wanyu/IteraTeR_v2 huggingface dataset:
Original:  In particular, under the \ell_\infty constraint with \epsilon=8/255 on the CIFAR10 dataset, our MMA trained model achieved 9%DIFDELCMD < \\%%% %DIF < higher robust accuracy than the best prior work reported in Madry et al. (2017) .
Revised:  In particular, under the \ell_\infty constraint with \epsilon=8/255 on the CIFAR10 dataset, our MMA trained model achieved 9%DIFDELCMD < \\%%% %DIF < higher robust accuracy than the best prior work reported in robustness .
Edit intent: clarity
Original:  In theory, we show that maximizing margins can be achieved by minimizing the adversarial loss on the decision boundary at the "shortest successful perturbation" .
Revised:  Our study shows that maximizing margins can be achieved by minimizing the adversarial loss on the decision boundary at the "shortest successful perturbation" .
Edit intent: clarity
Original:  Instead of adversarial training with a fixed \epsilon, MMA offers an improvement by selecting the margin as the "correct" \epsilon  individually for each point.
Revised:  Instead of adversarial training with a fixed \epsilon, MMA offers an improvement by enabling adaptive selection of the "correct" \epsilon individually for each point.
Edit intent: clarity
Original:  We demonstrate MMA training's efficacy and analyze its properties on the MNIST and CIFAR10 datasets w.r.t. \ell_\infty and \ell_2 robustness. 
Revised:  We demonstrate MMA training's efficacy on the MNIST and CIFAR10 datasets w.r.t. \ell_\infty and \ell_2 robustness. 
Edit intent: clarity
Original:  Our first algorithm is a simple private implementation of the  post-processing approach of [Hardt et al.  2016].
Revised:  Our first algorithm is a private implementation of the post-processing approach of [Hardt et al. 2016].
Edit intent: clarity
Original:  Our first algorithm is a simple private implementation of the  post-processing approach of [Hardt et al.  2016].
Revised:  Our first algorithm is a simple private implementation of the post-processing approach of [Hardt et al. , 2016].
Edit intent: fluency
Original:  This algorithm has the merit of being exceedingly simple, but must be able to use protected group membership explicitly at test time, which can be viewed as  'disparate treatment'.
Revised:  This algorithm is appealingly simple, but must be able to use protected group membership explicitly at test time, which can be viewed as 'disparate treatment'.
Edit intent: clarity
Original:  This algorithm has the merit of being exceedingly simple, but must be able to use protected group membership explicitly at test time, which can be viewed as  'disparate treatment'.
Revised:  This algorithm has the merit of being exceedingly simple, but must be able to use protected group membership explicitly at test time, which can be viewed as a form of 'disparate treatment'.
Edit intent: clarity
Original:  The second algorithm is a differentially private version of the algorithm of [Agarwal et al.  2018] , an oracle-efficient algorithm that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem.
Revised:  Our second algorithm is a differentially private version of the algorithm of [Agarwal et al. 2018] , an oracle-efficient algorithm that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem.
Edit intent: fluency
Original:  The second algorithm is a differentially private version of the algorithm of [Agarwal et al.  2018] , an oracle-efficient algorithm that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem.
Revised:  The second algorithm is a differentially private version of the algorithm of [Agarwal et al. , 2018] , an oracle-efficient algorithm that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem.
Edit intent: fluency
Original:  The second algorithm is a differentially private version of the algorithm of [Agarwal et al.  2018] , an oracle-efficient algorithm that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem.
Revised:  The second algorithm is a differentially private version of the algorithm of [Agarwal et al. 2018] that can be used to find the optimal fair classifier, given access to a subroutine that can solve the original (not necessarily fair) learning problem.
Edit intent: clarity
Original:  We propose a generalization of the MAL algorithm by performing the exit wave reconstruction and the registration of the image series simultaneously.
Revised:  We propose a generalization of these methods by performing the exit wave reconstruction and the registration of the image series simultaneously.
Edit intent: clarity
Original:  By replacing conventional decoders by our  decoder for representation learning and generative modeling of shapes , we demonstrate superior results for tasks such as shape autoencoding, generation , interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
Revised:  By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes , we demonstrate superior results for tasks such as generative shape modeling , interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
Edit intent: clarity
Original: Current global environmental challenges require firm, yet diverse resolutions in the energy sector.
Revised: Current global environmental challenges require vigorous and diverse actions in the energy sector.
Edit intent: clarity
Original:  One promising solution consists in harnessing high-quality variable renewable energy (VRE) resources in remote locations, while using transmission links to wheel the power towards end users.
Revised:  One solution that has recently attracted interest consists in harnessing high-quality variable renewable energy (VRE) resources in remote locations, while using transmission links to wheel the power towards end users.
