wanyu/IteraTeR_v2 huggingface dataset:
Original:  Specifically, for every \delta \in (0,1), we show that any correlated sampling scheme should have disagreement probability at least 2\delta/(1+\delta).
Revised:  Specifically, for every \delta \in (0,1), we show that any correlated sampling strategy should have disagreement probability at least 2\delta/(1+\delta).
Edit intent: clarity
Original:  Our proof is based on studying a new problem  we call "constrained agreement".
Revised:  Our proof is based on studying a new problem that we call "constrained agreement".
Edit intent: fluency
Original:  Here, Alice is given a subset A \subseteq [n] and is required to output an element i \in A, Bob is given a subset B \subseteq [n] and is required to output an element  j \in B , and the goal is to minimize the probability that i \neq j.
Revised:  Here, Alice is given a subset A \subseteq [n] and is required to output an element i \in A, Bob is given a subset B \subseteq [n] respectively and their goal is to output an element j \in B , and the goal is to minimize the probability that i \neq j.
Edit intent: coherence
Original:  Here, Alice is given a subset A \subseteq [n] and is required to output an element i \in A, Bob is given a subset B \subseteq [n] and is required to output an element  j \in B , and the goal is to minimize the probability that i \neq j.
Revised:  Here, Alice is given a subset A \subseteq [n] and is required to output an element i \in A, Bob is given a subset B \subseteq [n] and is required to output an element j \in B respectively while minimizing the probability that i \neq j.
Edit intent: coherence
Original:  We prove tight bounds on this question, which turn out to imply tight bounds for correlated sampling.
Revised:  We prove tight bounds for this question, which turn out to imply tight bounds for correlated sampling.
Edit intent: fluency
Original:  We prove tight bounds on this question, which turn out to imply tight bounds for correlated sampling.
Revised:  We prove tight bounds on this question, which in turn imply tight bounds for correlated sampling.
Edit intent: coherence
Original:  Though we settle basic questions about the two problems, our formulation also leads to several questions that remain open.
Revised:  Though we settle basic questions about the two problems, our formulation leads to more fine-grained questions that remain open.
Edit intent: clarity
Original: In the "correlated sampling" problem, two players are given probability measures P and Q  respectively, over the same measurable space and access to shared randomness.
Revised: In the "correlated sampling" problem, two players are given probability distributions P and Q respectively, over the same measurable space and access to shared randomness.
Edit intent: clarity
Original: In the "correlated sampling" problem, two players are given probability measures P and Q  respectively, over the same measurable space and access to shared randomness.
Revised: In the "correlated sampling" problem, two players are given probability measures P and Q , respectively, over the same measurable space and access to shared randomness.
Edit intent: fluency
Original: In the "correlated sampling" problem, two players are given probability measures P and Q  respectively, over the same measurable space and access to shared randomness.
Revised: In the "correlated sampling" problem, two players are given probability measures P and Q respectively, over the same finite set, with access to shared randomness.
Edit intent: clarity
Original:  Without any interaction , the two players are each required to output an element sampled according to their respective measures , while trying to minimize the probability that their outputs disagree.
Revised:  Without any communication , the two players are each required to output an element sampled according to their respective measures , while trying to minimize the probability that their outputs disagree.
Edit intent: clarity
Original:  Without any interaction , the two players are each required to output an element sampled according to their respective measures , while trying to minimize the probability that their outputs disagree.
Revised:  Without any interaction , the two players are each required to output an element sampled according to their respective distributions , while trying to minimize the probability that their outputs disagree.
Edit intent: clarity
Original:  A well-known strategy due to Kleinberg Tardos and Holenstein, with a close variant (for a similar problem) due to Broder, solves this task with disagreement probability at most 2 \delta/(1+\delta), where \delta is the total variation distance between P and Q.
Revised:  A well known strategy due to Kleinberg Tardos and Holenstein, with a close variant (for a similar problem) due to Broder, solves this task with disagreement probability at most 2 \delta/(1+\delta), where \delta is the total variation distance between P and Q.
Edit intent: fluency
Original:  A well-known strategy due to Kleinberg Tardos and Holenstein, with a close variant (for a similar problem) due to Broder, solves this task with disagreement probability at most 2 \delta/(1+\delta), where \delta is the total variation distance between P and Q.
Revised:  A well-known strategy due to Tardos and Holenstein, with a close variant (for a similar problem) due to Broder, solves this task with disagreement probability at most 2 \delta/(1+\delta), where \delta is the total variation distance between P and Q.
