wanyu/IteraTeR_v2 huggingface dataset:
Original:  We show that by employing similar discretization schemes  to Newton's classical equation of motion with an additional dissipative force, which we refer to as the accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms ;
Revised:  We show that by employing similar discretization schemes to Newton's equation with an additional dissipative force, which we refer to as the accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms ;
Edit intent: clarity
Original:  We show that by employing similar discretization schemes  to Newton's classical equation of motion with an additional dissipative force, which we refer to as the accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms ;
Revised:  We show that by employing similar discretization schemes to Newton's classical equation of motion with an additional dissipative force, which we refer to as accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms ;
Edit intent: clarity
Original:  We show that by employing similar discretization schemes  to Newton's classical equation of motion with an additional dissipative force, which we refer to as the accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms ;
Revised:  We show that by employing similar discretization schemes to Newton's classical equation of motion with an additional dissipative force, which we refer to as the accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms --
Edit intent: fluency
Original:  Moreover , we extend these algorithms to stochastic optimization settings, allowing us to make connections with Langevin and Fokker-Planck equations.
Revised:  Furthermore , we extend these algorithms to stochastic optimization settings, allowing us to make connections with Langevin and Fokker-Planck equations.
Edit intent: fluency
Original:  Moreover , we extend these algorithms to stochastic optimization settings, allowing us to make connections with Langevin and Fokker-Planck equations.
Revised:  Moreover , we extend these methods to stochastic settings, allowing us to make connections with Langevin and Fokker-Planck equations.
Edit intent: clarity
Original:  These results thus provide a unified framework from which several optimization methods can be derived from basic physical systems.
Revised:  Our results therefore provide a unified framework from which several optimization methods can be derived from basic physical systems.
Edit intent: coherence
Original: Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction methods . Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times  .
Revised: Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction algorithms . Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times .
Edit intent: clarity
Original:  As a possible solution to these restrictions we propose a multi-scale learned iterative reconstruction algorithm that computes iterates on discretisations of increasing resolution.
Revised:  As a possible solution to these restrictions we propose a multi-scale learned iterative reconstruction scheme that computes iterates on discretisations of increasing resolution.
Edit intent: clarity
Original:  Feasibility of the proposed method to speed up training and computation times in comparison to established learned reconstruction methods in 2D is demonstrated for low dose computed tomography (CT), for which we utilise the data base of abdominal CT scans provided for the 2016 AAPM low-dose CT grand challenge .
Revised:  Feasibility of the proposed method to speed up training and computation times in comparison to established learned reconstruction methods in two dimensions for low dose computed tomography (CT), for which we utilise the data base of abdominal CT scans provided for the 2016 AAPM low-dose CT grand challenge .
Edit intent: clarity
Original:  Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times  due to computationally expensive forward models.
Revised:  Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times , the latter due to computationally expensive forward models.
Edit intent: coherence
Original: The availability of large-scale household energy consumption datasets boosts the studies on energy disaggregation,
Revised: Energy disaggregation,
Edit intent: clarity
Original:  a.k.a. non-intrusive load monitoring, that aims to separate the energy consumption of individual appliances from the readings of a mains power meter measuring the total consumption of multiple appliances for example in a house. various neural network models such as convolutional neural network and recurrent neural network have been investigated to solve the energy disaggregation problem.
Revised:  a.k.a. Non-Intrusive Load Monitoring, aims to separate the energy consumption of individual appliances from the readings of a mains power meter measuring the total consumption of multiple appliances for example in a house. various neural network models such as convolutional neural network and recurrent neural network have been investigated to solve the energy disaggregation problem.
Edit intent: coherence
Original:  a.k.a. non-intrusive load monitoring, that aims to separate the energy consumption of individual appliances from the readings of a mains power meter measuring the total consumption of multiple appliances for example in a house. various neural network models such as convolutional neural network and recurrent neural network have been investigated to solve the energy disaggregation problem.
Revised:  a.k.a. non-intrusive load monitoring, that aims to separate the energy consumption of individual appliances from the readings of a mains power meter measuring the total consumption of multiple appliances for example in a house. various neural network models such as convolutional neural networks and recurrent neural network have been investigated to solve the energy disaggregation problem.
