wanyu/IteraTeR_v2 huggingface dataset:
Original:   On the hardness front , for p \in (1,2), we show under the Small Set Expansion Hypothesis and  Exponential Time Hypothesis (ETH), there is no constant factor approximation algorithm running in time 2^{k^{\delta} for a constant \delta }  > 0 , showing an exponential dependence on k is necessary.
Revised:  On the hardness front , for p \in (1,2), assuming the Small Set Expansion Hypothesis and Exponential Time Hypothesis (ETH), there is no constant factor approximation algorithm running in time 2^{k^{\delta} for a constant \delta } > 0 , showing an exponential dependence on k is necessary.
Edit intent: clarity
Original:   On the hardness front , for p \in (1,2), we show under the Small Set Expansion Hypothesis and  Exponential Time Hypothesis (ETH), there is no constant factor approximation algorithm running in time 2^{k^{\delta} for a constant \delta }  > 0 , showing an exponential dependence on k is necessary.
Revised:  On the hardness front , for p \in (1,2), we show under the Small Set Expansion Hypothesis and the Exponential Time Hypothesis (ETH), there is no constant factor approximation algorithm running in time 2^{k^{\delta} for a constant \delta } > 0 , showing an exponential dependence on k is necessary.
Edit intent: fluency
Original:   On the hardness front , for p \in (1,2), we show under the Small Set Expansion Hypothesis and  Exponential Time Hypothesis (ETH), there is no constant factor approximation algorithm running in time 2^{k^{\delta} for a constant \delta }  > 0 , showing an exponential dependence on k is necessary.
Revised:  On the hardness front , for p \in (1,2), we show under the Small Set Expansion Hypothesis and Exponential Time Hypothesis (ETH), } for a constant \delta } > 0 , showing an exponential dependence on k is necessary.
Edit intent: coherence
Original:  For p = 0, we observe that there is no approximation algorithm for the Generalized Binary \ell_0 -Rank-k Approximation problem running in time 2 ^{2^{\delta k} for a constant \delta > 0. We also show for finite fields of constant size, under the ETH, that any fixed constant factor approximation algorithm requires 2^{k^{\delta}}time for a constant \delta > 0.} 
Revised:  For p = 0, we observe that there is no approximation algorithm for the Generalized Binary \ell_0 -Rank-k Approximation problem running in time 2 } for a constant \delta > 0. We also show for finite fields of constant size, under the ETH, that any fixed constant factor approximation algorithm requires 2^{k^{\delta}}time for a constant \delta > 0.} 
Edit intent: coherence
Original:  Our results are: 1. We give a black-box algorithm for computing  the sum of the coefficients of the degree-k multilinear monomials in a polynomial over a field of characteristic zero.
Revised:  Our results are: 1. We give a black-box algorithm for computing the sum of the coefficients of the multilinear monomials in a polynomial over a field of characteristic zero.
Edit intent: clarity
Original:  Our algorithm runs in time O^*(n^{k/2 1%DIFDELCMD < ]%%% . 2. We give a randomized O^*((3e/2)^k) \approx O^*(4.08^k) time, polynomial space, black-box algorithm for detecting multilinear monomials of degree k over a field of characteristic zero.
Revised:  Our algorithm runs in time O^*(n^{k/2 %DIFDELCMD < ]%%% . 2. We give a randomized O^*((3e/2)^k) \approx O^*(4.08^k) time, polynomial space, black-box algorithm for detecting multilinear monomials of degree k over a field of characteristic zero.
Edit intent: clarity
Original:  This improves on the O^*(4.32^k) time, exponential space algorithm given in 2%DIFDELCMD < ]%%% . We note that there is a O^*(2^k) lower bound on our approach .
Revised:  This improves on the O^*(4.32^k) time, exponential space algorithm given in %DIFDELCMD < ]%%% . We note that there is a O^*(2^k) lower bound on our approach .
Edit intent: fluency
Original:  Along the way we give an exact answer to an open problem of Koutis and Williams and sharpen an upper bound on the size of perfectly balanced hash families given by Alon and Gutner.
Revised:  Along the way we give an exact answer to an open problem of Koutis and Williams and sharpen a lower bound on the size of perfectly balanced hash families given by Alon and Gutner.
