wanyu/IteraTeR_full_sent huggingface dataset:
Original: We analyze the popular kernel polynomial method (KPM) for approximating the spectral density (eigenvalue distribution) of a real symmetric (or Hermitian ) matrix A\in \mathbb{R^{n\times n}}  . We prove that a simple and practical variant of the KPM algorithm can approximate the spectral density to \epsilon accuracy in the Wasserstein-1 distance with roughly O({1}/{\epsilon}) matrix-vector multiplications with A.
Revised: We analyze the popular kernel polynomial method (KPM) for approximating the spectral density (eigenvalue distribution) of ^{n\times n}} . We prove that a simple and practical variant of the KPM algorithm can approximate the spectral density to \epsilon accuracy in the Wasserstein-1 distance with roughly O({1}/{\epsilon}) matrix-vector multiplications with A.
Edit intent: clarity
Original: We analyze the popular kernel polynomial method (KPM) for approximating the spectral density (eigenvalue distribution) of a real symmetric (or Hermitian ) matrix A\in \mathbb{R^{n\times n}}  . We prove that a simple and practical variant of the KPM algorithm can approximate the spectral density to \epsilon accuracy in the Wasserstein-1 distance with roughly O({1}/{\epsilon}) matrix-vector multiplications with A.
Revised: We analyze the popular kernel polynomial method (KPM) for approximating the spectral density (eigenvalue distribution) of a real symmetric (or Hermitian ) matrix A\in \mathbb{R^{n\times n}} an n\times n Hermitian matrix A . We prove that a simple and practical variant of the KPM algorithm can approximate the spectral density to \epsilon accuracy in the Wasserstein-1 distance with roughly O({1}/{\epsilon}) matrix-vector multiplications with A.
Edit intent: meaning-changed
Original:  As an application, we develop an O(n /\text{poly \epsilon)) time algorithm for computing the spectral density of any n\times n normalized graph adjacency or Laplacian matrix.
Revised:  As an application, we develop an O(n \cdot \text{poly \epsilon)) time algorithm for computing the spectral density of any n\times n normalized graph adjacency or Laplacian matrix.
Edit intent: meaning-changed
Original: The support/query (S/Q) training protocol is widely used in meta-learning. S/Q protocol trains a task-specific model on S and then evaluates it on Q to optimize the meta-model using query loss , which depends on size and quality of Q. In this paper, we study a new S / T protocolfor meta-learning.
Revised: Meta-learning can extract an inductive bias from previous learning experience and assist the training processes of new tasks. It is often realized through optimizing a meta-model using query loss , which depends on size and quality of Q. In this paper, we study a new S / T protocolfor meta-learning.
Edit intent: meaning-changed
Original: The support/query (S/Q) training protocol is widely used in meta-learning. S/Q protocol trains a task-specific model on S and then evaluates it on Q to optimize the meta-model using query loss , which depends on size and quality of Q. In this paper, we study a new S / T protocolfor meta-learning.
Revised: The support/query (S/Q) training protocol is widely used in meta-learning. S/Q protocol trains a task-specific model on S and then evaluates it on Q to optimize the meta-model with the evaluation loss of a series of task-specific solvers. Most existing algorithms sample non-overlapping \mathit{support / T protocolfor meta-learning.
Edit intent: meaning-changed
Original: The support/query (S/Q) training protocol is widely used in meta-learning. S/Q protocol trains a task-specific model on S and then evaluates it on Q to optimize the meta-model using query loss , which depends on size and quality of Q. In this paper, we study a new S / T protocolfor meta-learning. Assuming that we have access to the theoretically optimal model T for a task, we can directly match the task-specific model trained on S to T. S / T protocol offers a more accurate evaluation since it does not rely on possibly biased and noisy query instances.
