wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this work . two approaches are discussed for this strategy  and theoretical analysis is provided for the accuracy and stability implications of each approach.
Revised:  In this work , two approaches are discussed for this strategy and theoretical analysis is provided for the accuracy and stability implications of each approach.
Edit intent: fluency
Original:  In this work . two approaches are discussed for this strategy  and theoretical analysis is provided for the accuracy and stability implications of each approach.
Revised:  In this work . two approaches are discussed for this strategy , and theoretical analysis is provided for the accuracy and stability implications of each approach.
Edit intent: fluency
Original: Many traditional time integration methods which use a common timestep across an entire problem can perform poorly when the problem exhibits multiple characteristic time scales.
Revised: Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the problem exhibits multiple characteristic time scales.
Edit intent: clarity
Original: Many traditional time integration methods which use a common timestep across an entire problem can perform poorly when the problem exhibits multiple characteristic time scales.
Revised: Many traditional time integration methods which use a common timestep across an entire problem can perform poorly when the dynamics of the system exhibits a wide range of time scales.
Edit intent: clarity
Original:  Implicit-explicit (IMEX) methods, multirate methods, and other multimethods combine different methods or timesteps to efficiently solve these systems.
Edit intent: coherence
Original:  Multirate infinitesimal step (MIS) methods , first introduced by Knoth and Wolke, offer another flexible solution and are especially well-suited to problems with widely disparate time scales .
Revised:  Multirate infinitesimal step (MIS) methods ( Knoth and Wolke, offer another flexible solution and are especially well-suited to problems with widely disparate time scales .
Edit intent: coherence
Original:  The slow part of a system is discretized by a Runge-Kutta method, and the fast part is resolved by exactly integrating a modified fast ODE.
Revised:  The slow components are discretized by a Runge-Kutta method, and the fast part is resolved by exactly integrating a modified fast ODE.
Edit intent: clarity
Original:  This works extends the MRI-GARK framework by introducing coupled implicit methods to solve stiff multiscale systems.
Revised:  This work extends the MRI-GARK framework by introducing coupled implicit methods to solve stiff multiscale systems.
Edit intent: fluency
Original:  The gradient flow is well-defined and converges exponentially fast to an eigenfunction.
Revised:  The gradient flow is well-defined and converges to an eigenfunction.
Edit intent: clarity
Original: We consider the mutation-selection differential equation with pairwise interaction and establish the corresponding ancestral process, which is a specific random tree and a variant of the ancestral selection graph.
Revised: We consider the mutation-selection differential equation with pairwise interaction and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral selection graph.
Edit intent: clarity
Original:  The latter is dual to the mutation-selection equation and provides a stochastic representation of its solution .
Revised:  The latter also satisfies a duality relation with the mutation-selection equation and provides a stochastic representation of its solution .
Edit intent: clarity
Original:  The latter is dual to the mutation-selection equation and provides a stochastic representation of its solution .
Revised:  The latter is dual to the mutation-selection equation . Each of the dualities provides a stochastic representation of its solution .
Edit intent: clarity
Original:  It also allows to reveal the genealogical structures inherent in the bifurcations of the equilibria of the differential equation.
Edit intent: coherence
Original:  Furthermore, we establish constructions, again based on the stratified ancestral selection graph, that allow to trace back the ancestral lines into the distant past and obtain explicit results about the ancestral population in the case of unidirectional mutation.
Revised:  Furthermore, we establish constructions, again based on the stratified ancestral selection graph, we obtain explicit results about the ancestral population in the case of unidirectional mutation.
Edit intent: clarity
Original: We consider the mutation-selection differential equation with pairwise interaction  and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral selection graph.
Revised: We consider the mutation--selection differential equation with pairwise interaction and establish the corresponding ancestral process, which is a random tree and a variant of the ancestral selection graph.
Edit intent: fluency
Original:  The formal relation to the forward model is given via a dualityrelation .
Revised:  The formal relation to the forward model is given via duality .
