wanyu/IteraTeR_v2 huggingface dataset:
Original: We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form E(\mathbf{u f(u)+\tau_1 \|u\|_1 + \tau_2 \|D\,u\|_1, where f is a smooth convex function and D represents a linear operator, e.g. a finite difference operator, as in anisotropic Total Variation and fused-lasso regularizations.
Revised: We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form f(u)+\tau_1 \|u\|_1 + \tau_2 \|D\,u\|_1, where f is a smooth convex function and D represents a linear operator, e.g. a finite difference operator, as in anisotropic Total Variation and fused-lasso regularizations.
Edit intent: coherence
Original:  we study a generalization of the fundamental makespan scheduling P||Cmax problem which we call the " bounded job start scheduling problem " . Given a set of jobs, each specified by an integer processing time p_j, that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound g<=m on the number of jobs that may simultaneously begin per unit of time.
Revised:  we study a generalization of the fundamental makespan scheduling P||Cmax problem which we call the bounded job start scheduling problem " . Given a set of jobs, each specified by an integer processing time p_j, that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound g<=m on the number of jobs that may simultaneously begin per unit of time.
Edit intent: fluency
Original:  we study a generalization of the fundamental makespan scheduling P||Cmax problem which we call the " bounded job start scheduling problem " . Given a set of jobs, each specified by an integer processing time p_j, that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound g<=m on the number of jobs that may simultaneously begin per unit of time.
Revised:  we study a generalization of the fundamental makespan scheduling P||Cmax problem which we call the " bounded job start scheduling problem . Given a set of jobs, each specified by an integer processing time p_j, that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound g<=m on the number of jobs that may simultaneously begin per unit of time.
Edit intent: fluency
Original:  Then, we explore the idea of scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints.
Revised:  Then, we explore scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints.
Edit intent: clarity
Original:  Finally , we exploit machine augmentation and lexicographic optimization , which is useful for P||Cmax under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in good trade-offs in terms of makespan and number of used machines.
Revised:  Finally , we exploit machine augmentation and lexicographic optimization to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in good trade-offs in terms of makespan and number of used machines.
Edit intent: coherence
Original:  Finally , we exploit machine augmentation and lexicographic optimization , which is useful for P||Cmax under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in good trade-offs in terms of makespan and number of used machines.
Revised:  Finally , we exploit machine augmentation and lexicographic optimization , which is useful for P||Cmax under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in a low number of used machines.
Edit intent: clarity
Original: For several years , scholars have studied cooperative learning and its outcomes in the educational context.
Revised: For several decades , scholars have studied cooperative learning and its outcomes in the educational context.
Edit intent: clarity
Original: For several years , scholars have studied cooperative learning and its outcomes in the educational context.
Revised: For several years , scholars have studied cooperation and its outcomes in the educational context.
Edit intent: clarity
Original:  Yet, little is known on how different instructional strategies impact the relationship between cooperation and learning.
Revised:  Yet, we lack a complete understanding of how different instructional strategies impact the relationship between cooperation and learning.
Edit intent: clarity
Original:  Here we studied how different instructional strategies lead to different social configurations and their differences in academic performance.
Revised:  Here we studied how different instructional strategies led to different social configurations and their differences in academic performance.
Edit intent: fluency
Original:   In a highly clustered networks (which contains highly redundant information) students perform well-structured problems better than ill-structured problems.
Revised:  In a highly clustered network (which contains highly redundant information) students perform well-structured problems better than ill-structured problems.
Edit intent: fluency
Original:   In a highly clustered networks (which contains highly redundant information) students perform well-structured problems better than ill-structured problems.
Revised:  In a highly clustered networks (which contains redundant information) students perform well-structured problems better than ill-structured problems.
Edit intent: fluency
Original:   In a highly clustered networks (which contains highly redundant information) students perform well-structured problems better than ill-structured problems.
Revised:  In a highly clustered networks (which contains highly redundant information) , students performed well-structured problems better than ill-structured problems.
Edit intent: fluency
Original:  In contrast, students with access to network structural holes (which enable access to more diverse information) perform ill-structured problems better than well-structured problems.
Revised:  In contrast, students with access to network structural holes (which enable access to more diverse information) performed ill-structured problems better than well-structured problems.
Edit intent: fluency
Original:  Finally, ill-structured problems can promote creative thinking, but only if instructors guide the solving process and motivate students to engage in the appropriate cognitive demands these problems entail.
Revised:  Finally, ill-structured problems could promote creative thinking, but only if instructors guide the solving process and motivate students to engage in the appropriate cognitive demands these problems entail.
