wanyu/IteraTeR_v2 huggingface dataset:
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that computes such polynomials efficiently -- the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: coherence
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: clarity
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Edit intent: coherence
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of quantifier elimination combined with that of " \epsilon-samples ".
Edit intent: fluency
Original:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of " \epsilon-samples ".
Revised:  sets from \mathcal{S . Such a polynomial is called a " generalized partitioning polynomial " . We present a randomized algorithm that efficiently computes such a polynomial P. Specifically, the expected running time of our algorithm is only linear in | \mathcal{S | , where the constant of proportionality depends on d, D, and the complexity of the description of~S . Our approach exploits the technique of "quantifier elimination " combined with that of \epsilon-samples ".
Edit intent: fluency
Original:  the second is data structure for answering range search queries with semi-algebraic ranges in  O(\log n) time ;
Revised:  the second is data structure for answering range-searching queries with semi-algebraic ranges in O(\log n) time ;
Edit intent: fluency
Original: Neuromorphic computing methods and artificial neurons can enhance the possibilities of solving complex problems more efficiently.
Revised: Neuromorphic computing methods and artificial neurons can improve the possibilities of solving complex problems more efficiently.
Edit intent: clarity
Original:  We propose a neuron circuit formed by a double-junction SQUID interfered with a resistor (threshold loop), a resistor-inductor structure (decaying loop), and mutual inductance between threshold loop and decaying loop.
Revised:  We propose a neuron circuit formed by a double-junction SQUID interfered with a resistor (threshold loop), a resistor - inductor structure (decaying loop), and mutual inductance between threshold loop and decaying loop.
Edit intent: fluency
Original:  Designed artificial neuron has the following main properties  (i) ultra-high-speed operation with minimal power consumption, (ii) compatibility with standard foundry processes so that it can be fabricated with the available infrastructure, (iii) compatibility with conventional logic gates so that complicated networks can be designed and implemented.
Revised:  Designed artificial neuron has the following main properties : (i) ultra-high-speed operation with minimal power consumption, (ii) compatibility with standard foundry processes so that it can be fabricated with the available infrastructure, (iii) compatibility with conventional logic gates so that complicated networks can be designed and implemented.
Edit intent: fluency
Original:  Designed artificial neuron has the following main properties  (i) ultra-high-speed operation with minimal power consumption, (ii) compatibility with standard foundry processes so that it can be fabricated with the available infrastructure, (iii) compatibility with conventional logic gates so that complicated networks can be designed and implemented.
Revised:  Designed artificial neuron has the following main properties (i) ultra-high-speed operation with minimal power consumption, (ii) compatibility with standard foundry processes that allows fabrication with the available infrastructure, (iii) compatibility with conventional logic gates so that complicated networks can be designed and implemented.
Edit intent: clarity
Original:  Designed artificial neuron has the following main properties  (i) ultra-high-speed operation with minimal power consumption, (ii) compatibility with standard foundry processes so that it can be fabricated with the available infrastructure, (iii) compatibility with conventional logic gates so that complicated networks can be designed and implemented.
Revised:  Designed artificial neuron has the following main properties (i) ultra-high-speed operation with minimal power consumption, (ii) compatibility with standard foundry processes so that it can be fabricated with the available infrastructure, (iii) compatibility with conventional logic gates which enable complicated networks to be designed and implemented.
Edit intent: clarity
Original:  Operation speed of the neuron is about 50 GHz with about 5x10-19 J/spike energy.
Revised:  Firing frequency of the neuron is about 50 GHz with about 5x10-19 J/spike energy.
Edit intent: clarity
Original: Neuromorphic computing methods and artificial neurons can improve the possibilities of solving complex problems more efficiently.
Revised: Artificial neural networks inspired by brain operations can improve the possibilities of solving complex problems more efficiently.
Edit intent: clarity
Original: Deep neural networks (DNNs) have been widely applied in various applications involving image , text, audio, and graph data  .
Revised: Deep neural networks (DNNs) have been widely applied in various applications involving image , and graph data .
Edit intent: clarity
Original: Deep neural networks (DNNs) have been widely applied in various applications involving image , text, audio, and graph data  .