Edit intent: fluency
Original:  The hierarchies inherent in the tree are encoded systematically via ternary trees with weighted leaves;
Revised:  The hierarchies inherent in the tree are encoded systematically via tripod trees with weighted leaves;
Edit intent: clarity
Original:  The latter also satisfies a duality relation with the mutation-selection equation.
Revised:  The latter also satisfies a duality relation with the mutation--selection equation.
Edit intent: fluency
Original: In this paper, we develop the intelligent networking framework for Flying Ad-hoc Networks (FANETs), where a coalition-based model is designed .
Revised: In this paper, we develop a task-driven networking framework for Flying Ad-hoc Networks (FANETs), where a coalition-based model is designed .
Edit intent: clarity
Original: In this paper, we develop the intelligent networking framework for Flying Ad-hoc Networks (FANETs), where a coalition-based model is designed .
Revised: In this paper, we develop the intelligent networking framework for Flying Ad-hoc Networks (FANETs), where a coalition-based model is outlined .
Edit intent: clarity
Original:  Firstly, we present a brief survey to show the state-of-the art studies on the intra-communication of unmanned aerial vehicle (UAV) swarms.
Revised:  Firstly, we present a brief survey to show the state-of-the-art studies on the intra-communication of unmanned aerial vehicle (UAV) swarms.
Edit intent: fluency
Original:  To tackle the problem, we design an artificial intelligence-based optimization architecture, which mainly includes the game model, machine learning and the real-time decision.
Revised:  To tackle the problem, we design an intelligence-based optimization architecture, which mainly includes the game model, machine learning and the real-time decision.
Edit intent: clarity
Original:  To tackle the problem, we design an artificial intelligence-based optimization architecture, which mainly includes the game model, machine learning and the real-time decision.
Revised:  To tackle the problem, we design an artificial intelligence-based optimization architecture, which mainly includes the game model, machine learning and real-time decision.
Edit intent: fluency
Original:  Under the guidance of game theories and machine learning, UAVs can make comprehensive decisions by combining the previous training results with their own sensing, information interaction  and game strategies.
Revised:  Under the guidance of game theories and machine learning, UAVs can make comprehensive decisions by combining the previous training results with their sensing, information interaction and game strategies.
Edit intent: clarity
Original:  Under the guidance of game theories and machine learning, UAVs can make comprehensive decisions by combining the previous training results with their own sensing, information interaction  and game strategies.
Revised:  Under the guidance of game theories and machine learning, UAVs can make comprehensive decisions by combining the previous training results with their own sensing, information interaction , and game strategies.
Edit intent: fluency
Original:  Roughly, a local obfuscation mechanism with distribution privacy perturbs each single input so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an output of the mechanism.
Revised:  Roughly, a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an output of the mechanism.
Edit intent: clarity
Original:  To provide a stronger level of distribution privacy, we introduce an obfuscation mechanism, called the tupling mechanism, that perturbs a given input and adds random dummy data.
Revised:  To provide a stronger level of distribution privacy, we introduce an obfuscation mechanism, called a tupling mechanism, that perturbs a given input and adds random dummy data.
Edit intent: fluency
Original:  Then we apply the tupling mechanism to the protection of user attributes in location based services, and demonstrate by experiments that the tupling mechanism outperforms the popular local (extended) differentially private mechanisms in terms of distribution privacy and utility .
Revised:  Then we apply the tupling mechanism to the protection of user attributes in location based services, and demonstrate by experiments that the tupling mechanism outperforms the popular local (extended) differentially private mechanisms in terms of distribution privacy and service quality .
Edit intent: clarity
Original:  Finally, we discuss the relationships among utility, privacy, and the cost of adding dummy data .
Revised:  Finally, we discuss the relationships among the privacy, quality, and cost of obfuscation mechanisms .
Edit intent: clarity
Original: We propose a formal model for the privacy of user attributes in terms of differential privacy.
Revised: We introduce a formal model for the privacy of user attributes in terms of differential privacy.
Edit intent: clarity
Original:  In particular, we introduce a notion , called distribution privacy , as the differential privacy for probability distributions . Roughly,  a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an outputof the mechanism .
