wanyu/IteraTeR_v2 huggingface dataset:
Original:  We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion and sensing --- a model referred to as deep matrix factorization.
Revised:  We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion and sensing , a model referred to as deep matrix factorization.
Edit intent: fluency
Original:  We calculate this measure of systemic network concentration on a few data sets reporting exposures of financial institutions and show that typically the effect of common exposures is not fully contained by information at the level of single portfolio concentration  .
Revised:  This network metric is applied to synthetic and real world data to illustrate that the effect of common exposures is not fully contained by information at the level of single portfolio concentration .
Edit intent: clarity
Original:  We calculate this measure of systemic network concentration on a few data sets reporting exposures of financial institutions and show that typically the effect of common exposures is not fully contained by information at the level of single portfolio concentration  .
Revised:  We calculate this measure of systemic network concentration on a few data sets reporting exposures of financial institutions and show that typically the effect of common exposures is not fully reflected in single portfolio concentration .
Edit intent: clarity
Original:  As a result, we show that an optimal solution that minimizes systemic risk is to be found in a balance between these two, typically different and rather divergent, effects.
Edit intent: coherence
Original:  Using this network measure, we calculate the additional capital  corresponding to the systemic risk arising from credit concentration interconnectedness.
Revised:  Using this network measure, we calculate the additional capital requirement corresponding to the systemic risk arising from credit concentration interconnectedness.
Edit intent: clarity
Original: Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as the vanishing/exploding gradients problem .
Revised: Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as vanishing/exploding gradients problem .
Edit intent: fluency
Original: Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as the vanishing/exploding gradients problem .
Revised: Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as the vanishing/exploding gradients .
Edit intent: coherence
Original:  Short of designing new RNN architectures, various methods for dealing with this problem that have been previously proposed usually boil down to orthogonalization of the recurrent dynamics, either at initialization or during the entire training period.
Revised:  Short of designing new RNN architectures, previous methods for dealing with this problem that have been previously proposed usually boil down to orthogonalization of the recurrent dynamics, either at initialization or during the entire training period.
Edit intent: clarity
Original:  Short of designing new RNN architectures, various methods for dealing with this problem that have been previously proposed usually boil down to orthogonalization of the recurrent dynamics, either at initialization or during the entire training period.
Revised:  Short of designing new RNN architectures, various methods for dealing with this problem usually boil down to orthogonalization of the recurrent dynamics, either at initialization or during the entire training period.
Edit intent: coherence
Original:  The basic motivation behind these methods is that orthogonal transformations are isometries of the Euclidean space, hence they preserve (Euclidean) norms and effectively deal with the vanishing/exploding gradients problem .
Revised:  The basic motivation behind these methods is that orthogonal transformations are isometries of the Euclidean space, hence they preserve (Euclidean) norms and effectively deal with vanishing/exploding gradients problem .
Edit intent: fluency
Original:  The basic motivation behind these methods is that orthogonal transformations are isometries of the Euclidean space, hence they preserve (Euclidean) norms and effectively deal with the vanishing/exploding gradients problem .
Revised:  The basic motivation behind these methods is that orthogonal transformations are isometries of the Euclidean space, hence they preserve (Euclidean) norms and effectively deal with the vanishing/exploding gradients .
Edit intent: clarity
Original:  However, this idea ignores the crucial effects of non-linearity and noise.
Revised:  However, this ignores the crucial effects of non-linearity and noise.
Edit intent: clarity
Original:  Motivated by this finding, in this paper, we investigate the potential of non-normal RNNs, i.e. RNNs with a non-normal recurrent connectivity matrix, in sequential processing tasks.
Revised:  Motivated by this finding, here we investigate the potential of non-normal RNNs, i.e. RNNs with a non-normal recurrent connectivity matrix, in sequential processing tasks.
Edit intent: clarity
Original:  Our experimental results show that non-normal RNNs significantly outperform their orthogonal counterparts in a diverse range of benchmarks.
Revised:  Our experimental results show that non-normal RNNs outperform their orthogonal counterparts in a diverse range of benchmarks.
Edit intent: clarity
Original:  We also find evidence for increased non-normality and hidden chain-like feedforward structures in trained RNNs initialized with orthogonal recurrent connectivity matrices.
