wanyu/IteraTeR_v2 huggingface dataset:
Original:  The interdisciplinarity of the portfolios can be measured using Rao-Stirling diversity or Zhang et al.'s (in press) improved measure 2D3.
Revised:  The interdisciplinarity of the portfolios is measured using Rao-Stirling diversity or Zhang et al.'s (in press) improved measure 2D3.
Edit intent: clarity
Original:  Further instruction is provided online at URL 
Revised:  Further instruction is provided online at URL .
Edit intent: fluency
Original:  Below the same threshold no local algorithm can achieve this goal.
Revised:  Below the same threshold no local algorithm can achieve this goal.
Edit intent: fluency
Original:  Automatic differentiation (AD) is a technique for calculating derivatives  efficiently and accurately, established in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences.
Revised:  Automatic differentiation (AD) is a technique for calculating derivatives efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences.
Edit intent: coherence
Original:  We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on the recent developments in the adoption  this technique.
Revised:  We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption this technique.
Edit intent: clarity
Original:  We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on the recent developments in the adoption  this technique.
Revised:  We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on the recent developments in the adoption of this technique.
Edit intent: fluency
Original:  We also aim to dispel some misconceptions that we think have impeded the widespread awareness of AD within the machine learning community.
Revised:  We aim to dispel some misconceptions that we think have impeded the widespread awareness of AD within the machine learning community.
Edit intent: coherence
Original:  We also aim to dispel some misconceptions that we think have impeded the widespread awareness of AD within the machine learning community.
Revised:  We also aim to dispel some misconceptions that we contend have impeded the widespread awareness of AD within the machine learning community.
Edit intent: clarity
Original:  We also aim to dispel some misconceptions that we think have impeded the widespread awareness of AD within the machine learning community.
Revised:  We also aim to dispel some misconceptions that we think have impeded the use of AD within the machine learning community.
Edit intent: clarity
Original:  Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences.
Revised:  Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs . AD is a small but established field with applications in areas including computational fluid dynamics, nuclear engineering, and atmospheric sciences.
Edit intent: clarity
Original:  Despite its relevance, general-purpose AD has been missing from the toolbox of the machine learning community , a situation slowly changing with its ongoing adoption in mainstream machine learning frameworks .
Revised:  Despite its relevance, general-purpose AD has been missing from the machine learning toolbox , a situation slowly changing with its ongoing adoption in mainstream machine learning frameworks .
Edit intent: clarity
Original:  We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main techniques of implementation .
Revised:  We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques .
Edit intent: clarity
Original:  By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of  terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.
Revised:  By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.
Edit intent: fluency
Original:  Recently, these questions were ans\-wered by Pham [6], using linear algebraic methods.
Revised:  Recently, these questions were answered by Pham [6], using linear algebraic methods.
Edit intent: fluency
Original:  The elements of the stream have {\em keys} (cookies, users, queries) and elements with different keys interleave in the stream .
Revised:  Data elements have {\em keys} (cookies, users, queries) and elements with different keys interleave in the stream .
Edit intent: clarity
Original:  The elements of the stream have {\em keys} (cookies, users, queries) and elements with different keys interleave in the stream .
Revised:  The elements of the stream have {\em keys} (cookies, users, queries) and elements with different keys interleave .
Edit intent: clarity
Original:  The two most common statistics are {\em distinct keys }, which is the number of active keys in a specified segment, and {\em sum}, which is the sum of the frequencies of keys in the segment.
Revised:  The two most common statistics are {\em distinct }, which is the number of active keys in a specified segment, and {\em sum}, which is the sum of the frequencies of keys in the segment.
Edit intent: fluency
Original:  These are two special cases of {\em frequency cap} statistics, defined as the sum of frequencies {\em capped} by a parameter T, which are popular in online advertising platforms.
Revised:  These are two special cases of {\em cap} statistics, defined as the sum of frequencies {\em capped} by a parameter T, which are popular in online advertising platforms.
Edit intent: fluency
Original:  We propose a novel general framework for sampling unaggregated streams which provides the first effective stream sampling solution for general frequency cap statistics.
Revised:  We propose a novel general framework for sampling unaggregated streams which provides the first effective solution for general frequency cap statistics.
Edit intent: clarity
Original:  That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) each sample path, the average-level stability is just a direct result of it by averaging stochastic samples.
Revised:  That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability is just a direct result of it by averaging stochastic samples.
Edit intent: fluency
Original:  That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) each sample path, the average-level stability is just a direct result of it by averaging stochastic samples.
Revised:  That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) each sample path, the average-level stability just follows from it by averaging stochastic samples.
Edit intent: clarity
Original: Many works have investigated the expressive power of various kinds of neural networks.
