wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch, and the results demonstrate that PAGE  converges much faster than SGD in training and also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Revised:  Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch, and the results demonstrate that PAGE not only converges much faster than SGD in training and also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Edit intent: clarity
Original:  Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch, and the results demonstrate that PAGE  converges much faster than SGD in training and also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Revised:  Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch, and the results demonstrate that PAGE converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Edit intent: fluency
Original:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p  or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p  . We give a simple formula for the optimal choice of p . We prove tight lower bounds for nonconvex}{\epsilon^2}) for nonconvex finite-sum } problems, which are of independent interest.
Revised:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p _t or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p . We give a simple formula for the optimal choice of p . We prove tight lower bounds for nonconvex}{\epsilon^2}) for nonconvex finite-sum } problems, which are of independent interest.
Edit intent: meaning-changed
Original:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p  or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p  . We give a simple formula for the optimal choice of p . We prove tight lower bounds for nonconvex}{\epsilon^2}) for nonconvex finite-sum } problems, which are of independent interest.
Revised:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p _t . We give a simple formula for the optimal choice of p . We prove tight lower bounds for nonconvex}{\epsilon^2}) for nonconvex finite-sum } problems, which are of independent interest.
Edit intent: clarity
Original:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p  or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p  . We give a simple formula for the optimal choice of p . We prove tight lower bounds for nonconvex}{\epsilon^2}) for nonconvex finite-sum } problems, which are of independent interest.
Revised:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p . We give a simple formula for the optimal choice of p _t. Moreover, we prove the first tight lower bound \Omega(n+\frac{\sqrt{n}{\epsilon^2}) for nonconvex finite-sum } problems, which are of independent interest.
Edit intent: meaning-changed
Original:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p  or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p  . We give a simple formula for the optimal choice of p . We prove tight lower bounds for nonconvex}{\epsilon^2}) for nonconvex finite-sum } problems, which are of independent interest. Moreover, we prove matching upper bounds both in the}{\epsilon^2}) for nonconvex online problems, where b:= \min\{\sigma^2{\epsilon^2}, n\}.
Revised:  PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability p or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability 1-p . We give a simple formula for the optimal choice of p . We prove tight lower bounds for nonconvex}{\epsilon^2}) for nonconvex finite-sum } problems, which also leads to a tight lower bound \Omega(b+\frac{\sqrt{b}{\epsilon^2}) for nonconvex online problems, where b:= \min\{\sigma^2{\epsilon^2}, n\}.
Edit intent: meaning-changed
Original:  Then, we show that PAGE obtains the optimal convergence results O(n+\sqrt{n}{\epsilon^2}) (} finite-sum }{\epsilon^2}) (online) matching our lower bounds for both nonconvex finite-sum } and online regimes, which establish that PAGE is an optimal method .
Revised:  Then, we show that PAGE obtains the optimal convergence results O(n+\sqrt{n}{\epsilon^2}) (} finite-sum ) and O(b+\frac{\sqrt{b}{\epsilon^2}) (online) matching our lower bounds for both nonconvex finite-sum } and online regimes, which establish that PAGE is an optimal method .
Edit intent: meaning-changed
Original:  Then, we show that PAGE obtains the optimal convergence results O(n+\sqrt{n}{\epsilon^2}) (} finite-sum }{\epsilon^2}) (online) matching our lower bounds for both nonconvex finite-sum } and online regimes, which establish that PAGE is an optimal method .
Revised:  Then, we show that PAGE obtains the optimal convergence results O(n+\sqrt{n}{\epsilon^2}) (} finite-sum }{\epsilon^2}) (online) matching our lower bounds for both nonconvex finite-sum } and online problems .
Edit intent: clarity
Original:  condition, PAGE can automatically switch to a faster linear convergence rate {\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch , and the results demonstrate that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Revised:  condition, PAGE can automatically switch to a faster linear convergence rate O(\cdot\log \frac{1{\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch , and the results demonstrate that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Edit intent: meaning-changed
Original:  condition, PAGE can automatically switch to a faster linear convergence rate {\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch , and the results demonstrate that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Revised:  condition, PAGE can automatically switch to a faster linear convergence rate {\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch showing that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Edit intent: coherence
Original:  condition, PAGE can automatically switch to a faster linear convergence rate {\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch , and the results demonstrate that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
Revised:  condition, PAGE can automatically switch to a faster linear convergence rate {\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch , and the results demonstrate that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating the optimal theoretical results and confirming the practical superiority of PAGE.
