wanyu/IteraTeR_v2 huggingface dataset:
Original:  Furthermore, we characterize optimal step sizes and prove that , for a broad class of random matrices including the Gaussian ensemble, momentum does not accelerate the refreshed embeddings method.
Revised:  Furthermore, we prove that momentum does not accelerate the refreshed embeddings method.
Edit intent: coherence
Original:  Our choice of the sketch size yields an algorithm , for solving overdetermined least-squares problem, with a lower computational complexity compared to current state-of-the-art least-squares iterative methods based on randomized pre-conditioners .
Revised:  Our resulting algorithm yields a smaller complexity compared to current state-of-the-art least-squares iterative methods based on randomized pre-conditioners .
Edit intent: clarity
Original:  Our choice of the sketch size yields an algorithm , for solving overdetermined least-squares problem, with a lower computational complexity compared to current state-of-the-art least-squares iterative methods based on randomized pre-conditioners .
Revised:  Our choice of the sketch size yields an algorithm , for solving overdetermined least-squares problem, with a lower computational complexity compared to current state-of-the-art randomized pre-conditioning methods .
Edit intent: clarity
Original:  In particular, given the sketched data matrix, as the sample size grows, the resulting computational complexity becomes sub-linear in the problem dimensions.
Revised:  In particular, as the sample size grows, the resulting computational complexity becomes sub-linear in the problem dimensions.
Edit intent: clarity
Original:  In particular, given the sketched data matrix, as the sample size grows, the resulting computational complexity becomes sub-linear in the problem dimensions.
Revised:  In particular, given the sketched data matrix, as the sample size grows, the resulting complexity becomes sub-linear in the problem dimensions.
Edit intent: clarity
Original: We investigate randomized methods for solving overdetermined linear least-squares problems, where the Hessian is approximated based on a random projection of the data matrix.
Revised: We investigate randomized methods for solving overdetermined least-squares problems, where the Hessian is approximated based on a random projection of the data matrix.
Edit intent: clarity
Original: We investigate randomized methods for solving overdetermined linear least-squares problems, where the Hessian is approximated based on a random projection of the data matrix.
Revised: We investigate randomized methods for solving overdetermined linear least-squares problems, where the preconditioners are based on a random projection of the data matrix.
Edit intent: clarity
Original:  Given a stream of k-bit words, we seek to compute k ~ distinct sums corresponding to bit values at indexes 0, 1, 2, ..., k-1.
Revised:  Given a stream of k-bit words, we seek to compute k distinct sums corresponding to bit values at indexes 0, 1, 2, ..., k-1.
Edit intent: fluency
Original:  Nodes in the brain connectome graph correspond to different regions of interest (ROIs) while edges correspond to white matter fiber connections between these ROIs.
Revised:  Nodes in the brain connectome graph correspond to different regions of interest (ROIs) and edges to connection strengths between ROIs.
Edit intent: clarity
Original:  Methods: To address the problem and obtain more stable correlation estimates, we propose a novel windowless approach for computing dynamic correlations via heat kernel smoothing.
Revised:  Methods: To address the problem and obtain more robust correlation estimates, we propose a novel windowless approach for computing dynamic correlations via heat kernel smoothing.
Edit intent: clarity
Original:  However, these efforts still suffer from two types of latencies: (a) the computational latency (synthesize {\em   time), which grows linearly with the sentence length even with parallel approaches, and (b) the input latency {\em  in scenarios where the input text is incrementally generated (such as in simultaneous translation, dialog generation, and assistive technologies).
Revised:  However, these efforts still suffer from two types of latencies: (a) the {\em time), which grows linearly with the sentence length even with parallel approaches, and (b) the input latency {\em in scenarios where the input text is incrementally generated (such as in simultaneous translation, dialog generation, and assistive technologies).