Revised: We study the expressive power of various kinds of neural networks.
Edit intent: clarity
Original:  In particular, we study positive neural networks with multiple input neurons , and where neurons only excite each other and do not inhibit each other . Different behaviors can be expressed by varying the connection strengths between the neurons .
Revised:  In particular, we study positive neural networks with multiple input neurons . Different behaviors can be expressed by varying the connection strengths between the neurons .
Edit intent: coherence
Original:  In particular, we study positive neural networks with multiple input neurons , and where neurons only excite each other and do not inhibit each other . Different behaviors can be expressed by varying the connection strengths between the neurons .
Revised:  In particular, we study positive neural networks with multiple input neurons , and where neurons only excite each other and do not inhibit each other . Different behaviors can be expressed by varying the connection weights .
Edit intent: clarity
Original:  Finally, the complexities of the incremental approaches are compared on the theoretical and empirical points of view.
Revised:  Finally, the complexities of the incremental approaches are compared from the theoretical and empirical points of view.
Edit intent: fluency
Original: This study , based on contemporary mathematical foundations, presents an abelian group approach to analyzing inconsistency in pairwise comparisons.
Revised: This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons.
Edit intent: clarity
Original:  A general and precise notion of an inconsistency indicator map on a group, taking values in an abelian linearly ordered group, is introduced.
Revised:  A notion of an inconsistency indicator map on a group, taking values in an abelian linearly ordered group, is introduced.
Edit intent: clarity
Original:  For it, metrics and generalized metrics are investigated .
Revised:  For it, metrics and generalized metrics are utilized .
Edit intent: clarity
Original:  Every inconsistency indicator map generates an inconsistency index of a pairwise comparisons matrix .
Revised:  Every inconsistency indicator map generates an inconsistency indicator of a pairwise comparisons matrix .
Edit intent: clarity
Original:  A notion of an inconsistency indicator map on a group, taking values in an abelian linearly ordered group , is introduced.
Revised:  However, it wrongly assumes that an inconsistency indicator map on a group, taking values in an abelian linearly ordered group , is introduced.
Edit intent: coherence
Original:  A notion of an inconsistency indicator map on a group, taking values in an abelian linearly ordered group , is introduced.
Revised:  A notion of an inconsistency indicator can take values in any abelian linearly ordered group , is introduced.
Edit intent: clarity
Original:  Given two polygons with holes, we can fill in all the holes of one polygon, transforming it into a simple polygon, and still obtain the exactly same Minkowski sum.
Revised:  Given two polygons with holes, we can fill in all the holes of one polygon, transforming it into a simple polygon, and still obtain exactly the same Minkowski sum.
Edit intent: fluency
Original:  We also present an empirical comparison of the performance of Minkowski sum constructions, where we show that the implementation of the new algorithm exhibits better performance than all other implementations in many cases.
Revised:  We also present an empirical comparison of the performance of Minkowski sum constructions, where we show that the implementation of the new algorithm exhibits better performance than several other implementations in many cases.
Edit intent: clarity
Original:  Its efficiency stems in part from a property for Minkowski sums of polygons with holes, which we prove to hold in any dimension.
Revised:  Its efficiency stems in part from a property for Minkowski sums of polygons with holes, which in fact holds in any dimension:
Edit intent: clarity
Original:  Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) Strengthen the signal by adding the previous denoised image to the degraded input image, (ii) Operate the denoising method on the strengthened image, and (iii) Subtract the previous denoised image from the restored signal-strengthened outcome.
Revised:  Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) (S)trengthen the signal by adding the previous denoised image to the degraded input image, (ii) Operate the denoising method on the strengthened image, and (iii) Subtract the previous denoised image from the restored signal-strengthened outcome.
Edit intent: fluency
Original:  Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) Strengthen the signal by adding the previous denoised image to the degraded input image, (ii) Operate the denoising method on the strengthened image, and (iii) Subtract the previous denoised image from the restored signal-strengthened outcome.
Revised:  Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) Strengthen the signal by adding the previous denoised image to the degraded input image, (ii) (O)perate the denoising method on the strengthened image, and (iii) Subtract the previous denoised image from the restored signal-strengthened outcome.
Edit intent: clarity
Original:  Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) Strengthen the signal by adding the previous denoised image to the degraded input image, (ii) Operate the denoising method on the strengthened image, and (iii) Subtract the previous denoised image from the restored signal-strengthened outcome.
Revised:  Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) Strengthen the signal by adding the previous denoised image to the degraded input image, (ii) Operate the denoising method on the strengthened image, and (iii) (S)ubtract the previous denoised image from the restored signal-strengthened outcome.