Edit intent: clarity
Original:  In an experimental study, we compare a variety of algorithms with respect to their index-building and query times as well as their memory footprint . All of them yield a time/space trade-off for queries.
Revised:  In an experimental study, we compare a variety of algorithms with respect to their index-building and query times as well as their memory footprint on a diverse set of instances. Our experiments indicate that the query performance often depends strongly not only on the type of graph, but also on the result, i.e., reachable or unreachable. Furthermore, we show that previous algorithms are significantly sped up when combined with our new approach in almost all scenarios.
Edit intent: meaning-changed
Original:  Surprisingly, due to cache effects, a higher investment in space doesn't necessarily pay off: Reachability queries can often be answered even significantly faster than single memory accesses in a precomputed full reachability matrix.
Revised:  Surprisingly, due to cache effects, a higher investment in space doesn't necessarily pay off: Reachability queries can often be answered even faster than single memory accesses in a precomputed full reachability matrix.
Edit intent: clarity
Original:  From 1820 to 1920, the linearity between global PEC and world GDP justifies basic equations where, originally, PEC incorporates unskilled human labor that consumes and converts food energy .
Revised:  From 1820 to 1920, the linearity between global PEC and world GDP justifies basic equations where, originally, PEC incorporates unskilled human labor that consumes and converts energy from food .
Edit intent: clarity
Original:  In the following century, 1920-2016 , GDP grows quicker than PEC , displaying periods of linearity of the two variables , separated by distinct jumps  interpreted as radical technology shifts.
Revised:  In the following century, from 1920 to 2016 , GDP grows quicker than PEC , displaying periods of linearity of the two variables , separated by distinct jumps interpreted as radical technology shifts.
Edit intent: clarity
Original:  In the following century, 1920-2016 , GDP grows quicker than PEC , displaying periods of linearity of the two variables , separated by distinct jumps  interpreted as radical technology shifts.
Revised:  In the following century, 1920-2016 , GDP grows quicker than PEC , displaying periods of linearity of the two variables , separated by distinct jumps , which can be interpreted as radical technology shifts.
Edit intent: clarity
Original:  This paper is concerned with a fundamental robustness analysis for instability of an equilibrium point in the presence of a dynamic perturbation. Our analysis is based on the linearized system around the equilibrium point, which may move due to the perturbation .
Revised:  This paper is concerned with a robust instability analysis for the single-input-single-output unstable linear time-invariant (LTI) system under dynamic perturbations. The nominal system itself is possibly perturbed by the static gain of the uncertainty, which would be the case when a nonlinear uncertain system is linearized around an equilibrium point .
Edit intent: meaning-changed
Original:  one is on characterizations of linear systems for which the robust instability radius can be calculated exactly  and the other is on the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account .
Revised:  one is on a partial characterization of unperturbed nominal systems for which the robust instability radius can be calculated exactly and the other is on the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account .
Edit intent: meaning-changed
Original:  one is on characterizations of linear systems for which the robust instability radius can be calculated exactly  and the other is on the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account .
Revised:  one is on characterizations of linear systems for which the robust instability radius can be calculated exactly , and the other is on the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account .
Edit intent: fluency
Original:  one is on characterizations of linear systems for which the robust instability radius can be calculated exactly  and the other is on the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account .
Revised:  one is on characterizations of linear systems for which the robust instability radius can be calculated exactly and the other is a numerically tractable procedure for calculating the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account .
Edit intent: meaning-changed
Original:  one is on characterizations of linear systems for which the robust instability radius can be calculated exactly  and the other is on the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account .
Revised:  one is on characterizations of linear systems for which the robust instability radius can be calculated exactly and the other is on the exact instability margin for nominal systems parametrized by a perturbation parameter .
