wanyu/IteraTeR_full_sent huggingface dataset:
Original:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent  bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Revised:  for any function f\in H^\alpha_\infty( %DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Edit intent: fluency
Original:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent  bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Revised:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% of mixed smoothness, we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Edit intent: meaning-changed
Original:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent  bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Revised:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Edit intent: meaning-changed
Original:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent  bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Revised:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p %DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Edit intent: fluency
Original:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent  bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Revised:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% with a prescribed accuracy \varepsilon, and prove tight dimension-dependent bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Edit intent: clarity
Original:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent  bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Revised:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent upper and lower bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Edit intent: meaning-changed
Original:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent  bounds of the computation complexity of this approximation, characterized as the number of weights and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Revised:  for any function f\in H^\alpha_\infty( \mathbb I%DIFDELCMD < }%%% ^d), we explicitly construct a deep ReLU neural network having an output that approximates f in the W_0^{1,p \mathbb I%DIFDELCMD < }%%% ^d)-norm with a prescribed accuracy \varepsilon, and prove tight dimension-dependent bounds of the computation complexity of this approximation, characterized as the size and the depth of this deep ReLU neural network, explicitly in d and \varepsilon.
Edit intent: clarity
Original:  In this paper, a range of neural architecture search (NAS) techniques are used to automatically learn two  hyper-parameters that heavily affect the performance and model complexity of state-of-the-art factored time delay neural network (TDNN-F)acoustic models : i) the left and right splicing context offsets;
Revised:  In this paper, a range of neural architecture search (NAS) techniques are used to automatically learn two types of hyper-parameters that heavily affect the performance and model complexity of state-of-the-art factored time delay neural network (TDNN-F)acoustic models : i) the left and right splicing context offsets;
Edit intent: clarity
Original:  In this paper, a range of neural architecture search (NAS) techniques are used to automatically learn two  hyper-parameters that heavily affect the performance and model complexity of state-of-the-art factored time delay neural network (TDNN-F)acoustic models : i) the left and right splicing context offsets;
Revised:  In this paper, a range of neural architecture search (NAS) techniques are used to automatically learn two hyper-parameters of state-of-the-art factored time delay neural network (TDNN-F)acoustic models : i) the left and right splicing context offsets;
Edit intent: clarity
Original:  In this paper, a range of neural architecture search (NAS) techniques are used to automatically learn two  hyper-parameters that heavily affect the performance and model complexity of state-of-the-art factored time delay neural network (TDNN-F)acoustic models : i) the left and right splicing context offsets;
Revised:  In this paper, a range of neural architecture search (NAS) techniques are used to automatically learn two hyper-parameters that heavily affect the performance and model complexity of state-of-the-art factored time delay neural networks (TDNNs) : i) the left and right splicing context offsets;
Edit intent: clarity
Original:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Revised:  Experiments conducted on the 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Edit intent: fluency
Original:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Revised:  Experiments conducted on a 300-hour Switchboard corpus suggest the auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Edit intent: clarity
Original:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Revised:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Edit intent: fluency
Original:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Revised:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI TDNN systems using manual expert configurations .
Edit intent: clarity
Original:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual expert configurations .
Revised:  Experiments conducted on a 300-hour Switchboard conversational telephone speech recognition task suggest the NAS auto-configured TDNN-F systems consistently outperform the baseline LF-MMI trained TDNN-F systems using manual network design or random architecture search after LHUC speaker adaptation and RNNLM rescoring .
Edit intent: meaning-changed
Original: In 12%DIFDELCMD < ]%%% , the authors introduce an adaptive, stabilized finite element method (FEM), which solves a stable saddle-point problem .
Revised: In 12%DIFDELCMD < ]%%% , the authors introduce an adaptive, stabilized finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem .
Edit intent: meaning-changed
Original: In 12%DIFDELCMD < ]%%% , the authors introduce an adaptive, stabilized finite element method (FEM), which solves a stable saddle-point problem . The method delivers a stable continuous approximation and projects the residual onto a broken polynomial space .
Revised: In 12%DIFDELCMD < ]%%% , the authors introduce an adaptive, stabilized finite element method (FEM), which solves a stable saddle-point problem , this residual minimization delivers a stable continuous approximation and projects the residual onto a broken polynomial space .
Edit intent: meaning-changed
Original:  Studying the impact of the lockdown, trough the lens of social media , offers an unprecedented opportunity for analyzing the susceptibility and the resilience of circadian rhythms to large-scale exogenous shocks.
Revised:  Studying the impact of the lockdown, trough the lens of social media offers an unprecedented opportunity for analyzing the susceptibility and the resilience of circadian rhythms to large-scale exogenous shocks.
Edit intent: fluency
Original:  Studying the impact of the lockdown, trough the lens of social media , offers an unprecedented opportunity for analyzing the susceptibility and the resilience of circadian rhythms to large-scale exogenous shocks.
Revised:  Studying the impact of the lockdown, trough the lens of social media , offers an unprecedented opportunity to understand the susceptibility and the resilience of circadian rhythms to large-scale exogenous shocks.