Edit intent: clarity
Original:  This strategy has been used in several different contexts  including sketching algorithms, approximation algorithms based on rounding linear programming relaxations, the study of parallel repetition and cryptography.
Revised:  This strategy has been used in several different contexts , including sketching algorithms, approximation algorithms based on rounding linear programming relaxations, the study of parallel repetition and cryptography.
Edit intent: fluency
Original:  In this paper, we give a surprisingly simple proof that this strategy is in fact tight . Specifically, for every \delta \in (0,1), we show that any correlated sampling strategy should have disagreement probability at least 2\delta/(1+\delta)  .
Revised:  In this paper, we give a surprisingly simple proof that this strategy is essentially optimal . Specifically, for every \delta \in (0,1), we show that any correlated sampling strategy should have disagreement probability at least 2\delta/(1+\delta) .
Edit intent: clarity
Original:  In this paper, we give a surprisingly simple proof that this strategy is in fact tight . Specifically, for every \delta \in (0,1), we show that any correlated sampling strategy should have disagreement probability at least 2\delta/(1+\delta)  .
Revised:  In this paper, we give a surprisingly simple proof that this strategy is in fact tight . Specifically, for every \delta \in (0,1), we show that any correlated sampling strategy incurs a disagreement probability of essentially 2\delta/(1+\delta) .
Edit intent: clarity
Original:  Here, the two players are given subsets A \subseteq [n] and B \subseteq [n] respectively and their goal is to output an element i \in A and j \in B respectively while minimizing the probability that i \neq j.
Revised:  Here, the two players are given subsets A \subseteq [n] and B \subseteq [n] , respectively, and their goal is to output an element i \in A and j \in B respectively while minimizing the probability that i \neq j.
Edit intent: fluency
Original:  Here, the two players are given subsets A \subseteq [n] and B \subseteq [n] respectively and their goal is to output an element i \in A and j \in B respectively while minimizing the probability that i \neq j.
Revised:  Here, the two players are given subsets A \subseteq [n] and B \subseteq [n] respectively and their goal is to output an element i \in A and j \in B , respectively, while minimizing the probability that i \neq j.
Edit intent: fluency
Original:  In current use, however, clinicians set the patient's stimulator to apply stimulation at all times -whether it is needed or not.
Revised:  In current use, however, clinicians set the patient's stimulator to apply stimulation at all times- whether it is needed or not.
Edit intent: fluency
Original: Meeting the diverse delay requirements of next-generation wireless communication networks is one of the most critical goals of wireless system design .
Revised: Meeting the diverse delay requirements of emerging wireless applications is one of the most critical goals of wireless system design .
Edit intent: clarity
Original:  In this article, we elaborate on the main challenges of delay analysis in large wireless networks.
Revised:  In this article, we elaborate on the main challenges in the delay analysis in large wireless networks.
Edit intent: clarity
Original: In addition to their unusually long life cycle, periodical cicadas, Magicicada {\it  spp., provide an exceptional example of spatially synchronized life stage phenology in nature.
Revised: In addition to their unusually long life cycle, periodical cicadas, {\it spp., provide an exceptional example of spatially synchronized life stage phenology in nature.
Edit intent: clarity
Original:  Within regions ( broods ) spanning 50,000 to 500,000 km^2, adults emerge synchronously every 13 or 17 years.
Revised:  Within regions ( "broods" ) spanning 50,000 to 500,000 km^2, adults emerge synchronously every 13 or 17 years.
Edit intent: fluency
Original:  We develop non-linear Leslie matrix-type models of periodical cicadas that include predation-driven Allee effects and competition in addition to reproduction and survival.
Revised:  We develop nonlinear Leslie matrix-type models of periodical cicadas that include predation-driven Allee effects and competition in addition to reproduction and survival.
Edit intent: fluency
Original:  Using both numerical and analytical techniques, we demonstrate the observed presence of a single brood critically depends on the relationship between fecundity, competition, and predation.
Revised:  Using both analytical and numerical techniques, we demonstrate the observed presence of a single brood critically depends on the relationship between fecundity, competition, and predation.
Edit intent: fluency
Original:  It is shown that the single-brood equilibrium is stable while two-brood and all-brood equilibria are unstable.
Revised:  It is shown that the single-brood and unstable two-brood and all-brood equilibria are unstable.
