wanyu/IteraTeR_v2 huggingface dataset:
Original: In this work , we present an information propagation game on a network where the information is originated from a sponsor and the sponsor is willing to pay a fixed total budget to the nodes who propagate the information.
Revised: In this paper , we present an information propagation game on a network where the information is originated from a sponsor and the sponsor is willing to pay a fixed total budget to the nodes who propagate the information.
Edit intent: clarity
Original: In this work , we present an information propagation game on a network where the information is originated from a sponsor and the sponsor is willing to pay a fixed total budget to the nodes who propagate the information.
Revised: In this work , we present an information propagation game on a network where the information is originated from a sponsor who is willing to pay a fixed total budget to the nodes who propagate the information.
Edit intent: coherence
Original: In this work , we present an information propagation game on a network where the information is originated from a sponsor and the sponsor is willing to pay a fixed total budget to the nodes who propagate the information.
Revised: In this work , we present an information propagation game on a network where the information is originated from a sponsor and the sponsor is willing to pay a fixed total budget to the players who propagate the information.
Edit intent: clarity
Original:   The goal is to design a mechanism to share the budget such that all nodes are incentivized to propagate the information to all their neighbours.
Revised:  The goal is to design a mechanism to distribute the budget such that all nodes are incentivized to propagate the information to all their neighbours.
Edit intent: fluency
Original:   The goal is to design a mechanism to share the budget such that all nodes are incentivized to propagate the information to all their neighbours.
Revised:  The goal is to design a mechanism to share the budget such that all players in the social network are incentivized to propagate the information to all their neighbours.
Edit intent: clarity
Original:   The goal is to design a mechanism to share the budget such that all nodes are incentivized to propagate the information to all their neighbours.
Revised:  The goal is to design a mechanism to share the budget such that all nodes are incentivized to propagate information to all their neighbours.
Edit intent: fluency
Original:  We also consider the cases whether the budget has to be completely shared .
Revised:  We also consider the cases where the budget has to be completely shared .
Edit intent: clarity
Original: We consider the problem of recovering communities of users and communities of items (such as movies) based on a partially observed rating matrix as well as side-information in the form of similarity graphs of the users and items.
Revised: We consider the problem of recovering communities of users and items based on a partially observed rating matrix as well as side-information in the form of similarity graphs of the users and items.
Edit intent: coherence
Original: We consider the problem of recovering communities of users and communities of items (such as movies) based on a partially observed rating matrix as well as side-information in the form of similarity graphs of the users and items.
Revised: We consider the problem of recovering communities of users and communities of items (such as movies) based on a partially observed matrix together with side-information in the form of similarity graphs of the users and items.
Edit intent: clarity
Original:  Our information-theoretic results quantify the benefits of the two-sided graph side-information for recovery, and further analysis reveals that the two pieces of graph side-information produce an interesting synergistic effect under certain scenarios .
Revised:  Our information-theoretic results quantify the benefits of the two-sided graph side-information for recovery, and further analysis reveals that the two pieces of graph side-information produce an interesting synergistic effect .
Edit intent: clarity
Original: The damaging effects of hate speech in social media are evident during the last few years, and several organizations, researchers and the social media platforms themselves have tried to harness them without great success.
Revised: The damaging effects of hate speech on social media are evident during the last few years, and several organizations, researchers and the social media platforms themselves have tried to harness them without great success.
Edit intent: clarity
Original: The damaging effects of hate speech in social media are evident during the last few years, and several organizations, researchers and the social media platforms themselves have tried to harness them without great success.
Revised: The damaging effects of hate speech in social media are evident during the last few years, and several organizations, researchers and social media platforms themselves have tried to harness them without great success.
Edit intent: clarity
Original: The damaging effects of hate speech in social media are evident during the last few years, and several organizations, researchers and the social media platforms themselves have tried to harness them without great success.
Revised: The damaging effects of hate speech in social media are evident during the last few years, and several organizations, researchers and the social media platforms tried to harness them without great success.
Edit intent: clarity
Original:  Additionally, we present a number of state-of-the-art deep learning architectures for hate speech detection and use these datasets to train and evaluate them.
Revised:  Additionally, we experiment with state-of-the-art deep learning architectures for hate speech detection and use these datasets to train and evaluate them.
Edit intent: clarity
Original:  Experimentally, BNet2 and the Fourier transform initialization strategy are tested on various tasks, including approximating Fourier transform operator, end-to-end solvers of linear and nonlinear PDEs in 1D , and denoising and deblurring of 1D signals.
Revised:  Experimentally, BNet2 and the Fourier transform initialization strategy are tested on various tasks, including approximating Fourier transform operator, end-to-end solvers of linear and nonlinear PDEs , and denoising and deblurring of 1D signals.
