wanyu/IteraTeR_v2 huggingface dataset:
Original:  algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms , which are of the order%DIFDELCMD < \mathcal{O}%%% (\frac{n^{2}{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose }  a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent \emph{ (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Revised:  algorithms %DIFDELCMD < \mathcal{O}%%% (\frac{n^{2}{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose } a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent \emph{ (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Edit intent: coherence
Original:  algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms , which are of the order%DIFDELCMD < \mathcal{O}%%% (\frac{n^{2}{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose }  a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent \emph{ (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Revised:  algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms , which are of the order%DIFDELCMD < \mathcal{O}%%% }{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose } a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent \emph{ (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Edit intent: clarity
Original:  algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms , which are of the order%DIFDELCMD < \mathcal{O}%%% (\frac{n^{2}{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose }  a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent \emph{ (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Revised:  algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms , which are of the order%DIFDELCMD < \mathcal{O}%%% (\frac{n^{2}{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose } a greedy version of it, which we refer to as the accelerated primal-dual greedy coordinate descent \emph{ (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Edit intent: clarity
Original:  algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms , which are of the order%DIFDELCMD < \mathcal{O}%%% (\frac{n^{2}{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose }  a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent \emph{ (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Revised:  algorithms while it is better than those of Sinkhorn and Greenkhorn algorithms , which are of the order%DIFDELCMD < \mathcal{O}%%% (\frac{n^{2}{\varepsilon^2}), in terms of the desired accuracy \varepsilon > 0. Furthermore, we propose } a greedy version of APDRCD algorithm that we refer to as the accelerated primal-dual greedy coordinate descent \emph{accelerated primal-dual greedy coordinate descent (APDGCD) algorithm and demonstrate that it has a better practical performance than the APDRCD algorithm.
Edit intent: fluency
Original: Human flexible cognition and behavior indicate that the human brain can effectively use its internal feature representations acquired through limited experiences for new experiences in different domains.
Revised: Human flexible cognition and behavior indicate that the brain can transfer its prior knowledge to solve tasks in different domains.
Edit intent: clarity
Original:  To address this , we introduce a method for TL mediated by human brains to improve the performance of TL especially on pattern recognition in which human high-level cognition is considered .
Revised:  To address this , we introduce a method for TL mediated by human brains .
Edit intent: coherence
Original:  To explain the effectiveness of random sampling in theory, we introduce a "significance" criterion and prove that the performance of our framework depends on the significance degree of the given instance.
Revised:  To explain the effectiveness of random sampling in theory, we introduce a `significance' criterion and prove that the performance of our framework depends on the significance degree of the given instance.
Edit intent: fluency
Original:  Actually, our result can be viewed as a new step along the direction of beyond worst-case analysis in terms of clustering with outliers.
Revised:  The result proposed in this paper falls under the umbrella of beyond worst-case analysis in terms of clustering with outliers.
Edit intent: clarity
Original:  Moreover, the existence of outliers can make the clustering problems to be much more challenging.
Revised:  Moreover, the presence of outliers can make the clustering problems to be much more challenging.
Edit intent: clarity
Original:  The framework actually is very simple, where we just need to take a small sample  from input and run  existing approximation algorithm on the sample.
Revised:  The framework actually is very simple, where we just need to take a small sample from input and run an existing approximation algorithm on the sample.
Edit intent: fluency
Original:  To explain the effectiveness of random sampling in theory, we introduce a `significance' criterion and prove that the performance of our framework depends on the significance degree of the given instance.
Revised:  To explain the effectiveness of random sampling in theory, we introduce a `significance' criterion and prove that the performance of uniform sampling depends on the significance degree of the given instance.
Edit intent: clarity
Original:  The experiments suggest that our framework can achieve comparable clustering result with existing methods, but greatly reduce the running time .
Revised:  The experiments suggest that the uniform sampling method can achieve comparable clustering result with existing methods, but greatly reduce the running time .
