wanyu/IteraTeR_v2 huggingface dataset:
Original:  The superiority of the predictive densities , over the single regime random walk model , relies on the fact that the states capture alternating periods with distinct returns' characteristics.
Revised:  The superiority of the predictive densities , over the single regime random walk model relies on the fact that the states capture alternating periods with distinct returns' characteristics.
Edit intent: fluency
Original:  The superiority of the predictive densities , over the single regime random walk model , relies on the fact that the states capture alternating periods with distinct returns' characteristics.
Revised:  The superiority of the predictive densities , over the single regime random walk model , relies on the fact that the states capture alternating periods with distinct return characteristics.
Edit intent: clarity
Original:  Finally, we observe that conditionally on the hidden states, the predictors have different linear and non-linear effects  .
Revised:  Also, conditionally on the hidden states, the predictors have different linear and non-linear effects .
Edit intent: coherence
Original:  Finally, we observe that conditionally on the hidden states, the predictors have different linear and non-linear effects  .
Revised:  Finally, we observe that conditionally on the hidden states, it identifies predictors with different linear and non-linear effects .
Edit intent: clarity
Original:  These results reveal how tree species and their specific traits influence forest floor C stock and mineral soil C concentration and stock at the global scale.
Revised:  These results reveal how tree species and their specific traits influence forest floor C stock and mineral soil C concentration and stock at a global scale.
Edit intent: fluency
Original:  The problem is important not only as a fundamental problem in probability theory and statistics, but also because of its critical roles in many other important issues such as indecisiveness of voting, strategic voting, privacy of voting, voting power, voter turn out, etc.
Edit intent: coherence
Original:  In particular, little progress was made after Marchant Mar01 explicitly posed the likelihood of k-way ties under IC as an open question in 2001.
Revised:  In particular, little progress was made after Marchant explicitly posed the likelihood of k-way ties under IC as an open question in 2001.
Edit intent: fluency
Original:  Our main approach is a new technique called states compression, which generalizes the "mark/unmark" paradigm of Moitra (Moitra, JACM, 2019), and can give fast local-lemma-based sampling algorithms.
Revised:  Our main approach is a new technique called state compression, which generalizes the "mark/unmark" paradigm of Moitra (Moitra, JACM, 2019), and can give fast local-lemma-based sampling algorithms.
Edit intent: fluency
Original:  The new method admits a more extensive permitted range of the parameters in the mapping functions , that it enjoys some mathematical advantages in achieving optimal convergence rates .
Revised:  The new method admits a more extensive permitted range of the parameters in the mapping functions . Consequently, they have the capacity to achieve optimal convergence rates .
Edit intent: clarity
Original: Recently, Transformers have shown competitive automatic speech recognition (ASR) results .
Revised: Recently, Transformers have shown competitive automatic speech recognition (ASR) performance .
Edit intent: clarity
Original:  One key factor to the success of these models is the multi-head attention mechanism.
Revised:  One key factor in the success of these models is the multi-head attention mechanism.
Edit intent: fluency
Original:  However, we observed in trained models, the diagonal attention matrices indicating the redundancy of the corresponding attention heads.
Revised:  However, for trained models, the diagonal attention matrices indicating the redundancy of the corresponding attention heads.
Edit intent: coherence
Original:  Furthermore, we found some architectures with reduced numbers of attention heads have better performance.
Revised:  We have also found that some architectures with reduced numbers of attention heads have better performance.
Edit intent: coherence
Original:  In this paper, we develop  a novel version of such a graded dependent type system , including functions, tensor products, additive sums, and a unit type.
Revised:  In this paper, we develop a novel version of such a graded dependent type system that includes functions, tensor products, additive sums, and a unit type.
Edit intent: coherence
Original:  Since standard operational semantics is resource-agnostic, we develop a heap-based operational semantics and prove a soundness theorem that shows correct usage of resources .
Revised:  Since standard operational semantics is resource-agnostic, we develop a heap-based operational semantics and prove a soundness theorem that shows correct accounting of resource usage .
Edit intent: clarity
Original:  We expect that our work will provide a base for integrating linearity, irrelevance and dependent types in practical programming languages like Haskell.
