wanyu/IteraTeR_v2 huggingface dataset:
Original:  We assume that the bond market consist of entire family of rolling bonds and the investment strategy is a general signed measure distributed on all real numbers representing time to maturity specifications for different rolling bonds.
Revised:  We assume that the bond market consists of entire family of rolling bonds and the investment strategy is a general signed measure distributed on all real numbers representing time to maturity specifications for different rolling bonds.
Edit intent: fluency
Original:  Explicit calculations for certain particular models are presented.
Revised:  Explicit calculations for affine models are presented.
Edit intent: clarity
Original:  Guided by this intuition we formulate a system of session types based on Classical Linear Logic with coexponentials, which is well-suited for modelling client-server interactions.
Revised:  Guided by this intuition we formulate a system of session types based on Classical Linear Logic with coexponentials, which is suited to modelling client-server interactions.
Edit intent: clarity
Original: We propose a new general approach for the treatment of parameterized geometries in projection-based model order reduction.
Revised: We present a general approach for the treatment of parameterized geometries in projection-based model order reduction.
Edit intent: clarity
Original:  To ensure safety, self-driving vehicles must reliably sense and detect humans, other vehicles, and road infrastructure accurately, robustly, and timely.
Revised:  To ensure safety, self-driving vehicles must sense and detect humans, other vehicles, and road infrastructure accurately, robustly, and timely.
Edit intent: clarity
Original:  The signal-to-noise ratio (SNR) of the return signal is further enhanced by canceling out irrelevant reflections , using destructive interference.
Revised:  The signal-to-noise ratio (SNR) of the return signal by canceling out irrelevant reflections , using destructive interference.
Edit intent: clarity
Original:  Specifically, this paper proposes a new notion of algorithmic stability termed }\textit{locally elastic stability in light of a certain phenomenon in the training of neural networks \mbox{ he2020local   that locally elastic stability implies a tighter generalization bound than that derived based on uniform stability in many situations .
Revised:  Specifically, this paper proposes a new notion of algorithmic stability termed }\textit{ in light of a certain phenomenon in the training of neural networks \mbox{ he2020local that locally elastic stability implies a tighter generalization bound than that derived based on uniform stability in many situations .
Edit intent: fluency
Original:  Specifically, this paper proposes a new notion of algorithmic stability termed }\textit{locally elastic stability in light of a certain phenomenon in the training of neural networks \mbox{ he2020local   that locally elastic stability implies a tighter generalization bound than that derived based on uniform stability in many situations .
Revised:  Specifically, this paper proposes a new notion of algorithmic stability termed }\textit{locally elastic stability in light of a certain phenomenon in the training of neural networks \mbox{ he2020local that locally elastic stability implies tighter generalization bounds than those derived based on uniform stability in many situations .
Edit intent: fluency
Original:  The key idea is to compact the genuine speech representation and inject an angular margin to separate the spoofing attacks in the embedding space.
Revised:  The key idea is to compact the bona fide speech representation and inject an angular margin to separate the spoofing attacks in the embedding space.
Edit intent: fluency
Original:  Then, it proceeds to discretization by an implicit scheme, and a recursive expression for convergence speed is derived.
Revised:  Then, it proceeds to an implicit scheme, and a recursive expression for convergence speed is derived.
Edit intent: clarity
Original:  An optimal interface condition for Schwarz waveform relaxation is also obtained, which leads to "perfect convergence", that is, convergence within two times of iteration.
Revised:  An optimal interface condition for the Schwarz iteration is obtained, and it leads to "perfect convergence", that is, convergence within two times of iteration.
Edit intent: clarity
Original:  Numerical experiments indicate that the conclusions, such as the "perfect convergence ", drawn in the linear situations may remain mostly in the computation of the Burgers equations .
Revised:  Numerical experiments indicate that the conclusions, such as the "perfect convergence , " drawn in the linear situations may remain mostly in the computation of the Burgers equations .
Edit intent: fluency
Original:  Numerical experiments indicate that the conclusions, such as the "perfect convergence ", drawn in the linear situations may remain mostly in the computation of the Burgers equations .
Revised:  Numerical experiments indicate that the conclusions, such as the "perfect convergence ", drawn in the linear situations may remain in the Burgers equations' computation .
Edit intent: clarity
Original:  This network is built with the Floor function (\lfloor x\rfloor), the exponential function (2^x), the step function ( %DIFDELCMD < \one%%%  _{x\geq 0}), or their compositions as activation functions in each neuron and hence we call such networks as Floor-Exponential-Step (FLES) networks.
Revised:  This network is built with the Floor function (\lfloor x\rfloor), the exponential function (2^x), the step function ( %DIFDELCMD < \one%%% _{x\geq 0}), or their compositions as the activation function in each neuron and hence we call such networks as Floor-Exponential-Step (FLES) networks.
Edit intent: fluency
Original:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Revised:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Edit intent: fluency
Original:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Revised:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Edit intent: fluency
Original:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Revised:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Edit intent: fluency
Original:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Revised:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H %DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Edit intent: fluency
Original:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Revised:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Edit intent: clarity
Original:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H \"o%DIFDELCMD < }%%% lder order and constant, respectively.
