wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The proposed algorithms are two-level methods that optimize the Hamiltonian eigenvalue of smallest positive real part over perturbations of a fixed size in the inner iteration, using a constrained gradient flow , and optimize over the perturbation size in the outer iteration  .
Revised:  The proposed algorithms are two-level methods that optimize the Hamiltonian eigenvalue of smallest positive real part over perturbations of a fixed size in the inner iteration, using a constrained gradient flow . They optimize over the perturbation size in the outer iteration .
Edit intent: coherence
Original:  The proposed algorithms are two-level methods that optimize the Hamiltonian eigenvalue of smallest positive real part over perturbations of a fixed size in the inner iteration, using a constrained gradient flow , and optimize over the perturbation size in the outer iteration  .
Revised:  The proposed algorithms are two-level methods that optimize the Hamiltonian eigenvalue of smallest positive real part over perturbations of a fixed size in the inner iteration, using a constrained gradient flow , and optimize over the perturbation size in the outer iteration , which is shown to converge quadratically in the typical case of a defective coalescence of simple eigenvalues approaching the imaginary axis .
Edit intent: meaning-changed
Original:  Within the framework of the developed phenomenological model, based on the approach of DNA conformational vibrations, the modes of H-bond stretching, backbone vibrations  and water translational vibrations have been established.
Revised:  Within the framework of the developed phenomenological model, based on the approach of DNA conformational vibrations, the modes of H-bond stretching, backbone vibrations , and water translational vibrations have been established.
Edit intent: fluency
Original: Recent studies about learning multilingual representations have achieved significant performance gains across a wide range of downstream cross-lingual tasks. They train either an encoder-only Transformer mainly for understanding tasks, or an encoder-decoder Transformer specifically for generation tasks, ignoring the correlation between the two tasks and frameworks. In contrast, this paperpresents a variable encoder-decoder (VECO) pre-training approach to unify the two mainstreams in both model architectures and pre-training tasks. VECO splits the standard Transformer block into several sub-modules trained with both inner-sequence and cross-sequence masked language modeling, and correspondingly URLanizes certain sub-modules for understanding and generation tasksduring inference. Such a workflow not only ensures to train the most streamlined parameters necessary for two kinds of tasks, but also enables them to boost each other via sharing common sub-modules .
Revised: Recent studies about learning multilingual representations have achieved significant performance gains across a wide range of downstream cross-lingual transferability by training a unified Transformer encoder for multiple languages. However, much of this work only relies on the shared vocabulary and bilingual contexts to encourage the correlation across languages, which is loose and implicit for aligning the contextual representations between languages. In this paper, we plug a cross-attention module into the Transformer encoder to explicitly build the interdependence between languages. It can effectively avoid the degeneration of predicting masked words only conditioned on the context in its own language. More importantly, when fine-tuning on downstream tasks, the cross-attention module can be plugged in or out on-demand, thus naturally benefiting a wider range of cross-lingual tasks, from language understanding to generation .
Edit intent: meaning-changed
Original:  As a result, VECO delivers new state-of-the-art results on various cross-lingual understanding tasks of the XTREME benchmark  covering text classification, sequence labeling, question answering, and sentence retrieval.
Revised:  As a result, the proposed cross-lingual model delivers new state-of-the-art results on various cross-lingual understanding tasks of the XTREME benchmark covering text classification, sequence labeling, question answering, and sentence retrieval.
Edit intent: meaning-changed
Original:  As a result, VECO delivers new state-of-the-art results on various cross-lingual understanding tasks of the XTREME benchmark  covering text classification, sequence labeling, question answering, and sentence retrieval.
Revised:  As a result, VECO delivers new state-of-the-art results on various cross-lingual understanding tasks of the XTREME benchmark , covering text classification, sequence labeling, question answering, and sentence retrieval.
Edit intent: fluency
Original:  For  generation tasks, VECO also outperforms all existing cross-lingual models and state-of-the-art Transformer variants on WMT14 English-to-German and English-to-French translation datasets, with gains of up to 1 %DIFDELCMD < \sim2 %%%  BLEU.
