wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Hierarchical variational inference is employed to jointly detect and typologize block-structures as local signals or global noise. These principles are incorporated into novel community detection algorithm called Stochastic Block (with) Ambient Noise Model(SBANM) for multilayer weighted networks.
Revised:  Hierarchical variational inference is employed to jointly detect and typologize blocks as signal or noise. We call this model for multilayer weighted networks the Stochastic Block (with) Ambient Noise Model(SBANM) for multilayer weighted networks.
Edit intent: clarity
Original:  These principles are incorporated into novel community detection algorithm called Stochastic Block (with) Ambient Noise Model(SBANM) for multilayer weighted networks. We apply this method to several different domains.
Revised:  These principles are incorporated into novel community detection algorithm called Stochastic Block (with) Ambient Noise Model(SBANM) and develop an associated community detection algorithm. Then we apply this method to several different domains.
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Original:  We perform a parametric study to evaluate the (theoretical) performance of the algorithm using a Van der Pol oscillator , and conduct a series of simulated experiments in Gazebo using a non-holonomic wheeled robot.
Revised:  We perform a parametric study to evaluate the (theoretical) performance of the algorithm using a Van der Pol oscillator and conduct a series of simulated experiments in Gazebo using a non-holonomic wheeled robot.
Edit intent: fluency
Original: We prove a rate of convergence of order 1/N for the N-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common noise  for the L^2-error on its L-derivative \partial_\mu v} .
Revised: We prove a rate of convergence for the N-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common noise for the L^2-error on its L-derivative \partial_\mu v} .
Edit intent: clarity
Original: We prove a rate of convergence of order 1/N for the N-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common noise  for the L^2-error on its L-derivative \partial_\mu v} .
Revised: We prove a rate of convergence of order 1/N for the N-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common noise . The rate is of order 1/N for the pathwise error on the solution v and of order 1/\sqrt{N for the L^2-error on its L-derivative \partial_\mu v} .
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Original:  We  end with suggesting a conceptual framework that is supposed to be used in  very early stages of technology development and integration for and in work contexts.
Revised:  We deliberately aim at a networked way of thinking in scientific contexts and thus combine multidisciplinary subject areas in one paper to present an innovative way to deal with multi-faceted problems in a human-centred way. We end with suggesting a conceptual framework that is supposed to be used in very early stages of technology development and integration for and in work contexts.
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Original:  The efficiency of the applied method in fHRs extraction has been evaluated with 15 real fHR signals, along with the simulated fPCGs public database available at PhysioBank.
Revised:  The efficiency of the applied method in fHRs extraction has been evaluated with 15 real fPCG signals, along with the simulated fPCGs public database available at PhysioBank.
Edit intent: fluency
Original:  Let us consider a different, seemingly unrelated problem in graph theory: given three arbitrary square matrices P, I and C with elements in \mathbb{R\cup\{-\infty\}, find all real values of parameter \lambda such that the parametric directed graph having arcs weights of the form w((j,i)) = \max(P_{ij} + \lambda, I_{ij} - \lambda, C_{ij}) (for all arcs (j,i)) }  does not contain circuits with positive weight.
Revised:  \cup\{-\infty\}, find all real values of parameter \lambda such that the parametric directed graph having arcs weights of the form w((j,i)) = \max(P_{ij} + \lambda, I_{ij} - \lambda, C_{ij}) (for all arcs (j,i)) } does not contain circuits with positive weight.
Edit intent: coherence
Original:  Let us consider a different, seemingly unrelated problem in graph theory: given three arbitrary square matrices P, I and C with elements in \mathbb{R\cup\{-\infty\}, find all real values of parameter \lambda such that the parametric directed graph having arcs weights of the form w((j,i)) = \max(P_{ij} + \lambda, I_{ij} - \lambda, C_{ij}) (for all arcs (j,i)) }  does not contain circuits with positive weight.
Revised:  Let us consider a different, seemingly unrelated problem in graph theory: given three arbitrary square matrices P, I and C with elements in \mathbb{R\cup\{-\infty\}, find all real values of parameter \lambda such that the parametric directed graph having arcs weights of the form w((j,i)) = \max(P_{ij} + \lambda, I_{ij} - \lambda, C_{ij}) (for all arcs (j,i)) } In graph theory, the Proportional-Inverse-Constant-Non-positive Circuit weight Problem (PIC-NCP) consists in finding all the values of a parameter such that a particular parametric weighted directed graph does not contain circuits with positive weight.
