-like architectures that incorporate our model-based constraints, but can be trained discriminatively to perform accurate inference within a fixed network size .
Edit intent: clarity
Original:  In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but their architectures are rather generic and it can be unclear how to incorporate problem domain knowledge.
Revised:  In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but their architectures are generic and it can be unclear how to incorporate problem domain knowledge.
Edit intent: coherence
Original:  In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but their architectures are rather generic and it can be unclear how to incorporate problem domain knowledge.
Revised:  In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but their architectures are rather generic and it is unclear how to incorporate problem domain knowledge.
Edit intent: coherence
Original:  In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but their architectures are rather generic and it can be unclear how to incorporate problem domain knowledge.
Revised:  In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but their architectures are rather generic and it can be unclear how to incorporate knowledge.
Edit intent: clarity
Original:  Rather than optimizing the original model, we untie the model parameters across layers, in order to create a more powerful novel deep architecture which still maintains the model-based constraints, yet allowing a broader class of inference algorithms .
Revised:  Rather than optimizing the original model, we untie the model parameters across layers, in order to create a more powerful network .
Edit intent: clarity
Original:  The resulting network can be trained discriminatively to perform accurate inference within a fixed network size.
Revised:  The resulting architecture can be trained discriminatively to perform accurate inference within a fixed network size.
Edit intent: clarity
Original:  A reduction from Disjoint-Cycles shows that this problem has no polynomial kernel when parameterized by r, unless NP \subseteq coNP/poly, according to the results in Bodlaender, Thomass\'e, Yeo, 2012%DIFDELCMD < ]%%% . In this paper, we show that the problem Induced-Cycles parameterized by the r and the maximum degree \Delta has an O(\Delta^2 )-kernel for  r=2 and an O(r\Delta ^2 \log (r\Delta) )-kernel for ~r>2.
Revised:  A reduction from Disjoint-Cycles shows that this problem has no polynomial kernel when parameterized by r, unless NP \subseteq coNP/poly, according to the results in %DIFDELCMD < ]%%% . In this paper, we show that the problem Induced-Cycles parameterized by the r and the maximum degree \Delta has an O(\Delta^2 )-kernel for r=2 and an O(r\Delta ^2 \log (r\Delta) )-kernel for ~r>2.
Edit intent: coherence
Original:  A reduction from Disjoint-Cycles shows that this problem has no polynomial kernel when parameterized by r, unless NP \subseteq coNP/poly, according to the results in Bodlaender, Thomass\'e, Yeo, 2012%DIFDELCMD < ]%%% . In this paper, we show that the problem Induced-Cycles parameterized by the r and the maximum degree \Delta has an O(\Delta^2 )-kernel for  r=2 and an O(r\Delta ^2 \log (r\Delta) )-kernel for ~r>2.
Revised:  A reduction from Disjoint-Cycles shows that this problem has no polynomial kernel when parameterized by r, unless NP \subseteq coNP/poly, according to the results in Bodlaender, Thomass\'e, Yeo, 2012%DIFDELCMD < ]%%% . In this paper, we show that the problem Induced-Cycles parameterized by the r and the maximum degree \Delta has an O(\Delta^2 )-kernel for the case r=2 and an O(r\Delta ^2 \log (r\Delta) )-kernel for ~r>2.
Edit intent: clarity
Original:  We take a more direct approach and describe a way to train convolutional autoencoders layer by layer, where in each layer sparsityis achieved using a winner-take-all activation function within each feature map . Learning is computationally efficient and we show that our method can be used to train shallow and deep convolutional autoencoders whose representations can be used to achieve classification rates on the MNIST, CIFAR-10 and NORB datasetsthat are competitive with the state of the art .
Revised:  We take a more direct approach and describe a way to train convolutional autoencoders layer by layer, where in addition to lifetime sparsity, a spatial sparsity within each feature map . Learning is computationally efficient and we show that our method can be used to train shallow and deep convolutional autoencoders whose representations can be used to achieve classification rates on the MNIST, CIFAR-10 and NORB datasetsthat are competitive with the state of the art .