Edit intent: clarity
Original:  One promising solution consists in harnessing high-quality variable renewable energy (VRE) resources in remote locations, while using transmission links to wheel the power towards end users.
Revised:  One promising solution consists in harnessing high-quality variable renewable energy resources in remote locations, while using transmission links to wheel the power towards end users.
Edit intent: clarity
Original:  One promising solution consists in harnessing high-quality variable renewable energy (VRE) resources in remote locations, while using transmission links to wheel the power towards end users.
Revised:  One promising solution consists in harnessing high-quality variable renewable energy (VRE) resources in remote locations, while using transmission links to transport the power to end users.
Edit intent: clarity
Original:  In this context, a comparison of western Europe and Greenland wind regimes is proposed.
Revised:  In this context, a comparison of western European and Greenland wind regimes is proposed.
Edit intent: fluency
Original:  local climate associated with southern Greenland is identified to exhibit specific characteristics that facilitate extensive VRE generation levels . A methodology to assess the added value of wind harnessing in remote locations is introduced and applied on the aforementioned case study, showing superior and complementary wind generation potential in this region of Greenland with respect to selected European sites.
Revised:  local climate associated with southern Greenland is identified to exhibit specific characteristics that facilitate extensive VRE generation levels . A methodology to assess the added value of wind harnessing in remote locations is introduced and applied to the aforementioned Europe-Greenland case study, showing superior and complementary wind generation potential in this region of Greenland with respect to selected European sites.
Edit intent: clarity
Original:  local climate associated with southern Greenland is identified to exhibit specific characteristics that facilitate extensive VRE generation levels . A methodology to assess the added value of wind harnessing in remote locations is introduced and applied on the aforementioned case study, showing superior and complementary wind generation potential in this region of Greenland with respect to selected European sites.
Revised:  local climate associated with southern Greenland is identified to exhibit specific characteristics that facilitate extensive VRE generation levels . A methodology to assess the added value of wind harnessing in remote locations is introduced and applied on the aforementioned case study, showing superior and complementary wind generation potential in the considered region of Greenland with respect to selected European sites.
Edit intent: clarity
Original:  Second , we show that individual and collective knowhow correlate with measures of urban economic performance, suggesting the theory can provide testable implications for why some cities are more prosperous than others.
Revised:  Second , we show how the quantities are associated with metrics of economic performance, suggesting the theory can provide testable implications for why some cities are more prosperous than others.
Edit intent: clarity
Original:  Second , we show that individual and collective knowhow correlate with measures of urban economic performance, suggesting the theory can provide testable implications for why some cities are more prosperous than others.
Revised:  Second , we show that individual and collective knowhow correlate with measures of urban economic performance, suggesting our theory can provide testable implications for why some cities are more prosperous than others.
Edit intent: fluency
Original: We consider numerical certification of approximate solutions to an overdetermined system of N polynomial equations in n variables where n < N by passing to a square subsystem.
Revised: We consider numerical certification of approximate solutions to a system of polynomial equations with more equations than unknowns by first certifying solutions to a square subsystem.
Edit intent: clarity
Original: We propose a novel methodology for feature extraction from time series data based on topological data analysis.
Revised: We develop a novel algorithm for feature extraction from time series data based on topological data analysis.
Edit intent: clarity
Original: We propose a novel methodology for feature extraction from time series data based on topological data analysis.
Revised: We propose a novel methodology for feature extraction in time series data based on topological data analysis.
Edit intent: fluency
Original: We propose a novel methodology for feature extraction from time series data based on topological data analysis.
Revised: We propose a novel methodology for feature extraction from time series data by leveraging tools from topological data analysis.
Edit intent: clarity
Original:  We further apply our method to the problem of trend forecasting for cryptocurrency prices, where we manage to achieve significantly lower error rates than more standard, non TDA-based methodologies in complex pattern classification tasks.
Edit intent: coherence
Original:  We expect our method to provide a new insight on feature engineering for granular, noisy time series data.
Revised:  We expect our method to provide new insights on feature extraction from granular, noisy time series data.
Edit intent: clarity
Original:  The main feature of the scheme is the possibility to stabilize an a priori unstable high-order scheme  via a filter function which allows to combine a high-order scheme in the regularity regions and a monotone scheme elsewhere, in presence of singularities.
Revised:  The main feature of the scheme is the possibility to stabilize an a priori unstable high-order scheme ) via a filter function which allows to combine a high-order scheme in the regularity regions and a monotone scheme elsewhere, in presence of singularities.
Edit intent: fluency
Original:   ]  Within the framework  , the Moore-Penrose and weighted Moore-Penrose inverse for arbitrary-order tensors via the Einstein product is defined.
