wanyu/IteraTeR_v2 huggingface dataset:
Original:  We use structured sampling to overcome such scalability challenges and manage to compute accurately the importance of different data sources, even when their number ranges in the thousands, as in the case of all the taxi drivers in a large metropolis .
Revised:  We resort to structured sampling and manage to compute accurately the importance of different data sources, even when their number ranges in the thousands, as in the case of all the taxi drivers in a large metropolis .
Edit intent: clarity
Original:  The contexts are mapped to vector states in the two-dimensional quantum Hilbert space describing a dichotomic decision alternative in relation to which the contexts are subjectively recognized.
Revised:  The contexts are represented as quantum qubit states in two-dimensional quantum Hilbert space describing a dichotomic decision alternative in relation to which the contexts are subjectively recognized.
Edit intent: clarity
Original:  In this paper, we show a quantitative trade-off between rotation invariance and robustness.
Revised:  In this paper, we prove a quantitative trade-off between rotation invariance and robustness.
Edit intent: coherence
Original:  We empirically study the following two cases: (a) change in adversarial robustness as we improve only the invariance of equivariant models via training augmentation  , (b) change in invariance as we improve only the adversarial robustness using adversarial training.
Revised:  We empirically study the following two cases: (a) change in adversarial robustness as we improve only the invariance of equivariant models via training augmentation in equivariant models , (b) change in invariance as we improve only the adversarial robustness using adversarial training.
Edit intent: clarity
Original:  We observe that the rotation invariance of equivariant models (StdCNNs and GCNNs) improves by training augmentation with progressively larger random rotations but while doing so,  their adversarial robustness drops progressively, and very significantly on MNIST.
Revised:  We observe that the spatial robustness of equivariant models (StdCNNs and GCNNs) improves by training augmentation with progressively larger random rotations but while doing so, their adversarial robustness drops progressively, and very significantly on MNIST.
Edit intent: clarity
Original:  We observe that the rotation invariance of equivariant models (StdCNNs and GCNNs) improves by training augmentation with progressively larger random rotations but while doing so,  their adversarial robustness drops progressively, and very significantly on MNIST.
Revised:  We observe that the rotation invariance of equivariant models improves when their training is augmented with progressively larger random rotations but while doing so, their adversarial robustness drops progressively, and very significantly on MNIST.
Edit intent: clarity
Original:  We observe that the rotation invariance of equivariant models (StdCNNs and GCNNs) improves by training augmentation with progressively larger random rotations but while doing so,  their adversarial robustness drops progressively, and very significantly on MNIST.
Revised:  We observe that the rotation invariance of equivariant models (StdCNNs and GCNNs) improves by training augmentation with progressively larger transformations but while doing so, their adversarial robustness drops progressively, and very significantly on MNIST.
Edit intent: clarity
Original: Neural network models are known to be vulnerable to small, adversarial pixel-wise perturbations .
Revised: (Non-)robustness of neural networks to small, adversarial pixel-wise perturbations .
Edit intent: clarity
Original:  We complement this by empirically studying the following two cases : (a) change in adversarial robustness as we improve only the spatial robustness via training augmentation in equivariant models, (b) change in spatial robustness as we improve only the adversarial robustness using adversarial training.
Revised:  We complement this empirically by showing that : (a) change in adversarial robustness as we improve only the spatial robustness via training augmentation in equivariant models, (b) change in spatial robustness as we improve only the adversarial robustness using adversarial training.
Edit intent: clarity
Original:  We complement this by empirically studying the following two cases : (a) change in adversarial robustness as we improve only the spatial robustness via training augmentation in equivariant models, (b) change in spatial robustness as we improve only the adversarial robustness using adversarial training.
Revised:  We complement this by empirically studying the following two cases : (a) as the spatial robustness via training augmentation in equivariant models, (b) change in spatial robustness as we improve only the adversarial robustness using adversarial training.
Edit intent: fluency
Original:  We observe that the spatial robustness of equivariant models improves when their training is augmented with progressively larger transformations but while doing so, it progressively worsens their adversarial robustness .
Revised:  We observe that the spatial robustness of equivariant models improves by training augmentation with progressively larger transformations but while doing so, it progressively worsens their adversarial robustness .
Edit intent: clarity
Original:  We observe that the spatial robustness of equivariant models improves when their training is augmented with progressively larger transformations but while doing so, it progressively worsens their adversarial robustness .
Revised:  We observe that the spatial robustness of equivariant models improves when their training is augmented with progressively larger transformations , their adversarial robustness .
Edit intent: coherence
Original:  On the other hand, we take state-of-the-art adversarially trained models, and observe that adversarial training with progressively larger perturbations results in a progressive drop in their spatial robustness .