Revised: The support/query (S/Q) training protocol is widely used in meta-learning. S/Q protocol trains a task-specific model on S and then evaluates it on Q to optimize the meta-model using query loss , which depends on size and quality of Q. In this paper, we study a new S / \mathcal{Q / T protocol offers a more accurate evaluation since it does not rely on possibly biased and noisy query instances.
Edit intent: meaning-changed
Original:  Assuming that we have access to the theoretically optimal model T for a task, we can directly match the task-specific model trained on S to T. S / T protocol offers a more accurate evaluation since it does not rely on possibly biased and noisy query instances. There are two challenges in putting S / T protocol into practice.
Revised:  Assuming that we have access to the theoretically optimal model T for a task, we can directly match the task-specific model trained on S to T. S / \mathcal{T / T protocol into practice.
Edit intent: coherence
Original:  Firstly, we have to determine how to match the task-specific model to T. To this end, we minimize the discrepancy between them on a fictitious dataset generated by adversarial learning, and distill the prediction ability of T to the task-specific model. Secondly, we usually do not have ready-made optimal models. As an alternative, we construct surrogate/\mathcal{T} protocol in a typical application of meta-learning, \mathit{i.e.}, few-shot learning.
Revised:  We find that with a small ratio of tasks armed with target models, classic meta-learning algorithms can be improved a lot without consuming many resources. Furthermore, we empirically verify the effectiveness of \mathcal{S/\mathcal{T} protocol in a typical application of meta-learning, \mathit{i.e.}, few-shot learning.
Edit intent: coherence
Original:  In detail, after constructing } target models by fine-tuning on local tasks the globally pre-trained meta-model, maintaining both efficiency and veracity .
Revised:  In detail, after constructing } target models by fine-tuning on local tasks the globally pre-trained network on those hard tasks, we match the task-specific solvers to target models via knowledge distillation. Experiments demonstrate the superiority of our proposal .
Edit intent: meaning-changed
Original: Information about the potential environmental impacts of  post-lithium batteries is scarce. For this reason, this work provides a prospective life-cycle assessment of a hypothetical commercial MgS battery based on primary information obtained for a prototype cell. The Mg-S battery is found to have a good environmental performance with potential to outperform also current lithium-ion batteries in terms of environmental impacts.
Revised: Information about the potential environmental impacts of post-lithium systems such as the magnesium-sulfur (MgS) battery. Therefore, we use life cycle assessment following a cradle-to-gate perspective to quantify the cumulative energy demand and potential environmental impacts per Wh of the storage capacity of a hypothetical MgS battery (46 Wh/kg). Furthermore, we also estimate global warming potential (0.33 kg CO2 eq/Wh) , fossil depletion potential (0.09 kg oil eq / Wh), ozone depletion potential (2.5E-08 kg CFC-11/Wh) and metal depletion potential (0.044 kg Fe eq/Wh), associated with the MgS battery production. The battery is modelled based on an existing prototype MgS pouch cell and hypothetically optimised according to the current state of the art in lithium-ion batteries in terms of environmental impacts.
Edit intent: meaning-changed
Original:  The Mg-S battery is found to have a good environmental performance with potential to outperform also current lithium-ion batteries in terms of environmental impacts. However, this applies only if the assumed evolutions of the cell composition are achieved together with comparable performance in terms of battery lifespan. The initial (non-optimized ) prototype cell cannot compete with current LIB in terms of energy density or environmental friendliness , mainly due to the high share of non-active components, decreasing its performance substantially.
Revised:  The Mg-S battery is found to have a good environmental performance with potential to outperform also current lithium-ion batteries (LIB), exploring future improvement potentials. It turns out that the initial (non-optimised ) prototype cell cannot compete with current LIB in terms of energy density or environmental friendliness , mainly due to the high share of non-active components, decreasing its performance substantially.
Edit intent: clarity
Original:  The initial (non-optimized ) prototype cell cannot compete with current LIB in terms of energy density or environmental friendliness , mainly due to the high share of non-active components, decreasing its performance substantially.
