wanyu/IteraTeR_v2 huggingface dataset:
Original:  The current literature has predominantly focused on analyzing the characteristics of network games in the scenario where the structure of the network, which is represented by a graph, is known beforehand.
Revised:  The current literature has largely focused on analyzing the characteristics of network games in the scenario where the structure of the network, which is represented by a graph, is known beforehand.
Edit intent: clarity
Original:  Moreover, with experiments on three real-world examples, we show that our methods can effectively and more accurately learn the games than the baselines.
Revised:  Moreover, with experiments on three real world examples, we show that our methods can effectively and more accurately learn the games than the baselines.
Edit intent: fluency
Original:  In the economics literature, such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only on her action but also  that of her neighbors.
Revised:  Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only on her action but also that of her neighbors.
Edit intent: clarity
Original:  In the economics literature, such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only on her action but also  that of her neighbors.
Revised:  In the economics literature, such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only on her action but also on that of her neighbors.
Edit intent: fluency
Original:  In this paper, we propose two novel frameworks for learning, from the observations on individual actions, network games with linear-quadratic payoffs, and in particular  the structure of the interaction network.
Revised:  In this paper, we propose two novel frameworks for learning, from the observations on individual actions, network games with linear-quadratic payoffs, and in particular , the structure of the interaction network.
Edit intent: fluency
Original: We consider  a large portfolio limit where the asset prices evolve according  certain stochastic volatility models with default upon hitting a lower barrier.
Revised: We consider a large portfolio limit model where the underlying asset prices evolve according certain stochastic volatility models with default upon hitting a lower barrier.
Edit intent: clarity
Original: We consider  a large portfolio limit where the asset prices evolve according  certain stochastic volatility models with default upon hitting a lower barrier.
Revised: We consider a large portfolio limit where the asset prices evolve according to certain stochastic volatility models with default upon hitting a lower barrier.
Edit intent: fluency
Original:  When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions which has been studied in \mbox{ HK17 .
Revised:  The asset prices and the volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions which has been studied in \mbox{ HK17 .
Edit intent: coherence
Original:  When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions which has been studied in \mbox{ HK17 .
Revised:  When the asset prices and their volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions which has been studied in \mbox{ HK17 .
Edit intent: fluency
Original:  When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions which has been studied in \mbox{ HK17 .
Revised:  When the asset prices and the volatilities are correlated via systemic Brownian motions, and the resulting SPDE is defined on the positive half-space with Dirichlet boundary conditions which has been studied in \mbox{ HK17 .
Edit intent: clarity
Original:  When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions which has been studied in \mbox{ HK17 .
Revised:  When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions .
Edit intent: clarity
Original:  We present a tool implementing a recently developed partition refinement algorithm that is generic in the transition type of the given system and typically runs in time either \mathcal{O(m\cdot \log n) or O(m\cdot \log n\cdot\log m) for systems with m edges and n states.
Revised:  Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and typically runs in time either \mathcal{O(m\cdot \log n) or O(m\cdot \log n\cdot\log m) for systems with m edges and n states.
Edit intent: clarity
Original:  We present a tool implementing a recently developed partition refinement algorithm that is generic in the transition type of the given system and typically runs in time either \mathcal{O(m\cdot \log n) or O(m\cdot \log n\cdot\log m) for systems with m edges and n states.
Revised:  We present a tool implementing a recently developed partition refinement algorithm that is generic in the transition type of the given system and (m\cdot \log n) or O(m\cdot \log n\cdot\log m) for systems with m edges and n states.
Edit intent: clarity
Original:  This } matches the runtime of the best known algorithms for several fixed types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems , and in the case of weighted systems over non-cancellative monoids , such as (the additive monoid of) the tropical semiring , even improves the asymptotic runtime . Genericity is achieved by modelling transition types as endofunctors on sets and state-based systems as coalgebras.
Revised:  This } matches the runtime of the best known algorithms for many concrete types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems , and in the case of weighted systems over non-cancellative monoids , such as (the additive monoid of) the tropical semiring , even improves the asymptotic runtime . Genericity is achieved by modelling transition types as endofunctors on sets and state-based systems as coalgebras.
Edit intent: clarity
Original:  This } matches the runtime of the best known algorithms for several fixed types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems , and in the case of weighted systems over non-cancellative monoids , such as (the additive monoid of) the tropical semiring , even improves the asymptotic runtime . Genericity is achieved by modelling transition types as endofunctors on sets and state-based systems as coalgebras.