Edit intent: meaning-changed
Original:  The results are applied to the Repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness  is confirmed by numerical simulations.
Revised:  The results are applied to the Repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness of our linear robust instability analysis is confirmed by numerical simulations.
Edit intent: meaning-changed
Original:  In the field of Non-Intrusive Load Monitoring (NILM), performance evaluation can be conducted on real-world aggregate signals, provided by smart energy meters , or artificial superpositions of individual load signals (i.e., denoised aggregates).
Revised:  In the field of Non-Intrusive Load Monitoring (NILM), performance evaluation can be conducted on real-world aggregate signals, provided by smart energy meters or artificial superpositions of individual load signals (i.e., denoised aggregates).
Edit intent: fluency
Original:  On a large spreadsheet corpus with 196k tables and 306k charts, we show that Table2Charts could learn a shared representation of table fields so that tasks on different chart types could mutually enhance each other.
Revised:  On a large spreadsheet corpus with 167k tables and 271k charts, we show that Table2Charts could learn a shared representation of table fields so that tasks on different chart types could mutually enhance each other.
Edit intent: meaning-changed
Original:  Table2Charts has >0.61 recall at top-3 and >0.49 recall at top-1 for both single-type and multi-type chart recommendation tasks .
Revised:  Table2Charts has >0.61 recall at top-3 and >0.49 recall at top-1 for both single-type and multi-type task (with almost doubled recall numbers R@3=0.62 and R@1=0.44) and human evaluations .
Edit intent: meaning-changed
Original:  On a large spreadsheet corpus with 167k tables and 271k charts, we show that Table2Charts could learn a shared representation of table fields so that  tasks on different chart types could mutually enhance each other.
Revised:  On a large spreadsheet corpus with 165k tables and 266k charts, we show that Table2Charts could learn a shared representation of table fields so that tasks on different chart types could mutually enhance each other.
Edit intent: meaning-changed
Original:  On a large spreadsheet corpus with 167k tables and 271k charts, we show that Table2Charts could learn a shared representation of table fields so that  tasks on different chart types could mutually enhance each other.
Revised:  On a large spreadsheet corpus with 167k tables and 271k charts, we show that Table2Charts could learn a shared representation of table fields so that recommendation tasks on different chart types could mutually enhance each other.
Edit intent: meaning-changed
Original:  Table2Charts outperforms other chart recommendation systems in both multi-type task (with almost doubled recall numbers R@3= 0.62 and R@1= 0.44 ) and human evaluations.
Revised:  Table2Charts outperforms other chart recommendation systems in both multi-type task (with doubled recall numbers R@3= 0.62 and R@1= 0.44 ) and human evaluations.
Edit intent: clarity
Original:  Table2Charts outperforms other chart recommendation systems in both multi-type task (with almost doubled recall numbers R@3= 0.62 and R@1= 0.44 ) and human evaluations.
Revised:  Table2Charts outperforms other chart recommendation systems in both multi-type task (with almost doubled recall numbers R@3= 0.61 and R@1= 0.44 ) and human evaluations.
Edit intent: meaning-changed
Original:  Table2Charts outperforms other chart recommendation systems in both multi-type task (with almost doubled recall numbers R@3= 0.62 and R@1= 0.44 ) and human evaluations.
Revised:  Table2Charts outperforms other chart recommendation systems in both multi-type task (with almost doubled recall numbers R@3= 0.62 and R@1= 0.43 ) and human evaluations.
Edit intent: meaning-changed
Original:  We introduce here a new family of fixed point iterations that include the classical iterations for the numerical computation of G . We perform a detailed convergence analysis and prove that the iterations in the new class converge faster than the classical iterations.
Revised:  A new family of fixed point iterations that include the classical iterations for the numerical computation of G . We perform a detailed convergence analysis and prove that the iterations in the new class converge faster than the classical iterations.
Edit intent: clarity
Original:  We introduce here a new family of fixed point iterations that include the classical iterations for the numerical computation of G . We perform a detailed convergence analysis and prove that the iterations in the new class converge faster than the classical iterations.