Revised:  ] to tensors of arbitrary-order. Within the framework , the Moore-Penrose and weighted Moore-Penrose inverse for arbitrary-order tensors via the Einstein product is defined.
Edit intent: clarity
Original:  We then obtain a few necessary and sufficient conditions of the reverse-order law for weighted Moore-Penrose inverses of arbitrary-order tensors.
Revised:  We then obtain some necessary and sufficient conditions of the reverse-order law for weighted Moore-Penrose inverses of arbitrary-order tensors.
Edit intent: clarity
Original: We explore the singular value decomposition and full rank decomposition of arbitrary-order tensors using reshape operation.
Revised: We explore the singular value decomposition and full-rank decomposition of arbitrary-order tensors using reshape operation.
Edit intent: fluency
Original:  We then obtain some necessary and sufficient conditions of the reverse-order law  for weighted Moore-Penrose inverses of arbitrary-order tensors.
Revised:  We then obtain some necessary and sufficient conditions for the reverse-order law for weighted Moore-Penrose inverses of arbitrary-order tensors.
Edit intent: clarity
Original:  We then obtain some necessary and sufficient conditions of the reverse-order law  for weighted Moore-Penrose inverses of arbitrary-order tensors.
Revised:  We then obtain some necessary and sufficient conditions of the reverse-order law to hold for weighted Moore-Penrose inverses of arbitrary-order tensors.
Edit intent: clarity
Original:  For this reason, wells are typically modelled as lower-dimensional source terms .
Revised:  For this reason, wells are typically modelled as lower-dimensional sources .
Edit intent: clarity
Original:  We present here a splitting method for the solution, where the reservoir pressure is split into a low regularity term that explicitly captures the singularity, and a well-behaved, regular component v . The singularities can then be removed from the system by subtracting them from the governing equations.
Revised:  We present here a singularity removal method for the solution, where the reservoir pressure is split into a low regularity term that explicitly captures the singularity, and a well-behaved, regular component v . The singularities can then be removed from the system by subtracting them from the governing equations.
Edit intent: clarity
Original:  This results in a reformulated coupled 1D-3D model in which all variables are smooth.
Revised:  Finally, the coupled 1D-3D model in which all variables are smooth.
Edit intent: clarity
Original: This article aims to establish a fundamental mean-square convergence theorem for general one-step numerical approximations of L\'{e}vy noise driven stochastic differential equations (SDEs), with non-globally Lipschitz coefficients.
Revised: This paper first establishes a fundamental mean-square convergence theorem for general one-step numerical approximations of L\'{e}vy noise driven stochastic differential equations (SDEs), with non-globally Lipschitz coefficients.
Edit intent: clarity
Original: This article aims to establish a fundamental mean-square convergence theorem for general one-step numerical approximations of L\'{e}vy noise driven stochastic differential equations (SDEs), with non-globally Lipschitz coefficients.
Revised: This article aims to establish a fundamental mean-square convergence theorem for general one-step numerical approximations of L\'{e}vy noise driven stochastic differential equations with non-globally Lipschitz coefficients.
Edit intent: clarity
Original:  As applications of the obtained fundamental convergence theorem, two novel explicit schemes are designed and their convergence rates are exactly identified for problems subject to both multiplicative and additive noises.
Revised:  Then two novel explicit schemes are designed and their convergence rates are exactly identified for problems subject to both multiplicative and additive noises.
Edit intent: clarity
Original:  A price to pay for such a more relaxed condition is assuming finite L\'{e}vy measure . Moreover, new arguments are developed to handle essential difficulties in the convergence analysis, caused by the super-linear growth of the jump coefficient and the fact that higher moment bounds of the Poisson increments \int_t^{t+h} \int_Z \,N(ds,dz), t \geq 0, h >0 contribute to magnitude not more than O(h).
Revised:  However, we require that the L\'{e}vy measure . Moreover, new arguments are developed to handle essential difficulties in the convergence analysis, caused by the super-linear growth of the jump coefficient and the fact that higher moment bounds of the Poisson increments \int_t^{t+h} \int_Z \,N(ds,dz), t \geq 0, h >0 contribute to magnitude not more than O(h).
Edit intent: coherence
Original: It was observed before that in neuronal systems with convergence , a possible amplification can be as large as the degree of convergence.
Revised: It was observed before that due to convergence in the olfactory system a possible amplification can be as large as the degree of convergence.
Edit intent: clarity
Original: This paper studies the distributed reinforcement learning (DRL) problem involving a central controller and a group of learners.
Revised: This paper deals with distributed reinforcement learning (DRL) problem involving a central controller and a group of learners.
Edit intent: clarity
Original: This paper studies the distributed reinforcement learning (DRL) problem involving a central controller and a group of learners.
Revised: This paper studies the distributed reinforcement learning (DRL) , which involves a central controller and a group of learners.