Edit intent: coherence
Original:  However, these efforts still suffer from two types of latencies: (a) the computational latency (synthesize {\em   time), which grows linearly with the sentence length even with parallel approaches, and (b) the input latency {\em  in scenarios where the input text is incrementally generated (such as in simultaneous translation, dialog generation, and assistive technologies).
Revised:  However, these efforts still suffer from two types of latencies: (a) the computational latency (synthesize {\em time), which grows linearly with the sentence length even with parallel approaches, and (b) the {\em in scenarios where the input text is incrementally generated (such as in simultaneous translation, dialog generation, and assistive technologies).
Edit intent: coherence
Original:  In-line citation mentions in  full text are  linked to their corresponding bibliography entries, which are in turn linked to in-corpus cited papers, forming the edges of a contextual citation graph .
Revised:  In-line citation mentions in the full text are linked to their corresponding bibliography entries, which are in turn linked to in-corpus cited papers, forming the edges of a contextual citation graph .
Edit intent: fluency
Original:  In-line citation mentions in  full text are  linked to their corresponding bibliography entries, which are in turn linked to in-corpus cited papers, forming the edges of a contextual citation graph .
Revised:  In-line citation mentions in full text are linked to their corresponding bibliography entries, which are linked to their referenced papers, forming the edges of a contextual citation graph .
Edit intent: clarity
Original:  In-line citation mentions in  full text are  linked to their corresponding bibliography entries, which are in turn linked to in-corpus cited papers, forming the edges of a contextual citation graph .
Revised:  In-line citation mentions in full text are linked to their corresponding bibliography entries, which are in turn linked to in-corpus cited papers, forming contextual citation edges .
Edit intent: clarity
Original:  To our knowledge, this is the largest publicly available contextual citation graph ;
Revised:  To our knowledge, this is the largest publicly-available contextual citation graph ;
Edit intent: fluency
Original:  We release S2ORC to facilitate research and development of tools and tasks for the analysis of scientific text.
Revised:  We hope this resource will facilitate research and development of tools and tasks for the analysis of scientific text.
Edit intent: clarity
Original:  We release S2ORC to facilitate research and development of tools and tasks for the analysis of scientific text.
Revised:  We release S2ORC to facilitate research and development of tools and tasks for text mining over academic text.
Edit intent: clarity
Original:  First, an identifiability result is proved for partial boundary data without restrictive conditions on the inaccessible part of the boundary .
Revised:  The aim is to recover the missing data on the inaccessible part of the boundary .
Edit intent: clarity
Original:  The quasi-reversibility method is studied , and different mixed  formulations are proposed.
Revised:  The quasi-reversibility method is studied and different mixed formulations are proposed.
Edit intent: fluency
Original:  The quasi-reversibility method is studied , and different mixed  formulations are proposed.
Revised:  The quasi-reversibility method is studied , and different mixed variational formulations are proposed.
Edit intent: clarity
Original:  Well-posedness and convergence results are proved.
Revised:  Well-posedness , convergence and regularity results are proved.
Edit intent: clarity
Original:   Various two- and three dimensional numerical simulations attest the efficiency of the method, in particular for noisy data.
Revised:  Various two- and three-dimensional numerical simulations attest the efficiency of the method, in particular for noisy data.
Edit intent: fluency
Original:  Moreover the proposed heuristic yields structure which size can be bounded both by |S|H_{m-1}(S) and by |S|/m(H_0(S) + \cdots + H_{m-1}), where H_{k}(S) is the k-th order empirical entropy of S.
Revised:  Moreover the proposed heuristic yields structure whose size can be bounded both by |S|H_{m-1}(S) and by |S|/m(H_0(S) + \cdots + H_{m-1}), where H_{k}(S) is the k-th order empirical entropy of S.
Edit intent: fluency
Original:  However, the solutions obtained are not wholly understood.
Revised:  However, the solutions obtained are not fully understood.
Edit intent: clarity
Original:  Empirical results suggest that the training favors regularized solutions.
Revised:  Empirical results suggest that typical training algorithms favor regularized solutions.