Revised:  We hope that our work will provide a base for integrating linearity, irrelevance and dependent types in practical programming languages like Haskell.
Edit intent: clarity
Original:  Although the denoised problem turns out to be NP-hard, we give a linear-programming based approximation algorithm for it.
Revised:  Although this denoised problem turns out to be NP-hard, we give a linear-programming based approximation algorithm for it.
Edit intent: fluency
Original:  We empirically evaluate our approach on both synthetic and real-world datasets.
Revised:  We evaluate this approach on both synthetic and real-world datasets.
Edit intent: clarity
Original:  An AG code C = C(C, P, D) is a vector space associated to evaluations on P of functions in the Riemann-Roch space L _{\mathcal{C (D).
Revised:  An AG code C = C(C, P, D) is a vector space associated to evaluations on P of functions in the Riemann-Roch space L _\mathcal{C (D).
Edit intent: fluency
Original:  We take advantage of the algebraic geometry framework that makes any group action on the curve that fixes the divisor D translate into a decomposition of the code C. Concretely, our approach relies on Kani's result that splits the Riemann-Roch space of any invariant divisor under this action into several explicit Riemann-Roch spaces on the quotient curve.
Revised:  We take advantage of the algebraic geometry framework that makes any group action on the curve that fixes the divisor D translate into a decomposition of the code C. Concretely, our approach relies on Kani's result that splits the Riemann-Roch space of any invariant divisor under a group action on a curve into several explicit Riemann-Roch spaces on the quotient curve.
Edit intent: clarity
Original:  Under some hypotheses, these spaces behave well enough to define an AG code C' on the quotient curve so that a proximity test to C can  be reduced to one to  C'.
Revised:  Under some hypotheses, a proximity test to C can be reduced to one to C'.
Edit intent: clarity
Original:  The most popular method to address this issue is known as knowledge distillation in deep learning literature (in addition to model compression) where a large pretrained network known as the teacher is used to train a smaller student network.
Revised:  The most popular method to address this issue is known as knowledge distillation in deep learning literature (in addition to model compression) where a large pre-trained network known as the teacher is used to train a smaller student network.
Edit intent: fluency
Original:  We develop and apply multilevel Monte Carlo (MLMC) strategies for ensemble Kalman--Bucy filters (EnKBFs).
Revised:  We develop and apply multilevel Monte Carlo (MLMC) strategies for ensemble Kalman-Bucy filters (EnKBFs).
Edit intent: fluency
Original:  These filters can be viewed as approximations of conditional McKean--Vlasov-type diffusion processes.
Revised:  These filters can be viewed as approximations of conditional McKean-Vlasov-type diffusion processes.
Edit intent: fluency
Original:  They are also interpreted as the continuous-time analogue of the ensemble Kalman filter , which has proven to be successful due to its applicability and computational cost.
Revised:  They are also interpreted as the continuous-time analogue of the ensemble Kalman filter , which has proven to be successful due to its applicability and computational cost.
Edit intent: fluency
Original:  We test our theory on a linear problem, which we motivate through a relatively high-dimensional example of order \sim  10 ^3 .
Revised:  We test our theory on a linear problem, which we motivate through high-dimensional example of order \sim 10 ^3 .
Edit intent: clarity
Original:  We test our theory on a linear problem, which we motivate through a relatively high-dimensional example of order \sim  10 ^3 .
Revised:  We test our theory on a linear problem, which we motivate through a relatively high-dimensional examples of order \sim 10 ^3 .
Edit intent: fluency
Original:  In the rest of this paper, what will follow is a paradigm to set the stage for how peer lending can be conceived from a matching market perspective with sequential design making embedded in it.
Revised:  In the rest of this paper, what will follow is a paradigm to set the stage for how peer to peer investments can be conceived from a matching market perspective with sequential design making embedded in it.
Edit intent: clarity
Original: Neuromorphic engineering is a rapidly developing field that aims to take inspiration from the biological organization of neural systems to develop novel technology for computing, sensing  and actuating.
Revised: Neuromorphic engineering is a rapidly developing field that aims to take inspiration from the biological organization of neural systems to develop novel technology for computing, sensing , and actuating.