Revised: Deep neural networks (DNNs) have been widely applied in various applications involving image , text, audio, and graph data analysis .
Edit intent: clarity
Original:  However, recent studies have shown that DNNs are vulnerable to adversarial attack .
Revised:  However, recent studies have shown that DNNs are vulnerable to adversarial attacks .
Edit intent: coherence
Original:  Though there are several works studying adversarial attack and defense  on domains such as images and text processing, it is  difficult to directly transfer the learned knowledge to graph  data due to its representation challenge .
Revised:  Though there are several works studying adversarial attack and defense on domains such as images and text processing, it is still difficult to directly transfer the learned knowledge to graph data due to its representation challenge .
Edit intent: coherence
Original:  Though there are several works studying adversarial attack and defense  on domains such as images and text processing, it is  difficult to directly transfer the learned knowledge to graph  data due to its representation challenge .
Revised:  Though there are several works studying adversarial attack and defense on domains such as images and text processing, it is difficult to directly transfer the learned knowledge to graph data due to its representation challenges .
Edit intent: fluency
Original:  Given the importance of graph analysis,  increasing number of works start to analyze the robustness of machine learning models on graph  . Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions.
Revised:  Given the importance of graph analysis, an increasing number of works start to analyze the robustness of machine learning models on graph . Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions.
Edit intent: fluency
Original:  Given the importance of graph analysis,  increasing number of works start to analyze the robustness of machine learning models on graph  . Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions.
Revised:  Given the importance of graph analysis, increasing number of works start to analyze the robustness of machine learning models on graph data . Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions.
Edit intent: fluency
Original:  Therefore, in this paper, we aim to survey existing adversarial attack strategies on graph data and provide an unified problem formulation which can cover all current adversarial learning studies on graph.
Revised:  Therefore, in this paper, we aim to survey existing adversarial learning strategies on graph data and provide an unified problem formulation which can cover all current adversarial learning studies on graph.
Edit intent: clarity
Original:  We also compare different attacks  on graph data and discuss their corresponding contributions and limitations.
Revised:  Moreover, we also compare different attacks on graph data and discuss their corresponding contributions and limitations.
Edit intent: coherence
Original:  We also compare different attacks  on graph data and discuss their corresponding contributions and limitations.
Revised:  We also compare different attacks and defenses on graph data and discuss their corresponding contributions and limitations.
Edit intent: clarity
Original: The goal of statistical compressive sensing is to efficiently acquire and reconstruct high-dimensional signals with much fewer measurements than the data dimensionality, given access to a finite set of training signals . Current approaches do not learn the acquisition and recovery procedures end-to-end and are typically hand-crafted for sparsity based priors.
Revised: Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional signals with much fewer measurements than the data dimensionality, given access to a finite set of training signals . Current approaches do not learn the acquisition and recovery procedures end-to-end and are typically hand-crafted for sparsity based priors.
Edit intent: clarity
Original:  We propose Uncertainty Autoencoders, a framework that jointly learns the acquisition (i.e., encoding) and  recovery (i.e., decoding) procedures while implicitly modeling domain structure .
Revised:  We propose Uncertainty Autoencoders, a framework that jointly learns the acquisition (i.e., encoding) and recovery (i.e., decoding) procedures .
Edit intent: clarity
Original:  Our learning objective optimizes for a  variational lower bound to the mutual information between the signal and the measurements .
Revised:  Our learning objective optimizes for a tractable variational lower bound to the mutual information between the signal and the measurements .
Edit intent: clarity
Original:  Our learning objective optimizes for a  variational lower bound to the mutual information between the signal and the measurements .
Revised:  Our learning objective optimizes for a variational lower bound to the mutual information between the datapoints and the latent representations .
Edit intent: clarity
Original:  We show how our framework provides a unified treatment to several lines of research in dimensionality reduction, compressive sensing, and generative modeling.
Revised:  We show how our framework provides a unified treatment to several lines of research in dimensionality reduction, compressed sensing, and generative modeling.
Edit intent: fluency
Original:  Empirically, we demonstrate improvements of 32\%  on average over competing approaches for statistical compressive sensing of high-dimensional datasets.
Revised:  Empirically, we demonstrate a 32\% on average over competing approaches for statistical compressive sensing of high-dimensional datasets.