Edit intent: clarity
Original:  We show , that the resulting solution converges to the smooth spline interpolation of the training data as the number of hidden nodes tends to infinity  .
Revised:  We show that the resulting solution converges to the smooth spline interpolation of the training data as the number of hidden nodes tends to infinity .
Edit intent: fluency
Original:  However, the solutions obtained are not fully understood  . Empirical results suggest that typical training algorithms favor regularized solutions.
Revised:  However, the estimates obtained are not fully understood . Empirical results suggest that typical training algorithms favor regularized solutions.
Edit intent: clarity
Original:  These observations motivate us to analyze properties of the solutions found by gradient descent initialized close to zero, that is frequently employed to perform the training task.
Revised:  These observations motivate us to analyze properties of the neural networks found by gradient descent initialized close to zero, that is frequently employed to perform the training task.
Edit intent: clarity
Original:  This might give valuable insight on the properties of the solutions obtained using gradient descent methods in general settings.
Revised:  Our analysis might give valuable insight on the properties of the solutions obtained using gradient descent methods in general settings.
Edit intent: clarity
Original:  We prove that the decision version of this problem is NP-complete and cannot be solved in time 2^{o(\sigma  )} n unless the Exponential Time Hypothesis fails, where \sigma is the size of the alphabet  .
Revised:  We prove that the decision version of this problem is NP-complete and cannot be solved in time 2^{o(\sigma )} unless the Exponential Time Hypothesis fails, where \sigma is the size of the alphabet .
Edit intent: clarity
Original:  Moreover, we show that optimization variations of this problem yield strong inapproximability results.
Edit intent: coherence
Original:  In doing so  we relate two previously disparate topics: the size of a path cover of a graph and the number of runs in the BWT of a text .
Revised:  In doing so , we relate two previously disparate topics: the size of a path cover of a graph and the number of runs in the BWT of a text .
Edit intent: fluency
Original:  Finally, we provide an efficient algorithm for the more restricted problem of finding an optimal ordering on a subset of symbols (occurring only once) under ordering constraints which runs in optimal time for small values of \sigma.
Revised:  Finally, we provide an efficient algorithm for the problem of finding an optimal ordering on a subset of symbols (occurring only once) under ordering constraints which runs in optimal time for small values of \sigma.
Edit intent: clarity
Original: Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing  and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future.
Revised: Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing , and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future.
Edit intent: fluency
Original: Chaperone proteins -- the most disordered among all protein groups -- help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones.
Revised: Chaperone proteins - the most disordered among all protein groups -- help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones.
Edit intent: fluency
Original: Chaperone proteins -- the most disordered among all protein groups -- help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones.
Revised: Chaperone proteins -- the most disordered among all protein groups - help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones.
Edit intent: fluency
Original: Chaperone proteins - the most disordered among all protein groups - help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones.
Revised: Chaperone protein - the most disordered among all protein groups - help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones.
Edit intent: fluency
Original:  These designs aim to simultaneously balance all linear functions of the covariates, and the variance of an estimator of the average treatment effect is shown to be bounded by a quantity that is proportional to the loss function of a ridge regression of the potential outcomes on the covariates.
Revised:  These designs aim to simultaneously balance all linear functions of the covariates, and the minimum of the loss function of a ridge regression of the potential outcomes on the covariates.
Edit intent: clarity
Original:  No regression is actually conducted, and one may see the procedure as regression adjustment by design.
Revised:  One may thus interpret the approach as regression adjustment by design.
Edit intent: clarity
Original:  Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of the targeted covariates.
Revised:  Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of the covariates.
Edit intent: clarity
Original:  This paper introduces an experimental design that admits precise control over this trade-off  .
Revised:  This paper introduces an experimental design that admits precise control over an inescapable trade-off .
Edit intent: clarity
Original:  The design is specified by a  parameter that bounds the worst-case mean square error of an estimator of the average treatment effect.