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Original:  consequently, we prove that the same algorithm can be used to find d-periodic trajectories in P-TEGs faster than with previous approaches .
Revised:  consequently, we prove that the same algorithm can be used to find d-periodic trajectories in P-TEGs . Morever, exploiting the connection between the PIC-NCP and max-plus algebra, we prove that the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d .
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Original:  Morever , exploiting the connection between the PIC-NCP and max-plus algebra , we prove that  the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.
Revised:  Moreover , exploiting the connection between the PIC-NCP and max-plus algebra , we prove that the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.
Edit intent: coherence
Original:  Morever , exploiting the connection between the PIC-NCP and max-plus algebra , we prove that  the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.
Revised:  Morever , exploiting the connection between the PIC-NCP and max-plus algebra we prove that the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.
Edit intent: fluency
Original:  Morever , exploiting the connection between the PIC-NCP and max-plus algebra , we prove that  the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.
Revised:  Morever , exploiting the connection between the PIC-NCP and max-plus algebra , we prove that , given a P-TEG, the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.
Edit intent: meaning-changed
Original: Continual Learning (CL) algorithms have recently received a lot of attention as they attempt to overcome the need to train with an i.i.d. sample from some unknown target data distribution. Building on prior work, we study principled ways to tackle the CL problem by adopting a Bayesian perspective and focus on continually learning a task-specific posterior distribution via a shared meta-model, a task-conditioned hypernetwork.
Revised: Continual Learning (CL) algorithms have recently received a lot of attention as they attempt to overcome the need to train with an i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off Bayesian updates yield the same result. In practice, however, recursive updating often leads to poor trade-off solutions across tasks because approximate inference is necessary for most models of interest. Here, we describe an alternative Bayesian approach where task-conditioned hypernetwork.
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Original:  Building on prior work, we study principled ways to tackle the CL problem by adopting a Bayesian perspective and focus on continually learning a task-specific posterior distribution via a shared meta-model, a task-conditioned hypernetwork. This approach, which we term Posterior-replay CL, is in sharp contrast to most Bayesian CL approaches that focus on the recursive update of a single posterior distribution. The benefits of our approach are (1) an increased flexibility to model solutions in weight space and therewith less susceptibility to task dissimilarity, (2) access to principled task-specific predictive uncertainty estimates, that can be used to infer task identity during test time and to detect task boundaries during training, and (3) the ability to revisit and update task-specific posteriors in a principled manner without requiring access to past data. The proposed framework is versatile, which we demonstrate using simple posterior approximations (such as Gaussians) as well as powerful, implicit distributions modelled via a neural network. We illustrate the conceptual advance of our framework on low-dimensional problems and show performance gains on computer vision benchmarks .
Revised:  Building on prior work, we study principled ways to tackle the CL problem by adopting a Bayesian perspective and focus on continually learning a task-specific posterior distribution via a shared meta-model, a task-conditioned parameter distributions are continually inferred from data. We offer a practical deep learning implementation of our framework based on probabilistic task-conditioned hypernetworks, an approach we term "posterior meta-replay". Experiments on standard benchmarks show that our probabilistic hypernetworks compress sequences of posterior parameter distributions with virtually no URLetting. We obtain considerable performance gains compared to existing Bayesian CL methods, and identify task inference as our major limiting factor. This limitation has several causes that are independent of the considered sequential setting, opening up new avenues for progress in CL .
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Original:  This paper establishes a new convergence analysis of neural TD learningwithout any projection . We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(%DIFDELCMD < \nu%%% , 1/\epsilon) converges to the true value function with error \epsilon given poly(%DIFDELCMD < \nu%%% , 1/\epsilon) iterations or samples, where%DIFDELCMD < \nu %%% is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel.
Revised:  This paper establishes a new convergence analysis of neural TD learningwithout any projection %DIFDELCMD < \nu%%% , 1/\epsilon) converges to the true value function with error \epsilon given poly(%DIFDELCMD < \nu%%% , 1/\epsilon) iterations or samples, where%DIFDELCMD < \nu %%% is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel.