Edit intent: clarity
Original:  We take a more direct approach and describe a way to train convolutional autoencoders layer by layer, where in each layer sparsityis achieved using a winner-take-all activation function within each feature map . Learning is computationally efficient and we show that our method can be used to train shallow and deep convolutional autoencoders whose representations can be used to achieve classification rates on the MNIST, CIFAR-10 and NORB datasetsthat are competitive with the state of the art .
Revised:  We take a more direct approach and describe a way to train convolutional autoencoders layer by layer, where in each layer sparsityis achieved using a winner-take-all activation function within each feature map is achieved using winner-take-all activation functions. We will show that winner-take-all autoencoders can be used to train shallow and deep convolutional autoencoders whose representations can be used to achieve classification rates on the MNIST, CIFAR-10 and NORB datasetsthat are competitive with the state of the art .
Edit intent: clarity
Original:  The algorithm builds on a recent variance-reduced stochastic gradient technique, which was previously analyzed for strongly convex optimization, whereas here we apply it to the non-convex PCA problem, using a very different analysis.
Revised:  The algorithm builds on a recent variance-reduced stochastic gradient technique, which was previously analyzed for strongly convex optimization, whereas here we apply it to an inherently non-convex PCA problem, using a very different analysis.
Edit intent: clarity
Original:  The algorithm builds on a recent variance-reduced stochastic gradient technique, which was previously analyzed for strongly convex optimization, whereas here we apply it to the non-convex PCA problem, using a very different analysis.
Revised:  The algorithm builds on a recent variance-reduced stochastic gradient technique, which was previously analyzed for strongly convex optimization, whereas here we apply it to the non-convex problem, using a very different analysis.
Edit intent: clarity
Original: Purpose: In scientometrics, altmetrics are seen as an interesting possibility for measuring the broad impact of research.
Revised: Purpose: 
Edit intent: coherence
Original:  The present  study investigates the usefulness of altmetrics for measuring the broader impact of research.
Revised:  The present case study investigates the usefulness of altmetrics for measuring the broader impact of research.
Edit intent: clarity
Original:  This dataset was augmented with altmetrics (such as Twitter counts) which were downloaded from the homepage of PLOS (the Public Library of Science).
Revised:  The dataset was augmented with altmetrics (such as Twitter counts) which were downloaded from the homepage of PLOS (the Public Library of Science).
Edit intent: fluency
Original:  This dataset was augmented with altmetrics (such as Twitter counts) which were downloaded from the homepage of PLOS (the Public Library of Science).
Revised:  This dataset was augmented with altmetrics (such as Twitter counts) which were provided by PLOS (the Public Library of Science).
Edit intent: clarity
Original:  This study covers a total of 1,082 papers.
Revised:  In total, the case study covers a total of 1,082 papers.
Edit intent: coherence
Original: The desire to understand network systems in increasing detail has resulted in the development of a diversity of generative models that describe large-scale structure in a variety of ways, and allow its characterization in a principled and powerful manner.
Revised: The effort to understand network systems in increasing detail has resulted in the development of a diversity of generative models that describe large-scale structure in a variety of ways, and allow its characterization in a principled and powerful manner.
Edit intent: clarity
Original: The desire to understand network systems in increasing detail has resulted in the development of a diversity of generative models that describe large-scale structure in a variety of ways, and allow its characterization in a principled and powerful manner.
Revised: The desire to understand network systems in increasing detail has resulted in a diversity of generative models that describe large-scale structure in a variety of ways, and allow its characterization in a principled and powerful manner.
Edit intent: clarity
Original:  However, such elaborations invariably result in an increased number of parameters, which make these model variants prone to overfitting.
Revised:  However, such elaborations invariably result in an increased number of parameters, which makes these model variants prone to overfitting.
Edit intent: fluency
Original: The effort to understand network systems in increasing detail has resulted in a diversity of generative models that describe large-scale structure in a variety of ways, and allow its characterization in a principled and powerful manner.
Revised: The effort to understand network systems in increasing detail has resulted in a diversity of methods designed to extract their large-scale structure in a variety of ways, and allow its characterization in a principled and powerful manner.
Edit intent: clarity
Original:  However, such elaborations invariably result in an increased number of parameters, which makes these model variants prone to overfitting.