Revised:  This } matches the runtime of the best known algorithms for several fixed types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems , and in the case of weighted systems over non-cancellative monoids such as (the additive monoid of) the tropical semiring , even improves the asymptotic runtime . Genericity is achieved by modelling transition types as endofunctors on sets and state-based systems as coalgebras.
Edit intent: fluency
Original:  This } matches the runtime of the best known algorithms for several fixed types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems , and in the case of weighted systems over non-cancellative monoids , such as (the additive monoid of) the tropical semiring , even improves the asymptotic runtime . Genericity is achieved by modelling transition types as endofunctors on sets and state-based systems as coalgebras.
Revised:  This } matches the runtime of the best known algorithms for several fixed types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems , and in the case of weighted systems over non-cancellative monoids , such as (the additive monoid of) the tropical semiring even substantially improve, the asymptotic runtime . Genericity is achieved by modelling transition types as endofunctors on sets and state-based systems as coalgebras.
Edit intent: clarity
Original:  Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the runtime of the best known algorithms for many concrete types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems.
Revised:  Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run time of the best known algorithms for many concrete types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems.
Edit intent: clarity
Original:  Genericity is achieved by modelling transition types as endofunctors on sets, and systems as coalgebras.
Revised:  Genericity is achieved by modelling transition types as functors on sets, and systems as coalgebras.
Edit intent: fluency
Original:  In the present work, we refine the runtime analysis of our algorithm to cover additional instances, notably weighted automata and, more generally, weighted tree automata.
Revised:  In the present work, we refine the run time analysis of our algorithm to cover additional instances, notably weighted automata and, more generally, weighted tree automata.
Edit intent: clarity
Original:  For weights in a cancellative monoid we match, and for non-cancellative monoids such as (the additive monoid of) the tropical semiring even substantially improve, the asymptotic runtime of the best known algorithms.
Revised:  For weights in a cancellative monoid we match, and for non-cancellative monoids such as (the additive monoid of) the tropical semiring even substantially improve, the asymptotic run time of the best known algorithms.
Edit intent: clarity
Original: A set function is called XOS if it can be represented by the maximum of additive functions , where a set function f is additive if f(X) = \sum_{x \in Xf(\{x\}) for each X} . When such a representation is fixed, the number of additive functions to define the XOS function is called the width.
Revised: A set function is called XOS if it can be represented by the maximum of additive functions f(\{x\}) for each X} . When such a representation is fixed, the number of additive functions to define the XOS function is called the width.
Edit intent: coherence
Original:  We show two types of tight bounds on  polynomial-time approximability for this problem.
Revised:  We show two types of tight bounds on the polynomial-time approximability for this problem.
Edit intent: fluency
Original:  First, in general, the approximation bound is between \mathrm{O (n) and \Omega(n^{1-\epsilon}) for any \epsilon > 0, where n is the ground set size.
Revised:  First, in general, the approximation bound is between O (n) and \Omega(n^{1-\epsilon}) for any \epsilon > 0, where n is the ground set size.
Edit intent: clarity
Original:  When such a representation is fixed, the number of additive functions  to define the XOS function is called the width.
Revised:  When such a representation is fixed, the number of additive functions required to define the XOS function is called the width.
Edit intent: clarity
Original:  The method has the attractive properties of full hybridized methods, namely a H({\rm div})-conforming velocity field, pointwise satisfaction of the continuity equation and \emph{a priori} error estimates for the velocity that are independent of the pressure.
Revised:  The method has the attractive properties of full hybridized methods, namely an H({\rm div})-conforming velocity field, pointwise satisfaction of the continuity equation and \emph{a priori} error estimates for the velocity that are independent of the pressure.
Edit intent: fluency
Original:  The analysis results are supported by a range of numerical examples that demonstrate rates of convergence, and which show substantial computational efficiency gains over a full hybridized formulation.
Revised:  The analysis results are supported by a range of numerical examples that demonstrate rates of convergence, and which show computational efficiency gains over a full hybridized formulation.
Edit intent: clarity
Original:  We show that object-oriented languages, such as C++, can be interpreted as parallel programming languages , and standard sequential programs can be parallelized automatically . Parallel C++ code is typically more than ten times shorter than the equivalent C++ code with MPI.