Revised:  We also find evidence for increased non-normality and hidden chain-like feedforward motifs in trained RNNs initialized with orthogonal recurrent connectivity matrices.
Edit intent: clarity
Original:  Arrays are important for the performance of many memory-intensive applications due to the design of modern memory hierarchies: contiguous storage facilitates spatial locality and predictive access patterns which enables prefetching. perations on large arrays often lend themselves well to parallelisation, such as a fork-join style divide-and-conquer algorithm for sorting.
Revised:  Arrays are important for the performance of many memory-intensive applications due to the design of modern memory hierarchies: contiguous storage facilitates spatial locality and predictive access patterns which enables prefetching. Operations on large arrays often lend themselves well to parallelisation, such as a fork-join style divide-and-conquer algorithm for sorting.
Edit intent: fluency
Original:  This paper presents the first extension of reference capabilities---called array capabilities---that support concurrent and parallel operations on arrays of both primitive and non-primitive values.
Revised:  This paper presents the first extension of reference capabilities -- called array capabilities -- that support concurrent and parallel operations on arrays of both primitive and non-primitive values.
Edit intent: fluency
Original:  (edited) his paper presents the array capability design space and show how it applies to a number of array use cases.
Revised:  This paper presents the array capability design space and show how it applies to a number of array use cases.
Edit intent: coherence
Original: In this paper, we discuss singularity formation for the focusing cubic wave equation in the energy supercritical regime.
Revised: We consider the focusing cubic wave equation in the energy supercritical regime.
Edit intent: clarity
Original:  In the seven dimensional case it was proven to be stable along a co-dimension one manifold of initial data.
Revised:  Furthermore, the solution is proven to be stable along a co-dimension one manifold of initial data.
Edit intent: coherence
Original:  In the seven dimensional case it was proven to be stable along a co-dimension one manifold of initial data.
Revised:  In the seven dimensional case it was proven to be co-dimension one manifold of initial data.
Edit intent: clarity
Original:  Here , we provide numerical evidence that this solution is in fact a critical solution at the threshold between finite-time blowup and dispersion.
Revised:  Here , we provide evidence that this solution is in fact a critical solution at the threshold between finite-time blowup and dispersion.
Edit intent: clarity
Original:  Here , we provide numerical evidence that this solution is in fact a critical solution at the threshold between finite-time blowup and dispersion.
Revised:  Here , we provide numerical evidence that this solution is at the threshold between finite-time blowup and dispersion.
Edit intent: clarity
Original:  Furthermore, we discuss the spectral problem arising in the stability analysis in general dimensions d \geq 5.
Revised:  In addition, we investigate the spectral problem arising in the stability analysis in general dimensions d \geq 5.
Edit intent: clarity
Original:  Furthermore, we discuss the spectral problem arising in the stability analysis in general dimensions d \geq 5.
Revised:  Furthermore, we discuss the spectral problem that underlies the stability analysis in general dimensions d \geq 5.
Edit intent: clarity
Original: In this work we introduce and study a novel Quasi Newton minimization method based on a Hessian approximation Broyden Class-type updating scheme, where a suitable matrix B_k is updated instead of the current Hessian approximation B_k.
Revised: In this work we introduce and study novel Quasi Newton minimization method based on a Hessian approximation Broyden Class-type updating scheme, where a suitable matrix B_k is updated instead of the current Hessian approximation B_k.
Edit intent: fluency
Original: In this work we introduce and study a novel Quasi Newton minimization method based on a Hessian approximation Broyden Class-type updating scheme, where a suitable matrix B_k is updated instead of the current Hessian approximation B_k.
Revised: In this work we introduce and study a novel Quasi Newton minimization methods based on a Hessian approximation Broyden Class-type updating scheme, where a suitable matrix B_k is updated instead of the current Hessian approximation B_k.
Edit intent: fluency
Original:  such conditions can be ensured using low complexity matrices B_k obtained projecting B_k onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step . Extended experimental tests show that the introduction of the adaptive criterion  considerably improves the performance of the minimization scheme when compared with a non-adaptive choice and confirm that the method could be particularly suitable to solve large scale problems  .
Revised:  such conditions can be ensured using low complexity matrices B_k obtained projecting B_k onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step . Extended experimental tests show that the introduction of the adaptive criterion considerably improves the robustness of the minimization scheme when compared with a non-adaptive choice and confirm that the method could be particularly suitable to solve large scale problems .
