wanyu/IteraTeR_v2 huggingface dataset:
Original:  where the parameters are the treewidth of G and the number of FPQ-trees associated with every vertex of G. We also show that if one of these two parameters is dropped, then the problem is not fixed-parameter tractable ] . Besides being interesting on its own right, the study of planarity testing with hierarchical embedding constraints can be used to address other planarity testing problems.
Revised:  where the parameters are the treewidth of G and the number of FPQ-trees associated with every vertex of G. We also show that the problem is NP-complete if parameterized by the number of FPQ-trees only, and W ] . Besides being interesting on its own right, the study of planarity testing with hierarchical embedding constraints can be used to address other planarity testing problems.
Edit intent: clarity
Original:  Such an information-based approach is in sharp contrast to the conventional mathematical modelling of information-driven systems whereby one attempts to come up with essentially ad hoc {\it  models for the outputs.
Revised:  Such an information-based approach is in sharp contrast to the conventional mathematical modelling of information-driven systems whereby one attempts to come up with essentially {\it models for the outputs.
Edit intent: clarity
Original:  In this paper, we focus on the popular k-median and k-means variants which, given a set P of points from a metric space and a parameter k<|P|, require to identify a set S of k centers minimizing respectively the sum of the distances and of the squared distances of all points in P from their closest centers.
Revised:  In this paper, we focus on the popular k-median and k-means variants which, given a set P of points from a metric space and a parameter k<|P|, require to identify a set S of k centers minimizing , respectively, the sum of the distances and of the squared distances of all points in P from their closest centers.
Edit intent: fluency
Original:  Our specific focus is on general metric spaces  for which it is reasonable to require that the centers belong to the input set (i.e., S \subseteq P).
Revised:  Our specific focus is on general metric spaces , for which it is reasonable to require that the centers belong to the input set (i.e., S \subseteq P).
Edit intent: fluency
Original:  Remarkably, the algorithms attain approximation ratios that can be made arbitrarily close to those achievable by the best known polynomial-time sequential approximations, and they are very space efficient for small D, requiring local memories sizes substantially sublinear in the input size.
Revised:  Remarkably, the algorithms attain approximation ratios that can be made arbitrarily close to those achievable by the best known polynomial-time sequential approximations, and they are very space efficient for small D, requiring local memory sizes substantially sublinear in the input size.
Edit intent: fluency
Original: Modern microprocessors enable aggressive hardware virtualization that exposes the microarchitecture state of the processor due to temporal sharing of hardware resources .
Revised: Microprocessors enable aggressive hardware virtualization that exposes the microarchitecture state of the processor due to temporal sharing of hardware resources .
Edit intent: clarity
Original:  However, temporal sharing of hardware resources exposes the processor to various microarchitecture state attack vectors . State-of-the-art secure processor , such as MI6 adopts Intel's SGX enclave execution model.
Revised:  However, temporal sharing of hardware resources exposes the processor to various microarchitecture state attacks . State-of-the-art secure processor , such as MI6 adopts Intel's SGX enclave execution model.
Edit intent: clarity
Original:  However, temporal sharing of hardware resources exposes the processor to various microarchitecture state attack vectors . State-of-the-art secure processor , such as MI6 adopts Intel's SGX enclave execution model.
Revised:  However, temporal sharing of hardware resources exposes the processor to various microarchitecture state attack vectors . State-of-the-art secure processors , such as MI6 adopts Intel's SGX enclave execution model.
Edit intent: fluency
Original:  However, temporal sharing of hardware resources exposes the processor to various microarchitecture state attack vectors . State-of-the-art secure processor , such as MI6 adopts Intel's SGX enclave execution model.
Revised:  However, temporal sharing of hardware resources exposes the processor to various microarchitecture state attack vectors . State-of-the-art secure processor , such as MI6 adopt Intel's SGX enclave execution model.
Edit intent: fluency
Original:  MI6 architects strong isolation against these vulnerabilities by isolating large memory components , and purging the microarchitecture state of private state resources on every enclave entry / exit.
Revised:  MI6 architects strong isolation by statically isolating shared memory state , and purging the microarchitecture state of private state resources on every enclave entry / exit.
Edit intent: clarity
Original:  MI6 architects strong isolation against these vulnerabilities by isolating large memory components , and purging the microarchitecture state of private state resources on every enclave entry / exit.
Revised:  MI6 architects strong isolation against these vulnerabilities by isolating large memory components , and purging the microarchitecture state of private state resources on every enclave entry and exit.
Edit intent: fluency
Original:  For a given secure-insecure process tuple of an interactive application  , IRONHIDE pins the secure process  to the secure cluster, and it executes and interacts with the insecure process(es) without incurring the overheads of purging microarchitecture state on each interaction event.