Edit intent: fluency
Original:  Finally, ill-structured problems can promote creative thinking, but only if instructors guide the solving process and motivate students to engage in the appropriate cognitive demands these problems entail.
Revised:  Finally, ill-structured problems can promote creative thinking, provided that instructors guide the solving process and motivate students to engage in the appropriate cognitive demands these problems entail.
Edit intent: clarity
Original:  Our results suggest that teaching and instructional strategies have a key role in cooperative learning;
Revised:  Our results suggest that teaching and instructional strategies play an important role in cooperative learning;
Edit intent: clarity
Original:  therefore, educators implementing cooperative learning methods have to accompany them with a proper instructional strategy
Revised:  therefore, educators implementing cooperative learning methods have to accompany them with adequate instructional strategy.
Edit intent: clarity
Original: A novel multiscale method for non M-matrices using Multiscale Restricted Smoothed Basis (MsRSB) functions is presented.
Revised: A novel method to enable application of the Multiscale Restricted Smoothed Basis (MsRSB) functions is presented.
Edit intent: clarity
Original: A novel multiscale method for non M-matrices using Multiscale Restricted Smoothed Basis (MsRSB) functions is presented.
Revised: A novel multiscale method for non M-matrices using Multiscale Restricted Smoothed Basis (MsRSB) method to non M-matrices is presented.
Edit intent: clarity
Original: The traditional time series models , such as VAR, ARIMA, Holt-Winters, are frequently used for short-term forecasts  .
Revised: The models VAR, ARIMA, Holt-Winters, are frequently used for short-term forecasts .
Edit intent: clarity
Original:  Our goal is to fit (with high precision) the data into a multi-dimensional system of differential equations, which has a simple form and exhibits clear long-term trends , which characterize various scenarios ( influenced by externalities ) of the process's future outcomes .
Revised:  Our goal is to fit (with high precision) the data into a multi-dimensional system of differential equations, which has a simple form and exhibits clear long-term trends , which characterize various scenarios ( influenced by externalities .
Edit intent: clarity
Original:  The beliefs of the market about yet unobserved extreme jumps and pricing kernel and can be recovered: the market prices allow one to see "the shape of things to come".
Revised:  The beliefs of the market about yet unobserved extreme jumps and pricing kernel can be recovered: the market prices allow one to see "the shape of things to come".
Edit intent: fluency
Original:  To address this issue, we propose a new  approach, NIS (Neural Index Search), which searches for the optimal index structure using a neural network.
Revised:  To address this issue, we propose a new indexing approach, NIS (Neural Index Search), which searches for the optimal index structure using a neural network.
Edit intent: clarity
Original:  Experiments show that the auto-generated index by NIS can achieve a comparable performance with the state-of-the-art index.
Revised:  Experiments show that the auto-tuned index built by NIS can achieve a comparable performance with the state-of-the-art index.
Edit intent: clarity
Original:  Experiments show that the auto-generated index by NIS can achieve a comparable performance with the state-of-the-art index.
Revised:  Experiments show that the auto-generated index by NIS can achieve a better performance than the state-of-the-art index.
Edit intent: clarity
Original: Rate-distortion (RD) analysis is at the heart of lossy data compression.
Revised: Rate-distortion (RD) theory is at the heart of lossy data compression.
Edit intent: clarity
Original:  Here we extend the idea to generalized RD (GRD) functions of compressed videos that characterize the visual quality of a  video and its encoding profile, which includes not only bit rate but also other attributes such as video resolution .
Revised:  Here we aim to model the generalized RD (GRD) functions of compressed videos that characterize the visual quality of a video and its encoding profile, which includes not only bit rate but also other attributes such as video resolution .
Edit intent: clarity
Original:  Here we extend the idea to generalized RD (GRD) functions of compressed videos that characterize the visual quality of a  video and its encoding profile, which includes not only bit rate but also other attributes such as video resolution .
Revised:  Here we extend the idea to generalized RD (GRD) trade-off between the visual quality of a video and its encoding profile, which includes not only bit rate but also other attributes such as video resolution .
Edit intent: clarity
Original:  Here we extend the idea to generalized RD (GRD) functions of compressed videos that characterize the visual quality of a  video and its encoding profile, which includes not only bit rate but also other attributes such as video resolution .
Revised:  Here we extend the idea to generalized RD (GRD) functions of compressed videos that characterize the visual quality of a compressed video and its encoding profile, which includes not only bit rate but also other attributes such as video resolution .