Revised:  For any width hyper-parameter N\inN^+, it is shown that FLES networks with a width \max\{d, \, N\} and three hidden layers can uniformly approximate a H \"o%DIFDELCMD < }%%% lder function f on [0,1]^d with an exponential approximation rate 3\lambda d^{\alpha/2 2 )^{\alpha} 2} ^{-\alpha N}, where \alpha \in(0,1] and \lambda are the H %DIFDELCMD < }%%% lder order and constant, respectively.
Edit intent: fluency
Original:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is  \omega_f( \sqrt{d\,}  2^{-N} ) + 2 \omega_f( \sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Revised:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is 2 \omega_f( \sqrt{d\,} 2^{-N} ) + 2 \omega_f( \sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Edit intent: fluency
Original:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is  \omega_f( \sqrt{d\,}  2^{-N} ) + 2 \omega_f( \sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Revised:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f( \,} 2^{-N} ) + 2 \omega_f( \sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Edit intent: fluency
Original:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is  \omega_f( \sqrt{d\,}  2^{-N} ) + 2 \omega_f( \sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Revised:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f( \sqrt{d\,} 2^{-N} + 2 \omega_f( \sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Edit intent: fluency
Original:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is  \omega_f( \sqrt{d\,}  2^{-N} ) + 2 \omega_f( \sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Revised:  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f( \sqrt{d\,} 2^{-N} ) + 2 \omega_f( 2\sqrt{d\,} 2^{-N} . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r)
Edit intent: fluency
Original:  as r\rightarrow 0 is moderate (e.g., \omega_f(r) \lesssim r^\alpha for H \"o%DIFDELCMD < }%%% lder continuous functions), since the major term to be concerned in our approximation rate is essentially \sqrt{d} times a function of N independent of d within the modulus of continuity   .
Revised:  as r\rightarrow 0 is moderate (e.g., \omega_f(r) \lesssim r^\alpha for \"o%DIFDELCMD < }%%% lder continuous functions), since the major term to be concerned in our approximation rate is essentially \sqrt{d} times a function of N independent of d within the modulus of continuity .
Edit intent: clarity
Original:  as r\rightarrow 0 is moderate (e.g., \omega_f(r) \lesssim r^\alpha for H \"o%DIFDELCMD < }%%% lder continuous functions), since the major term to be concerned in our approximation rate is essentially \sqrt{d} times a function of N independent of d within the modulus of continuity   .
Revised:  as r\rightarrow 0 is moderate (e.g., \omega_f(r) \lesssim r^\alpha for H %DIFDELCMD < }%%% lder continuous functions), since the major term to be concerned in our approximation rate is essentially \sqrt{d} times a function of N independent of d within the modulus of continuity .
Edit intent: clarity
Original:  This network is built with the Floor function (\lfloor x\rfloor), the exponential function (2^x), the step function ( 1 \hspace{-3.6pt _{x\geq 0}), or their compositions as the activation function in each neuron and hence we call such networks as Floor-Exponential-Step (FLES) networks.
Revised:  This network is built with the floor function (\lfloor x\rfloor), the exponential function (2^x), the step function ( 1 \hspace{-3.6pt _{x\geq 0}), or their compositions as the activation function in each neuron and hence we call such networks as Floor-Exponential-Step (FLES) networks.
Edit intent: fluency
Original: The quest of this work is to present a discussion of some fundamental questions of economics in the era of quantum technology, which require a treatment different from economics studied thus far in the literature.
Revised: The quest of this work is to present discussions of some fundamental questions of economics in the era of quantum technology, which require a treatment different from economics studied thus far in the literature.
Edit intent: fluency
Original:  These "corona apps" may require widespread adoption to be effective, which has sparked public debates about the privacy, security, and societal implications of government-backed health applications.
Revised:  Many "corona apps" may require widespread adoption to be effective, which has sparked public debates about the privacy, security, and societal implications of government-backed health applications.
Edit intent: fluency
Original:  These "corona apps" may require widespread adoption to be effective, which has sparked public debates about the privacy, security, and societal implications of government-backed health applications.
Revised:  These "corona apps" require widespread adoption to be effective, which has sparked public debates about the privacy, security, and societal implications of government-backed health applications.
Edit intent: clarity
Original:  The embedding space should ideally capture the variations between all possible speakers, encoding the multiple  aspects that make up speaker identity.
Revised:  The embedding space should ideally capture the variations between all possible speakers, encoding the multiple acoustic aspects that make up speaker identity.
Edit intent: clarity
Original:  In this work, utilizing speaker age as an auxiliary variable in US Supreme Court recordings and speaker nationality with VoxCeleb , we show that by leveraging additional speaker attribute information in a multi task learning setting, deep speaker embedding performance can be increased for verification and diarization tasks, achieving a relative improvement of 17.8 \% in DER and 8.9 \% in EER for Supreme Court audio compared to omitting the auxiliary task.
