wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime). Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers  .
Revised:  We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation . The Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers .
Edit intent: clarity
Original:  Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers  .
Revised:  Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers . Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution .
Edit intent: meaning-changed
Original:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics  , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.
Revised:  reachability, and goal stability. To find a domain in which a learned control-affine approximation of the true dynamics , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.
Edit intent: clarity
Original:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics  , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.
Revised:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics can be trusted , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.
Edit intent: meaning-changed
Original:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics  , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.
Revised:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics , we estimate the Lipschitz constant of the difference between the true and learned dynamics , and ensure the estimate is valid with a given probability . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.
Edit intent: clarity
Original:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics  , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists.
Revised:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we also derive existence conditions for a one-step feedback law exists.
Edit intent: clarity
Original:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics  , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists. This allows fora small bound on the tracking error when the trajectory is executed on the real system .
Revised:  reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law which can keep the real system within a small bound of a nominal trajectory planned with the learned dynamics .
Edit intent: clarity
Original:  Our method imposes a check for the existence of the feedback law as constraints in a sampling-based planner, which returns a feedback policy ensuring that under the true dynamics, the goal is reachable, the path is safe in execution, and the closed-loop system is invariant in a small set about the goal.
Revised:  Our method imposes the feedback law existence as a constraint in a sampling-based planner, which returns a feedback policy ensuring that under the true dynamics, the goal is reachable, the path is safe in execution, and the closed-loop system is invariant in a small set about the goal.
Edit intent: clarity
Original:  Our method imposes a check for the existence of the feedback law as constraints in a sampling-based planner, which returns a feedback policy ensuring that under the true dynamics, the goal is reachable, the path is safe in execution, and the closed-loop system is invariant in a small set about the goal.
Revised:  Our method imposes a check for the existence of the feedback law as constraints in a sampling-based planner, which returns a feedback policy around a nominal plan ensuring that, if the Lipschitz constant estimate is valid, the true system is safe during plan execution, reaches the goal, and is ultimately invariant in a small set about the goal.
Edit intent: meaning-changed
Original:  CHECKED provides ground-truth on credibility,carefully obtained by ensuring the specific sources are used. CHECKED includes microblogs related to COVID-19  , identified by using a specific list of keywords  , covering a total 2120 microblogs published from December 2019 to August 2020.
Revised:  CHECKED provides a total 2,104 verified microblogs related to COVID-19 , identified by using a specific list of keywords , covering a total 2120 microblogs published from December 2019 to August 2020.
Edit intent: meaning-changed
Original:  CHECKED includes microblogs related to COVID-19  , identified by using a specific list of keywords  , covering a total 2120 microblogs published from December 2019 to August 2020.
Revised:  CHECKED includes microblogs related to COVID-19 from December 2019 to August 2020 , identified by using a specific list of keywords , covering a total 2120 microblogs published from December 2019 to August 2020.
Edit intent: fluency
Original:  CHECKED includes microblogs related to COVID-19  , identified by using a specific list of keywords  , covering a total 2120 microblogs published from December 2019 to August 2020.
Revised:  CHECKED includes microblogs related to COVID-19 , identified by using a specific list of keywords . Correspondingly, CHECKED includes 1 , covering a total 2120 microblogs published from December 2019 to August 2020.
Edit intent: meaning-changed
Original:  CHECKED includes microblogs related to COVID-19  , identified by using a specific list of keywords  , covering a total 2120 microblogs published from December 2019 to August 2020.
Revised:  CHECKED includes microblogs related to COVID-19 , identified by using a specific list of keywords , 868,175 reposts, 1,185,702 comments, and 56,852,736 likes that reveal how these verified microblogs are spread and reacted on Weibo.
Edit intent: meaning-changed
Original:  To address this issue, this paper presents a  meta-learning algorithm for unsupervised neural machine translation (UNMT) that trains the model to adapt to another domain by utilizing only a small amount of training data.
Revised:  To address this issue, this paper presents a novel meta-learning algorithm for unsupervised neural machine translation (UNMT) that trains the model to adapt to another domain by utilizing only a small amount of training data.