Edit intent: clarity
Original:  Two DRL settings that find broad applications are considered: multi-agent reinforcement learning (RL) and parallel RL . In both settings, frequent information exchange between the learners and the controller are required.
Revised:  In particular, two DRL settings encountered in several applications are considered: multi-agent reinforcement learning (RL) and parallel RL . In both settings, frequent information exchange between the learners and the controller are required.
Edit intent: clarity
Original:  Two DRL settings that find broad applications are considered: multi-agent reinforcement learning (RL) and parallel RL . In both settings, frequent information exchange between the learners and the controller are required.
Revised:  Two DRL settings that find broad applications are considered: multi-agent reinforcement learning (RL) and parallel RL , where frequent information exchanges between the learners and the controller are required.
Edit intent: clarity
Original:  However, for many distributed systems, e.g., parallel machines for training deep RL algorithms, and multi-robot systems for learning the optimal coordination strategies, the overhead caused by frequent communication is not negligible and becomes the bottleneck of the overall performance.
Revised:  However, for many distributed systems, however, such as those involving parallel machines for training deep RL algorithms, and multi-robot systems for learning the optimal coordination strategies, the overhead caused by frequent communication is not negligible and becomes the bottleneck of the overall performance.
Edit intent: clarity
Original:  However, for many distributed systems, e.g., parallel machines for training deep RL algorithms, and multi-robot systems for learning the optimal coordination strategies, the overhead caused by frequent communication is not negligible and becomes the bottleneck of the overall performance.
Revised:  However, for many distributed systems, e.g., parallel machines for training deep RL algorithms, and multi-robot systems for learning the optimal coordination strategies, the overhead caused by these frequent communication exchanges is considerable, and becomes the bottleneck of the overall performance.
Edit intent: clarity
Original:  To overcome this challenge, we develop a new policy gradient method that is amenable to efficient implementation in such communication-constrained settings.
Revised:  To address this challenge, we develop a new policy gradient method that is amenable to efficient implementation in such communication-constrained settings.
Edit intent: clarity
Original:  To overcome this challenge, we develop a new policy gradient method that is amenable to efficient implementation in such communication-constrained settings.
Revised:  To overcome this challenge, a novel policy gradient method that is amenable to efficient implementation in such communication-constrained settings.
Edit intent: clarity
Original:  To overcome this challenge, we develop a new policy gradient method that is amenable to efficient implementation in such communication-constrained settings.
Revised:  To overcome this challenge, we develop a new policy gradient method is developed here to cope with such communication-constrained settings.
Edit intent: clarity
Original:  Analytically, we can establish that i) the convergence rate of our algorithm is the same as the vanilla policy gradient for the DRLtasks;
Revised:  Analytically, we can establish that i) the novel algorithm has convergence rate identical to that of the plain-vanilla policy gradient for the DRLtasks;
Edit intent: clarity
Original:  and, ii) if the distributed computing units are heterogeneous in terms of their reward functions and initial state distributions, the number of communication rounds needed to achieve a targeted learning accuracy is  reduced.
Revised:  and, ii) if the distributed computing units are heterogeneous in terms of their reward functions and initial state distributions, the number of communication rounds needed to achieve a desirable learning accuracy is reduced.
Edit intent: clarity
Original:  and, ii) if the distributed computing units are heterogeneous in terms of their reward functions and initial state distributions, the number of communication rounds needed to achieve a targeted learning accuracy is  reduced.
Revised:  and, ii) if the distributed computing units are heterogeneous in terms of their reward functions and initial state distributions, the number of communication rounds needed to achieve a targeted learning accuracy is markedly reduced.
Edit intent: clarity
Original:  Numerical experiments on a popular multi-agent RL benchmark corroborate the significant communication reduction of our algorithm compared to the alternatives.
Revised:  Numerical experiments on a popular multi-agent RL benchmark corroborate the significant communication reduction of our algorithm compared to alternatives.
Edit intent: fluency
Original:  In particular, two DRL settings encountered in several applications are considered: multi-agent reinforcement learning (RL) and parallel RL, where frequent information exchanges between the learners and the controller are required.
Revised:  In particular, two typical settings encountered in several applications are considered: multi-agent reinforcement learning (RL) and parallel RL, where frequent information exchanges between the learners and the controller are required.
Edit intent: clarity
Original:  For many practical distributed systems, however, such as those involving parallel machines for training deep RL algorithms, and multi-robot systems for learning the optimal coordination strategies, the overhead caused by these frequent communication exchanges is considerable, and becomes the bottleneck of the overall performance.
Revised:  For many practical distributed systems, however, the overhead caused by these frequent communication exchanges is considerable, and becomes the bottleneck of the overall performance.
Edit intent: clarity