Revised:  For an interactive application , IRONHIDE pins the secure process to the secure cluster, and it executes and interacts with the insecure process(es) without incurring the overheads of purging microarchitecture state on each interaction event.
Edit intent: clarity
Original:  For a given secure-insecure process tuple of an interactive application  , IRONHIDE pins the secure process  to the secure cluster, and it executes and interacts with the insecure process(es) without incurring the overheads of purging microarchitecture state on each interaction event.
Revised:  For a given secure-insecure process tuple of an interactive application , IRONHIDE pins the secure process (es) to the secure cluster, and it executes and interacts with the insecure process(es) without incurring the overheads of purging microarchitecture state on each interaction event.
Edit intent: fluency
Original:  For a given secure-insecure process tuple of an interactive application  , IRONHIDE pins the secure process  to the secure cluster, and it executes and interacts with the insecure process(es) without incurring the overheads of purging microarchitecture state on each interaction event.
Revised:  For a given secure-insecure process tuple of an interactive application , IRONHIDE pins the secure process to the secure cluster, where they execute and interact with the insecure process(es) without incurring the overheads of purging microarchitecture state on each interaction event.
Edit intent: clarity
Original:  For a given secure-insecure process tuple of an interactive application  , IRONHIDE pins the secure process  to the secure cluster, and it executes and interacts with the insecure process(es) without incurring the overheads of purging microarchitecture state on each interaction event.
Revised:  For a given secure-insecure process tuple of an interactive application , IRONHIDE pins the secure process to the secure cluster, and it executes and interacts with the insecure process(es) without incurring the microarchitecture state purging overheads on every interaction event.
Edit intent: clarity
Original: A function f:[n  ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n  ]\toF_2 \dots\dots .
Revised: A function f:[n _1 ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n ]\toF_2 \dots\dots .
Edit intent: fluency
Original: A function f:[n  ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n  ]\toF_2 \dots\dots .
Revised: A function f:[n ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n ]\toF_2 \dots\dots .
Edit intent: fluency
Original: A function f:[n  ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n  ]\toF_2 \dots\dots .
Revised: A function f:[n ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n ]\toF_2 \dots\dots .
Edit intent: fluency
Original: A function f:[n  ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n  ]\toF_2 \dots\dots .
Revised: A function f:[n ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) \oplus \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n ]\toF_2 \dots\dots .
Edit intent: clarity
Original: A function f:[n  ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f _1,%DIFDELCMD < \dots%%% ,f_d :[n  ]\toF_2 \dots\dots .
Revised: A function f:[n ] ^d\dots \toF_2 is a direct sum if it is of the form f\left( ( a_1,\dots,a_d ) \right) = f_1(a_1) + \dots + f_d (a_d), for some d functions f %DIFDELCMD < \dots%%% ,f_d :[n ]\toF_2 \dots\dots .
Edit intent: fluency
Original:  In multiplicative \pm 1 notation, the above reads as follows.
Revised:  In multiplicative \pm 1 notation, our result reads as follows.
Edit intent: clarity
Original:  At each iteration, these agents update their beliefs about the true state based on noisy observations of the true state and the beliefs of a subset of other agents.
Revised:  At each iteration, agents update their beliefs about the true state based on noisy observations of the true state and the beliefs of a subset of other agents.
Edit intent: clarity
Original:  These subsets may include a special type of agent we call bots , who attempt to convince others of an erroneous true state rather than learn (modeling users spreading fake news).
Revised:  These subsets may include stubborn agents , who attempt to convince others of an erroneous true state rather than learn (modeling users spreading fake news).
Edit intent: clarity
Original:  These subsets may include a special type of agent we call bots , who attempt to convince others of an erroneous true state rather than learn (modeling users spreading fake news).
Revised:  These subsets may include a special type of agent we call bots , who attempt to convince others of an erroneous true state (modeling users spreading fake news).
Edit intent: clarity
Original:  At each iteration, agents update their beliefs about the true state in a non-Bayesian fashion, using noisy observations of the true state and the beliefs of a subset of other agents .
Revised:  At each iteration, agents update their beliefs about the true state of the world using private signals and the beliefs of a subset of other agents .
Edit intent: clarity
Original:  These subsets may include stubborn agents , who attempt to convince others of an erroneous true state (modeling users spreading fake news).
Revised:  These subsets may include stubborn agents , who attempt to convince others of an erroneous true state (modeling fake news).
Edit intent: clarity
Original:  As a demonstration, we show that an inversely-designed inhomogeneous medium can perform vowel classification on raw audio data by simple propagation of waves through such a medium , achieving performance that is comparable to a standard digital implementation of a recurrent neural network.
