wanyu/IteraTeR_v2 huggingface dataset:
Original:  Importantly, it is the first theoretical result that canexactly recover the rate of the centralized SGD, and has optimal dependence on the algebraic connectivity of the networks when using stochastic gradients .
Revised:  Importantly, it is the first theoretical result that canexactly recover the rate of the centralized SGD, and has optimal dependence on the algebraic connectivity and can exactly recover the rate of the centralized stochastic gradient method .
Edit intent: clarity
Original: This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for a non-convex empirical risk minimization problem over a peer-to-peer network  , which is in sharp contrast to the existing DSGT works only for the convex problem.
Revised: This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for non-convex empirical risk minimization problem over a peer-to-peer network , which is in sharp contrast to the existing DSGT works only for the convex problem.
Edit intent: fluency
Original: This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for a non-convex empirical risk minimization problem over a peer-to-peer network  , which is in sharp contrast to the existing DSGT works only for the convex problem.
Revised: This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for a non-convex empirical risk minimization problems over a peer-to-peer network , which is in sharp contrast to the existing DSGT works only for the convex problem.
Edit intent: fluency
Original:  To handle the variance among decentralized datasets, the mini-batch in each node of the network is designed to be proportional to the size of its local dataset.
Revised:  To handle the variance among decentralized datasets, the mini-batch in each node of the network is designed to be proportional to the size of the local dataset.
Edit intent: clarity
Original:  Moreover, we demonstrate that DSGT could achieve a linear speedup while a sublinear speedup is also possible, depending on the problem at hand.
Edit intent: coherence
Original:  Numerical experiments for neural networks and logistic regression problems on CIFAR-10 finally illustrate the advantages of DSGT for decentralized training .
Revised:  Numerical experiments for neural networks and logistic regression problems on CIFAR-10 finally illustrate the advantages of DSGT .
Edit intent: clarity
Original: This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for non-convex empirical risk minimization problems over a peer-to-peer network of nodes, which is in sharp contrast to the existing DSGT works only for convex problems.
Revised: This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for non-convex empirical risk minimization problems over a peer-to-peer network of nodes, which is in sharp contrast to the existing DSGT only for convex problems.
Edit intent: clarity
Original:  We explicitly evaluate the convergence rate of DSGT with both constant and decreasing stepsizes in terms of algebraic connectivity of the network, mini-batch size, gradient variance, etc.
Revised:  We explicitly evaluate the convergence rate of DSGT with respect to the number of iterations in terms of algebraic connectivity of the network, mini-batch size, gradient variance, etc.
Edit intent: clarity
Original:  Furthermore, we show that DSGT has a network independence property under certain conditions, which means that the network topology only affects the convergence rate up to a constant factor.
Revised:  Under certain conditions, we further show that DSGT has a network independence property under certain conditions, which means that the network topology only affects the convergence rate up to a constant factor.
Edit intent: clarity
Original:  Furthermore, we show that DSGT has a network independence property under certain conditions, which means that the network topology only affects the convergence rate up to a constant factor.
Revised:  Furthermore, we show that DSGT has a network independence property in the sense that the network topology only affects the convergence rate up to a constant factor.
Edit intent: clarity
Original:  Hence, the convergence rate of DSGT with respect to the number of iterations can be comparable to the centralized stochastic gradient method (SGD ).
Revised:  Hence, the convergence rate of DSGT can be comparable to the centralized stochastic gradient method (SGD ).
Edit intent: clarity
Original: A substring u of a string T is called a minimal unique substring ~ (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. A string w is called a minimal absent word ~ (MAW) of T if w does not occur in T and any proper substring of w occurs in T.
Revised: A substring u of a string T is called a minimal unique substring (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. A string w is called a minimal absent word ~ (MAW) of T if w does not occur in T and any proper substring of w occurs in T.
Edit intent: fluency
Original: A substring u of a string T is called a minimal unique substring ~ (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. A string w is called a minimal absent word ~ (MAW) of T if w does not occur in T and any proper substring of w occurs in T.
Revised: A substring u of a string T is called a minimal unique substring ~ (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. A string w is called a minimal absent word (MAW) of T if w does not occur in T and any proper substring of w occurs in T.