Revised:  The design is specified by a parameter that bounds the worst-case mean squared error of an estimator of the average treatment effect.
Edit intent: fluency
Original:  Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of the covariates.
Revised:  Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of potentially many covariates.
Edit intent: clarity
Original:  The achieved level of balance is  considerably better than what a fully random assignment would produce, and it is close to optimal given the desired level of robustness.
Revised:  The achieved level of balance is considerably better than what a fully random assignment would produce, and close to optimal given the desired level of robustness.
Edit intent: coherence
Original:  We show that the mean square error of the estimator is bounded by the minimum of the loss function of a ridge regression of the potential outcomes on the covariates.
Revised:  We show that the mean squared error of the estimator is bounded by the minimum of the loss function of a ridge regression of the potential outcomes on the covariates.
Edit intent: fluency
Original:  Prompt-LTL is an extension of LTL that allows to specify parametric bounds on the satisfaction of eventualities, thereby adding a quantitative aspect to the specification language.
Revised:  Prompt-LTL is an extension of LTL that allows to specify parametric bounds on the satisfaction of eventualities, thus adding a quantitative aspect to the specification language.
Edit intent: fluency
Original: Recently, the finite-rate-of-innovation (FRI) based continuous domain restoration is emerging as an alternative to the conventional on-the-grid  compressed sensing (CS) MRI restoration due to its ability to alleviate the basis mismatch between the true support of the shape in the continuous domain and the discrete grid.
Revised: Recently, the finite-rate-of-innovation (FRI) based continuous domain restoration is emerging as an alternative to the conventional on-the-grid compressed sensing (CS) due to its ability to alleviate the basis mismatch between the true support of the shape in the continuous domain and the discrete grid.
Edit intent: clarity
Original:  Based on this observation, we propose a data driven tight frame based off-the-grid CS-MRI reconstruction model for the MR image reconstruction.
Revised:  Based on this observation, we propose a data driven tight frame based off-the-grid CS-MRI reconstruction model for the CS-MRI reconstruction.
Edit intent: clarity
Original: Kahan introduced an explicit method of discretization for systems of forst order differential equations with nonlinearities of degree at most two (quadratic vector fields).
Revised: Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields).
Edit intent: fluency
Original:  be the size of maximum independent sets in G. For any F \subseteq E, V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle]
Revised:  be the size of maximum independent sets in %DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle]
Edit intent: clarity
Original:  be the size of maximum independent sets in G. For any F \subseteq E, V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle]
Revised:  be the size of maximum independent sets in G. For any F \subseteq E, V%DIFDELCMD < \langle %%% %DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle]
Edit intent: fluency
Original:  be the size of maximum independent sets in G. For any F \subseteq E, V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle]
Revised:  be the size of maximum independent sets in G. For any F \subseteq E, V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G %DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle]
Edit intent: fluency
Original:  be the size of maximum independent sets in G. For any F \subseteq E, V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle]
Revised:  be the size of maximum independent sets in G. For any F \subseteq E, V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle %%% denotes the set of vertices incident only to edges in F, and G V%DIFDELCMD < \langle %%% %DIFDELCMD < \rangle]
Edit intent: fluency
Original:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Revised:  %DIFDELCMD < %%% %DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Edit intent: clarity
Original:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Revised:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% %DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Edit intent: coherence
Original:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Revised:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game %DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Edit intent: fluency
Original:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Revised:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, %DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Edit intent: fluency
Original:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and \gamma%DIFDELCMD < } %%% :
Revised:  %DIFDELCMD < %%% denotes the induced subgraph on V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle%%% . An independent set game on G is a cooperative game \Gamma%DIFDELCMD < }%%% _G = (E, \gamma%DIFDELCMD < }%%% ), where E is the set of players and %DIFDELCMD < } %%% :
Edit intent: fluency
Original:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Revised:  2^E \rightarrow \mathbb{R %DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Edit intent: clarity