Edit intent: clarity
Original:  The experiments suggest that our framework can achieve comparable clustering result with existing methods, but greatly reduce the running time .
Revised:  The experiments suggest that our framework can achieve comparable clustering results with other existing methods, but greatly reduce the running time .
Edit intent: clarity
Original:  The experiments suggest that our framework can achieve comparable clustering result with existing methods, but greatly reduce the running time .
Revised:  The experiments suggest that our framework can achieve comparable clustering result with existing methods, but greatly reduce the running times .
Edit intent: fluency
Original: Many events are followed by absolute refractoriness , when for some time after the event a repetition of a similar event is impossible.
Revised: Many events are followed by an absolute refractory state , when for some time after the event a repetition of a similar event is impossible.
Edit intent: clarity
Original: Many events are followed by an absolute refractory state, when for some time after the event a repetition of a similar event is impossible.
Revised: Many events are followed by an absolute refractory period during which the occurrence of a subsequent event is impossible.
Edit intent: clarity
Original:  If uniform events, each of which is followed by the same period of absolute refractoriness, occur randomly, as in the Bernoulli scheme, then the event probability as a function of time can exhibit damped transient oscillations caused by a specific initial condition.
Revised:  If uniform events, each of which is followed by the absolute refractory period, the event probability as a function of time can exhibit damped transient oscillations caused by a specific initial condition.
Edit intent: clarity
Original:   The resulting formulas stand out for their relative simplicity, enabling analytical calculation of the damping coefficients for the second and third peaks of the event probability.
Revised:  The resulting formulas stand out for their relative simplicity, allowing one to analytically obtain the amplitude damping of the 2nd and 3rd peaks of the event probability.
Edit intent: clarity
Original:  Driven by both intrinsic and external factors, the environment is subject to continuous change in nature.
Revised:  Driven by both intrinsic and external factors, the environment is subject to continual change in nature.
Edit intent: fluency
Original:  We show that even if each individual game opposes cooperation , allowing for a transition between them can result in a favorable outcome for cooperation.
Revised:  Even if cooperation cannot be favored in each individual game opposes cooperation , allowing for a transition between them can result in a favorable outcome for cooperation.
Edit intent: clarity
Original:  We show that even if each individual game opposes cooperation , allowing for a transition between them can result in a favorable outcome for cooperation.
Revised:  We show that even if each individual game , allowing for a transition between them can result in a favorable outcome for cooperation.
Edit intent: clarity
Original:  Even small variations in different games being played can promote cooperation markedly.
Revised:  In particular, small variations in different games being played can promote cooperation markedly.
Edit intent: coherence
Original:  Our work suggests that interdependence between the environment and the individuals' behaviors may explain the large-scale cooperation in realistic systems even when cooperation is expensive relative to its benefit .
Revised:  Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly-connected populations .
Edit intent: clarity
Original:  In guaranteeing consistency of ABQ, weak adaptivity is notionally similar to the ideas of detailed balance and ergodicity in Markov Chain Monte Carlo methods, which allow sufficient conditions for consistency of MCMC. Likewise, our results identify a large and flexible class of adaptive Bayesian quadrature rules as consistent, within which practitioners can develop empirically efficient methods.
Revised:  Our results identify a large and flexible class of adaptive Bayesian quadrature rules as consistent, within which practitioners can develop empirically efficient methods.
Edit intent: clarity
Original: How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96\%, while other methods, especially kernel methods, fall far behind?
Revised: How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96\%, while other methods, especially kernel methods, fall far behind?
Edit intent: fluency
Original: How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96\%, while other methods, especially kernel methods, fall far behind?
Revised: How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96\%, while other methods, especially kernel methods, fall relatively behind?
Edit intent: clarity
Original:  There is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving that they can learn certain concept class that is also learnable by kernels , with similar test error.
Revised:  Recently, there is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving that they can learn certain concept class that is also learnable by kernels , with similar test error.
