wanyu/IteraTeR_v2 huggingface dataset:
Original: Recent advances in deep learning have set the focus on neural networks (NNs) that can successfully replace traditional numerical solvers in many applications, achieving impressive computing gains.
Revised: Recent advances in deep learning have allowed neural networks (NNs) that can successfully replace traditional numerical solvers in many applications, achieving impressive computing gains.
Edit intent: clarity
Original: Recent advances in deep learning have set the focus on neural networks (NNs) that can successfully replace traditional numerical solvers in many applications, achieving impressive computing gains.
Revised: Recent advances in deep learning have set the focus on neural networks (NNs) to successfully replace traditional numerical solvers in many applications, achieving impressive computing gains.
Edit intent: clarity
Original: Recent advances in deep learning have set the focus on neural networks (NNs) that can successfully replace traditional numerical solvers in many applications, achieving impressive computing gains.
Revised: Recent advances in deep learning have set the focus on neural networks (NNs) that can successfully replace traditional numerical solvers in many applications, thus enabling impressive computing gains.
Edit intent: clarity
Original:  A variety of NN-based methodologies have been shown to successfully approximate the dynamical trajectories computed by numerical time domain solvers at a fraction of the time.
Revised:  A variety of NN-based methodologies have been shown to successfully approximate the trajectories computed by numerical time domain solvers at a fraction of the time.
Edit intent: clarity
Original:  A variety of NN-based methodologies have been shown to successfully approximate the dynamical trajectories computed by numerical time domain solvers at a fraction of the time.
Revised:  A variety of NN-based methodologies have been shown to successfully approximate the dynamical trajectories computed by numerical solvers at a fraction of the time.
Edit intent: clarity
Original: In this work, we investigate an inverse problem of recovering multiple orders in  time-fractional diffusion type problems from the data observed at one single point on the boundary.
Revised: In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion type problems from the data observed at one single point on the boundary.
Edit intent: fluency
Original: In this work, we investigate an inverse problem of recovering multiple orders in  time-fractional diffusion type problems from the data observed at one single point on the boundary.
Revised: In this work, we investigate an inverse problem of recovering multiple orders in time-fractional diffusion model from the data observed at one single point on the boundary.
Edit intent: clarity
Original:  We prove the unique recovery of the orders together with their weights, which does not require a full knowledge of the domain or medium properties, e.g., the diffusion and potential coefficients, initial condition and source in the model.
Revised:  We prove the unique recovery of the orders together with their weights, which does not require a full knowledge of the domain or medium properties, e.g., diffusion and potential coefficients, initial condition and source in the model.
Edit intent: fluency
Original:  Further, inspired by the analysis, we propose a numerical procedure for recovering these parameters based on a nonlinear least-squares fitting with either fractional polynomials or rational approximations as the model function, and provide numerical experiments to illustrate the approach at small time t.
Revised:  Further, inspired by the analysis, we propose a numerical procedure for recovering these parameters based on a nonlinear least-squares fitting with either fractional polynomials or rational approximations as the model function, and provide numerical experiments to illustrate the approach for small time t.
Edit intent: fluency
Original:  Questionnaires were distributed through a university forum, student group chats, and Tencent Survey Service.
Edit intent: coherence
Original:  We introduce the second such algorithm,Consensus MWU , for which we prove local convergence and show empirically that it enjoys faster and more robust convergence than OMWU.
Revised:  We introduce the second such algorithm, , for which we prove local convergence and show empirically that it enjoys faster and more robust convergence than OMWU.
Edit intent: clarity
Original:  As for OMWU, CMWU has convergence guarantees in the zero-sum case only, but Cheung and Piliouras (2020) recently showed that  OMWU and MWU  display opposite convergence properties depending on whether the game is zero-sum or cooperative.
Revised:  As for OMWU, CMWU has convergence guarantees in the zero-sum case only, but Cheung and Piliouras (2020) recently showed that OMWU and MWU - display opposite convergence properties depending on whether the game is zero-sum or cooperative.
Edit intent: fluency
Original:  Inspired by this work and the recent literature on learning to optimize for single functions, we extend CMWU to non zero-sum games by introducing a new framework for online learning in games, where the update rule's gradient and Hessian coefficients along a trajectory are learnt by a reinforcement learning policy that is conditioned on the nature of the game: \textit{the game signature}.
Revised:  Inspired by this work and the recent literature on learning to optimize for single functions, we introduce a new framework for online learning in games, where the update rule's gradient and Hessian coefficients along a trajectory are learnt by a reinforcement learning policy that is conditioned on the nature of the game: \textit{the game signature}.