Edit intent: clarity
Original: Network functions virtualization (NFV) -- deploying network functions in software on commodity machines -- allows operators to employ rich chains of NFs to realize custom performance, security, and compliance policies, and ensure high performance by dynamically adding instances and /or failing over.
Revised: Network functions virtualization (NFV) allows operators to employ rich chains of NFs to realize custom performance, security, and compliance policies, and ensure high performance by dynamically adding instances and /or failing over.
Edit intent: coherence
Original: Network functions virtualization (NFV) -- deploying network functions in software on commodity machines -- allows operators to employ rich chains of NFs to realize custom performance, security, and compliance policies, and ensure high performance by dynamically adding instances and /or failing over.
Revised: Network functions virtualization (NFV) -- deploying network functions in software on commodity machines -- allows operators to employ NF chains to realize custom performance, security, and compliance policies, and ensure high performance by dynamically adding instances and /or failing over.
Edit intent: clarity
Original: Network functions virtualization (NFV) -- deploying network functions in software on commodity machines -- allows operators to employ rich chains of NFs to realize custom performance, security, and compliance policies, and ensure high performance by dynamically adding instances and /or failing over.
Revised: Network functions virtualization (NFV) -- deploying network functions in software on commodity machines -- allows operators to employ rich chains of NFs to realize custom policies, and ensure high performance by dynamically adding instances and /or failing over.
Edit intent: clarity
Original: Network functions virtualization (NFV) -- deploying network functions in software on commodity machines -- allows operators to employ rich chains of NFs to realize custom performance, security, and compliance policies, and ensure high performance by dynamically adding instances and /or failing over.
Revised: Network functions virtualization (NFV) -- deploying network functions in software on commodity machines -- allows operators to employ rich chains of NFs to realize custom performance, security, and compliance policies, and dynamically add instances to meet demand or for failover. NFs maintain detailed per- and /or failing over.
Edit intent: clarity
Original:  Because NFs are stateful, it is important to carefully manage their state , especially during such dynamic actions.
Revised:  Because NFs are stateful, it is important to carefully manage their state , especially during dynamic actions.
Edit intent: clarity
Original:  We present StreamNF,\name an NFV framework that satisfies the above requirements.
Revised:  We present StreamNF,\name, an NFV framework that satisfies the above requirements.
Edit intent: fluency
Original:  Extensive evaluation of a StreamNF prototype built atop Apache Storm shows that the significant benefits of StreamNF in terms of state management performance and chain-wide properties come at a modest per-packet latency cost.
Revised:  Extensive evaluation of a StreamNF prototype built atop Apache Storm shows that the significant benefits of StreamNF in terms of state management performance and chain-wide correctness at little additional cost.
Edit intent: clarity
Original: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1  \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant  ;
Revised: We show that the KLS constant for n-dimensional isotropic logconcave measures is O(n ^{ o( 1 \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant ;
Edit intent: fluency
Original: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1  \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant  ;
Revised: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ 1 \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant ;
Edit intent: clarity
Original: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1  \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant  ;
Revised: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1 \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant ;
Edit intent: coherence
Original: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1  \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant  ;
Revised: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1 \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same improved bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant ;
Edit intent: clarity
Original: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1  \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, isotropic constant , Poincar\'e constant and exponential concentration constant  ;
Revised: We show that the KLS constant for n-dimensional isotropic logconcave measures is n ^{ o( 1 \log n} ) %DIFDELCMD < \MBLOCKRIGHTBRACE%%% , thus approaching the conjecture that it is O(1) . As corollaries we obtain the same almost constant bound on the thin-shell estimate, Poincare constant and exponential concentration constant ;
Edit intent: fluency
Original: We show that the KLS constant for n-dimensional isotropic logconcave measures is O(n^{1/4}), improving on the current best bound of O(n^{1/3}\log n).
Revised: We show that the KLS constant for n-dimensional isotropic logconcave measures is O(n^{1/4}), improving on the previous best bound of O(n^{1/3}\log n).
Edit intent: clarity
Original:  it also follows that the ball walk for sampling from an isotropic logconcave density in {\bf R}^{n} converges in O^{*}(n^{2.5}) steps from a warm start {\bf   with support of diameter D is \Omega(1/D), resolving a question posed by Frieze and Kannan in 1997.
Revised:  it also follows that the ball walk for sampling from an isotropic logconcave density in {\bf R}^{n} converges in O^{*}(n^{2.5}) steps from a warm start {\bf R with support of diameter D is \Omega(1/D), resolving a question posed by Frieze and Kannan in 1997.