Revised:  We show that object-oriented languages, such as C++, can be interpreted as parallel programming languages . Parallel C++ code is typically more than ten times shorter than the equivalent C++ code with MPI.
Edit intent: coherence
Original:  We believe that implementation and standardization of parallel object-oriented languages will drastically reduce the cost of parallel programming.
Revised:  We believe that implementation and standardization of parallel object-oriented framework has the potential to drastically reduce the cost of parallel programming.
Edit intent: clarity
Original:  We describe a novel compiler architecture with a dedicated back end for the interconnect fabric, making the network a part of a multiprocessor computer, rather than a collection of pipes between processor nodes.
Revised:  We describe a novel compiler architecture with a dedicated backend for the interconnect fabric, making the network a part of a multiprocessor computer, rather than a collection of pipes between processor nodes.
Edit intent: fluency
Original:  To overcome this, we introduce a budgeted regularized pruning framework for deep convolutional neural networks .
Revised:  To overcome this, we introduce a budgeted regularized pruning framework for deep CNNs .
Edit intent: clarity
Original:  this allows us to attain pruning factors up to 16x without significantly affecting the accuracy .
Revised:  this allows us to attain pruning factors up to 16x without significant accuracy drop .
Edit intent: clarity
Original: Adam and RMSProp , as two of the most influential adaptive stochastic algorithms for training deep neural networks,  have been pointed out to be divergent even in the convex setting via a few simple counterexamples.
Revised: Adam and RMSProp are two of the most influential adaptive stochastic algorithms for training deep neural networks, have been pointed out to be divergent even in the convex setting via a few simple counterexamples.
Edit intent: fluency
Original: Adam and RMSProp , as two of the most influential adaptive stochastic algorithms for training deep neural networks,  have been pointed out to be divergent even in the convex setting via a few simple counterexamples.
Revised: Adam and RMSProp , as two of the most influential adaptive stochastic algorithms for training deep neural networks, which have been pointed out to be divergent even in the convex setting via a few simple counterexamples.
Edit intent: coherence
Original:  Many attempts, such as decreasing an adaptive learning rate, adopting a big batch size, incorporating a temporal decorrelation technique, seeking an analogous surrogate, etc. , have been tried to promote Adam/RMSProp-type algorithms to converge.
Revised:  Many attempts, such as decreasing an adaptive learning rate, adopting a big batch size, incorporating a temporal decorrelation technique, seeking an analogous surrogate, etc. , have been tried to promote Adam/RMSProp-type algorithms to converge.
Edit intent: fluency
Original:  Moreover, we show that the convergences of several variants of Adam, such as AdamNC, AdaEMA, etc. , can be directly implied via the proposed sufficient condition in the non-convex setting.
Revised:  Moreover, we show that the convergences of several variants of Adam, such as AdamNC, AdaEMA, etc. , can be directly implied via the proposed sufficient condition in the non-convex setting.
Edit intent: fluency
Original:  This observation together with this sufficient condition gives much deeper interpretations on their divergences.
Revised:  This observation coupled with this sufficient condition gives much deeper interpretations on their divergences.
Edit intent: fluency
Original:  At last, we validate the sufficient condition by applying Adam and RMSProp to tackle the counterexamples and train deep neural networks.
Revised:  At last, we validate the sufficient condition by applying Adam and RMSProp to tackle a certain counterexample and train deep neural networks.
Edit intent: clarity
Original:  Numerical results are exactly in accord with the analysisin theory .
Revised:  Numerical results are exactly in accord with our theoretical analysis .
Edit intent: fluency
Original: Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong  such that at most k edges are weak and for each induced P_3 in G at least one edge is weak.
Revised: Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak such that at most k edges are weak and for each induced P_3 in G at least one edge is weak.
Edit intent: clarity
Original: Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong  such that at most k edges are weak and for each induced P_3 in G at least one edge is weak.
Revised: Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong and such that at most k edges are weak and for each induced P_3 in G at least one edge is weak.
Edit intent: fluency
Original:  In Edge-List Multi-STC and Vertex-List Multi-STC we may additionally restrict the set of permitted colors for each edge of G. We show that, under the ETH , Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2^{o(|V|^2)} , and that Multi-STC is NP-hard for every fixed~c .