Revised:  For cross-lingual generation tasks, VECO also outperforms all existing cross-lingual models and state-of-the-art Transformer variants on WMT14 English-to-German and English-to-French translation datasets, with gains of up to 1 %DIFDELCMD < \sim2 %%% BLEU.
Edit intent: meaning-changed
Original:  For  generation tasks, VECO also outperforms all existing cross-lingual models and state-of-the-art Transformer variants on WMT14 English-to-German and English-to-French translation datasets, with gains of up to 1 %DIFDELCMD < \sim2 %%%  BLEU.
Revised:  For generation tasks, it also outperforms all existing cross-lingual models and state-of-the-art Transformer variants on WMT14 English-to-German and English-to-French translation datasets, with gains of up to 1 %DIFDELCMD < \sim2 %%% BLEU.
Edit intent: clarity
Original:  For  generation tasks, VECO also outperforms all existing cross-lingual models and state-of-the-art Transformer variants on WMT14 English-to-German and English-to-French translation datasets, with gains of up to 1 %DIFDELCMD < \sim2 %%%  BLEU.
Revised:  For generation tasks, VECO also outperforms all existing cross-lingual models and state-of-the-art Transformer variants on WMT14 English-to-German and English-to-French translation datasets, with gains of up to 1 %DIFDELCMD < \sim2 %%% ~2 BLEU.
Edit intent: meaning-changed
Original:  Thus, we propose meta-algorithms, namely multi-agent plan segmenting -X (MAPS-X) and its lazy variant, that can be plugged on existing centralized sampling-based tree planners X to produce plans with good explanations using a desirable number of images.
Revised:  Thus, we propose meta-algorithms, namely -X (MAPS-X) and its lazy variant, that can be plugged on existing centralized sampling-based tree planners X to produce plans with good explanations using a desirable number of images.
Edit intent: clarity
Original:  Thus, we propose meta-algorithms, namely multi-agent plan segmenting -X (MAPS-X) and its lazy variant, that can be plugged on existing centralized sampling-based tree planners X to produce plans with good explanations using a desirable number of images.
Revised:  Thus, we propose meta-algorithms, namely multi-agent plan segmenting multi-agent plan segmenting-X (MAPS-X) and its lazy variant, that can be plugged on existing centralized sampling-based tree planners X to produce plans with good explanations using a desirable number of images.
Edit intent: fluency
Original:  The numerical scheme is constructed based on a recently developed energetic variational formulation, in which the reaction part is reformulated in terms of reaction trajectories , and both the reaction and the diffusion parts dissipate the same free energy .
Revised:  The numerical scheme is constructed based on a recently developed energetic variational formulation, in which the reaction part is reformulated in terms of reaction trajectories . The fact that both the reaction and the diffusion parts dissipate the same free energy .
Edit intent: coherence
Original:  The numerical scheme is constructed based on a recently developed energetic variational formulation, in which the reaction part is reformulated in terms of reaction trajectories , and both the reaction and the diffusion parts dissipate the same free energy . This subtle fact opens a path of an  operator splitting scheme for these systems.
Revised:  The numerical scheme is constructed based on a recently developed energetic variational formulation, in which the reaction part is reformulated in terms of reaction trajectories , and both the reaction and the diffusion parts dissipate the same free energy opens a path of an operator splitting scheme for these systems.
Edit intent: coherence
Original:  Flimma URL addresses this issue by implementing the state-of-the-art gene expression workflow limma voom in a federated, privacy-preserving manner  . Flimma results are identical to those generated by limma voom on combined datasets even in imbalanced scenarios where meta-analysis approaches fail.
Revised:  Flimma URL addresses this issue by implementing the state-of-the-art workflow limma voom in a federated, privacy-preserving manner . Flimma results are identical to those generated by limma voom on combined datasets even in imbalanced scenarios where meta-analysis approaches fail.
Edit intent: clarity
Original:  Flimma URL addresses this issue by implementing the state-of-the-art gene expression workflow limma voom in a federated, privacy-preserving manner  . Flimma results are identical to those generated by limma voom on combined datasets even in imbalanced scenarios where meta-analysis approaches fail.