Edit intent: clarity
Original:  Studying the impact of the lockdown, trough the lens of social media , offers an unprecedented opportunity for analyzing the susceptibility and the resilience of circadian rhythms to large-scale exogenous shocks.
Revised:  Studying the impact of the lockdown, trough the lens of social media , offers an unprecedented opportunity for analyzing the susceptibility and the resilience of human activity patterns to large-scale exogenous shocks.
Edit intent: clarity
Original:  In this context, we address two interconnected research questions: Can variations of online activity cycles provide information on the impact of lockdown on human activities? How do onlinecircadian rhythms react to such a disruption? Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of  YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Revised:  Firstly, we investigate the changes that this upheaval has caused in online activity in terms of time spent online, themes and emotion shared on the platforms, and rhythms of content consumption. Secondly, we examine the resilience of certain platform characteristics, such as the daily rhythms of emotion expression. Data. Two independent datasets about the French cyberspace: a fine-grained temporal record of YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Edit intent: clarity
Original:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of  YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Revised:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of almost 100 thousand YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Edit intent: meaning-changed
Original:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of  YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Revised:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of YouTube videos and a Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Edit intent: clarity
Original:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of  YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Revised:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of YouTube videos and a large collection of Tweets on %DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Edit intent: coherence
Original:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of  YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Revised:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% collection of 8 million Tweets between February 17 and April 14, 2020. Findings. In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Edit intent: meaning-changed
Original:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of  YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with a substantial increase of night activity during the lockdown.
Revised:  Data: We base our research on the analysis and comparison of two independent databases about the French cyberspace: a fine-grained temporal record of YouTube videos and a large collection of Tweets on Covid-19%DIFDELCMD < }%%% . Findings: In both datasets we observe a reshaping of the circadian rhythms with an increase of night activity during the lockdown.
Edit intent: clarity
Original:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Revised:  Specifically, a (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Edit intent: clarity
Original:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Revised:  We show that in this setting one can construct (k,\eps) %DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Edit intent: clarity
Original:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Revised:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% %DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Edit intent: coherence
Original:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Revised:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors.
Edit intent: meaning-changed
Original:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% hides polylogarithmic factors. That is , there is a set of m k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.
Revised:  We show that in this setting one can construct (k,\eps) -nets of size m =%DIFDELCMD < \tldO%%% (1/%DIFDELCMD < \eps%%% ^{1-k/d), where }%DIFDELCMD < \tldO %%% -net is a set of m k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.
Edit intent: meaning-changed
Original:  That is , there is a set of m k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.
Revised:  That is , there is a set of k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.
Edit intent: clarity
Original:  We also prove that any such net must have size at least \Omega(1/}\eps As a concrete example, in three dimensions all \eps-heavy bodies in [0,1]^3 can be stabbed by %DIFDELCMD < \tldO%%%  (1/\eps^{2/3}) lines.
Revised:  We also prove that any such net must have size at least \Omega(1/}\eps^{1-k/d As a concrete example, in three dimensions all \eps-heavy bodies in [0,1]^3 can be stabbed by %DIFDELCMD < \tldO%%% (1/\eps^{2/3}) lines.
Edit intent: meaning-changed
Original:  We also prove that any such net must have size at least \Omega(1/}\eps As a concrete example, in three dimensions all \eps-heavy bodies in [0,1]^3 can be stabbed by %DIFDELCMD < \tldO%%%  (1/\eps^{2/3}) lines.
Revised:  We also prove that any such net must have size at least \Omega(1/}\eps As a concrete example, in three dimensions all \eps-heavy bodies in [0,1]^3 can be stabbed by %DIFDELCMD < \tldO%%% \Theta (1/\eps^{2/3}) lines.
Edit intent: meaning-changed
Original:  Note, that these bounds are sublinear in 1/\eps, and are thus somewhat surprising . We also present deterministic constructions of weak%DIFDELCMD < \eps%%% -nets, under the same volume measure of 0,1%DIFDELCMD < ]%%% ^d.
Revised:  Note, that these bounds are sublinear in 1/\eps, and are thus somewhat surprising %DIFDELCMD < \eps%%% -nets, under the same volume measure of 0,1%DIFDELCMD < ]%%% ^d.
Edit intent: clarity
Original:  We also present deterministic constructions of weak%DIFDELCMD < \eps%%% -nets, under the same volume measure of 0,1%DIFDELCMD < ]%%% ^d.
Revised:  We also present deterministic constructions of weak%DIFDELCMD < \eps%%% -nets, under the same volume measure of %DIFDELCMD < ]%%% ^d.
Edit intent: meaning-changed
Original:  We also present deterministic constructions of weak%DIFDELCMD < \eps%%% -nets, under the same volume measure of 0,1%DIFDELCMD < ]%%% ^d. While our bounds are still weaker than known bounds, the new constructions are simple and explicit, unlike previous constructions .
Revised:  We also present deterministic constructions of weak%DIFDELCMD < \eps%%% -nets, under the same volume measure of 0,1%DIFDELCMD < ]%%% .
Edit intent: coherence