Revised:  We introduce here a new family of fixed point iterations that include the classical iterations for the numerical computation of G , that includes the classical iterations, is introduced. A detailed convergence analysis and prove that the iterations in the new class converge faster than the classical iterations.
Edit intent: meaning-changed
Original:  We introduce here a new family of fixed point iterations that include the classical iterations for the numerical computation of G . We perform a detailed convergence analysis and prove that the iterations in the new class converge faster than the classical iterations.
Revised:  We introduce here a new family of fixed point iterations that include the classical iterations for the numerical computation of G . We perform a detailed convergence analysis proves that the iterations in the new class converge faster than the classical iterations.
Edit intent: coherence
Original:  To find out how developers and their productivity were affected, we distributed two surveys (with  3,634 responses )---weeks apart to understand the presence and prevalence of the benefits, challenges, and opportunities to improve this special circumstance of remote work.
Revised:  To find out how developers and their productivity were affected, we distributed two surveys (with a combined total of 3,634 responses )---weeks apart to understand the presence and prevalence of the benefits, challenges, and opportunities to improve this special circumstance of remote work.
Edit intent: meaning-changed
Original:  To find out how developers and their productivity were affected, we distributed two surveys (with  3,634 responses )---weeks apart to understand the presence and prevalence of the benefits, challenges, and opportunities to improve this special circumstance of remote work.
Revised:  To find out how developers and their productivity were affected, we distributed two surveys (with 3,634 responses that answered all required questions) -- weeks apart to understand the presence and prevalence of the benefits, challenges, and opportunities to improve this special circumstance of remote work.
Edit intent: meaning-changed
Original: We study the least squares problem x_{b,\omega} := \min _{x \in S} \|(A + \omega I)^{-1/2} (b - Ax)\|_2, with A = A^*, for a subspace S of F^n (F = R or C), and \omega > -min(A).
Revised: We study the problem x_{b,\omega} := \min _{x \in S} \|(A + \omega I)^{-1/2} (b - Ax)\|_2, with A = A^*, for a subspace S of F^n (F = R or C), and \omega > -min(A).
Edit intent: clarity
Original: We study the least squares problem x_{b,\omega} := \min _{x \in S} \|(A + \omega I)^{-1/2} (b - Ax)\|_2, with A = A^*, for a subspace S of F^n (F = R or C), and \omega > -min(A).
Revised: We study the least squares problem x_{b,\omega} := \text{arg min _{x \in S} \|(A + \omega I)^{-1/2} (b - Ax)\|_2, with A = A^*, for a subspace S of F^n (F = R or C), and \omega > -min(A).
Edit intent: meaning-changed
Original:  \to  We study several properties of \mathbf{Ind}_A(\mathcal{S}) in relation to A and \mathcal{S}.
Revised:  The problem is also such that when A is positive and S is a Krylov subspace, it reduces to CG for \omega = 0 and to MINRES for \omega\to We study several properties of \mathbf{Ind}_A(\mathcal{S}) in relation to A and \mathcal{S}.
Edit intent: meaning-changed
Original:  We show that in general, the dimension of the affine subspace \mathcal{X}_b containing the solutions x_{b,\omega} can be smaller than \mathbf{Ind}_A(\mathcal{S}) for all b.
Revised:  We show that the dimension of the affine subspace \mathcal{X}_b containing the solutions x_{b,\omega} can be smaller than \mathbf{Ind}_A(\mathcal{S}) for all b.
Edit intent: clarity
Original:  However, we also exhibit some sufficient conditions on A and \mathcal{S}, under which a related set \mathcal{X} := \text{Span}{\{x_{b,\omega} - x_{b,\mu} \mid b \in \mathbb{F}^n, \omega,\mu > -\lambda_{min}(A)\}} has dimension equal to \mathbf{Ind}_A(\mathcal{S}).
Revised:  However, we also exhibit some sufficient conditions on A and \mathcal{S}, under which \mathcal{X} := \text{Span}{\{x_{b,\omega} - x_{b,\mu} \mid b \in \mathbb{F}^n, \omega,\mu > -\lambda_{min}(A)\}} has dimension equal to \mathbf{Ind}_A(\mathcal{S}).
Edit intent: clarity