Edit intent: fluency
Original:  a.k.a. non-intrusive load monitoring, that aims to separate the energy consumption of individual appliances from the readings of a mains power meter measuring the total consumption of multiple appliances for example in a house. various neural network models such as convolutional neural network and recurrent neural network have been investigated to solve the energy disaggregation problem.
Revised:  a.k.a. non-intrusive load monitoring, that aims to separate the energy consumption of individual appliances from the readings of a mains power meter measuring the total consumption of multiple appliances for example in a house. various neural network models such as convolutional neural network and recurrent neural networks have been investigated to solve the energy disaggregation problem.
Edit intent: fluency
Original:  Neural network models can learn complex patterns from large amount of data and have outperformed traditional machine learning methods such as  hidden Markov models.
Revised:  Neural network models can learn complex patterns from large amounts of data and have outperformed traditional machine learning methods such as hidden Markov models.
Edit intent: fluency
Original:  Neural network models can learn complex patterns from large amount of data and have outperformed traditional machine learning methods such as  hidden Markov models.
Revised:  Neural network models can learn complex patterns from large amount of data and have been shown to outperform the traditional machine learning methods such as hidden Markov models.
Edit intent: clarity
Original:  In this paper, we investigate the application of the recently developed WaveNet model for the task of energy disaggregation.
Revised:  In this paper, we investigate the application of the recently developed WaveNet models for the task of energy disaggregation.
Edit intent: fluency
Original:  Based on a real-world energy dataset collected from 20 households over two years, we show that the WaveNet model outperforms the state-of-the-art deep learning methods proposed in the literature for energy disaggregation in terms of both error measures and computational cost.
Revised:  Based on a real-world energy dataset collected from 20 households over two years, we show that WaveNet models outperforms the state-of-the-art deep learning methods proposed in the literature for energy disaggregation in terms of both error measures and computational cost.
Edit intent: clarity
Original:  An edge set E' \subseteq E is a {\em dominating induced matching} ({\em d.i.m.}) in G if every edge in E is intersected by exactly one edge of E'.
Revised:  An edge subset E' \subseteq E is a {\em dominating induced matching} ({\em d.i.m.}) in G if every edge in E is intersected by exactly one edge of E'.
Edit intent: clarity
Original:  this problem is also known as theEfficient Edge Domination problem;
Revised:  this problem is also known as the problem;
Edit intent: coherence
Original:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs , and in polynomial time for S_{1,2,4 -free graphs as well as for S_{2,2,2 . In this paper , combining two distinct approaches , we solve it in polynomial time for P_9-free graphs.
Revised:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but was solved in linear time for P_7-free graphs , and in polynomial time for S_{1,2,4 -free graphs as well as for S_{2,2,2 . In this paper , combining two distinct approaches , we solve it in polynomial time for P_9-free graphs.
Edit intent: clarity
Original:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs , and in polynomial time for S_{1,2,4 -free graphs as well as for S_{2,2,2 . In this paper , combining two distinct approaches , we solve it in polynomial time for P_9-free graphs.
Revised:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs and in polynomial time for S_{1,2,4 -free graphs as well as for S_{2,2,2 . In this paper , combining two distinct approaches , we solve it in polynomial time for P_9-free graphs.
Edit intent: fluency
Original:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs , and in polynomial time for S_{1,2,4 -free graphs as well as for S_{2,2,2 . In this paper , combining two distinct approaches , we solve it in polynomial time for P_9-free graphs.
Revised:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs , and in polynomial time for S_{1,2,4 -free graphs . In this paper , combining two distinct approaches , we solve it in polynomial time for P_9-free graphs.
Edit intent: coherence
Original:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs , and in polynomial time for S_{1,2,4 -free graphs as well as for S_{2,2,2 . In this paper , combining two distinct approaches , we solve it in polynomial time for P_9-free graphs.
Revised:  The DIM problem is \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs , and in polynomial time for S_{1,2,4 -free graphs as well as for S_{2,2,2 . In this paper , we solve it in polynomial time for P_9-free graphs.
Edit intent: coherence
Original:  However, privacy concern has to be attached prior importance in DML, since training data may contain sensitive information of users.
Revised:  However, privacy concerns have to be given priority in DML, since training data may contain sensitive information of users.
Edit intent: clarity
Original:  The new challenging issue is to reduce the accumulation of privacy losses over ADMM iterations as much as possible .
Revised:  The new challenging issue is to keep the accumulation of privacy losses over ADMM iterations as much as possible .