Edit intent: clarity
Original:  We construct the latter using a new canonical decomposition of two-player games into eight components corresponding to commutative projection operators, generalizing and unifying recent game concepts studied in the literature.
Revised:  We construct the latter using a new decomposition of two-player games into eight components corresponding to commutative projection operators, generalizing and unifying recent game concepts studied in the literature.
Edit intent: clarity
Original:   The manuscript concludes with the description of a Dynamic Mode Decomposition algorithm that converges when a dense collection of occupation kernels, arising from the data, are leveraged in the analysis.
Revised:  The manuscript concludes with the description of two Dynamic Mode Decomposition algorithm that converges when a dense collection of occupation kernels, arising from the data, are leveraged in the analysis.
Edit intent: clarity
Original:   The manuscript concludes with the description of a Dynamic Mode Decomposition algorithm that converges when a dense collection of occupation kernels, arising from the data, are leveraged in the analysis.
Revised:  The manuscript concludes with the description of a Dynamic Mode Decomposition algorithms that converges when a dense collection of occupation kernels, arising from the data, are leveraged in the analysis.
Edit intent: fluency
Original:  In this context, the Nash social welfare--defined as the geometric mean of agents' valuations for their assigned bundles--stands as a fundamental measure that quantifies the extent of fairness of an allocation.
Revised:  In this context, the Nash social welfare-defined as the geometric mean of agents' valuations for their assigned bundles--stands as a fundamental measure that quantifies the extent of fairness of an allocation.
Edit intent: fluency
Original:  In this context, the Nash social welfare--defined as the geometric mean of agents' valuations for their assigned bundles--stands as a fundamental measure that quantifies the extent of fairness of an allocation.
Revised:  In this context, the Nash social welfare--defined as the geometric mean of agents' valuations for their assigned bundles-stands as a fundamental measure that quantifies the extent of fairness of an allocation.
Edit intent: fluency
Original:  These results imply that--in the case of binary XOS valuations--there necessarily exists an allocation that simultaneously satisfies multiple (approximate) fairness and efficiency criteria.
Revised:  These results imply that-in the case of binary XOS valuations--there necessarily exists an allocation that simultaneously satisfies multiple (approximate) fairness and efficiency criteria.
Edit intent: fluency
Original:  These results imply that--in the case of binary XOS valuations--there necessarily exists an allocation that simultaneously satisfies multiple (approximate) fairness and efficiency criteria.
Revised:  These results imply that--in the case of binary XOS valuations-there necessarily exists an allocation that simultaneously satisfies multiple (approximate) fairness and efficiency criteria.
Edit intent: fluency
Original:  Our main result is a quasi-polynomial time algorithm to solve orbit recovery over SO(3) - i. e. the cryo-electron tomography problem which asks to recover the three-dimensional structure of a molecule from noisy measurements of randomly rotated copies of it.
Revised:  Our main result is a quasi-polynomial time algorithm for orbit recovery over SO(3) - i. e. the cryo-electron tomography problem which asks to recover the three-dimensional structure of a molecule from noisy measurements of randomly rotated copies of it.
Edit intent: clarity
Original:  Our main result is a quasi-polynomial time algorithm to solve orbit recovery over SO(3) - i. e. the cryo-electron tomography problem which asks to recover the three-dimensional structure of a molecule from noisy measurements of randomly rotated copies of it.
Revised:  Our main result is a quasi-polynomial time algorithm to solve orbit recovery over SO(3) in this model.
Edit intent: clarity
Original:  Our approach exploits the layered structure of the invariant polynomials, and simultaneously yields a new class of tensor decomposition algorithms that work in settings when the tensor is not low-rank but rather where the factors arealgebraically related to each other by a group action{\em   .
Revised:  Our approach exploits the layered structure of the system of polynomial equations by setting up a system of{\em .
Edit intent: clarity
Original:  Our approach exploits the layered structure of the invariant polynomials, and simultaneously yields a new class of tensor decomposition algorithms that work in settings when the tensor is not low-rank but rather where the factors arealgebraically related to each other by a group action{\em   .
Revised:  Our approach exploits the layered structure of the invariant polynomials, and simultaneously yields a new class of tensor decomposition algorithms that work in settings when the tensor is not low-rank but rather where the factors arealgebraically related to each other by a group action{\em linear .
Edit intent: fluency
Original:  This has opened up the possibility of introducing variational and symplectic integration methods using geometric integrators .
Revised:  This has opened up the possibility of introducing variational and symplectic methods using geometric integrators .
Edit intent: fluency
Original:  This has opened up the possibility of introducing variational and symplectic integration methods using geometric integrators .