Edit intent: clarity
Original:   Fourier transform initialized BNet2 and CNN consistently improve the training and testing accuracy over the randomly initialized CNN.
Revised:  And Fourier transform initialized BNet2 and CNN consistently improve the training and testing accuracy over the randomly initialized CNN.
Edit intent: fluency
Original: A standard approach to compute the roots of a univariate polynomial is to compute the eigenvalues of an associated confederate matrix instead, such as, for instance the companion or comrade matrix.
Revised: A standard approach to compute the roots of a univariate polynomial is to compute the eigenvalues of an associated confederate matrix instead, such as, for instance the companion or comrade matrix.
Edit intent: fluency
Original:  While a sample complexity lower bound precludes sublinear algorithms for arbitrary PSD matices , we provide the first sublinear time and query algorithms when the corruption on the diagonal entries is bounded.
Revised:  While a sample complexity lower bound precludes sublinear algorithms for arbitrary PSD matrices , we provide the first sublinear time and query algorithms when the corruption on the diagonal entries is bounded.
Edit intent: fluency
Original:  They also showed that any relative-error low-rank approximation algorithm must query %DIFDELCMD < \Omega%%%  (nk/\epsilon) entries of A, and closing this gap is an important openquestion .
Revised:  They also showed that any relative-error low-rank approximation algorithm must query %DIFDELCMD < \Omega%%% (nk/\epsilon) entries of A, this gap has since remained open .
Edit intent: clarity
Original:  Our main result is to resolve this question by showing an algorithm that queries an optimal (nk/\epsilon) entries of A and outputs a relative-error low-rank approximation in (n\cdot (k/\epsilon)^{\omega-1}) time.
Revised:  Our main result is to resolve this question by obtaining an optimal algorithm that queries an optimal (nk/\epsilon) entries of A and outputs a relative-error low-rank approximation in (n\cdot (k/\epsilon)^{\omega-1}) time.
Edit intent: clarity
Original:  Our main result is to resolve this question by showing an algorithm that queries an optimal (nk/\epsilon) entries of A and outputs a relative-error low-rank approximation in (n\cdot (k/\epsilon)^{\omega-1}) time.
Revised:  Our main result is to resolve this question by showing an algorithm that queries O (nk/\epsilon) entries of A and outputs a relative-error low-rank approximation in (n\cdot (k/\epsilon)^{\omega-1}) time.
Edit intent: clarity
Original:  Our main result is to resolve this question by showing an algorithm that queries an optimal (nk/\epsilon) entries of A and outputs a relative-error low-rank approximation in (n\cdot (k/\epsilon)^{\omega-1}) time.
Revised:  Our main result is to resolve this question by showing an algorithm that queries an optimal (nk/\epsilon) entries of A and outputs a relative-error low-rank approximation in O(n (k/\epsilon)^{\omega-1}) time.
Edit intent: clarity
Original:  One recent approach proposes self-supervision based on non-rigid reconstruction.
Edit intent: coherence
Original:  Our approach significantly outperforms both existing non-rigid reconstruction methods that do not use learned data terms, as well as learning-based approaches that only use self-supervision.
Revised:  Our approach significantly outperforms existing non-rigid reconstruction methods that do not use learned data terms, as well as learning-based approaches that only use self-supervision.
Edit intent: clarity
Original: In this paper, we develop an approximation theory for deep neural networks that is based on the concept of a catalog network . Catalog networks are generalizations of standard neural networks in which the nonlinear activation functions can vary from layer to layer as long as they are chosen from a predefined catalog of continuous functions.
Revised: In this paper, we develop an approximation theory for deep neural networks that is based on the notion of a catalog network . Catalog networks are generalizations of standard neural networks in which the nonlinear activation functions can vary from layer to layer as long as they are chosen from a predefined catalog of continuous functions.
Edit intent: fluency
Original: In this paper, we develop an approximation theory for deep neural networks that is based on the concept of a catalog network . Catalog networks are generalizations of standard neural networks in which the nonlinear activation functions can vary from layer to layer as long as they are chosen from a predefined catalog of continuous functions.
Revised: In this paper, we develop an approximation theory for deep neural networks that is based on the concept of a catalog network , which is a generalization of a standard neural network in which the nonlinear activation functions can vary from layer to layer as long as they are chosen from a predefined catalog of continuous functions.
Edit intent: coherence
Original: In this paper, we develop an approximation theory for deep neural networks that is based on the concept of a catalog network . Catalog networks are generalizations of standard neural networks in which the nonlinear activation functions can vary from layer to layer as long as they are chosen from a predefined catalog of continuous functions.
Revised: In this paper, we develop an approximation theory for deep neural networks that is based on the concept of a catalog network . Catalog networks are generalizations of standard neural networks in which the nonlinear activation functions can vary from layer to layer as long as they are chosen from a predefined catalog of functions.