Edit intent: clarity
Original:  Empirically, we demonstrate improvements of 32\%  on average over competing approaches for statistical compressive sensing of high-dimensional datasets.
Revised:  Empirically, we demonstrate improvements of 32\% on average over competing approaches for the task of statistical compressed sensing of high-dimensional datasets.
Edit intent: clarity
Original:  For example, the state-of-the-art technique requires 318,936 buckets (and over 8 seconds of refinement overhead per query) after observing only 300 queries.
Edit intent: coherence
Original: We develop random batch methods for interacting particle systems with large number of particles.
Revised: We develop Random Batch Methods for interacting particle systems with large number of particles.
Edit intent: fluency
Original:  Given a collection f_{ji: S_{i} }%DIFDELCMD < \to %DIFDELCMD < %%% S_{j a simple metric condition , which has a natural interpretation when considering the analogy of parallel transport, to construct a Gibbs measure on the space of correspondences between any pair of shapes that are generated by the f_{ji .
Revised:  Given a collection f_{ji: S_{i} }%DIFDELCMD < \to %DIFDELCMD < %%% S_{j a simple metric condition to construct a Gibbs measure on the space of correspondences between any pair of shapes that are generated by the f_{ji .
Edit intent: coherence
Original:  We demonstrate that this measure can be used to more accurately compute correspondences between feature points compared to currently employed, less robust methods .
Revised:  We demonstrate that this measure can improve correspondence accuracy between feature points compared to currently employed, less robust methods .
Edit intent: clarity
Original:  This is an axiomatic theory in bounded arithmetic which can formalize standard combinatorial arguments based on approximate counting.
Edit intent: coherence
Original:  In particular, the Ramsey and weak pigeonhole search problems lie in the  class.
Revised:  In particular, the Ramsey and weak pigeonhole search problems lie in the new class.
Edit intent: clarity
Original:  The goal is to find a path and delay for each demand so that no two trips occupy the same vertex at the same time, and so that the sum of trip times is minimized.
Revised:  The goal is to find a walk and delay for each demand so that no two trips occupy the same vertex at the same time, and so that the sum of trip times is minimized.
Edit intent: fluency
Original:  We also present a natural approximation algorithm  , and provide a tight analysis.
Revised:  We present a natural approximation algorithm , and provide a tight analysis.
Edit intent: clarity
Original: A propositional logic sentence in conjunctive normal form that has clauses with two literals (a 2-CNF) can be associated with a multigraph in which the vertices correspond to the variables and edges to clauses.
Revised: A propositional logic sentence in conjunctive normal form that has clauses of length two (a 2-CNF) can be associated with a multigraph in which the vertices correspond to the variables and edges to clauses.
Edit intent: clarity
Original:  Equivalently, all reduced 2-CNF sentences supported on a given simple graph are satisfiable if and only if those three graphs are forbidden as subgraphs in contractions of the original graph.
Revised:  Equivalently, all reduced 2-CNF sentences supported on a given simple graph are satisfiable if and only if those three graphs are forbidden as subgraphs of of the original graph.
Edit intent: clarity
Original: Previously we have introduced the cosine product-to-sum identity  \prodm = 1^M {\cos \left( {t{{{2^m}}}} \right)} = 1{{{2^{M - 1}}}}\summ = 1^{{2^{M - 1}}} {\cos \left( {{2m - 1}{{{2^M}}}t} \right)} and applied it for sampling  as an incomplete cosine expansion of the sinc function in order to obtain a rational approximation of the Voigt/complex error function that with only 16 summation terms can provide accuracy {\sim 10^{ - 14}}.
Revised: In our previous publications we have introduced the cosine product-to-sum identity \prodm = 1^M {\cos \left( {t{{{2^m}}}} \right)} = 1{{{2^{M - 1}}}}\summ = 1^{{2^{M - 1}}} {\cos \left( {{2m - 1}{{{2^M}}}t} \right)} and applied it for sampling as an incomplete cosine expansion of the sinc function in order to obtain a rational approximation of the Voigt/complex error function that with only 16 summation terms can provide accuracy {\sim 10^{ - 14}}.
Edit intent: clarity