Revised:  This has opened up the possibility of introducing variational and symplectic integration methods using geometric integration .
Edit intent: clarity
Original:  Using both, Hamilton's principle and Lagrange-d'Alembert's  , we derive two families of  optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of typical momentum methods.
Revised:  Using both, Hamilton's and Lagrange-d'Alembert's , we derive two families of optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of typical momentum methods.
Edit intent: coherence
Original:  Using both, Hamilton's principle and Lagrange-d'Alembert's  , we derive two families of  optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of typical momentum methods.
Revised:  Using both, Hamilton's principle and Lagrange-d'Alembert's principle , we derive two families of optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of typical momentum methods.
Edit intent: fluency
Original:  Using both, Hamilton's principle and Lagrange-d'Alembert's  , we derive two families of  optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of typical momentum methods.
Revised:  Using both, Hamilton's principle and Lagrange-d'Alembert's , we derive two families of optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, the second of which mimics the behavior of the latter which reduces the oscillations of typical momentum methods.
Edit intent: clarity
Original:  Using both, Hamilton's principle and Lagrange-d'Alembert's  , we derive two families of  optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of typical momentum methods.
Revised:  Using both, Hamilton's principle and Lagrange-d'Alembert's , we derive two families of optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the first reducing the oscillations of typical momentum methods.
Edit intent: coherence
Original:  Using both, Hamilton's principle and Lagrange-d'Alembert's  , we derive two families of  optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of typical momentum methods.
Revised:  Using both, Hamilton's principle and Lagrange-d'Alembert's , we derive two families of optimization methods in one-to-one correspondence that generalize Polyak's heavy ball and the well known Nesterov accelerated gradient method, mimicking the behavior of the latter which reduces the oscillations of classical momentum methods.
Edit intent: clarity
Original:  but not - or \cdot has the finite representation property , an extension of the result for ordered domain algebras \{0,1,D,R, \leq, 1', \smile,;\ . We survey the results in the area of the finite representation property and raise a number of open questions .
Revised:  but not - or \cdot has the finite representation property , an extension of the result for ordered domain algebras \{0,1,D,R, \leq, 1', \smile,;\ . We survey the results in the area of the finite representation property .
Edit intent: clarity
Original:  More central individuals had exceptionally similar neural responses to their peers and especially to each other in brain regions  associated with high-level interpretations and social cognition (e.g., in the default-mode network), whereas less-central individuals exhibited more idiosyncratic responses.
Revised:  We found that more central individuals had exceptionally similar neural responses to their peers and especially to each other in brain regions associated with high-level interpretations and social cognition (e.g., in the default-mode network), whereas less-central individuals exhibited more idiosyncratic responses.
Edit intent: coherence
Original:  More central individuals had exceptionally similar neural responses to their peers and especially to each other in brain regions  associated with high-level interpretations and social cognition (e.g., in the default-mode network), whereas less-central individuals exhibited more idiosyncratic responses.
Revised:  More central individuals had exceptionally similar neural responses to their peers and especially to each other in brain regions that are associated with high-level interpretations and social cognition (e.g., in the default-mode network), whereas less-central individuals exhibited more idiosyncratic responses.
Edit intent: clarity
Original:  These findings suggest an "Anna Karenina principle" in social networks: Highly-central individuals process the world in exceptionally similar ways, whereas less-central individuals process the world in idiosyncratic ways.
Revised:  These findings suggest that highly-central individuals process the world in exceptionally similar ways, whereas less-central individuals process the world in idiosyncratic ways.
Edit intent: clarity
Original:  In this paper  we introduce a framework, LMAC, based on meta-gradient descent that automates the discovery of the  update rule without explicit human design.
Revised:  In this paper , we introduce a framework, LMAC, based on meta-gradient descent that automates the discovery of the update rule without explicit human design.
Edit intent: fluency
Original:  In this paper  we introduce a framework, LMAC, based on meta-gradient descent that automates the discovery of the  update rule without explicit human design.
Revised:  In this paper we introduce a framework, LMAC, based on meta-gradient descent to automate the discovery of the update rule without explicit human design.
Edit intent: coherence
Original: The duality of sensory inference and optimal control was known since 1960s and has recently been recognized as common computations required for  posterior distributions in dynamic Bayesian inference and  value functions in optimal control.
Revised: The duality of sensory inference and optimal control was known since 1960s and has recently been recognized as common computations required for posterior distributions in Bayesian inference and value functions in optimal control.
Edit intent: clarity
Original:  Here we consider a hypothesis that the anterior and posterior cortical circuits evolved for dual computations for sensory inference and optimal control, or perceptual and value-based decision making, respectively.