Edit intent: fluency
Original:  Furthermore, still in the context of K-SVD image denoising, we introduce an interesting interpretation of the SOS algorithm as a technique for closing the gap between the local patch-modeling and the global restoration task, thereby leading to improved performance  .
Revised:  Still in the context of K-SVD image denoising, we introduce an interesting interpretation of the SOS algorithm as a technique for closing the gap between the local patch-modeling and the global restoration task, thereby leading to improved performance .
Edit intent: coherence
Original:  Within this general framework, we show in this work that spaced seeds provide a significant improvement of classification capacity as opposed to traditional contiguous k-mers.
Revised:  Within this general framework, we show in this work that spaced seeds provide a significant improvement of classification accuracy as opposed to traditional contiguous k-mers.
Edit intent: clarity
Original:  This allows to formulate a Strong Bernoulli property and a notion of cut-invariance  for convergent ergodic means , yielding a version of the Strong law of large numbers  for heap monoids with Bernoulli measures  .
Revised:  A Strong Bernoulli property and a notion of cut-invariance for convergent ergodic means , yielding a version of the Strong law of large numbers for heap monoids with Bernoulli measures .
Edit intent: coherence
Original:  This allows to formulate a Strong Bernoulli property and a notion of cut-invariance  for convergent ergodic means , yielding a version of the Strong law of large numbers  for heap monoids with Bernoulli measures  .
Revised:  This allows to formulate a Strong Bernoulli property and a notion of cut-invariance is formulated for convergent ergodic means , yielding a version of the Strong law of large numbers for heap monoids with Bernoulli measures .
Edit intent: clarity
Original:  This allows to formulate a Strong Bernoulli property and a notion of cut-invariance  for convergent ergodic means , yielding a version of the Strong law of large numbers  for heap monoids with Bernoulli measures  .
Revised:  This allows to formulate a Strong Bernoulli property and a notion of cut-invariance for convergent ergodic means . Then a version of the Strong law of large numbers for heap monoids with Bernoulli measures .
Edit intent: clarity
Original: We propose rectified factor networks (RFNs) as generative unsupervised models, which learn robust, very sparse, and non-linear codes with many code units . RFN learning is a variational expectation maximization (EM) algorithm with unknown prior which includes (i) rectified posterior means, (ii) normalized signals of hidden units, and (iii) dropout.
Revised: We propose rectified factor networks (RFNs) to efficiently construct very sparse, and non-linear codes with many code units . RFN learning is a variational expectation maximization (EM) algorithm with unknown prior which includes (i) rectified posterior means, (ii) normalized signals of hidden units, and (iii) dropout.
Edit intent: clarity
Original: We propose rectified factor networks (RFNs) as generative unsupervised models, which learn robust, very sparse, and non-linear codes with many code units . RFN learning is a variational expectation maximization (EM) algorithm with unknown prior which includes (i) rectified posterior means, (ii) normalized signals of hidden units, and (iii) dropout.
Revised: We propose rectified factor networks (RFNs) as generative unsupervised models, which learn robust, very sparse, non-linear codes with many code units . RFN learning is a variational expectation maximization (EM) algorithm with unknown prior which includes (i) rectified posterior means, (ii) normalized signals of hidden units, and (iii) dropout.
Edit intent: fluency
Original:  For pretraining of deep networks on MNIST, rectangle data, convex shapes, NORB, and CIFAR, RFNs were superior to restricted Boltzmann machines (RBMs ) and denoising autoencoders.
Revised:  For pretraining of deep networks on different vision datasets, where RFNs were superior to restricted Boltzmann machines (RBMs ) and denoising autoencoders.
Edit intent: clarity
Original:  For pretraining of deep networks on MNIST, rectangle data, convex shapes, NORB, and CIFAR, RFNs were superior to restricted Boltzmann machines (RBMs ) and denoising autoencoders.
Revised:  For pretraining of deep networks on MNIST, rectangle data, convex shapes, NORB, and CIFAR, RFNs were superior to RBMs and autoencoders.
Edit intent: clarity
Original:  (i) O( log n ) for \beta< %DIFDELCMD < \betau%%%  , (ii) O(n^{1/3}) for \beta= %DIFDELCMD < \betau%%%  , (iii) \exp(n ^\Omega(1)) for%DIFDELCMD < \betau%%% ) for \mathrm{u}} <\beta< %DIFDELCMD < \betarc%%%  , and (iv) O( log n ) for \beta\geq %DIFDELCMD < \betarc%%%  . These results complement refined results of Cuff et al. (2012) on the mixing time of the Glauber dynamics for the ferromagnetic Potts model.