Edit intent: clarity
Original:  Hence, we extend the meta-learning algorithm, which utilizes knowledge learned from high-resource domains  to boost the performance of low-resource UNMT. Our model surpasses a transfer learning-based approach by up to 2-4 BLEU scores.
Revised:  Hence, we extend the meta-learning algorithm, which utilizes knowledge learned from high-resource domains , to boost the performance of low-resource UNMT. Our model surpasses a transfer learning-based approach by up to 2-4 BLEU scores.
Edit intent: fluency
Original:  Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities exchange while facing the systemic and idiosyncratic noises as well as the stochastic order-flows from its over-the-counter clients. We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Revised:  In the previous work ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Edit intent: coherence
Original:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Revised:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the 15] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Edit intent: meaning-changed
Original:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Revised:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ], we have shown that a certain price process, which is given by the solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Edit intent: meaning-changed
Original:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Revised:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Edit intent: clarity
Original:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit.
Revised:  We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type , asymptotically clears the market in the large population limit.
Edit intent: clarity
Original:  In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit ] .
Revised:  In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit ]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size .
Edit intent: meaning-changed
Original:  On difficult query images from two benchmark datasets, we demonstrate that our approach matches and exceeds the performance of several alternative fusion approaches along with state-of-the-art techniques that are provided with a priori (unfair) knowledge of the best reference images.
Revised:  On difficult query images from two benchmark datasets, we demonstrate that our approach matches and exceeds the performance of several alternative fusion approaches along with state-of-the-art techniques that are provided with prior (unfair) knowledge of the best reference images.
Edit intent: clarity
Original:  By restructuring OpenMP offload directives, we gain an 18x speedup for the su3 proxy application on NERSC's Cori system with Clang , and a 15.7x speedup by switching max reductions to add reductions in the laplace mini-app , using the Cray-llvm compiler on Cori.
Revised:  By restructuring OpenMP offloading directives, we gain an 18x speedup for the su3 proxy application on NERSC's Cori system with Clang , and a 15.7x speedup by switching max reductions to add reductions in the laplace mini-app , using the Cray-llvm compiler on Cori.
Edit intent: fluency
Original:  By restructuring OpenMP offload directives, we gain an 18x speedup for the su3 proxy application on NERSC's Cori system with Clang , and a 15.7x speedup by switching max reductions to add reductions in the laplace mini-app , using the Cray-llvm compiler on Cori.
Revised:  By restructuring OpenMP offload directives, we gain an 18x speedup for the su3 proxy application on NERSC's Cori system when using the Clang compiler , and a 15.7x speedup by switching max reductions to add reductions in the laplace mini-app , using the Cray-llvm compiler on Cori.
Edit intent: clarity
Original:  By restructuring OpenMP offload directives, we gain an 18x speedup for the su3 proxy application on NERSC's Cori system with Clang , and a 15.7x speedup by switching max reductions to add reductions in the laplace mini-app , using the Cray-llvm compiler on Cori.
Revised:  By restructuring OpenMP offload directives, we gain an 18x speedup for the su3 proxy application on NERSC's Cori system with Clang , and a 15.7x speedup by switching max reductions to add reductions in the laplace mini-app when using the Cray-llvm compiler on Cori.
Edit intent: coherence
Original:  Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate  all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs.
Revised:  Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate the solution space of all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs.
Edit intent: meaning-changed
Original:  We then use this analytical characterization to rigorously analyze the solution space geometry and derive certainty conditions guaranteeing a non-zero synapse between neurons.
Revised:  We then use this analytical characterization to rigorously analyze the solution space geometry can undergo topological transitions as the allowed error increases, which could provide insight into both neuroscience and machine learning. We ultimately use this geometric characterization to derive certainty conditions guaranteeing a non-zero synapse between neurons.
Edit intent: meaning-changed
Original:  These dangerous eigenvalues contribute to large round-off errors in the first iteration, but are self-correcting in later iterations  .