Edit intent: fluency
Original: Network quantization is one of network compression techniques employed to reduce the redundancy of deep neural networks.
Revised: Network quantization is one of network compression techniques to reduce the redundancy of deep neural networks.
Edit intent: clarity
Original:  It compresses the size of the storage for a large number of network parameters in a neural network by quantizing them and encoding the quantized values into binary codewords of smaller sizes .
Revised:  It reduces the number of distinct network parameter values by quantization in order to save the storage for them .
Edit intent: clarity
Original:  In this paper, we aim to design network quantization schemes that minimize the expected loss due to quantization while maximizing the compression ratio .
Revised:  In this paper, we design network quantization schemes that minimize the expected loss due to quantization while maximizing the compression ratio .
Edit intent: clarity
Original:  In this paper, we aim to design network quantization schemes that minimize the expected loss due to quantization while maximizing the compression ratio .
Revised:  In this paper, we aim to design network quantization schemes that minimize the performance loss due to quantization while maximizing the compression ratio .
Edit intent: clarity
Original:  To this end, we analyze the quantitative relation of quantization errors to the loss function of a neural network and identify that the Hessian-weighted distortion measure is locally the right objective function that we need to optimize for minimizing the loss due to quantization.
Revised:  To this end, we analyze the quantitative relation of quantization errors to the neural network loss function and identify that the Hessian-weighted distortion measure is locally the right objective function that we need to optimize for minimizing the loss due to quantization.
Edit intent: clarity
Original:  To this end, we analyze the quantitative relation of quantization errors to the loss function of a neural network and identify that the Hessian-weighted distortion measure is locally the right objective function that we need to optimize for minimizing the loss due to quantization.
Revised:  To this end, we analyze the quantitative relation of quantization errors to the loss function of a neural network and identify that the Hessian-weighted distortion measure is locally the right objective function for the optimization of network quantization.
Edit intent: clarity
Original:  As a result, Hessian-weighted k-means clustering is proposed for clustering network parameters to quantize when fixed-length binary encoding follows .
Revised:  As a result, Hessian-weighted k-means clustering is proposed for clustering network parameters to quantize .
Edit intent: coherence
Original:  When optimal variable-length binary codes, e.g., Huffman codes, are employed for further compression of quantized values after clustering , we derive that the network quantization problem can be related to the entropy-constrained scalar quantization (ECSQ) problem in information theory and consequently propose two solutions of ECSQ for network quantization, i.e., uniform quantization and an iterative algorithm similar to Lloyd's algorithm for k-means clustering .
Revised:  When optimal variable-length binary codes, e.g., Huffman codes, are employed for further compression , we derive that the network quantization problem can be related to the entropy-constrained scalar quantization (ECSQ) problem in information theory and consequently propose two solutions of ECSQ for network quantization, i.e., uniform quantization and an iterative algorithm similar to Lloyd's algorithm for k-means clustering .
Edit intent: clarity
Original:  When optimal variable-length binary codes, e.g., Huffman codes, are employed for further compression of quantized values after clustering , we derive that the network quantization problem can be related to the entropy-constrained scalar quantization (ECSQ) problem in information theory and consequently propose two solutions of ECSQ for network quantization, i.e., uniform quantization and an iterative algorithm similar to Lloyd's algorithm for k-means clustering .
Revised:  When optimal variable-length binary codes, e.g., Huffman codes, are employed for further compression of quantized values after clustering , we derive that the network quantization problem can be related to the entropy-constrained scalar quantization (ECSQ) problem in information theory and consequently propose two solutions of ECSQ for network quantization, i.e., uniform quantization and an iterative solution similar to Lloyd's algorithm for k-means clustering .
Edit intent: fluency
Original:  When optimal variable-length binary codes, e.g., Huffman codes, are employed for further compression of quantized values after clustering , we derive that the network quantization problem can be related to the entropy-constrained scalar quantization (ECSQ) problem in information theory and consequently propose two solutions of ECSQ for network quantization, i.e., uniform quantization and an iterative algorithm similar to Lloyd's algorithm for k-means clustering .
Revised:  When optimal variable-length binary codes, e.g., Huffman codes, are employed for further compression of quantized values after clustering , we derive that the network quantization problem can be related to the entropy-constrained scalar quantization (ECSQ) problem in information theory and consequently propose two solutions of ECSQ for network quantization, i.e., uniform quantization and an iterative algorithm similar to Lloyd's algorithm .
Edit intent: clarity