Revised:  Here we consider the hypothesis that the anterior and posterior cortical circuits evolved for dual computations for sensory inference and optimal control, or perceptual and value-based decision making, respectively.
Edit intent: fluency
Original:  Here we consider a hypothesis that the anterior and posterior cortical circuits evolved for dual computations for sensory inference and optimal control, or perceptual and value-based decision making, respectively.
Revised:  Here we consider a hypothesis that the sensory and motor cortical circuits implement the dual computations for sensory inference and optimal control, or perceptual and value-based decision making, respectively.
Edit intent: clarity
Original:  We  explore how different types of cortical neurons may represent different variables , such as prior and posterior distributions and value functions, and what cortical dynamics may realize required computations.
Revised:  We explore how different cortical neurons may represent different variables , such as prior and posterior distributions and value functions, and what cortical dynamics may realize required computations.
Edit intent: clarity
Original:  Results show that MoleHD is able to outperform all the baseline methods on average across 30 classification tasks with significantly reduced computing cost  .
Revised:  Results show that MoleHD is able to outperform all the baseline methods on average across 30 classification tasks with significantly reduced computing cost and training efforts .
Edit intent: clarity
Original:  To the best of our knowledge, we develop the first HDC-based method for drug discovery.
Revised:  To the best of our knowledge, this is the first HDC-based method for drug discovery.
Edit intent: coherence
Original: Various applications of machines in Internet of Things (IoT) require different bandwidths.
Revised: Various applications of machines in Internet of Things require different bandwidths.
Edit intent: clarity
Original:  Each machine may choose its RF interface , according to required bandwidth for sending its data .
Revised:  Each machine may choose its RF interface , according to required bandwidth .
Edit intent: clarity
Original:  We propose an optimal next-hop selection framework with  dynamic RF interface settings for sources with  same requested bandwidth.
Revised:  We propose an optimal next-hop selection framework with a dynamic RF interface settings for sources with same requested bandwidth.
Edit intent: fluency
Original:  We propose an optimal next-hop selection framework with  dynamic RF interface settings for sources with  same requested bandwidth.
Revised:  We propose an optimal next-hop selection framework with dynamic RF interface setting for sources with same requested bandwidth.
Edit intent: fluency
Original:  We propose an optimal next-hop selection framework with  dynamic RF interface settings for sources with  same requested bandwidth.
Revised:  We propose an optimal next-hop selection framework with dynamic RF interface settings for sources with the same requested bandwidth.
Edit intent: fluency
Original:  In this way, the efficiency and correct use of RF network resources can be improved.
Revised:  In this way, the efficient use of RF network resources can be improved.
Edit intent: clarity
Original:  The simulations show that , the average data rate of sources improved between 11.1\% to 117\%  and the average unmatched source  improved between 1.9\% and 5.3\%.
Revised:  The simulations show that the average data rate of sources improved between 11.1\% to 117\% and the average unmatched source improved between 1.9\% and 5.3\%.
Edit intent: fluency
Original:  The simulations show that , the average data rate of sources improved between 11.1\% to 117\%  and the average unmatched source  improved between 1.9\% and 5.3\%.
Revised:  The simulations show that , the average data rate of sources improved between 11.1\% to 117\% , and the average unmatched source improved between 1.9\% and 5.3\%.
Edit intent: fluency
Original: Various applications of machines in Internet of Things require different bandwidths.
Revised: Various applications which run on the machines in a network such as Internet-of-Things require different bandwidths.
Edit intent: clarity
Original:  Each machine may choose its RF interface in machine-to-machines or machine-to-base stations communications according to required bandwidth.
Revised:  So each machine may select one of its multiple Radio Frequency (RF) interfaces for machine-to-machine or machine-to base-station communications according to required bandwidth.
Edit intent: clarity
Original:  We propose an optimal next-hop selection framework with a dynamic RF interface setting for sources with the same requested bandwidth.
Revised:  We have proposed a generalized framework for joint dynamic optimal RF interface setting for sources with the same requested bandwidth.
Edit intent: clarity
Original:  The simulations show that the average data rate of sources improved between 11.1\% to 117 \%, and the average unmatched source number improved between 1.9\% and 5.3 \%.
Revised:  The simulations show that the average data rate of sources improved between 11.1\% to 117 \%.
Edit intent: coherence
Original: - \`a la Nguyen and Onak FOCS'08%DIFDELCMD < ] %%% -
Revised: - \`a la Nguyen and Onak %DIFDELCMD < ] %%% -
Edit intent: coherence