Revised:  These dangerous eigenvalues contribute to large round-off errors in the first iteration, but are self-correcting in later iterations . For matrices with orthogonal eigenvectors (e.g., real-symmetric or complex Hermitian), two iterations is enough to reduce round-off errors to the order of the unit-round off .
Edit intent: meaning-changed
Original:  We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees  validity and asymptotic optimality . Validity: Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization.
Revised:  We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees the validity and asymptotic optimality . Validity: Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization.
Edit intent: fluency
Original:  We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees  validity and asymptotic optimality . Validity: Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization.
Revised:  We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees validity and asymptotic optimality for known environments. Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization.
Edit intent: meaning-changed
Original:  We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees  validity and asymptotic optimality . Validity: Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization.
Revised:  We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees validity and asymptotic optimality . Validity:Validity: Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization.
Edit intent: fluency
Original:  Existing solutions  include accounting for the fraction or count of treated neighbors in a user's network, among other strategies. Yet, there are often a high number of researcher degrees of freedom in specifying network interference conditions and most current methods do not account for the local network structure beyond simply counting the number of neighbors.
Revised:  Existing solutions include accounting for the fraction or count of treated neighbors in a user's network, yet most current methods do not account for the local network structure beyond simply counting the number of neighbors.
Edit intent: coherence
Original:   We test our method on a  real-world experiment on a large-scale network and a synthetic network setting , which highlight how accounting for local structures can better account for different interference patterns in networks.
Revised:  Our approach can account for social network theories, such as structural diversity and echo chambers, and also can help specify network interference conditions that are suitable to each experiment. We test our method on a real-world experiment on a large-scale network and a synthetic network setting , which highlight how accounting for local structures can better account for different interference patterns in networks.
Edit intent: meaning-changed
Original: While the estimation of risk is an important question in the daily business of banks and insurances, it is surprising that efficient procedures for this task are not well studied. Indeed, many existing plug-in approaches for the estimation of risk suffer from an unnecessary bias which leads to the underestimation of risk and negatively impacts backtesting results, especially in the small sample environment .
Revised: While the estimation of risk is an important question in the daily business of banks and insurances, many existing plug-in approaches for the estimation of risk suffer from an unnecessary bias which leads to the underestimation of risk and negatively impacts backtesting results, especially in the small sample environment .
Edit intent: coherence
Original:  Indeed, many existing plug-in approaches for the estimation of risk suffer from an unnecessary bias which leads to the underestimation of risk and negatively impacts backtesting results, especially in the small sample environment .
Revised:  Indeed, many existing plug-in approaches for the estimation of risk suffer from an unnecessary bias . This often leads to the underestimation of risk and negatively impacts backtesting results, especially in the small sample environment .
Edit intent: coherence
Original:  In this article , we consider efficient estimation of risk in practical situations and provide means to improve the accuracy of risk estimators and their performance in backtesting. In particular , we propose an algorithm for bias correction and show how to apply it for generalized Pareto distributions.
Revised:  In this article we show that the link between estimation bias and backtesting can be traced back to the dual relationship between risk measures and the corresponding performance measures, and discuss this in reference to value-at-risk and expected shortfall frameworks. Motivated by this finding , we propose an algorithm for bias correction and show how to apply it for generalized Pareto distributions.
Edit intent: meaning-changed
Original:  In particular, we developed a multimodal neural network model---using a partial, observed bounce trajectory and the audio resulting from drop impact as its inputs---to predict the full bounce trajectory and the end location of a dropped object.
Revised:  In particular, we developed a multimodal neural network model-using a partial, observed bounce trajectory and the audio resulting from drop impact as its inputs---to predict the full bounce trajectory and the end location of a dropped object.
Edit intent: fluency
Original:  In particular, we developed a multimodal neural network model---using a partial, observed bounce trajectory and the audio resulting from drop impact as its inputs---to predict the full bounce trajectory and the end location of a dropped object.
Revised:  In particular, we developed a multimodal neural network model---using a partial, observed bounce trajectory and the audio resulting from drop impact as its inputs-to predict the full bounce trajectory and the end location of a dropped object.
Edit intent: fluency