Revised:  In particular, we introduce a notion , called distribution privacy . Roughly, a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an outputof the mechanism .
Edit intent: clarity
Original:  In particular, we introduce a notion , called distribution privacy , as the differential privacy for probability distributions . Roughly,  a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an outputof the mechanism .
Revised:  In particular, we introduce a notion , called distribution privacy , as the differential privacy for probability distributions . Roughly, the distribution privacy of a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an outputof the mechanism .
Edit intent: clarity
Original:  In particular, we introduce a notion , called distribution privacy , as the differential privacy for probability distributions . Roughly,  a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an outputof the mechanism .
Revised:  In particular, we introduce a notion , called distribution privacy , as the differential privacy for probability distributions . Roughly, a local obfuscation mechanism means that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an outputof the mechanism .
Edit intent: clarity
Original:  In particular, we introduce a notion , called distribution privacy , as the differential privacy for probability distributions . Roughly,  a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the probability distribution of inputs by observing an outputof the mechanism .
Revised:  In particular, we introduce a notion , called distribution privacy , as the differential privacy for probability distributions . Roughly, a local obfuscation mechanism with distribution privacy perturbs its inputs so that the attacker cannot significantly gain any information on the distribution of the mechanism's input by observing its output .
Edit intent: clarity
Original:  For instance , we prove that , to provide distribution privacy w.r.t. the approximate max-divergence (resp. f-divergence), the amount of noise added by the Laplace mechanism should be proportional to the infinite Wasserstein (resp. the Earth mover's) distance between the two distributions we want to make indistinguishable.
Revised:  For instance , we prove that , to provide distribution privacy w.r.t. the approximate max-divergence (resp. f-divergence), the amount of noise proportionally to the infinite Wasserstein (resp. the Earth mover's) distance between the two distributions we want to make indistinguishable.
Edit intent: clarity
Original:  For instance , we prove that , to provide distribution privacy w.r.t. the approximate max-divergence (resp. f-divergence), the amount of noise added by the Laplace mechanism should be proportional to the infinite Wasserstein (resp. the Earth mover's) distance between the two distributions we want to make indistinguishable.
Revised:  For instance , we prove that , to provide distribution privacy w.r.t. the approximate max-divergence (resp. f-divergence), the amount of noise added by the Laplace mechanism should be proportional to the infinite Wasserstein distance between the two distributions we want to make indistinguishable.
Edit intent: clarity
Original:  To provide a stronger level of distribution privacy , we introduce an obfuscation mechanism, called a tupling mechanism, that perturbs a given input and adds random dummy data  .
Revised:  To provide a stronger level of distribution privacy , we introduce an obfuscation mechanism, called a tupling mechanism, that adds random dummy data .
Edit intent: clarity
Original:  To provide a stronger level of distribution privacy , we introduce an obfuscation mechanism, called a tupling mechanism, that perturbs a given input and adds random dummy data  .
Revised:  To provide a stronger level of distribution privacy , we introduce an obfuscation mechanism, called a tupling mechanism, that perturbs a given input and adds random dummy data to the output .
Edit intent: clarity
Original:  Then we apply the tupling mechanism to the protection of user attributes in location based services , and demonstrate by experiments that the tupling mechanism outperforms popular local differential privacy mechanisms in terms of distribution privacy and service quality .
Revised:  Then we apply this mechanism to the protection of user attributes in location based services , and demonstrate by experiments that the tupling mechanism outperforms popular local differential privacy mechanisms in terms of distribution privacy and service quality .
Edit intent: clarity
Original:  Then we apply the tupling mechanism to the protection of user attributes in location based services , and demonstrate by experiments that the tupling mechanism outperforms popular local differential privacy mechanisms in terms of distribution privacy and service quality .
Revised:  Then we apply the tupling mechanism to the protection of user attributes in location based services . By experiments, we demonstrate that the tupling mechanism outperforms popular local differential privacy mechanisms in terms of distribution privacy and service quality .