Edit intent: fluency
Original:  Using the database, we demonstrate that real-world GRD functions are clustered in a low-dimensional subspace in the theoretical space of all possible GRD functions . Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD (eGRD) method to accurately estimate the GRD function of a source video content from only a few queries.
Revised:  Using the database, we demonstrate that real-world GRD functions , which turn out to live in a low-dimensional subspace in the theoretical space of all possible GRD functions . Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD (eGRD) method to accurately estimate the GRD function of a source video content from only a few queries.
Edit intent: coherence
Original:  Using the database, we demonstrate that real-world GRD functions are clustered in a low-dimensional subspace in the theoretical space of all possible GRD functions . Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD (eGRD) method to accurately estimate the GRD function of a source video content from only a few queries.
Revised:  Using the database, we demonstrate that real-world GRD functions are clustered in a low-dimensional subspace of \mathcal{W . Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD (eGRD) method to accurately estimate the GRD function of a source video content from only a few queries.
Edit intent: clarity
Original:  Using the database, we demonstrate that real-world GRD functions are clustered in a low-dimensional subspace in the theoretical space of all possible GRD functions . Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD (eGRD) method to accurately estimate the GRD function of a source video content from only a few queries.
Revised:  Using the database, we demonstrate that real-world GRD functions are clustered in a low-dimensional subspace in the theoretical space of all possible GRD functions . Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD method to accurately estimate the GRD function of a source video content from only a few queries.
Edit intent: clarity
Original:  Experimental results  show that the proposed algorithm significantly outperforms state-of-the-art empirical RD estimation methods  in accuracy and efficiency.
Revised:  Experimental results show that the proposed algorithm significantly outperforms state-of-the-art empirical RD estimation methods both in accuracy and efficiency.
Edit intent: clarity
Original:  Finally , we demonstrate the usefulness of the proposed eGRD model in a practical application: video codec comparison.
Revised:  Last , we demonstrate the usefulness of the proposed eGRD model in a practical application: video codec comparison.
Edit intent: fluency
Original:  Finally , we demonstrate the usefulness of the proposed eGRD model in a practical application: video codec comparison.
Revised:  Finally , we demonstrate the promise of the proposed eGRD model in a practical application: video codec comparison.
Edit intent: clarity
Original:  Finally , we demonstrate the usefulness of the proposed eGRD model in a practical application: video codec comparison.
Revised:  Finally , we demonstrate the usefulness of the proposed model in video codec comparison.
Edit intent: clarity
Original:  This framework is developed in Pytorch, and it enables distributed-memory execution on cloud or supercomputer systems.
Revised:  This framework is developed in Pytorch, and it enables distributed-memory execution on both cloud and supercomputer systems.
Edit intent: clarity
Original:  PyHessian enables fast computations of the top Hessian eigenvalue , the Hessian trace, and the full Hessian eigenvalue  density.
Revised:  PyHessian enables fast computations of the top Hessian eigenvalues , the Hessian trace, and the full Hessian eigenvalue density.
Edit intent: fluency
Original:  To illustrate this, we apply PyHessian to analyze the effect of residual connections and Batch Normalization layers on the smoothness of the loss landscape  .
Revised:  To illustrate this, we apply PyHessian to analyze the effect of residual connections and Batch Normalization layers on the smoothness of the loss landscape during training .
Edit intent: clarity
Original:  One recent claim, based on simpler first-order analysis, is that residual connections and batch normalization make the loss landscape ``smoother '', thus making it easier for Stochastic Gradient Descent to converge to a good solution.
Revised:  One recent claim, based on simpler first-order analysis, is that residual connections and Batch Normalization make the loss landscape ``smoother '', thus making it easier for Stochastic Gradient Descent to converge to a good solution.
Edit intent: fluency
Original:  One recent claim, based on simpler first-order analysis, is that residual connections and batch normalization make the loss landscape ``smoother '', thus making it easier for Stochastic Gradient Descent to converge to a good solution.
Revised:  One recent claim, based on simpler first-order analysis, is that residual connections and batch normalization make the loss landscape ``smoother ,'' thus making it easier for Stochastic Gradient Descent to converge to a good solution.
Edit intent: fluency
Original:  In particular, we find that batch normalization layers do not necessarily make the loss landscape smoother, especially for shallow networks.
Revised:  In particular, we find that Batch Normalization layers do not necessarily make the loss landscape smoother, especially for shallow networks.
Edit intent: fluency
Original:  We have open-sourced our PyHessian framework for Hessian spectrum computation.