Revised:  In this work, utilizing speaker age as an auxiliary variable in US Supreme Court recordings , we show that by leveraging additional speaker attribute information in a multi task learning setting, deep speaker embedding performance can be increased for verification and diarization tasks, achieving a relative improvement of 17.8 \% in DER and 8.9 \% in EER for Supreme Court audio compared to omitting the auxiliary task.
Edit intent: coherence
Original:  In this work, utilizing speaker age as an auxiliary variable in US Supreme Court recordings and speaker nationality with VoxCeleb , we show that by leveraging additional speaker attribute information in a multi task learning setting, deep speaker embedding performance can be increased for verification and diarization tasks, achieving a relative improvement of 17.8 \% in DER and 8.9 \% in EER for Supreme Court audio compared to omitting the auxiliary task.
Revised:  In this work, utilizing speaker age as an auxiliary variable in US Supreme Court recordings and speaker nationality with VoxCeleb , we show that by leveraging two additional forms of speaker attribute information in a multi task learning setting, deep speaker embedding performance can be increased for verification and diarization tasks, achieving a relative improvement of 17.8 \% in DER and 8.9 \% in EER for Supreme Court audio compared to omitting the auxiliary task.
Edit intent: clarity
Original: A number of recent advances in  audio synthesis rely on neural upsamplers , which can introduce undesired artifacts.
Revised: A number of recent advances in neural audio synthesis rely on neural upsamplers , which can introduce undesired artifacts.
Edit intent: fluency
Original: A number of recent advances in  audio synthesis rely on neural upsamplers , which can introduce undesired artifacts.
Revised: A number of recent advances in audio synthesis rely on upsampling layers , which can introduce undesired artifacts.
Edit intent: clarity
Original:  We then compare different neural upsamplers , showing that nearest neighbor interpolation upsamplers can be an alternative to the problematic (but state-of-the-art) transposed and subpixel convolutions which are prone to introduce tonal artifacts.
Revised:  We then compare different upsampling layers , showing that nearest neighbor interpolation upsamplers can be an alternative to the problematic (but state-of-the-art) transposed and subpixel convolutions which are prone to introduce tonal artifacts.
Edit intent: clarity
Original:  We then compare different neural upsamplers , showing that nearest neighbor interpolation upsamplers can be an alternative to the problematic (but state-of-the-art) transposed and subpixel convolutions which are prone to introduce tonal artifacts.
Revised:  We then compare different neural upsamplers , showing that nearest neighbor upsamplers can be an alternative to the problematic (but state-of-the-art) transposed and subpixel convolutions which are prone to introduce tonal artifacts.
Edit intent: clarity
Original:  In particular, they show that loops can arise as a consequence of distinguishing different flow types, and complement previous results where loops, in the one-commodity case, were arising as a consequence of imposing dynamical rules to the sources and sinks or when enforcing robustness to damage.
Revised:  In particular, they show that loops can arise as a consequence of distinguishing different flow types, complementing previous results where loops, in the one-commodity case, were arising as a consequence of imposing dynamical rules to the sources and sinks or when enforcing robustness to damage.
Edit intent: coherence
Original:  In particular, they show that loops can arise as a consequence of distinguishing different flow types, and complement previous results where loops, in the one-commodity case, were arising as a consequence of imposing dynamical rules to the sources and sinks or when enforcing robustness to damage.
Revised:  In particular, they show that loops can arise as a consequence of distinguishing different flow types, and complement previous results where loops, in the one-commodity case, were obtained as a consequence of imposing dynamical rules to the sources and sinks or when enforcing robustness to damage.
Edit intent: clarity
Original: Sequential recommendation methods play a crucial role in modern recommender systems because of their ability to capture users'dynamic interests from their historical interactions.
Revised: Sequential recommendation methods play a crucial role in modern recommender systems because of their ability to capture a user's dynamic interest from her/his historical interactions.
Edit intent: clarity
Original:  We propose a novel model called Contrastive Pre-training for Sequential Recommendation (CP4Rec), which utilizes the contrastive pre-training framework to extract meaningful user patterns and further encode the user representation effectively.
Revised:  We propose a novel multi-task model called utilizes the contrastive pre-training framework to extract meaningful user patterns and further encode the user representation effectively.
Edit intent: clarity
Original:  We propose a novel model called Contrastive Pre-training for Sequential Recommendation (CP4Rec), which utilizes the contrastive pre-training framework to extract meaningful user patterns and further encode the user representation effectively.
Revised:  We propose a novel model called Contrastive Pre-training for Sequential Recommendation (CP4Rec), whichC utilizes the contrastive pre-training framework to extract meaningful user patterns and further encode the user representation effectively.
Edit intent: clarity
Original:  We propose a novel model called Contrastive Pre-training for Sequential Recommendation (CP4Rec), which utilizes the contrastive pre-training framework to extract meaningful user patterns and further encode the user representation effectively.
Revised:  We propose a novel model called Contrastive Pre-training for Sequential Recommendation (CP4Rec), whichontrastive utilizes the contrastive pre-training framework to extract meaningful user patterns and further encode the user representation effectively.
Edit intent: fluency