Edit intent: fluency
Original:  According to the measured data, the proposed DDAR-model can adjust its form to various regularization models at each discrete point of the estimated function, which makes this new model has the ability to characterize local smooth properties of the estimated function  .
Revised:  According to the measured data, the proposed DDAR-model can adjust its form to various regularization models at each discrete point of the estimated function, which makes the characterization of local smooth properties of the estimated function .
Edit intent: clarity
Original:  According to the measured data, the proposed DDAR-model can adjust its form to various regularization models at each discrete point of the estimated function, which makes this new model has the ability to characterize local smooth properties of the estimated function  .
Revised:  According to the measured data, the proposed DDAR-model can adjust its form to various regularization models at each discrete point of the estimated function, which makes this new model has the ability to characterize local smooth properties of the estimated function possible .
Edit intent: clarity
Original:  In the end, we provide some numerical examples which clearly indicate that the proposed DDAR-model always generates a favorable result  compared with several Tikhonov and Total-Variation regularization models.
Revised:  In the end, we provide some numerical examples which clearly indicate that the proposed AARM can generates a favorable result compared with several Tikhonov and Total-Variation regularization models.
Edit intent: clarity
Original: The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel  states that any nonzero polynomial f(x_1,\ldots, x_n) of degree at most s will evaluate to a nonzero value at some point on a grid S^n \subseteq F^n with |S| > s. Thus, there is a deterministic polynomial identity test (PIT) for all degree-s size-s algebraic circuits in n variables that runs in time poly(s) \cdot (s +1)^n.
Revised: The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel states that any nonzero polynomial f(x_1,\ldots, x_n) of degree at most s will evaluate to a nonzero value at some point on a grid S^n \subseteq F^n with |S| > s. Thus, there is an explicit hitting set for all n-variate degree s, size s algebraic circuits of size (s +1)^n.
Edit intent: clarity
Original:  In a surprising recent result, Agrawal, Ghosh and Saxena (STOC 2018)showed any deterministic blackbox PIT algorithm for degree-s, size-s, n-variate circuits with running time as bad as s^{n^{0.5 - \delta}Huge(n), where \delta }  > 0 and Huge(n) is an arbitrary function, can be used to construct blackbox PIT algorithms for degree-s size scircuits with running time s ^{\exp \circ \exp (O(\log ^\ast s)).
Revised:  In }Huge(n), where \delta } > 0 and Huge(n) is an arbitrary function, can be used to construct blackbox PIT algorithms for degree-s size scircuits with running time s ^{\exp \circ \exp (O(\log ^\ast s)).
Edit intent: clarity
Original:  We describe optimal quantum algorithms that performs O(n/m^{1/4}) and O(n/t^{1/6} + m^{3/4}/t) queries respectively.
Revised:  We describe optimal quantum algorithms that perform O(n/m^{1/4}) and O(n/t^{1/6} + m^{3/4}/t) queries respectively.
Edit intent: fluency
Original:  We design a P-pass quantum streaming algorithm with space memory M satisfying a tradeoff of P^2 M = O(n^{1-2/k}), whereas the best classical algorithm requires P M = \Theta(n^{1-2/k}).
Revised:  We design a P-pass quantum streaming algorithm with memory M satisfying a tradeoff of P^2 M = O(n^{1-2/k}), whereas the best classical algorithm requires P M = \Theta(n^{1-2/k}).
Edit intent: clarity
Original:  Our result is optimal and subsumes a previous result of Montanaro [Mon15].
Revised:  Our algorithm subsumes a previous result of Montanaro [Mon15].
Edit intent: clarity
Original:  This new paradigm is based on a refinement of the Amplitude Estimation algorithm of Brassard et al. [BHMT02] , and of previous quantum algorithms for the mean estimation problem.
Revised:  This new paradigm is based on a refinement of the Amplitude Estimation algorithm of Brassard et al. [BHMT02] and of previous quantum algorithms for the mean estimation problem.
Edit intent: fluency
Original:   For our applications, we also adapt the variable-time amplitude amplification technique of Ambainis [Amb10] into a variable-time amplitude estimation algorithm , improving a recent result of Chakraborty, Gily\'en and Jeffery CGJ18 .