Revised:  As a demonstration, we show that an inverse-designed inhomogeneous medium can perform vowel classification on raw audio data by simple propagation of waves through such a medium , achieving performance that is comparable to a standard digital implementation of a recurrent neural network.
Edit intent: fluency
Original:  As a demonstration, we show that an inversely-designed inhomogeneous medium can perform vowel classification on raw audio data by simple propagation of waves through such a medium , achieving performance that is comparable to a standard digital implementation of a recurrent neural network.
Revised:  As a demonstration, we show that an inversely-designed inhomogeneous medium can perform vowel classification on raw audio signals as their waveforms scatter and propagate through it , achieving performance that is comparable to a standard digital implementation of a recurrent neural network.
Edit intent: clarity
Original:  As a demonstration, we show that an inversely-designed inhomogeneous medium can perform vowel classification on raw audio data by simple propagation of waves through such a medium , achieving performance that is comparable to a standard digital implementation of a recurrent neural network.
Revised:  As a demonstration, we show that an inversely-designed inhomogeneous medium can perform vowel classification on raw audio data by simple propagation of waves through such a medium , achieving performance comparable to a standard digital implementation of a recurrent neural network.
Edit intent: clarity
Original:  Traditionally , the neural signal of interest for decoding visual scenes has been focused on fMRI data .
Revised:  Traditionally , the neural signal of interest for decoding visual scenes .
Edit intent: clarity
Original:  So far there are few studies of decoding by using spikes.
Revised:  There are few studies of decoding by using spikes.
Edit intent: coherence
Original:  Furthermore, with a pre-trained SID, one can decode any dynamic videos , with the aid of an encoder, to achieve real-time encoding and decoding  visual scenes by spikes.
Revised:  Furthermore, with a pre-trained SID, one can decode any dynamic videos to achieve real-time encoding and decoding visual scenes by spikes.
Edit intent: clarity
Original:  Furthermore, with a pre-trained SID, one can decode any dynamic videos , with the aid of an encoder, to achieve real-time encoding and decoding  visual scenes by spikes.
Revised:  Furthermore, with a pre-trained SID, one can decode any dynamic videos , with the aid of an encoder, to achieve real-time encoding and decoding of visual scenes by spikes.
Edit intent: fluency
Original: Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays  major role in the theory of sparse graph classes.
Revised: Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes.
Edit intent: fluency
Original:  We show that there exists a constant C such that for every  integers a,b \geq 2 and a graph G, if the treedepth of G is at least Cab \log a , then the treewidth of G is at least a or G contains a subcubic (i.e., of maximum degree at most 3) tree of treedepth at least b as a subgraph.
Revised:  We show that there exists a constant C such that for every integers a,b \geq 2 and a graph G, if the treedepth of G is at least Cab , then the treewidth of G is at least a or G contains a subcubic (i.e., of maximum degree at most 3) tree of treedepth at least b as a subgraph.
Edit intent: clarity
Original:  As a direct corollary, we obtain that every graph of treedepth \Omega(k^3 \log k ) is either of treewidth at least k, contains a subdivision of full binary tree of depth k, or contains a path of length 2^k.
Revised:  As a direct corollary, we obtain that every graph of treedepth \Omega(k^3 ) is either of treewidth at least k, contains a subdivision of full binary tree of depth k, or contains a path of length 2^k.
Edit intent: clarity
Original:  We also show an application  for approximation algorithms of treedepth: given a graph G of treedepth k and treewidth t, one can in polynomial time compute a treedepth decomposition of G of width O (kt \log^{3/2} t).
Revised:  We also show an application of our techniques for approximation algorithms of treedepth: given a graph G of treedepth k and treewidth t, one can in polynomial time compute a treedepth decomposition of G of width O (kt \log^{3/2} t).
Edit intent: clarity
Original:  The experimental results demonstrate that the proposed framework can significantly improve the SE performance in terms of perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI) on the TIMIT dataset.
Revised:  The experimental results demonstrate that the proposed framework can obtain notable performance improvement in terms of perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI) on the TIMIT dataset.
Edit intent: clarity
Original:  Our insight is that feed forward networks should be able to learn a decision logic that is captured in the activation patterns of its neurons.
Revised:  We observe that a significant part (if not all) of the logic of feed forward networks should be able to learn a decision logic that is captured in the activation patterns of its neurons.
Edit intent: clarity
Original:  Our insight is that feed forward networks should be able to learn a decision logic that is captured in the activation patterns of its neurons.
Revised:  Our insight is that feed forward networks is captured in the activation patterns of its neurons.
Edit intent: clarity
Original:  Our insight is that feed forward networks should be able to learn a decision logic that is captured in the activation patterns of its neurons.