Revised:  Flimma URL addresses this issue by implementing the state-of-the-art gene expression workflow limma voom in a privacy-preserving manner . Flimma results are identical to those generated by limma voom on combined datasets even in imbalanced scenarios where meta-analysis approaches fail.
Edit intent: clarity
Original:  Flimma URL addresses this issue by implementing the state-of-the-art gene expression workflow limma voom in a federated, privacy-preserving manner  . Flimma results are identical to those generated by limma voom on combined datasets even in imbalanced scenarios where meta-analysis approaches fail.
Revised:  Flimma URL addresses this issue by implementing the state-of-the-art gene expression workflow limma voom in a federated, privacy-preserving manner , i.e. patient data never leaves its source site . Flimma results are identical to those generated by limma voom on combined datasets even in imbalanced scenarios where meta-analysis approaches fail.
Edit intent: meaning-changed
Original: The truncated Milstein method, which was initial proposed in (Guo, Liu, Mao and Yue 2018), is extended to the non-autonomous stochastic differential equations with the super-linear state variable and the H\"older continuous time variable.
Revised: The truncated Milstein method, which was initially proposed in (Guo, Liu, Mao and Yue 2018), is extended to the non-autonomous stochastic differential equations with the super-linear state variable and the H\"older continuous time variable.
Edit intent: fluency
Original:  Our method works without any prior knowledge about the number of zeros , or their approximate location , as long as the number of zeros is finite. We give a complete convergence analysis, which relies on results on the caustics of f, and on convergence results for Newton's method.
Revised:  Our method works without any prior knowledge about the number of zeros , or their approximate location . We start by computing all solution of f(z) = \eta with |\eta| sufficiently large and then track all solutions as \eta tends to 0 to finally obtain all zeros of f. Using theoretical results on harmonic mappings we analyze where and how the number of solutions of f(z) = \eta changes and incorporate this into the method. We prove that our method is guaranteed to compute all zeros, as long as none of them is singular.
Edit intent: meaning-changed
Original:  Under local privacy constraints , we present a sample-optimal private-coin scheme that only sends a one-bit message per user.
Revised:  We characterize the sample complexity for sparse estimation under LDP constraints up to a constant factor and the sample complexity under communication constraints up to a logarithmic factor. Our upper bounds under LDP are based on the Hadamard Response, a private coin scheme that requires only one bit of communication per user.
Edit intent: meaning-changed
Original:  For communication constraints, we present a public-coin scheme based on random hashing functions , which we prove is optimal up to logarithmic factors. Our results show that the sample complexity only depends logarithmically on the ambient dimension, thus providing significant improvement in sample complexity under sparsity assumptions. Our lower bounds are based on a recently proposed chi-squared contraction method .
Revised:  For communication constraints, we present a public-coin scheme based on random hashing functions . Our tight lower bounds are based on a recently proposed chi-squared contraction method .
Edit intent: coherence
Original: Research and development of electroencephalogram (EEG) based brain-computer interfaces (BCIs) have advanced rapidly, partly due to the wide adoption of sophisticated machine learning approaches for decoding the EEG signals.
Revised: Research and development of electroencephalogram (EEG) based brain-computer interfaces (BCIs) have advanced rapidly, partly due to deeper understanding of the brain and wide adoption of sophisticated machine learning approaches for decoding the EEG signals.
Edit intent: meaning-changed
Original:  However, recent studies have shown that machine learning algorithms are vulnerable to adversarial attacks , e. g., the attacker can add tiny adversarial perturbations to a test sample to fool the model, or poison the training data to insert a secret backdoor. Previous research has shown that adversarial attacks are also possible for EEG-based BCIs. However, only adversarial perturbations have been considered, and the approaches are theoretically sound but very difficult to implement in practice.
Revised:  However, recent studies have shown that machine learning algorithms are vulnerable to adversarial attacks .