Edit intent: coherence
Original:  Then we apply the tupling mechanism to the protection of user attributes in location based services , and demonstrate by experiments that the tupling mechanism outperforms popular local differential privacy mechanisms in terms of distribution privacy and service quality .
Revised:  Then we apply the tupling mechanism to the protection of user attributes in location based services , and demonstrate by experiments that the tupling mechanism outperforms popular local mechanisms in terms of distribution privacy and service quality .
Edit intent: clarity
Original:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al, where%DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% _\al not found by the classical regularization.
Revised:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% %DIFDELCMD < \Bo%%% _\al, where%DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% _\al not found by the classical regularization.
Edit intent: fluency
Original:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al, where%DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% _\al not found by the classical regularization.
Revised:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% %DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% _\al not found by the classical regularization.
Edit intent: coherence
Original:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al, where%DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% _\al not found by the classical regularization.
Revised:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al, where%DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% %DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% _\al not found by the classical regularization.
Edit intent: fluency
Original:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al, where%DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% _\al not found by the classical regularization.
Revised:  In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form %DIFDELCMD < \Bo%%% _\al + %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al, where%DIFDELCMD < \Bo%%% _\al is a classical regularization and the network %DIFDELCMD < \nun%%% _\al%DIFDELCMD < \Bo%%% _\al is trained to recover the missing part %DIFDELCMD < \Id%%% _X - %DIFDELCMD < \Bo%%% B_\alpha not found by the classical regularization.
Edit intent: clarity
Original:  We demonstrate that our results recover existing convergence and convergence rates results for filter-based regularization methods as well as the recently introduced null-space network as special cases  .
Revised:  We demonstrate that our results recover existing convergence and convergence rates results for filter-based regularization methods as well as the recently introduced null space network as special cases .
Edit intent: fluency
Original:  Additionally, we derive convergence rates (quantitative error estimate ) assuming a sufficient decay of the associated distance function.
Revised:  Additionally, we derive convergence rates (quantitative error estimates ) assuming a sufficient decay of the associated distance function.
Edit intent: fluency
Original:  Numerical results are presented for a tomographic sparse data problem, which clearly demonstrate that the proposed RegNets improve the classical regularization as well as the previously proposed null space network.
Revised:  Numerical results are presented for a tomographic sparse data problem, which clearly demonstrate that the proposed RegNets improve the classical regularization as well as the null space network.
Edit intent: clarity
Original:  We associate each task with a manifold on which the training process travels from initialization to final parameters and construct a meta learning objective that minimizes the expected length of this path.
Revised:  We associate each task with a manifold on which the training process travels from initialization to final parameters and construct a meta-learning objective that minimizes the expected length of this path.
Edit intent: fluency
Original:  We demonstrate that our framework outperforms competing methods, both in meta learning and transfer learning, on a set of computer vision tasks.
Revised:  We demonstrate that our framework outperforms competing methods, both in meta-learning and transfer learning, on a set of computer vision tasks.
Edit intent: fluency
Original:  Finally, we demonstrate that Leap can transfer knowledge across learning processes in demanding Reinforcement Learning environments (Atari) that involve millions of gradient steps.
Revised:  Finally, we demonstrate that Leap can transfer knowledge across learning processes in demanding reinforcement learning environments (Atari) that involve millions of gradient steps.
Edit intent: fluency
Original:  We evaluate our model on multiple molecular optimization tasks and show that our model outperforms previous state-of-the-art baselines by a significant margin .
Revised:  We evaluate our model on multiple molecular optimization tasks and show that our model outperforms previous state-of-the-art baselines .
Edit intent: clarity
Original:  Thus, still many visual recognition problems  defined on arbitrary manifolds cannot benefit much from the success of CNNs, if at all .
Revised:  Thus, still many visual recognition problems are defined on arbitrary manifolds cannot benefit much from the success of CNNs, if at all .
Edit intent: clarity
Original:  Thus, still many visual recognition problems  defined on arbitrary manifolds cannot benefit much from the success of CNNs, if at all .
Revised:  Thus, still many visual recognition problems defined on arbitrary surfaces (2D-manifolds) .
Edit intent: clarity