Edit intent: clarity
Original:  We apply the theory of catalog networks to demonstrate that neural networks can overcome the curse of dimensionality in different high-dimensional approximation problems .
Revised:  We apply the theory of catalog networks to demonstrate that neural networks can overcome the curse of dimensionality .
Edit intent: clarity
Original:  The dataset consists of 5, 300 subjects generating 81, 658 labeled audio clips in Hindi, Marathi and English.
Revised:  The dataset consists of 5, 301 subjects generating 81, 658 labeled audio clips in Hindi, Marathi and English.
Edit intent: fluency
Original:  These labels represent expert opinions on the ability of the child to read at a specified level.
Revised:  These labels represent expert opinions on the child's ability to read at a specified level.
Edit intent: clarity
Original:  Early results indicate that we can achieve a prediction accuracy of 86 percent for the English language.
Revised:  Early results indicate that we can achieve a prediction accuracy of 86 \% for the English language.
Edit intent: fluency
Original:  The twist in the multistage setting is that the found solutions may not differ too much between subsequent layers.
Revised:  The twist in the multistage setting is that the solutions found must not differ too much between subsequent layers.
Edit intent: clarity
Original:  We relax on this notion by introducing a global instead of the so far local budget view  . More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is upper-bounded.
Revised:  We relax on this notion by introducing a global instead of the local budget view . More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is upper-bounded.
Edit intent: coherence
Original:  Studying several classic graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized angle, we encounter both fixed-parameter tractability and parameterized hardness results.
Revised:  Studying several classical graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized angle, we encounter both fixed-parameter tractability and parameterized hardness results.
Edit intent: fluency
Original:  Somewhat surprisingly, we find that sometimes the global multistage versions of NP-hard problems such as Vertex Cover turn out to be computationally easier than the ones of polynomial-time solvable problems such as Matching.
Revised:  Somewhat surprisingly, we find that sometimes the global multistage versions of NP-hard problems such as Vertex Cover turn out to be computationally more tractable than the ones of polynomial-time solvable problems such as Matching.
Edit intent: clarity
Original:  More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is upper-bounded . Studying several classical graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized  angle, we encounter both fixed-parameter tractability and parameterized hardness results.
Revised:  More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is moderate . Studying several classical graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized angle, we encounter both fixed-parameter tractability and parameterized hardness results.
Edit intent: clarity
Original:  More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is upper-bounded . Studying several classical graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized  angle, we encounter both fixed-parameter tractability and parameterized hardness results.
Revised:  More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is upper-bounded . Studying several classical graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized complexity angle, we encounter both fixed-parameter tractability and parameterized hardness results.
Edit intent: clarity
Original: The higher-order interactions of complex systems, such as the brain , are captured by their simplicial complex structure and have a significant effect on dynamics.
Revised: The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics.
Edit intent: fluency
Original:  However  the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes.
Revised:  However , the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes.
Edit intent: coherence
Original:  We show that higher-order Kuramoto dynamics can lead to  explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.
Revised:  We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.
Edit intent: fluency
Original: In this paper, we provide a deterministic O(\log N)-space algorithm for estimating the random walk probabilities on  Eulerian directed graphs (and thus also undirected graphs) to within inverse polynomial additive error (\epsilon=1/ \text{poly (N)) where N is the length of the input.
Revised: We provide a deterministic O(\log N)-space algorithm for estimating the random walk probabilities on Eulerian directed graphs (and thus also undirected graphs) to within inverse polynomial additive error (\epsilon=1/ \text{poly (N)) where N is the length of the input.
Edit intent: clarity
Original: In this paper, we provide a deterministic O(\log N)-space algorithm for estimating the random walk probabilities on  Eulerian directed graphs (and thus also undirected graphs) to within inverse polynomial additive error (\epsilon=1/ \text{poly (N)) where N is the length of the input.
Revised: In this paper, we provide a deterministic O(\log N)-space algorithm for estimating random walk probabilities on Eulerian directed graphs (and thus also undirected graphs) to within inverse polynomial additive error (\epsilon=1/ \text{poly (N)) where N is the length of the input.
Edit intent: fluency
Original: In this paper, we provide a deterministic O(\log N)-space algorithm for estimating the random walk probabilities on  Eulerian directed graphs (and thus also undirected graphs) to within inverse polynomial additive error (\epsilon=1/ \text{poly (N)) where N is the length of the input.
Revised: In this paper, we provide a deterministic O(\log N)-space algorithm for estimating the random walk probabilities on Eulerian directed graphs , to within inverse polynomial additive error (\epsilon=1/ \text{poly (N)) where N is the length of the input.