Revised:  On the other hand, we take state-of-the-art robust models are adversarially trained with progressively larger perturbations results in a progressive drop in their spatial robustness .
Edit intent: coherence
Original:  However, the vanilla gates in RNN (e.g.  the input gate in LSTM) suffer from the problem of gate undertraining mainly due to the saturating activation functions, which may result in failures of learning gating  roles and thus the weak performance.
Revised:  However, the vanilla gates in RNN (e.g. , the input gate in LSTM) suffer from the problem of gate undertraining mainly due to the saturating activation functions, which may result in failures of learning gating roles and thus the weak performance.
Edit intent: fluency
Original:  The refining mechanism allows enhancing gradient back-propagation as well as extending the gating activation scope, which , although simple, can guide RNN to reach possibly deeper minima.
Revised:  The refining mechanism allows enhancing gradient back-propagation as well as extending the gating activation scope, which can guide RNN to reach possibly deeper minima.
Edit intent: coherence
Original:  In this paper, we consider these problems in the streaming model where one string is available via oracle queries and the other string comes as a stream of characters .
Revised:  In this paper, we consider these problems in the streaming model where one string is available via oracle queries and the other string .
Edit intent: clarity
Original:  We also study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.
Revised:  We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.
Edit intent: clarity
Original:  We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior.
Revised:  We use our characterization to study joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior.
Edit intent: clarity
Original: We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state  and who observe some information structure.
Revised: We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state , and who observe some information structure.
Edit intent: fluency
Original:  Our main result is that, for the two agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility.
Revised:  For two agents we introduce a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility.
Edit intent: clarity
Original:  For any number of agents, a related " no trade " condition likewise provides a characterization of feasibility .
Revised:  For any number of agents, we characterize feasible distributions in terms of a " no trade " condition likewise provides a characterization of feasibility .
Edit intent: clarity
Original:  For any number of agents, a related " no trade " condition likewise provides a characterization of feasibility .
Revised:  For any number of agents, a related " no-trade " condition likewise provides a characterization of feasibility .
Edit intent: fluency
Original:  For any number of agents, a related " no trade " condition likewise provides a characterization of feasibility .
Revised:  For any number of agents, a related " no trade " condition .
Edit intent: clarity
Original:  We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.
Revised:  We study a related class of Bayesian persuasion problems with multiple receivers, and explore the extreme points of the set of feasible distributions.
Edit intent: clarity
Original:  We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.
Revised:  We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, exploring the extreme feasible distributions.
Edit intent: clarity
Original:  Our two main results are based on the analysis of thin flows with resetting  .
Revised:  Our two main results are based on the formulation of thin flows with resetting .
Edit intent: clarity
Original:  The modalities required for the formula are also synthesized on-the-fly, and we present a recipe for re-coding the formula with different modalities, given  a separating set of predicate liftings.
Revised:  The modalities required for the formula are also synthesized on-the-fly, and we present a recipe for re-coding the formula with different modalities, given by a separating set of predicate liftings.
Edit intent: coherence
Original:  the rate expression is sharp and improves on existing results;
Revised:  the rate expression improves on existing results;
Edit intent: coherence
Original:  Building on an unconditionally stable space-time DG formulation developed in [Moiola, Perugia 2018], we (a) prove optimal convergence rates for the space-time scheme with local isotropic corner mesh refinement on the spatial domain, and (b) demonstrate numerically optimal convergence rates of a suitable sparse space-time version of the DG scheme.
Revised:  Building on an unconditionally stable space-time DG formulation developed in [Moiola, Perugia 2018], we (a) prove optimal convergence rates for the space-time scheme with local isotropic corner mesh refinement on the spatial domain, and (b) demonstrate numerically optimal convergence rates of a suitable sparse space-time version of the DG scheme.
Edit intent: fluency
Original:  The latter scheme is based on the so-called combination formula , in conjunction with a family of anisotropic space-time DG-discretizations.
Revised:  The latter scheme is based on the so-called combination formula , in conjunction with a family of anisotropic space-time DG-discretizations.
Edit intent: fluency
Original: Summary: Recent advances in distance-based protein folding have led to a paradigm shift in protein structure prediction.
Revised:  Recent advances in distance-based protein folding have led to a paradigm shift in protein structure prediction.
Edit intent: coherence
Original:  Availability and implementation: Open source code of PolyFold is freely available for download at URL It is implemented in cross-platform Java and binary executables are available for macOS, Linux, and Windows.
Revised:  Open source code of PolyFold is freely available for download at URL It is implemented in cross-platform Java and binary executables are available for macOS, Linux, and Windows.
Edit intent: coherence
Original:  \emph{How do we design learning algorithms that are robust to the presence of arbitrarily irrational agents?
Revised:  \emph{How do we design learning algorithms that are robust to the presence of arbitrarily irrational agents?