Revised:  Our insight is that feed forward networks should be able to learn a decision logic that is captured in the activation status ('on' or 'off') of its neurons.
Edit intent: clarity
Original:  We propose to extract such decision patterns that can be considered as invariants of the network with respect to a certain output behavior .
Revised:  We propose to extract patterns based on neuron decisions as preconditions that imply certain desirable output property e.g., the prediction being a certain class .
Edit intent: clarity
Original:  We present techniques to extract input invariants as convex predicates on the input space , and layer invariants that represent features captured in the hidden layers  .
Revised:  We present techniques to extract input properties, encoding convex predicates on the input space , and layer invariants that represent features captured in the hidden layers .
Edit intent: clarity
Original:  We apply the techniques on the networks for the MNIST and ACASXU applications.
Revised:  We apply our techniques on networks for the MNIST and ACASXU applications.
Edit intent: fluency
Original:  Our experiments highlight the use of invariants in a variety of applications , such as explainability , providing robustness guarantees, detecting adversaries, simplifying proofs and network distillation.
Revised:  Our experiments highlight the use of invariants in a variety of tasks , such as explainability , providing robustness guarantees, detecting adversaries, simplifying proofs and network distillation.
Edit intent: clarity
Original:  Our experiments highlight the use of invariants in a variety of applications , such as explainability , providing robustness guarantees, detecting adversaries, simplifying proofs and network distillation.
Revised:  Our experiments highlight the use of invariants in a variety of applications , such as explaining predictions , providing robustness guarantees, detecting adversaries, simplifying proofs and network distillation.
Edit intent: clarity
Original:  Our experiments highlight the use of invariants in a variety of applications , such as explainability , providing robustness guarantees, detecting adversaries, simplifying proofs and network distillation.
Revised:  Our experiments highlight the use of invariants in a variety of applications , such as explainability , providing robustness guarantees, simplifying proofs, and network distillation.
Edit intent: clarity
Original: We consider dynamic risk measures induced by Backward Stochastic Differential Equations ( BSDE ) in enlargement of filtration setting.
Revised: We consider dynamic risk measures induced by Backward Stochastic Differential Equations ( BSDEs ) in enlargement of filtration setting.
Edit intent: clarity
Original:  Although numerous of cross-modal hashing algorithms are proposed to yield compact binary codes,  exhaustive search is impractical for large-scale datasets , and Hamming distance computation suffers inaccurate results.
Revised:  Although dozens of cross-modal hashing algorithms are proposed to yield compact binary codes, exhaustive search is impractical for large-scale datasets , and Hamming distance computation suffers inaccurate results.
Edit intent: clarity
Original:  Although numerous of cross-modal hashing algorithms are proposed to yield compact binary codes,  exhaustive search is impractical for large-scale datasets , and Hamming distance computation suffers inaccurate results.
Revised:  Although numerous of cross-modal hashing algorithms are proposed to yield compact binary codes, the exhaustive search is impractical for large-scale datasets , and Hamming distance computation suffers inaccurate results.
Edit intent: coherence
Original:  We construct an inverted index table based on index codes , and train a neural network to improve the indexing accuracy and efficiency.
Revised:  We construct an inverted index table based on index codes and train a neural network to improve the indexing accuracy and efficiency.
Edit intent: fluency
Original:  Results show the proposed method effectively boosts the performance on search accuracy, computation cost, and memory consumption in these datasets and hashing methods.
Revised:  Results show the proposed method effectively boost the performance on search accuracy, computation cost, and memory consumption in these datasets and hashing methods.
Edit intent: fluency
Original:  In this work we explore some nonlinear extensions that take these elements into account in the construction of the basis.
Revised:  In this paper, we investigate the construction of the basis.
Edit intent: clarity
Original:  MixHop requires no additional memory or computational complexity, and outperforms on challenging baselines.
Revised:  Mixhop requires no additional memory or computational complexity, and outperforms on challenging baselines.
Edit intent: fluency
Original: A hitting-set generator (HSG) is a polynomial map Gen :F^k \to F^n such that for all n-variate polynomials Q of small enough circuit size and degree, if Q is non-zero, then Q\circ Gen is non-zero .
Revised: A hitting-set generator (HSG) is a polynomial map G :F^k \to F^n such that for all n-variate polynomials Q of small enough circuit size and degree, if Q is non-zero, then Q\circ Gen is non-zero .
Edit intent: fluency
Original:  In this paper, we give a new construction of such a HSG assuming that we have an explicit polynomial of sufficient hardness in the sense of approximative or border complexity .
Revised:  In this paper, we give a new construction of such an HSG assuming that we have an explicit polynomial of sufficient hardness in the sense of approximative or border complexity .
Edit intent: fluency