Edit intent: coherence
Original:  Previously, this problem was known to be solvable by a randomized algorithm using space O(\log N) (  Aleliunas et al., FOCS ` 79) and by a deterministic algorithm using space O(\log^{3/2} N) (Saks and Zhou, FOCS ` 95 and JCSS ` 99), both of which held for arbitrary directed graphs but had not been improved even for undirected graphs.
Revised:  Previously, this problem was known to be solvable by a randomized algorithm using space O(\log N) ( Aleliunas et al., FOCS 79) and by a deterministic algorithm using space O(\log^{3/2} N) (Saks and Zhou, FOCS ` 95 and JCSS ` 99), both of which held for arbitrary directed graphs but had not been improved even for undirected graphs.
Edit intent: fluency
Original:  Previously, this problem was known to be solvable by a randomized algorithm using space O(\log N) (  Aleliunas et al., FOCS ` 79) and by a deterministic algorithm using space O(\log^{3/2} N) (Saks and Zhou, FOCS ` 95 and JCSS ` 99), both of which held for arbitrary directed graphs but had not been improved even for undirected graphs.
Revised:  Previously, this problem was known to be solvable by a randomized algorithm using space O(\log N) ( Aleliunas et al., FOCS ` 79) and by a deterministic algorithm using space O(\log^{3/2} N) (Saks and Zhou, FOCS 95 and JCSS ` 99), both of which held for arbitrary directed graphs but had not been improved even for undirected graphs.
Edit intent: fluency
Original:  Previously, this problem was known to be solvable by a randomized algorithm using space O(\log N) (  Aleliunas et al., FOCS ` 79) and by a deterministic algorithm using space O(\log^{3/2} N) (Saks and Zhou, FOCS ` 95 and JCSS ` 99), both of which held for arbitrary directed graphs but had not been improved even for undirected graphs.
Revised:  Previously, this problem was known to be solvable by a randomized algorithm using space O(\log N) ( Aleliunas et al., FOCS ` 79) and by a deterministic algorithm using space O(\log^{3/2} N) (Saks and Zhou, FOCS ` 95 and JCSS 99), both of which held for arbitrary directed graphs but had not been improved even for undirected graphs.
Edit intent: fluency
Original:  We also give improvements on the space complexity of both of these previous algorithms for non-Eulerian directed graphs when the error is negligible (\epsilon=1/N^{\omega(1)}), generalizing what Hoza and Zuckerman (FOCS ` 18) recently showed for the special case of distinguishing whether a random walk probability is 0 or greater than \epsilon.
Revised:  We also give improvements on the space complexity of both of these previous algorithms for non-Eulerian directed graphs when the error is negligible (\epsilon=1/N^{\omega(1)}), generalizing what Hoza and Zuckerman (FOCS 18) recently showed for the special case of distinguishing whether a random walk probability is 0 or greater than \epsilon.
Edit intent: clarity
Original:  The latter algorithm builds on the work of Murtagh et al. (FOCS ` 17) that gave a deterministic O(\log N)-space algorithm for inverting undirected Laplacian matrices, and the work of Cohen et al. (FOCS ` 19) that gave a randomized \tilde{O}(N)-time algorithm for inverting Eulerian Laplacian matrices.
Revised:  The latter algorithm builds on the work of Murtagh et al. (FOCS 17) that gave a deterministic O(\log N)-space algorithm for inverting undirected Laplacian matrices, and the work of Cohen et al. (FOCS ` 19) that gave a randomized \tilde{O}(N)-time algorithm for inverting Eulerian Laplacian matrices.
Edit intent: fluency
Original:  The latter algorithm builds on the work of Murtagh et al. (FOCS ` 17) that gave a deterministic O(\log N)-space algorithm for inverting undirected Laplacian matrices, and the work of Cohen et al. (FOCS ` 19) that gave a randomized \tilde{O}(N)-time algorithm for inverting Eulerian Laplacian matrices.
Revised:  The latter algorithm builds on the work of Murtagh et al. (FOCS ` 17) that gave a deterministic O(\log N)-space algorithm for inverting undirected Laplacian matrices, and the work of Cohen et al. (FOCS 19) that gave a randomized \tilde{O}(N)-time algorithm for inverting Eulerian Laplacian matrices.
Edit intent: fluency
Original:  A running theme throughout these contributions is an analysis of "cycle-lifted graphs , "  where we take a graph and "lift" it to a new graph whose adjacency matrix is the tensor product of the original adjacency matrix and a directed cycle (or variants of one).
Revised:  A running theme throughout these contributions is an analysis of "cycle-lifted graphs " where we take a graph and "lift" it to a new graph whose adjacency matrix is the tensor product of the original adjacency matrix and a directed cycle (or variants of one).
Edit intent: fluency