Revised:  The initial (non-optimized ) prototype cell cannot compete with current LIB in terms of energy density or environmental performance , mainly due to the high share of non-active components, decreasing its performance substantially.
Edit intent: clarity
Original:  The use of exclusively abundant materials with comparably low environmental impacts within the cell is the major strength of the  MgS battery , leaving the energy-intensive process steps as the remaining critical contributors to the total environmental impacts i.e., the cell manufacturing and magnesium and aluminium metal production.
Revised:  Therefore, if the assumed evolutions of the MgS battery , leaving the energy-intensive process steps as the remaining critical contributors to the total environmental impacts i.e., the cell manufacturing and magnesium and aluminium metal production.
Edit intent: meaning-changed
Original:  The use of exclusively abundant materials with comparably low environmental impacts within the cell is the major strength of the  MgS battery , leaving the energy-intensive process steps as the remaining critical contributors to the total environmental impacts i.e., the cell manufacturing and magnesium and aluminium metal production.
Revised:  The use of exclusively abundant materials with comparably low environmental impacts within the cell is the major strength of the MgS cell composition are achieved to overcome current design hurdles and reach a comparable lifespan, efficiency, cost and safety levels to that of existing LIB; then the MgS battery , leaving the energy-intensive process steps as the remaining critical contributors to the total environmental impacts i.e., the cell manufacturing and magnesium and aluminium metal production.
Edit intent: meaning-changed
Original:  The use of exclusively abundant materials with comparably low environmental impacts within the cell is the major strength of the  MgS battery , leaving the energy-intensive process steps as the remaining critical contributors to the total environmental impacts i.e., the cell manufacturing and magnesium and aluminium metal production. Here, the use of renewable electricity and non-fossil sources for process heat are the keys for further improving its environmental performance .
Revised:  The use of exclusively abundant materials with comparably low environmental impacts within the cell is the major strength of the MgS battery has significant potential to outperform both existing LIB, and lithium-sulfur batteries .
Edit intent: meaning-changed
Original: One of the biggest challenges raised by the Covid-19 outbreaks involves school openings and in-class vs. remote learning, affecting more than one billion students worldwide. One of the main issues herein concerns the potential effect of in person school activities on the spread of the epidemic: many studies have been conducted, often reaching divergent conclusions. In this paper, we first identify one apparently unobserved feature of the interrelation between virus transmissions in two subpopulations : as the contact rate of one subpopulation is varied, there is a phase transition between almost irrelevance to heavy influence of the transmission rate in the subpopulation on the overall outbreak; such transition is seen to occur during outbreaks or new strains upsurge, lockdowns, and vaccination campaigns , albeit at different transition points.
Revised: One of the biggest challenges raised by the Covid-19 pandemic. The mathematical analysis of compartmental models with subpopulations shows that the in-school contact rates affects the overall course of the pandemic only above a certain threshold that separates an influence phase from a non-influence one. The threshold, that we calculate via linear approximation in several cases, seems to appear in all contexts, including outbreaks or new strains upsurge, lockdowns, and vaccination campaigns , albeit at different transition points.
Edit intent: coherence
Original:  such transition is seen to occur during outbreaks or new strains upsurge, lockdowns, and vaccination campaigns , albeit at different transition points. Applied to schools, our results suggest that suitably, and possibly very tightly, controlled openings have no bearing on the overall spread of the pandemic. This is the case even during a widespread vaccination for which school age children arenot eligible. To curb the mathematical complexity of the results, we restrict here to SIR models, but we trust, and illustrate by simulations, that our conclusions apply in more general setting; our results provide a clarification to the diversity of opinions on school opening effects, and help envisioning plans for upcoming school activities. Case studies in the literature illustrate the occurrence of phase transitions .