Edit intent: coherence
Original:  It is not hard to see the clustered selected-internal Steiner tree problem is NP-hard. Hence, in this paper, we present the first known approximation algorithm with performance ratio  \rho+4  for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Revised:  In this paper, we present the first known approximation algorithm with performance ratio \rho+4 for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Edit intent: coherence
Original:  Hence, in this paper, we present the first known approximation algorithm with performance ratio  \rho+4  for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Revised:  Hence, in this paper, we present the first known approximation algorithm with performance ratio ( \rho+4 for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Edit intent: fluency
Original:  Hence, in this paper, we present the first known approximation algorithm with performance ratio  \rho+4  for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Revised:  Hence, in this paper, we present the first known approximation algorithm with performance ratio \rho+4 ) for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Edit intent: fluency
Original:  Hence, in this paper, we present the first known approximation algorithm with performance ratio  \rho+4  for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Revised:  Hence, in this paper, we present the first known approximation algorithm with performance ratio \rho+4 for the clustered selected-internal Steiner tree problem , where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Edit intent: coherence
Original:  Hence, in this paper, we present the first known approximation algorithm with performance ratio  \rho+4  for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Revised:  Hence, in this paper, we present the first known approximation algorithm with performance ratio \rho+4 for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Edit intent: meaning-changed
Original:  Hence, in this paper, we present the first known approximation algorithm with performance ratio  \rho+4  for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Revised:  Hence, in this paper, we present the first known approximation algorithm with performance ratio \rho+4 for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln %DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Edit intent: meaning-changed
Original:  Hence, in this paper, we present the first known approximation algorithm with performance ratio  \rho+4  for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% +\epsilon\approx 1.39 .
Revised:  Hence, in this paper, we present the first known approximation algorithm with performance ratio \rho+4 for the clustered selected-internal Steiner tree problem if the cost function is metric (i.e., the costs of edges satisfy the triangle inequality), where \rho is the best-known performance ratio for the Steiner tree problem whose performance ratio is \ln 4%DIFDELCMD < }%%% .
Edit intent: meaning-changed
Original:  In this paper, we propose the overlapping Domain Decomposition Methods(DDMs) to solve the nonconvex optimization problem in ptychographic imaging , that decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information on the interface of these subdomains,thus leading to highly parallel algorithms with good load balance.
Revised:  In this paper, we propose the overlapping Domain Decomposition Methods(DDMs) to solve the nonconvex optimization problem in ptychographic imaging . They decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information on the interface of these subdomains,thus leading to highly parallel algorithms with good load balance.
Edit intent: coherence
Original:  In this paper, we propose the overlapping Domain Decomposition Methods(DDMs) to solve the nonconvex optimization problem in ptychographic imaging , that decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information on the interface of these subdomains,thus leading to highly parallel algorithms with good load balance.
Revised:  In this paper, we propose the overlapping Domain Decomposition Methods(DDMs) to solve the nonconvex optimization problem in ptychographic imaging , that decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information in the overlapping regions of these subdomains,thus leading to highly parallel algorithms with good load balance.
Edit intent: clarity
Original:  More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping region for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric .
Revised:  More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping regions for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric .
Edit intent: fluency
Original:  More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping region for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric .
Revised:  More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping region for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric (ST-AGM). Such metric allows for fast calculation of the proximal mapping with closed form, and meanwhile provides the possibility for the convergence guarantee of the first-order nonconvex optimization algorithm due to its Lipschitz smoothness.
Edit intent: meaning-changed
Original:  Such platforms embed shopping experiences within IM apps, e.g.  WeChat, WhatsApp, where real-world friends post and recommend products from the platform in IM group chats and quite often form lasting recommending/buying relationships.
Revised:  Such platforms embed shopping experiences within IM apps, e.g. , WeChat, WhatsApp, where real-world friends post and recommend products from the platform in IM group chats and quite often form lasting recommending/buying relationships.
Edit intent: fluency
Original:  Such platforms embed shopping experiences within IM apps, e.g.  WeChat, WhatsApp, where real-world friends post and recommend products from the platform in IM group chats and quite often form lasting recommending/buying relationships.
Revised:  Such platforms embed shopping experiences within IM apps, e.g. WeChat, WhatsApp, where real-world friends post and recommend products from the platforms in IM group chats and quite often form lasting recommending/buying relationships.
Edit intent: clarity