Revised:  For our applications, we also adapt the variable-time amplitude amplification technique of Ambainis [Amb10] into a variable-time amplitude estimation algorithm CGJ18 .
Edit intent: coherence
Original:   For our applications, we also adapt the variable-time amplitude amplification technique of Ambainis [Amb10] into a variable-time amplitude estimation algorithm , improving a recent result of Chakraborty, Gily\'en and Jeffery CGJ18 .
Revised:  For our applications, we also adapt the variable-time amplitude amplification technique of Ambainis [Amb10] into a variable-time amplitude estimation algorithm , improving a recent result of Chakraborty, Gily\'en and Jeffery .
Edit intent: clarity
Original: The \ell_2 tracking problem is the task of obtaining a streaming algorithm that, given access to a stream of items a_1,a_2,a_3,\ldots from a universe [n], outputs at each time t an estimate to the \ell_2 norm of the frequency vector f^{(t)}\in R^n (where f^{(t)}_i is the number of occurrences of item i in the stream up to time t).
Revised: The \ell_2 tracking problem is the task of obtaining a streaming algorithm that, given access to a stream of items a_1,a_2,a_3,\ldots from a universe [n], outputs at each time t an estimate to the \ell_2 norm of the frequency vector f^{(t)}\in R^n (where f^{(t)}_i is the number of occurrences of item i in the stream up to time t).
Edit intent: fluency
Original:  Our algorithm is obtained using the Count Sketch of [Charilkar-Chen-Farach-Colton, ICALP 2002].
Revised:  Our algorithm is obtained using the CountSketch of [Charilkar-Chen-Farach-Colton, ICALP 2002].
Edit intent: fluency
Original: We study a new LLL-like framework for rejection sampling , which naturally generalizes the variable-framework for the Lov\'asz local lemma (LLL) and the LLL-based Partial Rejection Sampling of Guo, Jerrum and Liu STOC'17%DIFDELCMD < ]%%% . In this new framework, the occurrence of a bad event is biased by the current evaluation of variables, rather than being determined by them as in the standard setting of LLL.
Revised:  STOC'17%DIFDELCMD < ]%%% . In this new framework, the occurrence of a bad event is biased by the current evaluation of variables, rather than being determined by them as in the standard setting of LLL.
Edit intent: coherence
Original: We study a new LLL-like framework for rejection sampling , which naturally generalizes the variable-framework for the Lov\'asz local lemma (LLL) and the LLL-based Partial Rejection Sampling of Guo, Jerrum and Liu STOC'17%DIFDELCMD < ]%%% . In this new framework, the occurrence of a bad event is biased by the current evaluation of variables, rather than being determined by them as in the standard setting of LLL.
Revised: We study a new LLL-like framework for rejection sampling , which naturally generalizes the variable-framework for the Lov\'asz local lemma (LLL) and the LLL-based Partial Rejection Sampling of Guo, Jerrum and Liu %DIFDELCMD < ]%%% . In this new framework, the occurrence of a bad event is biased by the current evaluation of variables, rather than being determined by them as in the standard setting of LLL.
Edit intent: coherence
Original:  In Mode 4, vehicles autonomously select and manage their radio resources without any cellular infrastructure support . Mode 4 is highly relevant since V2V safety applications cannot depend on the availability of infrastructure-based cellular coverage.
Revised:  In Mode 4, vehicles autonomously select and manage their radio resources . Mode 4 is highly relevant since V2V safety applications cannot depend on the availability of infrastructure-based cellular coverage.
Edit intent: clarity
Original:  This paper presents a set of novel analytical models of the communication performance of C-V2X or LTE-V Mode 4.
Revised:  This paper presents the first analytical models of the communication performance of C-V2X or LTE-V Mode 4.
Edit intent: clarity
Original:  In particular, the paper presents analytical models for the average PDR (Packet Delivery Ratio) as a function of the distance between transmitter and receiver, and for the four different types of transmission errors that can be encountered in C-V2X or LTE-V Mode 4.