Revised:  such transition is seen to occur during outbreaks or new strains upsurge, lockdowns, and vaccination campaigns excluding children, albeit with different values. Our theoretical findings are then confirmed by several data-driven studies that have previously identified the phase transition in specific cases. Specific outcomes of this study are: opposite conclusions reached by studies of the same or similar situations might depend on, possibly small, differences in modeling or in parameter estimation from the very noisy Covid-19 data, that result in identifying different phases; it is possible to keep schools open at any stage of the Covid-19 pandemic, but suitably strict rules must be applied at all times or else this becomes highly detrimental to virus containment efforts; as the threshold during vaccination turns out to correspond to the internal transmission rate that would lead to virus extinction if the school population was isolated, the needed strict control can be sustained only for very brief periods; as a result, either schools will have to face a prolonged closure or children need to be vaccinated as well .
Edit intent: meaning-changed
Original: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: arXiv:2010.06774 (2020 )] and derive new a posteriori error estimates for Maxwell two-phase interface problems.
Revised: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: Computers \& Mathematics with Applications. )] and derive new a posteriori error estimates for Maxwell two-phase interface problems.
Edit intent: meaning-changed
Original: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: arXiv:2010.06774 (2020 )] and derive new a posteriori error estimates for Maxwell two-phase interface problems.
Revised: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: arXiv:2010.06774 (202091 )] and derive new a posteriori error estimates for Maxwell two-phase interface problems.
Edit intent: meaning-changed
Original: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: arXiv:2010.06774 (2020 )] and derive new a posteriori error estimates for Maxwell two-phase interface problems.
Revised: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: arXiv:2010.06774 (2020, 192-201 (2021 )] and derive new a posteriori error estimates for Maxwell two-phase interface problems.
Edit intent: meaning-changed
Original: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: arXiv:2010.06774 (2020 )] and derive new a posteriori error estimates for Maxwell two-phase interface problems.
Revised: We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: arXiv:2010.06774 (2020 )] and derive new a posteriori error estimates for H(curl)-elliptic two-phase interface problems.
Edit intent: meaning-changed
Original:  New methods of model parallelism such as tensor and pipeline parallelism have been proposed to address these challenges ; unfortunately , naive usage leads to fundamental scaling issues at thousands of GPUs due to various reasons, e.g., expensive cross-node communication or idle periods waiting on other devices.
Revised:  New methods of model parallelism such as tensor and pipeline parallelism have been proposed to address these challenges . Unfortunately , naive usage leads to fundamental scaling issues at thousands of GPUs due to various reasons, e.g., expensive cross-node communication or idle periods waiting on other devices.
Edit intent: fluency
Original:  In this work, we show how to compose different types of parallelism methods (tensor, pipeline, and data paralleism ) to scale to thousands of GPUs, achieving a two-order-of-magnitude increase in the sizes of models we can efficiently train compared to existing systems.
Revised:  In this work, we show how to compose different types of parallelism methods (tensor, pipeline, and data parallelism ) to scale to thousands of GPUs, achieving a two-order-of-magnitude increase in the sizes of models we can efficiently train compared to existing systems.
Edit intent: fluency
Original:  The composition of these techniques allows us to perform training iterations on a model with 1 trillion parameters at 502 petaFLOP/s on 3072 GPUs with achieved per-GPU throughput of 52\% of peak;
Revised:  Our approach allows us to perform training iterations on a model with 1 trillion parameters at 502 petaFLOP/s on 3072 GPUs with achieved per-GPU throughput of 52\% of peak;
Edit intent: clarity
Original:  We use reinforcement learning to train a high-level gait policy that specifies the contact schedules of each foot, while the low-level Model Predictive Controller (MPC) optimizes the motor torques so that the robot can walk at a desired velocity using that gait pattern.
Revised:  We use reinforcement learning to train a high-level gait policy that specifies gait patterns of each foot, while the low-level Model Predictive Controller (MPC) optimizes the motor torques so that the robot can walk at a desired velocity using that gait pattern.