Edit intent: fluency
Original:  The potential of neuronal control is illustrated on simple network examples that suggest the scalability of the mixed-feedback principles.
Revised:  The potential of neuronal control is illustrated on elementary network examples that suggest the scalability of the mixed-feedback principles.
Edit intent: clarity
Original:  Due to the NP-hardness of this problem, most previous attempts rely on heuristic techniques.
Revised:  Due to the hardness of this problem, most previous attempts rely on heuristic techniques.
Edit intent: clarity
Original:  Supervised metric learning can be categorized into entity-based learning and proxy-based learning %DIFDELCMD < \protect%%% \footnote{Different from the definition in \mbox{ Proxyanchor .
Revised:  Supervised metric learning can be categorized into entity-based learning and proxy-based learning %DIFDELCMD < \protect%%% \footnote{ .
Edit intent: coherence
Original:  Most of  existing metric learning objectives like Contrastive, Triplet, Prototypical, GE2E, etc all belong to the former division, the performance of which is either highly dependent on sample mining strategy or restricted by insufficient label information in the mini-batch.
Revised:  Most of the existing metric learning objectives like Contrastive, Triplet, Prototypical, GE2E, etc all belong to the former division, the performance of which is either highly dependent on sample mining strategy or restricted by insufficient label information in the mini-batch.
Edit intent: fluency
Original:  This paper proposes a Mask Proxy (MP) loss which directly incorporates both proxy-based relationship and entity-based relationship .
Revised:  This paper proposes a Masked Proxy (MP) loss which directly incorporates both proxy-based relationship and entity-based relationship .
Edit intent: fluency
Original:  We further propose Multinomial Mask Proxy (MMP) loss to leverage the hardness of entity-to-entity pairs.
Revised:  We further propose Multinomial Masked Proxy (MMP) loss to leverage the hardness of entity-to-entity pairs.
Edit intent: fluency
Original:  We further propose Multinomial Mask Proxy (MMP) loss to leverage the hardness of entity-to-entity pairs.
Revised:  We further propose Multinomial Mask Proxy (MMP) loss to leverage the hardness of speaker pairs.
Edit intent: clarity
Original:  Our approach allows us to derive new classes of kernels which unify popular random walk or diffusion-type sampling methods with more complicated "extended phase space" algorithms based on Hamiltonian dynamics.
Revised:  Our approach allows us to derive new classes of kernels which unify random walk or diffusion-type sampling methods with more complicated "extended phase space" algorithms based on Hamiltonian dynamics.
Edit intent: clarity
Original:  Our approach allows us to derive new classes of kernels which unify popular random walk or diffusion-type sampling methods with more complicated "extended phase space" algorithms based on Hamiltonian dynamics.
Revised:  Our approach allows us to derive new classes of kernels which unify popular random walk or diffusion-type sampling methods with more complicated "extended phase space" algorithms based around ideas from Hamiltonian dynamics.
Edit intent: clarity
Original:  The starting point for our approach is an abstract result developed in the generality of measurable state spaces that addresses proposal kernels that possess a certain involution structure.
Revised:  Our starting point is an abstract result developed in the generality of measurable state spaces that addresses proposal kernels that possess a certain involution structure.
Edit intent: clarity
Original: The purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions u of elliptic problems while assuming H ^1_0 -error estimation %DIFDELCMD < \left\|%%% u-%DIFDELCMD < u\right\|%%% _{H_{0^{1}} \leq \rho given some numerical approximation }%DIFDELCMD < u %%% and an explicit error bound \rho .
Revised: The purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions u of elliptic problems while assuming H ^1_0 -error estimation %DIFDELCMD < \left\|%%% %DIFDELCMD < u\right\|%%% _{H_{0^{1}} \leq \rho given some numerical approximation }%DIFDELCMD < u %%% and an explicit error bound \rho .
Edit intent: coherence
Original:  Appl. Math, Vol. 370, (2020) 112647], we achieved a method of verifying positivity for several semilinear elliptic problems by unifying two approaches .
Revised:  Appl. Math, Vol. 370, (2020) 112647], we proposed two approaches to verify the positivity of solutions of several semilinear elliptic problems by unifying two approaches .