Revised:  In particular, the paper presents analytical models for the average PDR (Packet Delivery Ratio) as a function of the distance between transmitter and receiver, and for the four different types of transmission errors that can be encountered in C-V2X Mode 4.
Edit intent: clarity
Original:  The models are validated in this study for a wide range of transmission parameters and traffic densities.
Revised:  The models are validated for a wide range of transmission parameters and traffic densities.
Edit intent: clarity
Original:  To this aim, this study compares the results obtained with the analytical models to those obtained with a C-V2X or LTE-V Mode 4 simulator implemented by the authors over the Veinssimulation platform.
Revised:  To this aim, this study compares the results obtained with the analytical models to those obtained with a C-V2X Mode 4 simulator implemented by the authors over the Veinssimulation platform.
Edit intent: clarity
Original: We study an iterative algorithm proposed by S. Armstrong, A. Hannukainen, T. Kuusi, J.-C.
Revised: We study the iterative algorithm proposed by S. Armstrong, A. Hannukainen, T. Kuusi, J.-C.
Edit intent: fluency
Original:  These problems with oscillating coefficients usually require very expensive numerical calculus , while this method uses some simple iterations to obtain exponential convergence .
Revised:  These problems with oscillating coefficients usually require very expensive numerical calculations , while this method uses some simple iterations to obtain exponential convergence .
Edit intent: clarity
Original:  These problems with oscillating coefficients usually require very expensive numerical calculus , while this method uses some simple iterations to obtain exponential convergence .
Revised:  These problems with oscillating coefficients usually require very expensive numerical calculus , while this iterative method is comparatively easy to compute .
Edit intent: clarity
Original:  In this article, we analyze in detail the mechanism of the algorithm and show a uniform estimate for the contraction factor , which is independent both of the size of the domain and function in iteration .
Revised:  In this article, we strengthen the estimate for the contraction factor , which is independent both of the size of the domain and function in iteration .
Edit intent: clarity
Original:  In this article, we analyze in detail the mechanism of the algorithm and show a uniform estimate for the contraction factor , which is independent both of the size of the domain and function in iteration .
Revised:  In this article, we analyze in detail the mechanism of the algorithm and show a uniform estimate for the contraction factor , which is independent both of the size of the domain .
Edit intent: clarity
Original: This paper explores meaning structures in the social practiceof small groups .
Revised: This paper explores meaning structures in practice .
Edit intent: clarity
Original:  The hard k-taxi problem is substantially more difficult than the easy version with at least an exponential deterministic competitive ratio, \Omega(2^k), admitting a reduction from the layered width-k graph traversal problem.
Revised:  The hard k-taxi problem is substantially more difficult than the easy version with at least an exponential deterministic competitive ratio, \Omega(2^k), admitting a reduction from the layered graph traversal problem.
Edit intent: clarity
Original:  For the hard k-taxi problem on hierarchically separated trees (HSTs), we present a memoryless randomized algorithm with competitive ratio 2^k-1 against adaptive online adversaries and provide a matching lower bound .
Revised:  We focus mainly on the hard version. For hierarchically separated trees (HSTs), we present a memoryless randomized algorithm with competitive ratio 2^k-1 against adaptive online adversaries and provide a matching lower bound .
Edit intent: clarity
Original:  Due to well-known HST embedding techniques, this yields a randomized O(2^k\log n)-competitive algorithm for arbitrary n-point metric spaces .
Revised:  Due to well-known HST embedding techniques, the algorithm implies a randomized O(2^k\log n)-competitive algorithm for arbitrary n-point metric spaces .
Edit intent: clarity
Original:  Due to well-known HST embedding techniques, this yields a randomized O(2^k\log n)-competitive algorithm for arbitrary n-point metric spaces .
Revised:  Due to well-known HST embedding techniques, this yields a randomized O(2^k\log n)-competitive algorithm for arbitrary n-point metrics .
Edit intent: clarity
Original:  We demonstrate that, whilst achieving over 99\% and 90\% accuracy on MNIST and CIFAR-10 datasets, ANTs benefit from (i) faster inference via conditional computation, (ii) increased interpretability via hierarchical clustering  e.g.  learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset .
Revised:  ANTs allow increased interpretability via hierarchical clustering e.g. learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset .
Edit intent: coherence
Original:  We demonstrate that, whilst achieving over 99\% and 90\% accuracy on MNIST and CIFAR-10 datasets, ANTs benefit from (i) faster inference via conditional computation, (ii) increased interpretability via hierarchical clustering  e.g.  learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset .
Revised:  We demonstrate that, whilst achieving over 99\% and 90\% accuracy on MNIST and CIFAR-10 datasets, ANTs benefit from (i) faster inference via conditional computation, (ii) increased interpretability via hierarchical clustering , e.g. learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset .
Edit intent: fluency
Original:  We demonstrate that, whilst achieving over 99\% and 90\% accuracy on MNIST and CIFAR-10 datasets, ANTs benefit from (i) faster inference via conditional computation, (ii) increased interpretability via hierarchical clustering  e.g.  learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset .
Revised:  We demonstrate that, whilst achieving over 99\% and 90\% accuracy on MNIST and CIFAR-10 datasets, ANTs benefit from (i) faster inference via conditional computation, (ii) increased interpretability via hierarchical clustering e.g. , learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset .
Edit intent: fluency
Original:  We demonstrate that, whilst achieving over 99\% and 90\% accuracy on MNIST and CIFAR-10 datasets, ANTs benefit from (i) faster inference via conditional computation, (ii) increased interpretability via hierarchical clustering  e.g.  learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset .
Revised:  We demonstrate that, whilst achieving over 99\% and 90\% accuracy on MNIST and CIFAR-10 datasets, ANTs benefit from (i) faster inference via conditional computation, (ii) increased interpretability via hierarchical clustering e.g. learning meaningful class associations, such as separating natural vs. man-made objects , and (iii) a mechanism to adapt the architecture to the size and complexity of the training data .
Edit intent: fluency
Original:  ANTs allow increased interpretability via hierarchical clustering, e.g. , learning meaningful class associations, such as separating natural vs. man-made objects .
Revised:  ANTs allow increased interpretability via hierarchical clustering, e.g. learning meaningful class associations, such as separating natural vs. man-made objects .
Edit intent: fluency
Original:  Furthermore, ANT optimisation naturally adapts the architecture to the size and complexity of the training data .
Revised:  Furthermore, ANT optimisation naturally adapts the architecture to the size and complexity of the training dataset .
Edit intent: fluency
Original:  We unite the two via adaptive neural trees (ANTs) , a model that incorporates representation learning into edges, routing functions and leaf nodes of a decision tree, along with a backpropagation-based training algorithm that adaptively grows the architecture from primitive modules (e.g., convolutional layers).
Revised:  We unite the two via adaptive neural trees (ANTs) that incorporates representation learning into edges, routing functions and leaf nodes of a decision tree, along with a backpropagation-based training algorithm that adaptively grows the architecture from primitive modules (e.g., convolutional layers).
Edit intent: clarity
Original:  We demonstrate that, whilst achieving competitive performance on classification and regression datasets, ANTs benefit from (i) lightweight inference via conditional computation, (ii) hierarchical separation of features useful to the predictive task e.g. learning meaningful class associations, such as separating natural vs. man-made objects, and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset.
Revised:  We demonstrate that, whilst achieving competitive performance on classification and regression datasets, ANTs benefit from (i) lightweight inference via conditional computation, (ii) hierarchical separation of features useful to the task e.g. learning meaningful class associations, such as separating natural vs. man-made objects, and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset.
Edit intent: clarity
Original:  Problems such as maximal independent set (MIS) or maximal matching are among the most intensively studied problems in the field and logarithmic round algorithms have been known for these problems from 1980s.
Revised:  Maximal independent set (MIS) or maximal matching are among the most intensively studied problems in the field and logarithmic round algorithms have been known for these problems from 1980s.
Edit intent: clarity
Original:  Problems such as maximal independent set (MIS) or maximal matching are among the most intensively studied problems in the field and logarithmic round algorithms have been known for these problems from 1980s.
Revised:  Problems such as maximal independent set (MIS) and maximal matching are among the most intensively studied problems in the field and logarithmic round algorithms have been known for these problems from 1980s.
Edit intent: fluency