Edit intent: coherence
Original:  There is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving that they can learn certain concept class that is also learnable by kernels , with similar test error.
Revised:  There is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving they can learn certain concept class that is also learnable by kernels , with similar test error.
Edit intent: fluency
Original:  There is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving that they can learn certain concept class that is also learnable by kernels , with similar test error.
Revised:  There is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving that they can learn certain concept class that is also learnable by kernels with similar test error.
Edit intent: fluency
Original:  Yet, can we show neural networks provably learn some concept class better than kernels?
Revised:  Yet, can neural networks provably learn some concept class better than kernels?
Edit intent: clarity
Original:  We answer this positively in the PAC learning language.
Revised:  We answer this positively in the PAC-learning language.
Edit intent: fluency
Original:  At the same time, we prove there are simple functions in this class that the test error obtained by neural networks can be much smaller than any "generic" kernel method, including neural tangent kernels , conjugate kernels, etc .
Revised:  At the same time, we prove there are simple functions in this class that the test error obtained by neural networks can be much smaller than any kernel method, including neural tangent kernels , conjugate kernels, etc .
Edit intent: clarity
Original:  At the same time, we prove there are simple functions in this class that the test error obtained by neural networks can be much smaller than any "generic" kernel method, including neural tangent kernels , conjugate kernels, etc .
Revised:  At the same time, we prove there are simple functions in this class that the test error obtained by neural networks can be much smaller than any "generic" kernel method, including neural tangent kernels (NTK) .
Edit intent: clarity
Original:  The main intuition is that \textit{multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to " one-shot " learning algorithms such as kernel methods  .
Revised:  The main intuition is that \textit{multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to " one-shot " learning algorithms such as kernel methods .
Edit intent: fluency
Original:  The main intuition is that \textit{multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to " one-shot " learning algorithms such as kernel methods  .
Revised:  The main intuition is that \textit{multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to `` one-shot " learning algorithms such as kernel methods .
Edit intent: fluency
Original:  The main intuition is that \textit{multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to " one-shot " learning algorithms such as kernel methods  .
Revised:  The main intuition is that \textit{multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to " one-shot '' learning algorithms such as kernel methods .
Edit intent: fluency
Original:  Yet, can neural networks provably learn some concept class better than kernels?
Revised:  Yet, can neural networks provably learn some concept class BETTER than kernels?
Edit intent: coherence
Original:  At the same time, we prove there are simple functions in this class such that with the same number of training examples, the test error obtained by neural networks can be much smaller thanany kernel method, including neural tangent kernels (NTK).
Revised:  At the same time, we prove there are simple functions in this class such that with the same number of training examples, the test error obtained by neural networks can be thanany kernel method, including neural tangent kernels (NTK).
Edit intent: clarity
Original:  At the same time, we prove there are simple functions in this class such that with the same number of training examples, the test error obtained by neural networks can be much smaller thanany kernel method, including neural tangent kernels (NTK).
Revised:  At the same time, we prove there are simple functions in this class such that with the same number of training examples, the test error obtained by neural networks can be much smaller any kernel method, including neural tangent kernels (NTK).
Edit intent: fluency
Original:  The main intuition is that multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to `` one-shot '' learning algorithms such as kernel methods  ] . In the end, we also prove a computation complexity advantage of ResNet with respect to other learning methods including linear regression over arbitrary feature mappings.
Revised:  The main intuition is that multi-layer neural networks can implicitly perform hierarchical learning using different layers, which reduces the sample complexity comparing to `` one-shot '' learning algorithms such as kernel methods ] . In the end, we also prove a computation complexity advantage of ResNet with respect to other learning methods including linear regression over arbitrary feature mappings.
Edit intent: fluency
Original:  The main intuition is that multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to `` one-shot '' learning algorithms such as kernel methods  ] . In the end, we also prove a computation complexity advantage of ResNet with respect to other learning methods including linear regression over arbitrary feature mappings.