Edit intent: clarity
Original:  In the proposed privacy-aware DML framework, a local randomization approach, which is proved to be differentially private, is adopted to provide users with self-controlled privacy guarantee for the most sensitive information.
Revised:  In the proposed framework, a local randomization approach, which is proved to be differentially private, is adopted to provide users with self-controlled privacy guarantee for the most sensitive information.
Edit intent: clarity
Original:  In the proposed privacy-aware DML framework, a local randomization approach, which is proved to be differentially private, is adopted to provide users with self-controlled privacy guarantee for the most sensitive information.
Revised:  In the proposed privacy-aware DML framework, a local randomization approach, which is differentially private, is adopted to provide users with self-controlled privacy guarantee for the most sensitive information.
Edit intent: coherence
Original:  Also, we analyze the performance of the trained model according to its generalization error.
Revised:  We provide detailed analyses on the performance of the trained model according to its generalization error.
Edit intent: clarity
Original:  Finally, we conduct extensive experiments using synthetic and real-world datasets to validate the theoretical results and evaluate the classification performance of the proposed framework.
Revised:  Finally, we conduct extensive experiments using real-world datasets to validate the theoretical results and evaluate the classification performance of the proposed framework.
Edit intent: clarity
Original:  Exploiting this new data source, a wide range of applications have emerged, from weather forecasting to stock market prediction, or the collection of intelligence about military and government movements.
Revised:  Exploiting this new data source, a wide range of applications have emerged, from weather forecasting to stock market prediction, or the collection of information about military and government movements.
Edit intent: clarity
Original:  Typically these applications require knowledge about the metadata of the aircraft, specifically its operator and the aircraft category. armasuisse Science + Technology, the R  D agency for the Swiss Armed Forces, has been developing Classi-Fly, a novel approach to obtain metadata about aircraft based on their movement patterns.
Revised:  Typically these applications require knowledge about the metadata of the aircraft, specifically its operator and the aircraft category. armasuisse Science + Technology, the R \& D agency for the Swiss Armed Forces, has been developing Classi-Fly, a novel approach to obtain metadata about aircraft based on their movement patterns.
Edit intent: fluency
Original:  We show that we can obtain the correct aircraft category with an accuracy of over 88\% . In cases, where no metadata is available, this approach can be used to create the data necessary for applications working with air traffic communication.
Revised:  We show that we can obtain the correct aircraft category with an accuracy of over 88\% , demonstrating that it can improve the meta data necessary for applications working with air traffic communication.
Edit intent: clarity
Original:  Finally, we show that it is feasible to automatically detect sensitive aircraft such as police and surveillance aircraft using this method .
Revised:  Finally, we show that it is feasible to automatically detect specific flights such as police and surveillance aircraft using this method .
Edit intent: clarity
Original:  Finally, we show that it is feasible to automatically detect sensitive aircraft such as police and surveillance aircraft using this method .
Revised:  Finally, we show that it is feasible to automatically detect sensitive aircraft such as police and surveillance missions .
Edit intent: clarity
Original:  Based on the obtained results , we study the asymptotic structure of the market when all the investors use the relatively growth optimal strategy.
Revised:  Based on the results obtained , we study the asymptotic structure of the market when all the investors use the relatively growth optimal strategy.
Edit intent: fluency
Original:  Based on the obtained results , we study the asymptotic structure of the market when all the investors use the relatively growth optimal strategy.
Revised:  Based on the obtained results , we study the asymptotic structure of the market when all the investors use the relative growth optimal strategy.
Edit intent: fluency
Original: In the Cograph Deletion  problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of  at most k edges whose removal from G  results a graph that does not contain an induced path with four vertices.
Revised: In the Cograph Deletion problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k whose removal from G results a graph that does not contain an induced path with four vertices.
Edit intent: clarity
Original:  In this paper we give an algorithm for Cograph Deletion whose running time is O^*(2.303^k)  .
Revised:  In this paper we give algorithms for Cograph Deletion whose running time is O^*(2.303^k) .
Edit intent: fluency
Original: In the Cograph Deletion (resp., Cograph Editing) problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of edges of size at most k whose removal from G (resp., removal and addition to G) results  a graph that does not contain an induced path with four vertices.