Edit intent: fluency
Original:  Standard game-theoretic formulations for settings like contextual pricing and security games assume that agents act in accordance with a specific behavioral model.
Revised:  Standard game-theoretic formulations of this problem assume that agents act in accordance with a specific behavioral model.
Edit intent: clarity
Original:  Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis , and may be of independent algorithmic interest .
Revised:  Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis .
Edit intent: clarity
Original:  In practice, however, some agents may not prescribe to the dominant behavioral model or may act in ways that are seemingly arbitrarily irrational.
Revised:  In practice, however, some agents may not subscribe to the dominant behavioral model or may act in ways that are seemingly arbitrarily irrational.
Edit intent: fluency
Original:  In practice, however, some agents may not prescribe to the dominant behavioral model or may act in ways that are seemingly arbitrarily irrational.
Revised:  In practice, however, some agents may not prescribe to the dominant behavioral model or may act in ways that seem to be arbitrarily irrational.
Edit intent: fluency
Original:  In particular, we provide two algorithms, one built on robustifying multidimensional binary search methods and one on translating the setting to a proxy setting appropriate for gradient descent .
Revised:  In particular, we provide two algorithms, one based on multidimensional binary search methods and one on translating the setting to a proxy setting appropriate for gradient descent .
Edit intent: clarity
Original:  however, they only provide approximate inference.
Revised:  however, they only provide approximate inference.
Edit intent: fluency
Original:  This paper presents dynamic-programming algorithms and proofs for exact inference in hierarchical clustering  .
Revised:  This paper presents dynamic-programming algorithms and proofs for exact inference in hierarchical clustering .
Edit intent: fluency
Original:  however, they only provideapproximate inference.
Revised:  however, they only provide inference.
Edit intent: clarity
Original:  This paper presents dynamic-programming algorithms and proofs for exact inference in hierarchical clustering at small but useful scales.
Revised:  This paper presents dynamic-programming algorithms for exact inference in hierarchical clustering at small but useful scales.
Edit intent: clarity
Original:  We are able to compute the partition function, MAP hierarchical clustering , and marginal probabilities of sub-hierarchies and clusters.
Revised:  We are able to compute the partition function, maximum likelihood hierarchy , and marginal probabilities of sub-hierarchies and clusters.
Edit intent: clarity
Original:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element  and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries  .
Revised:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \dsig \du inside each element and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries .
Edit intent: coherence
Original:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element  and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries  .
Revised:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig and displacement\du inside each element and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries .
Edit intent: clarity
Original:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element  and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries  .
Revised:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element , and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries .
Edit intent: fluency
Original:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element  and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries  .
Revised:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% %DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries .
Edit intent: coherence
Original:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element  and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries  .
Revised:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% \hsig \hu on elementary boundaries .
Edit intent: fluency
Original:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element  and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries  .
Revised:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig and\hu on elementary boundaries .
Edit intent: coherence
Original:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element  and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries  .
Revised:  The analysis is based on a unified Galerkin discretization formulation for the linear elasticity problem consisting of four discretization variables: strong symmetric stress tensor %DIFDELCMD < \boldsymbol %%% \sigma_h, displacement u_h \dsig \du inside each element and the modifications of these two variables %DIFDELCMD < \check \boldsymbol %%% \sigma_h and%DIFDELCMD < \check %DIFDELCMD < %%% u_h \hsig \hu on elementary boundaries of elements .
Edit intent: clarity
Original:  Motivated by many relevant methods in  literature, this formulation can be used to derive most existing discontinuous, nonconforming and conforming Galerkin methods for linear elasticity problem and especially to develop a number of new discontinuous Galerkin methods.
Revised:  Motivated by many relevant methods in the literature, this formulation can be used to derive most existing discontinuous, nonconforming and conforming Galerkin methods for linear elasticity problem and especially to develop a number of new discontinuous Galerkin methods.
Edit intent: fluency
Original:  Motivated by many relevant methods in  literature, this formulation can be used to derive most existing discontinuous, nonconforming and conforming Galerkin methods for linear elasticity problem and especially to develop a number of new discontinuous Galerkin methods.
Revised:  Motivated by many relevant methods in literature, this formulation can be used to derive most existing discontinuous, nonconforming and conforming Galerkin methods for linear elasticity problems and especially to develop a number of new discontinuous Galerkin methods.
Edit intent: fluency
Original:  As certain stabilization parameter tends to infinity , this four-field formulation is proved to converge to some conforming and nonconforming mixed methods for linear elasticity problem .
Revised:  As certain stabilization parameter tends to infinity , this four-field formulation is proved to converge to some conforming and nonconforming mixed methods for linear elasticity problems .
Edit intent: fluency