Revised:  In Edge-List Multi-STC and Vertex-List Multi-STC we may additionally restrict the set of permitted colors for each edge of G. We show that, under the ETH , Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2^{o(|V|^2)} .
Edit intent: coherence
Original:  Then, we show that no semi-direct product (and, thus, also no direct product) of an arbitrary semigroup with a (non-trivial) subsemigroup of the free monogenic semigroup is an automaton semigroup.
Revised:  Then, we show that no semidirect product (and, thus, also no direct product) of an arbitrary semigroup with a (non-trivial) subsemigroup of the free monogenic semigroup is an automaton semigroup.
Edit intent: fluency
Original:  We  will show that there is an equivalence between these two Gaussian processes when the domain is infinite -- for us, R or \mathbb{R ^2 -- which breaks down when the domain is finite due to the effect of boundary conditions on Green's functions of PDEs.
Revised:  We will show that there is an equivalence between these two Gaussian processes when the domain is infinite -- for us, R ^2 -- which breaks down when the domain is finite due to the effect of boundary conditions on Green's functions of PDEs.
Edit intent: clarity
Original:  We then introduce the semivariogram method for obtaining point estimates of the Mat\'ern covariance hyper-parameters, which specifies the Gaussian prior needed for stabilizing the inverse problem.
Revised:  We then introduce the semivariogram method for estimating the Mat\'ern covariance hyper-parameters, which specifies the Gaussian prior needed for stabilizing the inverse problem.
Edit intent: clarity
Original:  We then introduce the semivariogram method for obtaining point estimates of the Mat\'ern covariance hyper-parameters, which specifies the Gaussian prior needed for stabilizing the inverse problem.
Revised:  We then introduce the semivariogram method for obtaining point estimates of the Mat\'ern covariance parameters, which specify the Gaussian prior needed for stabilizing the inverse problem.
Edit intent: clarity
Original:  We consider rough set pairs (X_E,X^T), where the lower approximation X_E is defined as is customary in rough set theory, but because T is assumed to be E-compatible, X^T allows more elements to be possibly in X , because X^E\subseteq X^T.
Revised:  We consider rough set pairs (X_E,X^T), where the lower approximation X_E is defined as is customary in rough set theory, but X^T allows more elements to be possibly in X , because X^E\subseteq X^T.
Edit intent: coherence
Original:  The benchmarking framework is available as an open-source Python package.
Revised:  The benchmarking open-source Python package.
Edit intent: clarity
Original:  Furthermore, existing load balancers rely on one of two methods: host-level traffic redirection, which may add as much as 8.5 \% additional traffic to underlying networks, or connection tracking, which consumes a considerable amount of memory in load balancers and is prone to denial of service attacks .
Revised:  Furthermore, existing load balancers rely on one of two methods: host-level traffic redirection, which may add as much as 8.5 \% additional traffic to underlying networks, or connection tracking, which consumes a considerable amount of memory in load balancers .
Edit intent: coherence
Original:  Both of these methods result in inefficient usage of networking resources.
Revised:  Both of these methods result in inefficient usage of network resources.
Edit intent: fluency
Original:  We propose the In-Network Congestion-Aware load Balancer (INCAB) to achieve even load distribution and optimize network resources used for load balancing in addition to meeting the PCC requirement.
Revised:  We propose the in-network congestion-aware load Balancer (INCAB) to achieve even load distribution and optimize network resources used for load balancing in addition to meeting the PCC requirement.
Edit intent: fluency
Original:  We propose the In-Network Congestion-Aware load Balancer (INCAB) to achieve even load distribution and optimize network resources used for load balancing in addition to meeting the PCC requirement.
Revised:  We propose the In-Network Congestion-Aware load Balancer (INCAB) to achieve even load distribution among service instances and optimal network resources usage in addition to meeting the PCC requirement.
Edit intent: clarity
Original:  We show that our congestion-aware solution capable of identifying and monitoring each instance's most-utilized resource improves the load distribution among all service instances.
Revised:  We show that INCAB is capable of identifying and monitoring each instance's most-utilized resource improves the load distribution among all service instances.
Edit intent: clarity
Original:  We show that our congestion-aware solution capable of identifying and monitoring each instance's most-utilized resource improves the load distribution among all service instances.
Revised:  We show that our congestion-aware solution capable of identifying and monitoring each instance's most-utilized resource and can improve the load distribution among all service instances.
Edit intent: clarity