Edit intent: clarity
Original:  such conditions can be ensured using low complexity matrices B_k obtained projecting B_k onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step . Extended experimental tests show that the introduction of the adaptive criterion  considerably improves the performance of the minimization scheme when compared with a non-adaptive choice and confirm that the method could be particularly suitable to solve large scale problems  .
Revised:  such conditions can be ensured using low complexity matrices B_k obtained projecting B_k onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step . Extended experimental tests show that the introduction of the adaptive criterion considerably improves the performance of the minimization schemes when compared with a non-adaptive choice and confirm that the method could be particularly suitable to solve large scale problems .
Edit intent: fluency
Original:  such conditions can be ensured using low complexity matrices B_k obtained projecting B_k onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step . Extended experimental tests show that the introduction of the adaptive criterion  considerably improves the performance of the minimization scheme when compared with a non-adaptive choice and confirm that the method could be particularly suitable to solve large scale problems  .
Revised:  such conditions can be ensured using low complexity matrices B_k obtained projecting B_k onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step . Extended experimental tests show that the introduction of the adaptive criterion considerably improves the performance of the minimization scheme when compared with a non-adaptive choice ; moreover, they show that the proposed methods could be particularly suitable to solve large scale problems .
Edit intent: coherence
Original: We present " interaction trees" (ITrees) , a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment.
Revised:  " interaction trees" (ITrees) , a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment.
Edit intent: coherence
Original: We present " interaction trees" (ITrees) , a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment.
Revised: We present " Interaction trees" (ITrees) , a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment.
Edit intent: fluency
Original: We present " interaction trees" (ITrees) , a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment.
Revised: We present " interaction trees" (ITrees) are a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment.
Edit intent: clarity
Original: We present " interaction trees" (ITrees) , a general-purpose data structure in Coq for formalizing the behaviors of recursive programs that interact with their environment.
Revised: We present " interaction trees" (ITrees) , a general-purpose data structure for representing the behaviors of recursive programs that interact with their environment.
Edit intent: clarity
Original:  ITrees are built  of uninterpreted events and their continuations---a coinductive variant of a "free monad".
Revised:  ITrees are built out of uninterpreted events and their continuations---a coinductive variant of a "free monad".
Edit intent: fluency
Original:  Using this theory, we prove the termination-sensitive correctness of a compiler from a simple imperative source language to an assembly-like target whose meanings are given as an ITree-based denotational semantics.
Revised:  Using this theory, we prove the termination-sensitive correctness of a compiler from a simple imperative source language to an assembly-like target whose meanings are given in an ITree-based denotational semantics.
Edit intent: fluency
Original:  Here we introduce the Lipschitz matrix , a generalization of the scalar Lipschitz constant that alters the norm in which the distance between points is measured.
Revised:  Here we introduce the Lipschitz matrix : a generalization of the scalar Lipschitz constant that alters the norm in which the distance between points is measured.
Edit intent: fluency
Original:  Even if the Lipschitz matrix is not low rank, it can still reduce the constant associated with these tasks compared the Lipschitz constant when the singular values of the Lipschitz matrix decay.
Revised:  Even if the Lipschitz matrix is low-rank, this cost no longer depends on the dimension of the input, but instead on the rank of the Lipschitz matrix decay.
Edit intent: clarity
Original: We design and implement a novel algorithm for computing a Multilevel Monte Carlo (MLMC) estimator for the cumulative distribution function of a quantity of interest in problems with a random input parameter or initial condition .
Revised: We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator for the cumulative distribution function of a quantity of interest in problems with a random input parameter or initial condition .
Edit intent: fluency
Original: We design and implement a novel algorithm for computing a Multilevel Monte Carlo (MLMC) estimator for the cumulative distribution function of a quantity of interest in problems with a random input parameter or initial condition .
Revised: We design and implement a novel algorithm for computing a Multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with a random input parameter or initial condition .
Edit intent: fluency
Original: We design and implement a novel algorithm for computing a Multilevel Monte Carlo (MLMC) estimator for the cumulative distribution function of a quantity of interest in problems with a random input parameter or initial condition .
Revised: We design and implement a novel algorithm for computing a Multilevel Monte Carlo (MLMC) estimator for the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions .
Edit intent: fluency
Original:  Our approach combines a standard MLMC method with stratified sampling by replacing standard Monte Carlo at each level of discretization by stratified Monte Carlo with proportional allocation.
Revised:  Our approach combines a standard MLMC method with stratified sampling by replacing standard Monte Carlo at each level with stratified Monte Carlo with proportional allocation.
Edit intent: clarity
Original:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation may yield a more efficient algorithm compared to the typically used polynomial smoothing , with the difference in computational cost between both methods depending on the required error tolerance and the nature of the problem .
Revised:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation yields a more efficient algorithm compared to the typically used polynomial smoothing , with the difference in computational cost between both methods depending on the required error tolerance and the nature of the problem .
Edit intent: clarity
Original:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation may yield a more efficient algorithm compared to the typically used polynomial smoothing , with the difference in computational cost between both methods depending on the required error tolerance and the nature of the problem .
Revised:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation may yield a more efficient algorithm compared to the typically used polynomial smoothing . The difference in computational cost between both methods depending on the required error tolerance and the nature of the problem .
Edit intent: coherence
Original:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation may yield a more efficient algorithm compared to the typically used polynomial smoothing , with the difference in computational cost between both methods depending on the required error tolerance and the nature of the problem .
Revised:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation may yield a more efficient algorithm compared to the typically used polynomial smoothing , with the difference in computational cost between the smoothing methods depends on the required error tolerance and the nature of the problem .
Edit intent: clarity
Original:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation may yield a more efficient algorithm compared to the typically used polynomial smoothing , with the difference in computational cost between both methods depending on the required error tolerance and the nature of the problem .
Revised:  Furthermore, we find that a smoothing approximation for the indicator function based on kernel density estimation may yield a more efficient algorithm compared to the typically used polynomial smoothing , with the difference in computational cost between both methods depending on the required error tolerance .
Edit intent: clarity
Original:  In this paper , we present a declarative solution, EdgeUsher, to the problem of how to best place VNF chains onto Cloud-Edge infrastructures.
Revised:  In this paper , we present a declarative solution, EdgeUsher, to the problem of how to best place VNF chains to Cloud-Edge infrastructures.
Edit intent: fluency
Original:  EdgeUsher prototype can determine all eligible placements for a set of VNF chains onto an Edge infrastructure so to satisfy all the hardware, IoT, security, bandwidth, and latency requirements associated with the input VNF chains .
Revised:  EdgeUsher can determine all eligible placements for a set of VNF chains onto an Edge infrastructure so to satisfy all the hardware, IoT, security, bandwidth, and latency requirements associated with the input VNF chains .
Edit intent: clarity
Original:  EdgeUsher prototype can determine all eligible placements for a set of VNF chains onto an Edge infrastructure so to satisfy all the hardware, IoT, security, bandwidth, and latency requirements associated with the input VNF chains .
Revised:  EdgeUsher prototype can determine all eligible placements for a set of VNF chains onto an Edge infrastructure so to satisfy all of their hardware, IoT, security, bandwidth, and latency requirements associated with the input VNF chains .
Edit intent: clarity
Original:  EdgeUsher prototype can determine all eligible placements for a set of VNF chains onto an Edge infrastructure so to satisfy all the hardware, IoT, security, bandwidth, and latency requirements associated with the input VNF chains .
Revised:  EdgeUsher prototype can determine all eligible placements for a set of VNF chains onto an Edge infrastructure so to satisfy all the hardware, IoT, security, bandwidth, and latency requirements .
Edit intent: clarity
Original: With the rapid evolution of technological, economic, and regulatory landscapes, contemporary Blockchian platforms are all but certain to undergo major changes.
Revised: With the rapid evolution of technological, economic, and regulatory landscapes, contemporary blockchain platforms are all but certain to undergo major changes.
Edit intent: fluency
Original:  Therefore,  applications that rely on them will eventually need to migrate the Blockchain to remain competitive and secure, as well as to enhance the  performance, cost efficiency, privacy, and regulatory compliance.
Revised:  Therefore, the applications that rely on them will eventually need to migrate the Blockchain to remain competitive and secure, as well as to enhance the performance, cost efficiency, privacy, and regulatory compliance.
Edit intent: fluency