Edit intent: fluency
Original: We investigate  coexistence of an age optimizing network (AON) and a throughput optimizing network (TON) that access the same wireless spectrum bandusing a WiFi-like CSMA/CA based access .
Revised: We investigate the coexistence of an age optimizing network (AON) and a throughput optimizing network (TON) that access the same wireless spectrum bandusing a WiFi-like CSMA/CA based access .
Edit intent: fluency
Original: We investigate  coexistence of an age optimizing network (AON) and a throughput optimizing network (TON) that access the same wireless spectrum bandusing a WiFi-like CSMA/CA based access .
Revised: We investigate coexistence of an age optimizing network (AON) and a throughput optimizing network (TON) that share a common spectrum band .
Edit intent: clarity
Original:  We consider two modes of long run coexistence: (a) networks compete with each other for spectrum access  causing them to interfere and (b) networks cooperate and achieve non-interfering access.
Revised:  We consider two modes of long run coexistence: (a) networks compete with each other for spectrum access , causing them to interfere and (b) networks cooperate and achieve non-interfering access.
Edit intent: fluency
Original:  We consider two modes of long run coexistence: (a) networks compete with each other for spectrum access  causing them to interfere and (b) networks cooperate and achieve non-interfering access.
Revised:  We consider two modes of long run coexistence: (a) networks compete with each other for spectrum access causing them to interfere and (b) networks cooperate to achieve non-interfering access.
Edit intent: coherence
Original:  To model competition, we define a non-cooperative stage game parameterized by  average age of the AON at the beginning of the stage, derive its mixed strategy Nash equilibrium (MSNE), and analyze the evolution of age and throughput over an infinitely repeated game in which each network plays the MSNE in every stage.
Revised:  To model competition, we define a non-cooperative stage game parameterized by the average age of the AON at the beginning of the stage, derive its mixed strategy Nash equilibrium (MSNE), and analyze the evolution of age and throughput over an infinitely repeated game in which each network plays the MSNE in every stage.
Edit intent: fluency
Original:  To model competition, we define a non-cooperative stage game parameterized by  average age of the AON at the beginning of the stage, derive its mixed strategy Nash equilibrium (MSNE), and analyze the evolution of age and throughput over an infinitely repeated game in which each network plays the MSNE in every stage.
Revised:  To model competition, we define a non-cooperative stage game parameterized by average age of the AON at the beginning of the stage, derive its mixed strategy Nash equilibrium (MSNE), and analyze the evolution of age and throughput over an infinitely repeated game in which each network plays the MSNE at every stage.
Edit intent: fluency
Original:  Cooperation has a coordination device use a coin toss during each stage to select the network that must access the medium.
Revised:  Cooperation uses a coordination device use a coin toss during each stage to select the network that must access the medium.
Edit intent: fluency
Original:  Cooperation has a coordination device use a coin toss during each stage to select the network that must access the medium.
Revised:  Cooperation has a coordination device that performs a coin toss during each stage to select the network that must access the medium.
Edit intent: clarity
Original:  Networks use the grim trigger punishment strategy, reverting to playing the MSNE every stage forever , if the other disobeys the device.
Revised:  Networks use the grim trigger punishment strategy, reverting to playing the MSNE every stage forever if the other disobeys the device.
Edit intent: fluency
Original:  We determine if there exists a subgame perfect equilibrium, that is the networks obey the device forever as they find cooperation beneficial.
Revised:  We determine if there exists a subgame perfect equilibrium, i.e., the networks obey the device forever as they find cooperation beneficial.
Edit intent: clarity
Original:  We find that networks choose to cooperate only when they have a small enough number of nodes . Else, they would rather disobey the device and compete.
Revised:  We show that networks choose to cooperate only when they have a small enough number of nodes . Else, they would rather disobey the device and compete.
Edit intent: clarity
Original:  We find that networks choose to cooperate only when they have a small enough number of nodes . Else, they would rather disobey the device and compete.
Revised:  We find that networks choose to cooperate only when they consist of a sufficiently small number of nodes . Else, they would rather disobey the device and compete.
Edit intent: clarity
Original:  We find that networks choose to cooperate only when they have a small enough number of nodes . Else, they would rather disobey the device and compete.