Edit intent: clarity
Original:  We use reinforcement learning to train a high-level gait policy that specifies the contact schedules of each foot, while the low-level Model Predictive Controller (MPC) optimizes the motor torques so that the robot can walk at a desired velocity using that gait pattern.
Revised:  We use reinforcement learning to train a high-level gait policy that specifies the contact schedules of each foot, while the low-level whole-body controller optimizes the motor torques so that the robot can walk at a desired velocity using that gait pattern.
Edit intent: clarity
Original:  We use reinforcement learning to train a high-level gait policy that specifies the contact schedules of each foot, while the low-level Model Predictive Controller (MPC) optimizes the motor torques so that the robot can walk at a desired velocity using that gait pattern.
Revised:  We use reinforcement learning to train a high-level gait policy that specifies the contact schedules of each foot, while the low-level Model Predictive Controller (MPC) optimizes the motor commands so that the robot can walk at a desired velocity using that gait pattern.
Edit intent: clarity
Original:  We test our learning framework on a quadruped robot and demonstrate automatic gait transitions, from walking to trotting and to fly-trotting, as the robot increases its speed up to 2.5m/s (5 body lengths/s) . We show that the learned hierarchical controller consumes much less energy across a wide range of locomotion speed than baseline controllers.
Revised:  We test our learning framework on a quadruped robot and demonstrate automatic gait transitions, from walking to trotting and to fly-trotting, as the robot increases its speed . We show that the learned hierarchical controller consumes much less energy across a wide range of locomotion speed than baseline controllers.
Edit intent: clarity
Original:  In this work, we develop a corpus-driven approach to auto-validate machine-generated data by inferring suitable data-validation "patterns" that accurately describe the underlying data-domain , which minimizes false positives while maximizing data quality issues caught.
Revised:  In this work, we develop a corpus-driven approach to auto-validate machine-generated data by inferring suitable data-validation "patterns" that accurately describe the underlying data domain , which minimizes false positives while maximizing data quality issues caught.
Edit intent: fluency
Original: Self-attention based models have achieved remarkable success in natural language processing . However, the self-attention network design is questioned as suboptimal in recent studies, due to its veiled validity and high redundancy .
Revised: Self-attention based models have achieved remarkable success in natural language processing , they are susceptible to over-fitting due to unusual large model size. To this end, dropout serves as a therapy. However, existing methods like random-based, knowledge-based and search-based dropout are more general but less effective onto self-attention network design is questioned as suboptimal in recent studies, due to its veiled validity and high redundancy .
Edit intent: meaning-changed
Original:  We demonstrate that the lighter state-of-the-art models with nearly 80\% of self-attention layers pruned, may achieve even better resultson multiple tasks, including natural language understanding, document classification, named entity recognition and POS tagging, with nearly twice faster inference .
Revised:  We demonstrate that state-of-the-art models with nearly 80\% of self-attention layers pruned, may achieve even better resultson multiple tasks, including natural language understanding, document classification, named entity recognition and POS tagging, with nearly twice faster inference .
Edit intent: clarity
Original:  We demonstrate that the lighter state-of-the-art models with nearly 80\% of self-attention layers pruned, may achieve even better resultson multiple tasks, including natural language understanding, document classification, named entity recognition and POS tagging, with nearly twice faster inference .
Revised:  We demonstrate that the lighter state-of-the-art models with elaborate training design may achieve much stronger results. We verify the universality of our approach on extensive natural language processing tasks .
Edit intent: clarity
Original: We give a computer-based proof of the following fact: If a square is tiled by seven convex tiles which are congruent among themselves, then the tiles are rectangles . This confirms a new case of a conjecture posed by Yuen, Zamfirescu and Zamfirescu .
Revised: We give a computer-based proof of the following fact: If a square is tiled by seven convex tiles which are congruent among themselves, then the tiles are rectangles .
Edit intent: coherence