Revised:  The main intuition is that multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to " one-shot '' learning algorithms such as kernel methods ] . In the end, we also prove a computation complexity advantage of ResNet with respect to other learning methods including linear regression over arbitrary feature mappings.
Edit intent: fluency
Original:  The main intuition is that multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to `` one-shot '' learning algorithms such as kernel methods  ] . In the end, we also prove a computation complexity advantage of ResNet with respect to other learning methods including linear regression over arbitrary feature mappings.
Revised:  The main intuition is that multi-layer neural networks can implicitly perform hierarchal learning using different layers, which reduces the sample complexity comparing to `` one-shot " learning algorithms such as kernel methods ] . In the end, we also prove a computation complexity advantage of ResNet with respect to other learning methods including linear regression over arbitrary feature mappings.
Edit intent: fluency
Original:  It is often difficult to compare the different models with respect to their applicability and interpretation.
Edit intent: coherence
Original:  The models are divided according to generating processes, operating in discrete and continuous time , respectively .
Revised:  The models are divided according to generating processes, operating in discrete and continuous time .
Edit intent: clarity
Original:  First, we introduce the Temporal Exponential Random Graph Model (TERGM) and its extension, the Separable TERGM (STERGM), both being \newline time-discrete models.
Revised:  First, we introduce the Temporal Exponential Random Graph Model (TERGM) and the Separable TERGM (STERGM), both being \newline time-discrete models.
Edit intent: clarity
Original:  This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and a splitting scheme of the fourth-order governing equations in terms of two second-order elliptic operators.
Revised:  This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of two second-order elliptic operators.
Edit intent: fluency
Original:  This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and a splitting scheme of the fourth-order governing equations in terms of two second-order elliptic operators.
Revised:  This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and a splitting scheme of the fourth-order governing equations in terms of a system of second-order elliptic operators.
Edit intent: clarity
Original: The unsupervised detection of anomalies in time series data has important applications , e.g., in user behavioural modelling , fraud detection, and cybersecurity.
Revised: The unsupervised detection of anomalies in time series data has important applications in user behavioral modeling , fraud detection, and cybersecurity.
Edit intent: coherence
Original:  Anomaly detection has  been extensively studied in categorical sequences , however we often have access to time series data that contain paths through networks.
Revised:  Anomaly detection has been extensively studied in categorical sequences . However, we often have access to time series data that contain paths through networks.
Edit intent: fluency
Original:  Anomaly detection has  been extensively studied in categorical sequences , however we often have access to time series data that contain paths through networks.
Revised:  Anomaly detection has been extensively studied in categorical sequences , however we often have access to time series data that represent paths through networks.
Edit intent: clarity
Original:  To reliably detect anomalies  we must account for the fact that such data contain a large number of independent observations of short paths constrained by a graph topology.
Revised:  To reliably detect anomalies , we must account for the fact that such data contain a large number of independent observations of short paths constrained by a graph topology.
Edit intent: fluency
Original:  To reliably detect anomalies  we must account for the fact that such data contain a large number of independent observations of short paths constrained by a graph topology.
Revised:  To reliably detect anomalies we must account for the fact that such data contain a large number of independent observations of paths constrained by a graph topology.
Edit intent: clarity
Original: Finite mixture models for clustering can often be improved by adding a regularization that is specific to the topology of the data.
Revised: Finite mixture models for clustering can often be improved by adapting them to the topology of the data.
Edit intent: clarity
Original: Recent work studying clustering in undirected graphs has drawn attention to the distinction between measures of clustering that focus on the "center" node of a triangle vs. measures that focus on the "initiator," a distinction with considerable consequences.
Revised: Recent work studying clustering in undirected graphs has drawn attention to the distinction between measures that focus on the "center" node of a triangle vs. measures that focus on the "initiator," a distinction with considerable consequences.
Edit intent: clarity