Revised:  We find that networks choose to cooperate only when they have a small enough number of nodes , otherwise they prefer to disobey the device and compete.
Edit intent: clarity
Original:  Given a graphon, we endow the latent space of the nodes with the so-called neighborhood distance that measures the propensity of two nodes to be connected with similar nodes.
Revised:  Given a graphon, we endow the latent space of the nodes with the neighborhood distance that measures the propensity of two nodes to be connected with similar nodes.
Edit intent: clarity
Original:  However, many real-world problems require a joint objective that is non-linear and dynamic programming cannot be applied directly.
Revised:  However, many real-world problems require optimization of an objective that is non-linear and dynamic programming cannot be applied directly.
Edit intent: clarity
Original:  For example, in a resource allocation problem, one of the objective is to maximize long-term fairness among the users.
Revised:  For example, in a resource allocation problem, one of the objectives is to maximize long-term fairness among the users.
Edit intent: fluency
Original:   This paper addresses and formalizes the problem of joint objective optimization, where not only the sum of rewards of each agent but a function of the sum of rewardsof each agent needs to be optimized.
Revised:  This paper addresses and formalizes the problem of optimizing a non-linear function of the sum of rewardsof each agent needs to be optimized.
Edit intent: clarity
Original:  We propose both model-based and model-free algorithms  , where the model-based algorithm is shown to achieve (\sqrt{\frac{KO\left({T}}}\right)  .
Revised:  We propose both model-based and model-free algorithms , where the model-based policy is shown to achieve (\sqrt{\frac{KO\left({T}}}\right) .
Edit intent: clarity
Original:  Further, using  fairness in cellular base-station scheduling as an example , the proposed algorithms are shown to significantly outperform the state-of-the-art approaches.
Revised:  Further, using the fairness in cellular base-station scheduling as an example , the proposed algorithms are shown to significantly outperform the state-of-the-art approaches.
Edit intent: fluency
Original:  Further, using  fairness in cellular base-station scheduling as an example , the proposed algorithms are shown to significantly outperform the state-of-the-art approaches.
Revised:  Further, using fairness in cellular base-station scheduling as an example , the proposed algorithm is shown to significantly outperform the state-of-the-art approaches.
Edit intent: fluency
Original:  Global deviations of this dynamics on the other hand reflects pathological conditions.
Revised:  Global deviations from this dynamics on the other hand reflects pathological conditions.
Edit intent: clarity
Original:  The numerical simulations demonstrated however that the probability to exhibit the pathological dynamics in this case is maintained at <10\sim10 \\%DIF < , even when the population contains only a single cell that displays physiological dynamics .
Revised:  The numerical simulations demonstrated however that the probability to exhibit stable pathological dynamics in this case is maintained at <10\sim10 \\%DIF < , even when the population contains only a single cell that displays physiological dynamics .
Edit intent: clarity
Original:  The numerical simulations demonstrated however that the probability to exhibit the pathological dynamics in this case is maintained at <10\sim10 \\%DIF < , even when the population contains only a single cell that displays physiological dynamics .
Revised:  The numerical simulations demonstrated however that the probability to exhibit the pathological dynamics in this case is less than\sim10 \\%DIF < , even when the population contains only a single cell that displays physiological dynamics .
Edit intent: clarity
Original:  This results therefore suggest that the physiological bursting dynamics %DIF > . These results therefore suggest that the physiological bursting  of a population of beta-cells is cooperatively regulated, even when single-cells acquire disfunctional channels that induce intercellular communication defects  .
Revised:  This results therefore suggest that the physiological bursting dynamics %DIF > . These results therefore suggest that the physiological bursting dynamics of a population of beta-cells is cooperatively regulated, even when single-cells acquire disfunctional channels that induce intercellular communication defects .
Edit intent: fluency
Original:  This results therefore suggest that the physiological bursting dynamics %DIF > . These results therefore suggest that the physiological bursting  of a population of beta-cells is cooperatively regulated, even when single-cells acquire disfunctional channels that induce intercellular communication defects  .
Revised:  This results therefore suggest that the physiological bursting dynamics %DIF > . These results therefore suggest that the physiological bursting of a population of beta-cells is cooperatively regulated, even under intercellular communication defects .