Revised:  Because such model variants possess an increased number of parameters, which makes these model variants prone to overfitting.
Edit intent: clarity
Original:  However, such elaborations invariably result in an increased number of parameters, which makes these model variants prone to overfitting.
Revised:  However, such elaborations invariably result in an increased number of parameters, they become prone to overfitting.
Edit intent: clarity
Original:  Here we propose a principled method of model selection based on the minimum description length principle and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best model according to the statistical evidence available in the data.
Revised:  Here we propose a principled method of model selection based on the minimum description length criterion and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best model according to the statistical evidence available in the data.
Edit intent: clarity
Original:  Here we propose a principled method of model selection based on the minimum description length principle and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best model according to the statistical evidence available in the data.
Revised:  Here we propose a principled method of model selection based on the minimum description length principle and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best one according to the statistical evidence available in the data.
Edit intent: clarity
Original:  Contrary to other alternatives such as likelihood ratios and parametric bootstrapping, this method scales very well, and combined with efficient inference methods recently developed, allows for the analysis of very large networks with an arbitrarily large number of groups.
Edit intent: coherence
Original:  In applying this method to many empirical datasets from different fields, we observed that while degree correction tends to provide better fits for a majority of networks, community overlap does not , and is selected as  better model only for a minority of them  .
Revised:  In applying this method to many empirical datasets from different fields, we observed that while degree correction tends to provide better fits for a majority of networks, community overlap does not , and is selected as a better model only for a minority of them .
Edit intent: fluency
Original:  A possible solution to this outstanding issue is to shift the focus away from ad hoc methods , and move towards more principled approaches based on statistical inference of generative models.
Revised:  A possible solution to this outstanding issue is to shift the focus away from ad hoc methods and move towards more principled approaches based on statistical inference of generative models.
Edit intent: fluency
Original:  Here  we consider the comparison between a variety of generative models including features such as degree correction, where nodes with arbitrary degrees can belong to the same group, and community overlap, where nodes are allowed to belong to more than one group.
Revised:  Here , we consider the comparison between a variety of generative models including features such as degree correction, where nodes with arbitrary degrees can belong to the same group, and community overlap, where nodes are allowed to belong to more than one group.
Edit intent: fluency
Original:  Because such model variants possess an increased number of parameters, they become prone to overfitting.
Revised:  Because such model variants possess an increasing number of parameters, they become prone to overfitting.
Edit intent: fluency
Original:  In this work  we present a method of model selection based on the minimum description length criterion and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best one according to the statistical evidence available in the data.
Revised:  In this work , we present a method of model selection based on the minimum description length criterion and posterior odds ratios that is capable of fully accounting for the increased degrees of freedom of the larger models, and selects the best one according to the statistical evidence available in the data.
Edit intent: fluency
Original:  In applying this method to many empirical unweighted networks from different fields, we observe that community overlap is very often not supported by statistical evidence , and is selected as a better model only for a minority of them.
Revised:  In applying this method to many empirical unweighted networks from different fields, we observe that community overlap is very often not supported by statistical evidence and is selected as a better model only for a minority of them.
Edit intent: fluency
Original:  On the other hand, we find that degree correction tends to be almost universally favored by the available data, implying that intrinsic node proprieties (as opposed to group properties) is often an essential ingredient of network formation.
Revised:  On the other hand, we find that degree correction tends to be almost universally favored by the available data, implying that intrinsic node proprieties (as opposed to group properties) are often an essential ingredient of network formation.
Edit intent: fluency
Original:  Second, if the seller can commit not to raise prices upon purchase, while still retaining the possibility of lowering prices in future, we show that threshold equilibria always exist and for most distributionsthere is a unique threshold equilibrium .
Revised:  Second, if the seller can commit not to raise prices upon purchase, while still retaining the possibility of lowering prices in future, we show that threshold equilibria are guaranteed to exist for the power law family of distributions .
Edit intent: clarity
Original:  The buyer's  value for the item is unknown to the seller but is drawn initially from a publicly known distribution F and remains the same throughout.
Revised:  The buyer's value for the item is drawn initially from a publicly known distribution F and remains the same throughout.
Edit intent: clarity