Revised:  (i) O( log n ) for \beta< %DIFDELCMD < \betau%%% , (ii) O(n^{1/3}) for \beta= %DIFDELCMD < \betau%%% , (iii) \exp(n ^\Omega(1)) for%DIFDELCMD < \betau%%% ^{\Omega(1)) for \mathrm{u}} <\beta< %DIFDELCMD < \betarc%%% , and (iv) O( log n ) for \beta\geq %DIFDELCMD < \betarc%%% . These results complement refined results of Cuff et al. (2012) on the mixing time of the Glauber dynamics for the ferromagnetic Potts model.
Edit intent: fluency
Original:  (i) O( log n ) for \beta< %DIFDELCMD < \betau%%%  , (ii) O(n^{1/3}) for \beta= %DIFDELCMD < \betau%%%  , (iii) \exp(n ^\Omega(1)) for%DIFDELCMD < \betau%%% ) for \mathrm{u}} <\beta< %DIFDELCMD < \betarc%%%  , and (iv) O( log n ) for \beta\geq %DIFDELCMD < \betarc%%%  . These results complement refined results of Cuff et al. (2012) on the mixing time of the Glauber dynamics for the ferromagnetic Potts model.
Revised:  (i) O( log n ) for \beta< %DIFDELCMD < \betau%%% , (ii) O(n^{1/3}) for \beta= %DIFDELCMD < \betau%%% , (iii) \exp(n ^\Omega(1)) for%DIFDELCMD < \betau%%% ) for \mathrm{u}} <\beta< %DIFDELCMD < \betarc%%% , and (iv) O( \log{n ) for \beta\geq %DIFDELCMD < \betarc%%% . These results complement refined results of Cuff et al. (2012) on the mixing time of the Glauber dynamics for the ferromagnetic Potts model.
Edit intent: fluency
Original:  The case q=2 ( the Swendsen-Wang algorithm for the  ferromagnetic Ising model ) undergoes a slow-down at the uniqueness) for \beta=\beta_c, (iii) \Theta(\log n) for \beta>\beta_c, where \beta_c is the critical temperature for the ordered} / non-uniqueness critical temperature for the infinite \Delta-regular tree (Long et al., 2014) but yet still has polynomial mixing time at all (inverse) temperatures \beta>0 (Cooper et al., 2000) .
Revised:  Long et al. studied the case q=2 ( the Swendsen-Wang algorithm for the ferromagnetic Ising model ) undergoes a slow-down at the uniqueness) for \beta=\beta_c, (iii) \Theta(\log n) for \beta>\beta_c, where \beta_c is the critical temperature for the ordered} / non-uniqueness critical temperature for the infinite \Delta-regular tree (Long et al., 2014) but yet still has polynomial mixing time at all (inverse) temperatures \beta>0 (Cooper et al., 2000) .
Edit intent: clarity
Original:  The case q=2 ( the Swendsen-Wang algorithm for the  ferromagnetic Ising model ) undergoes a slow-down at the uniqueness) for \beta=\beta_c, (iii) \Theta(\log n) for \beta>\beta_c, where \beta_c is the critical temperature for the ordered} / non-uniqueness critical temperature for the infinite \Delta-regular tree (Long et al., 2014) but yet still has polynomial mixing time at all (inverse) temperatures \beta>0 (Cooper et al., 2000) .
Revised:  The case q=2 , the Swendsen-Wang algorithm for the ferromagnetic Ising model ) undergoes a slow-down at the uniqueness) for \beta=\beta_c, (iii) \Theta(\log n) for \beta>\beta_c, where \beta_c is the critical temperature for the ordered} / non-uniqueness critical temperature for the infinite \Delta-regular tree (Long et al., 2014) but yet still has polynomial mixing time at all (inverse) temperatures \beta>0 (Cooper et al., 2000) .
Edit intent: fluency
Original:  In contrast  for q\geq 3 there are two critical temperatures 0<\beta _{\mathrm{u < \mathrm{rc } that are relevant , these two critical points relate to phase transitions in the infinite tree .
Revised:  In contrast , for q\geq 3 there are two critical temperatures 0<\beta _{\mathrm{u < \mathrm{rc } that are relevant , these two critical points relate to phase transitions in the infinite tree .
Edit intent: fluency
Original:  In contrast  for q\geq 3 there are two critical temperatures 0<\beta _{\mathrm{u < \mathrm{rc } that are relevant , these two critical points relate to phase transitions in the infinite tree .
Revised:  In contrast for q\geq 3 there are two critical temperatures 0<\beta _{\mathrm{u < rc } that are relevant , these two critical points relate to phase transitions in the infinite tree .
Edit intent: fluency
Original:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Revised:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) \Theta(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Edit intent: clarity