Edit intent: coherence
Original:  We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(%DIFDELCMD < \nu%%% , 1/\epsilon) converges to the true value function with error \epsilon given poly(%DIFDELCMD < \nu%%% , 1/\epsilon) iterations or samples, where%DIFDELCMD < \nu %%% is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel.
Revised:  We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(%DIFDELCMD < \nu%%% %DIFDELCMD < \nu%%% , 1/\epsilon) iterations or samples, where%DIFDELCMD < \nu %%% is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel.
Edit intent: coherence
Original:  We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(%DIFDELCMD < \nu%%% , 1/\epsilon) converges to the true value function with error \epsilon given poly(%DIFDELCMD < \nu%%% , 1/\epsilon) iterations or samples, where%DIFDELCMD < \nu %%% is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel.
Revised:  We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(%DIFDELCMD < \nu%%% , 1/\epsilon) converges to the true value function with error \epsilon given poly(%DIFDELCMD < \nu%%% %DIFDELCMD < \nu %%% is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel.
Edit intent: clarity
Original:  We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(%DIFDELCMD < \nu%%% , 1/\epsilon) converges to the true value function with error \epsilon given poly(%DIFDELCMD < \nu%%% , 1/\epsilon) iterations or samples, where%DIFDELCMD < \nu %%% is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel. Our sample complexity and overparameterization bounds are based on a drift analysis of the network parameters as a stopped random process in the lazy training regime .
Revised:  We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(%DIFDELCMD < \nu%%% , 1/\epsilon) converges to the true value function with error \epsilon given poly(%DIFDELCMD < \nu%%% , 1/\epsilon) iterations or samples, where%DIFDELCMD < \nu %%% We consider two practically used algorithms, projection-free and max-norm regularized Neural TD learning, and establish the first convergence bounds for these algorithms. An interesting observation from our results is that max-norm regularization can dramatically improve the performance of TD learning algorithms, both in terms of sample complexity and overparameterization. In particular, we prove that max-norm regularization appears to be more effective than \ell_2-regularization, again both in terms of sample complexity and overparameterization bounds are based on a drift analysis of the network parameters as a stopped random process in the lazy training regime .
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Original:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in this case . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero  .
Revised:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in the binary linear classification . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero .
Edit intent: meaning-changed
Original:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in this case . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero  .
Revised:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in this case . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero . We extend the analysis to general cases and prove local smoothness in several cases. Our analysis reveals that the constraint of adversarial examples is a cause of the non-smoothness of adversarial loss. Moreover, we reveal the relation between the flatness of the loss function with respect to input data and the smoothness of the adversarial loss with respect to parameters. Our analysis implies that if we flatten the loss function with respect to input data, the smoothness of adversarial loss tends to decrease .
Edit intent: meaning-changed
Original:  Since adversarial attacks are the worst noise for the models, they should depend on the parameters of the models. In this study , we analyze the smoothness of the loss function of adversarial training for binary linear classification and for general cases considering the dependence .
Revised:  Since adversarial attacks are the worst noise for the models, they should depend on the parameters . Considering this dependence , we analyze the smoothness of the loss function of adversarial training for binary linear classification and for general cases considering the dependence .
Edit intent: clarity
Original:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in the binary linear classification . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero.
Revised:  We reveal that the constraint of adversarial attacks is one cause of the non-smoothness and that the smoothness depends on the types of constraints of adversarial attacks in the binary linear classification . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero.
Edit intent: meaning-changed
Original:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in the binary linear classification . Specifically, under the L2 constraints, the adversarial loss is smooth except at zero. We extend the analysis to general cases and prove local smoothness in several cases. Our analysis reveals that the constraint of adversarial examples is a cause of the non-smoothness of adversarial loss .
Revised:  We reveal that the Lipschitz continuity depends on the types of constraints of adversarial attacks in the binary linear classification . Specifically, the L_\infty constraint can cause non-smoothness of adversarial loss .
Edit intent: meaning-changed
Original:  Moreover, we reveal the relation between the flatness of the loss function with respect to input data and the smoothness of the adversarial loss with respect to parameters. Our analysis implies that if we flatten the loss function with respect to input data, the smoothness of adversarial loss tends to decrease .