Edit intent: clarity
Original:  To this end, we aim to provide a stack of declarative languages with R-like syntax for the different lifecycle tasks, and users with different expertise.
Revised:  To this end, we aim to provide a stack of declarative language abstractions for the different lifecycle tasks, and users with different expertise.
Edit intent: clarity
Original:  Using DRLViz, experts are assisted to interpret  using memory reduction interactions, to investigate parts of the memory role when errors have been made , and ultimately to improve the agent training process.
Revised:  Using DRLViz, experts are assisted to interpret decisions using memory reduction interactions, to investigate parts of the memory role when errors have been made , and ultimately to improve the agent training process.
Edit intent: clarity
Original:  Using DRLViz, experts are assisted to interpret  using memory reduction interactions, to investigate parts of the memory role when errors have been made , and ultimately to improve the agent training process.
Revised:  Using DRLViz, experts are assisted to interpret using memory reduction interactions, and to investigate the role of parts of the memory role when errors have been made , and ultimately to improve the agent training process.
Edit intent: clarity
Original:  Using DRLViz, experts are assisted to interpret  using memory reduction interactions, to investigate parts of the memory role when errors have been made , and ultimately to improve the agent training process.
Revised:  Using DRLViz, experts are assisted to interpret using memory reduction interactions, to investigate parts of the memory when errors have been made , and ultimately to improve the agent training process.
Edit intent: clarity
Original:  We report on several examples of use of DRLViz , in the context of video games simulators (ViZDoom) for a navigation scenario with item gathering tasks.
Revised:  We report on DRLViz applied in the context of video games simulators (ViZDoom) for a navigation scenario with item gathering tasks.
Edit intent: clarity
Original:  A trace FEM based on standard Taylor-Hood (continuous \mathbf P_2-P_1 ) bulk elements is proposed.
Revised:  A trace FEM based on standard Taylor-Hood (continuous P2-P1 ) bulk elements is proposed.
Edit intent: clarity
Original:  The key result proved in the paper is an inf-sup stability of the trace \mathbf P_2-P_1 finite element pair, with the stability constant uniformly bounded with respect to the discretization parameter and the position of the surface in the bulk mesh.
Revised:  The key result proved in the paper is an inf-sup stability of the trace P2-P1 finite element pair, with the stability constant uniformly bounded with respect to the discretization parameter and the position of the surface in the bulk mesh.
Edit intent: clarity
Original: Preferred walking speed is a widely-used performance measure for people with mobility issues . Often these speeds are measured walking in a straight line and walking over short distances .
Revised: Preferred walking speed is a widely-used performance measure for people with mobility issues , but is usually measured in straight line walking for fixed distances or durations .
Edit intent: clarity
Original:  Here, we observe walking for short distances and walking in circles in subjects with unilateral lower-limb amputation using a Jaipur Foot prosthetic leg.
Revised:  Here, we studied walking for short distances and walking in circles in subjects with unilateral lower-limb amputation using a Jaipur Foot prosthetic leg.
Edit intent: clarity
Original:  Here, we observe walking for short distances and walking in circles in subjects with unilateral lower-limb amputation using a Jaipur Foot prosthetic leg.
Revised:  Here, we observe walking for short distances and walking in circles in unilateral lower-limb amputation using a Jaipur Foot prosthetic leg.
Edit intent: clarity
Original: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em  {\em   .
Revised: We introduce the notion of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em {\em .
Edit intent: clarity
Original: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em  {\em   .
Revised: We introduce the problem of {\em stable manipulation } , where colluding manipulator(s) need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em {\em .
Edit intent: clarity
Original: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em  {\em   .
Revised: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em {\em .
Edit intent: clarity
Original: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em  {\em   .
Revised: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election when their knowledge about the others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em {\em .
Edit intent: clarity
Original: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em  {\em   .
Revised: We introduce the problem of {\em stable manipulation } where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes{\em {\em ) .
Edit intent: fluency
Original:  In contrast, stable manipulation becomes intractable for the Copeland^\alpha voting rule for every \alpha\in[0,1] even for  single manipulator.
Revised:  In contrast, stable manipulation becomes intractable for the Copeland^\alpha voting rule for every \alpha\in[0,1] even for a single manipulator.
Edit intent: fluency