Edit intent: clarity
Original:  However, some cases also require L^{\infty} -error estimation %DIFDELCMD < \left\|%%% u-%DIFDELCMD < u\right\|%%% _{L^{\infty} \leq \sigma given explicit \sigma>0 .
Revised:  However, some cases require L^{\infty} -error estimation %DIFDELCMD < \left\|%%% u-%DIFDELCMD < u\right\|%%% _{L^{\infty} \leq \sigma given explicit \sigma>0 .
Edit intent: clarity
Original:  However, some cases also require L^{\infty} -error estimation %DIFDELCMD < \left\|%%% u-%DIFDELCMD < u\right\|%%% _{L^{\infty} \leq \sigma given explicit \sigma>0 .
Revised:  However, some cases also require L^{\infty} -error estimation %DIFDELCMD < \left\|%%% %DIFDELCMD < u\right\|%%% _{L^{\infty} \leq \sigma given explicit \sigma>0 .
Edit intent: coherence
Original:  However, some cases also require L^{\infty} -error estimation %DIFDELCMD < \left\|%%% u-%DIFDELCMD < u\right\|%%% _{L^{\infty} \leq \sigma given explicit \sigma>0 .
Revised:  However, some cases also require L^{\infty} -error estimation %DIFDELCMD < \left\|%%% u-%DIFDELCMD < u\right\|%%% } \leq \sigma given explicit \sigma>0 .
Edit intent: coherence
Original:  We describe how to evaluate some constants calculated from approximation because the proposed method requires explicit estimates of them.
Revised:  We describe how to evaluate some constants because the proposed method requires explicit estimates of them.
Edit intent: clarity
Original: We present a simple deterministic distributed algorithm that computes a (\Delta+1)-vertex coloring in O(\log^2 \Delta \cdot \log n) rounds , in any graph with at most n nodes and maximum degree at most \Delta .
Revised: We present a simple deterministic distributed algorithm that computes a (\Delta+1)-vertex coloring in O(\log^2 \Delta \cdot \log n) rounds .
Edit intent: clarity
Original:  It can also be extended to the more general (degree+1)-list coloring problem.
Revised:  The algorithm can also be extended to the more general (degree+1)-list coloring problem.
Edit intent: clarity
Original:  It solves the coloring problem in a direct way, without using network decomposition, by gradually rounding a certain fractional color assignment until reaching an integral color assignment .
Revised:  It solves the coloring problem in a direct way, without using network decomposition, by gradually rounding a certain fractional color assignment until reaching an integral color assignments .
Edit intent: fluency
Original: We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size.
Revised: We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size.
Edit intent: fluency
Original:  Here \text{nnz  denotes the number of non-zero entries of a matrix M, and \omega is the exponent of matrix multiplication.
Revised:  Here nnz denotes the number of non-zero entries of a matrix M, and \omega is the exponent of matrix multiplication.
Edit intent: coherence
Original:  The desired components, thereby, are typically defined at the time of training .
Revised:  The DSCs are typically defined at the time of training .
Edit intent: clarity
Original:  Auxiliary information is, thereby, extracted from a reference snippet of the desired components by a second DNN, which estimates a set of adaptive weights ( AW ) of the first DNN.
Revised:  Auxiliary information is, thereby, extracted from a reference snippet of the desired components by a second DNN, which estimates a set of adaptive weights ( AWs ) of the first DNN.
Edit intent: clarity
Original:  Applications where the reference and desired signal cannot be assigned to a specific class and vary over time require a time-dependency .
Revised:  Applications where the reference and desired signal cannot be assigned to a specific class like speech, require time-variant AWs .
Edit intent: clarity
Original:  To avoid strong scaling between the estimate and the mixture, we propose  the dual scale-invariant signal-to-distortion ratio in a TASNET inspired DNN as the training objective .
Revised:  To avoid strong scaling between the estimate and the mixture, we propose to train with the dual scale-invariant signal-to-distortion ratio in a TASNET inspired DNN as the training objective .
Edit intent: clarity
Original:  To avoid strong scaling between the estimate and the mixture, we propose  the dual scale-invariant signal-to-distortion ratio in a TASNET inspired DNN as the training objective .