Revised:  We have open-sourced the PyHessian framework for Hessian spectrum computation.
Edit intent: fluency
Original: We present PyHessian , a new scalable framework that enables fast computation of Hessian (i.e., second-order derivative) information for deep neural networks.
Revised: We present PYHESSIAN , a new scalable framework that enables fast computation of Hessian (i.e., second-order derivative) information for deep neural networks.
Edit intent: fluency
Original:  To illustrate this, we apply PyHessian to analyze the effect of residual connections and Batch Normalization layers on the smoothness of the loss landscape during training .
Revised:  To illustrate this, we analyze the effect of residual connections and Batch Normalization layers on the smoothness of the loss landscape during training .
Edit intent: clarity
Original:  To illustrate this, we apply PyHessian to analyze the effect of residual connections and Batch Normalization layers on the smoothness of the loss landscape during training .
Revised:  To illustrate this, we apply PyHessian to analyze the effect of residual connections and Batch Normalization layers on the trainability of neural networks .
Edit intent: clarity
Original:  One recent claim, based on simpler first-order analysis, is that residual connections and Batch Normalization make the loss landscape ``smoother, '' thus making it easier for Stochastic Gradient Descent to converge to a good solution.
Revised:  One recent claim, based on simpler first-order analysis, is that residual connections and Batch Normalization make the loss landscape smoother, thus making it easier for Stochastic Gradient Descent to converge to a good solution.
Edit intent: fluency
Original:  This analysis leads to finer-scale insight , demonstrating that  while conventional wisdom is sometimes validated, in other cases it is simply incorrect.
Revised:  This analysis leads to finer-scale insights , demonstrating that while conventional wisdom is sometimes validated, in other cases it is simply incorrect.
Edit intent: fluency
Original:  This analysis leads to finer-scale insight , demonstrating that  while conventional wisdom is sometimes validated, in other cases it is simply incorrect.
Revised:  This analysis leads to finer-scale insight , demonstrating that , while conventional wisdom is sometimes validated, in other cases it is simply incorrect.
Edit intent: fluency
Original:  In particular, we find that Batch Normalization layers do not necessarily make the loss landscape smoother, especially for shallow networks.
Revised:  In particular, we find that Batch Normalization does not necessarily make the loss landscape smoother, especially for shallow networks.
Edit intent: clarity
Original: In this paper, we provide a control-theoretic perspective on optimal tensor optimization algorithms for minimizing a convex function in a finite-dimensional Euclidean space.
Revised: We provide a control-theoretic perspective on optimal tensor optimization algorithms for minimizing a convex function in a finite-dimensional Euclidean space.
Edit intent: clarity
Original: In this paper, we provide a control-theoretic perspective on optimal tensor optimization algorithms for minimizing a convex function in a finite-dimensional Euclidean space.
Revised: In this paper, we provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space.
Edit intent: clarity
Original:  Given a function \Phi: R^d \rightarrow R that is convex and twice-continuously differentiable, we study an ordinary differential equation (ODE) that is governed by the gradient operator \nabla \Phi and a positive control parameter \lambda(t) that tends to infinity as t \rightarrow +\infty.
Revised:  Given a function \Phi: R^d \rightarrow R that is convex and twice continuously differentiable, we study an ordinary differential equation (ODE) that is governed by the gradient operator \nabla \Phi and a positive control parameter \lambda(t) that tends to infinity as t \rightarrow +\infty.
Edit intent: clarity
Original:  Given a function \Phi: R^d \rightarrow R that is convex and twice-continuously differentiable, we study an ordinary differential equation (ODE) that is governed by the gradient operator \nabla \Phi and a positive control parameter \lambda(t) that tends to infinity as t \rightarrow +\infty.
Revised:  Given a function \Phi: R^d \rightarrow R that is convex and twice-continuously differentiable, we study a closed-loop control system that is governed by the gradient operator \nabla \Phi and a positive control parameter \lambda(t) that tends to infinity as t \rightarrow +\infty.
Edit intent: clarity
Original:  Given a function \Phi: R^d \rightarrow R that is convex and twice-continuously differentiable, we study an ordinary differential equation (ODE) that is governed by the gradient operator \nabla \Phi and a positive control parameter \lambda(t) that tends to infinity as t \rightarrow +\infty.
Revised:  Given a function \Phi: R^d \rightarrow R that is convex and twice-continuously differentiable, we study an ordinary differential equation (ODE) that is governed by the operators \nabla \Phi and a positive control parameter \lambda(t) that tends to infinity as t \rightarrow +\infty.
Edit intent: clarity