Revised: In the Cograph Deletion (resp., Cograph Editing) problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of edges of size at most k whose removal from G (resp., removal and addition to G) results in a graph that does not contain an induced path with four vertices.
Edit intent: fluency
Original: Gauge-invariance is a mathematical concept that has profound implications in Physics -- known to provide justification for the fundamental interactions -- and has recently been applied to the Cellular Automaton (CA) model in a restricted case.
Revised: Gauge-invariance is a mathematical concept that has profound implications in Physics---as it provides the justification of the fundamental interactions -- and has recently been applied to the Cellular Automaton (CA) model in a restricted case.
Edit intent: coherence
Original: Gauge-invariance is a mathematical concept that has profound implications in Physics -- known to provide justification for the fundamental interactions -- and has recently been applied to the Cellular Automaton (CA) model in a restricted case.
Revised: Gauge-invariance is a mathematical concept that has profound implications in Physics -- known to provide justification for the fundamental interactions . It was recently adapted to the Cellular Automaton (CA) model in a restricted case.
Edit intent: coherence
Original: Gauge-invariance is a mathematical concept that has profound implications in Physics -- known to provide justification for the fundamental interactions -- and has recently been applied to the Cellular Automaton (CA) model in a restricted case.
Revised: Gauge-invariance is a mathematical concept that has profound implications in Physics -- known to provide justification for the fundamental interactions -- and has recently been applied to the Cellular Automaton (CA) framework, in a restricted case.
Edit intent: clarity
Original:  In this paper, this invariance applied to CA is generalized to a case known as non-abelian gauge-invariance .
Revised:  In this paper, this treatment is generalized to a case known as non-abelian gauge-invariance .
Edit intent: clarity
Original:  In this paper, this invariance applied to CA is generalized to a case known as non-abelian gauge-invariance .
Revised:  In this paper, this invariance applied to CA is generalized to non-abelian gauge-invariance .
Edit intent: clarity
Original: We consider the task of tensor estimation, i.e. estimating a low-rank 3-order n \times n \times n tensor from noisy observations of randomly chosen entries in the sparse regime.
Revised: Consider the task of tensor estimation, i.e. estimating a low-rank 3-order n \times n \times n tensor from noisy observations of randomly chosen entries in the sparse regime.
Edit intent: clarity
Original:  As the main contribution of this work, we introduce a generalization of the collaborative filtering algorithm for the setting of tensor estimation and argue that it achieves sample complexity that (nearly ) matches the conjectured  lower bound on the sample complexity.
Revised:  As the main contribution of this work, we introduce a generalization of the collaborative filtering algorithm for the setting of tensor estimation and argue that it achieves sample complexity that nearly matches the conjectured lower bound on the sample complexity.
Edit intent: fluency
Original:  Interestingly, our generalization uses the matrix obtained from the ``flattened '' tensor to compute similarity as in the classical collaborative filtering but by defining a novel ``graph'' using it.
Revised:  Our algorithm uses the matrix obtained from the ``flattened '' tensor to compute similarity as in the classical collaborative filtering but by defining a novel ``graph'' using it.
Edit intent: clarity
Original:  Interestingly, our generalization uses the matrix obtained from the ``flattened '' tensor to compute similarity as in the classical collaborative filtering but by defining a novel ``graph'' using it.
Revised:  Interestingly, our generalization uses the matrix obtained from the flattened tensor to compute similarity as in the classical collaborative filtering but by defining a novel ``graph'' using it.
Edit intent: fluency
Original:  The algorithm recovers the tensor with  mean-squared-error (MSE) decaying to 0 as long as each entry is observed independently with probability p = \Omega(n^{-3/2 + \epsilon }) for any arbitrarily small \epsilon > 0. It turns out that p = \Omega(n^{-3/2 .
Revised:  The algorithm recovers the tensor with mean-squared-error (MSE) decaying to 0 as long as each entry is observed independently with probability p = \Omega(n^{-3/2 + \epsilon }) for any arbitrarily small \kappa > 0. It turns out that p = \Omega(n^{-3/2 .
Edit intent: clarity
Original: Consider the task of tensor estimation, i.e. estimating a low-rank 3-order n \times n \times n tensor from noisy observations of randomly chosen entries in the sparse regime.
Revised: Consider the task of estimating a 3-order n \times n \times n tensor from noisy observations of randomly chosen entries in the sparse regime.
Edit intent: clarity