Revised:  To avoid strong scaling between the estimate and the mixture, we propose the dual scale-invariant signal-to-distortion ratio in a TASNET inspired DNN .
Edit intent: clarity
Original:  We evaluate the proposed AW systems using a wide range of different acoustic conditions and show the scenario dependent advantages of time-variant over time-invariant AW .
Revised:  We evaluate the proposed AWs systems under various acoustic conditions and show the scenario dependent advantages of time-variant over time-invariant AW .
Edit intent: clarity
Original:  We evaluate the proposed AW systems using a wide range of different acoustic conditions and show the scenario dependent advantages of time-variant over time-invariant AW .
Revised:  We evaluate the proposed AW systems using a wide range of different acoustic conditions and show the scenario-dependent advantages of time-variant over time-invariant AW .
Edit intent: fluency
Original:  We evaluate the proposed AW systems using a wide range of different acoustic conditions and show the scenario dependent advantages of time-variant over time-invariant AW .
Revised:  We evaluate the proposed AW systems using a wide range of different acoustic conditions and show the scenario dependent advantages of time-variant over time-invariant AWs .
Edit intent: clarity
Original: State-of-the-art separation of desired signal components (DSCs) from a mixture is achieved using time-frequency masks or filters estimated by a deep neural network (DNN).
Revised: Informed speaker extraction aims to extract a target speech signal from a mixture is achieved using time-frequency masks or filters estimated by a deep neural network (DNN).
Edit intent: clarity
Original: Due to the high variability of the traffic in the radio access network (RAN), fixed network configurations are not flexible to achieve the optimal performance.
Revised: Due to the high variability of the traffic in the radio access network (RAN), fixed network configurations are not flexible enough to achieve optimal performance.
Edit intent: clarity
Original:  But the detailed mechanisms of the eNodeB configurations are usually very complicated and not disclosed, not to mention the large KPIs space needed to be considered.
Revised:  But the detailed mechanisms of the eNodeB configurations are usually very complicated and not disclosed, not to mention the large key performance indicators (KPIs) space needed to be considered.
Edit intent: clarity
Original:  These make constructing  simulator, offline tuning, or rule-based solutions difficult.
Revised:  These make constructing a simulator, offline tuning, or rule-based solutions difficult.
Edit intent: fluency
Original:  We aim to build an intelligent controller without strong assumption or domain knowledge about the RAN and can run for 24/7 without supervision.
Revised:  We aim to build an intelligent controller without strong assumption or domain knowledge about the RAN and can run 24/7 without supervision.
Edit intent: clarity
Original:  Next, we build a double Q network agent that is trained with the live feedbacks of the key performance indicators from the RAN.
Revised:  Next, we build a double Q network agent trained with the live feedbacks of the key performance indicators from the RAN.
Edit intent: clarity
Original:  Next, we build a double Q network agent that is trained with the live feedbacks of the key performance indicators from the RAN.
Revised:  Next, we build a double Q network agent that is trained with the live feedback of the key performance indicators from the RAN.
Edit intent: fluency
Original: In  recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network coding or public key cryptography.
Revised: In the recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network coding or public key cryptography.
Edit intent: fluency
Original:  In this article, we discuss the hardness of the code equivalence problem in rank metric for F_{q^m} --linear and general rank metric codes.
Revised:  In this article, we discuss the hardness of the code equivalence problem in rank metric for F_{q^m} -linear and general rank metric codes.
Edit intent: fluency
Original:  In the F_{q^m} --linear case, we reduce the underlying problem to another one called {\em Matrix Codes Right Equivalence Problem (MCREP) .
Revised:  In the F_{q^m} -linear case, we reduce the underlying problem to another one called {\em Matrix Codes Right Equivalence Problem (MCREP) .
Edit intent: fluency
Original:  In the F_{q^m} --linear case, we reduce the underlying problem to another one called {\em Matrix Codes Right Equivalence Problem (MCREP) .
Revised:  In the F_{q^m} --linear case, we reduce the underlying problem to another one called {\em Matrix Codes Right Equivalence Problem .
Edit intent: clarity