Revised:  Moreover, we reveal the relation between the flatness of the loss function with respect to input data , the Lipschitz constant of the gradient of adversarial loss tends to increase. To address the non-smoothness, we show that EntropySGD smoothens the non-smooth loss and improves the performance of adversarial training .
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Original:  We prove that for this requirement to hold , under certain conditions, it is necessary and sufficient for clusters to have low conductance, the ratio of edge boundary size to volume , which yields a measure of cluster quality.
Revised:  We prove under mild conditions that, in order for this requirement to hold , under certain conditions, it is necessary and sufficient for clusters to have low conductance, the ratio of edge boundary size to volume , which yields a measure of cluster quality.
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Original:  We prove that for this requirement to hold , under certain conditions, it is necessary and sufficient for clusters to have low conductance, the ratio of edge boundary size to volume , which yields a measure of cluster quality.
Revised:  We prove that for this requirement to hold for network-dependent data, it is necessary and sufficient for clusters to have low conductance, the ratio of edge boundary size to volume , which yields a measure of cluster quality.
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Original:  We show in simulations that,  for important classes of networks lacking low-conductance clusters, cluster-robust methods can exhibit substantial size distortion , whereas for networks with such clusters, they outperform HAC estimators .
Revised:  We find in simulations that, for important classes of networks lacking low-conductance clusters, cluster-robust methods can exhibit substantial size distortion , whereas for networks with such clusters, they outperform HAC estimators .
Edit intent: clarity
Original:  We show in simulations that,  for important classes of networks lacking low-conductance clusters, cluster-robust methods can exhibit substantial size distortion , whereas for networks with such clusters, they outperform HAC estimators .
Revised:  We show in simulations that, when clusters have low conductance, cluster-robust methods outperform HAC estimators in terms of size control. However, for important classes of networks lacking low-conductance clusters, cluster-robust methods can exhibit substantial size distortion , whereas for networks with such clusters, they outperform HAC estimators .
Edit intent: meaning-changed
Original:  We show in simulations that,  for important classes of networks lacking low-conductance clusters, cluster-robust methods can exhibit substantial size distortion , whereas for networks with such clusters, they outperform HAC estimators .
Revised:  We show in simulations that, for important classes of networks lacking low-conductance clusters, the methods can exhibit substantial size distortion , whereas for networks with such clusters, they outperform HAC estimators .
Edit intent: clarity
Original: Since the recent study ~\mbox{%DIFAUXCMD Krichene20@KDD20 done by Krichene and Rendle on the sampling-based top-k evaluation metric for recommendation, there has been a lot of debates on the validity of using sampling to evaluate recommendation algorithms.
Revised: Since the recent study (Krichene and Rendle 2020) done by Krichene and Rendle on the sampling-based top-k evaluation metric for recommendation, there has been a lot of debates on the validity of using sampling to evaluate recommendation algorithms.
Edit intent: clarity
Original:  Though their work and the recent work ~\mbox{%DIFAUXCMD Li@KDD20 have proposed some basic approaches for mapping the sampling-based metrics to their global counterparts which rank the entire set of items, there is still a lack of understanding and consensus on how sampling should be used for recommendation evaluation.
Revised:  Though their work and the recent work (Li et al.2020) have proposed some basic approaches for mapping the sampling-based metrics to their global counterparts which rank the entire set of items, there is still a lack of understanding and consensus on how sampling should be used for recommendation evaluation.
Edit intent: clarity
Original:  The proposed approaches either are rather uninformative (linking sampling to metric evaluation) or can only work on simple metrics, such as Recall/Precision ~\mbox{%DIFAUXCMD Krichene20@KDD20,Li@KDD20 In this paper, we introduce a new research problem on learning the empirical rank distribution, and a new approach based on the estimated rank distribution, to estimate the top-k metrics.
Revised:  The proposed approaches either are rather uninformative (linking sampling to metric evaluation) or can only work on simple metrics, such as Recall/Precision (Krichene and Rendle 2020; Li et al. 2020). In this paper, we introduce a new research problem on learning the empirical rank distribution, and a new approach based on the estimated rank distribution, to estimate the top-k metrics.
Edit intent: meaning-changed