wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } The problem of constructing an explicit family of matrices that are sufficiently rigid for Valiant's reduction (Valiant-rigid) still remains open. Moreover, since 2017 most of the long-studied candidates have been shown not to be Valiant-rigid. Some of those former candidates for rigidity are Kronecker products of small matrices. In a recent paper (STOC'21), Alman gave a general non-rigidity result for such matrices: he showed that if an n\times n matrix A (over any field) is a Kronecker product of d\times d matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: meaning-changed
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, ^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: clarity
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% \dots\ge ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: meaning-changed
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots, M_k (so n=d^k) (d\ge ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: meaning-changed
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge 2) then changing only n ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: meaning-changed
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge ^{ 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: fluency
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge ^{ ( 1+\varepsilon } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: clarity
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge ^{ ( 1+\varepsilon ) n } entries of A one can reduce its rank to\le , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: meaning-changed
Original:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary }  matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge  ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le  , where 1/\gamma is roughly 2^d/\varepsilon^2.
Revised:  Recently (arXiv 2021) , Alman proved that for any field \mathbb{F, d\geq 2 and arbitrary } matrices M_1, \ldots, M_n \in \mathbb{F^{d\times d}, one can get a d^n\times d^n matrix of rank }%DIFDELCMD < \le %%% d^{(1-\gamma)n \dots\ge ^{ ( 1+\varepsilon ) n } entries of the Kronecker product M = M_1\otimes M_2\otimes \ldots\otimes M_n\le n^{1-\gamma , where 1/\gamma is roughly 2^d/\varepsilon^2.
Edit intent: clarity
Original:  Second, we reduce 1/\gamma from exponential in d to roughly d^{3/2}/\varepsilon^2 (where d is the maximum size of the matrices  ), and to nearly linear (roughly d/\varepsilon^2) for matrices M_i of sizes within a constant factor of each other.
Revised:  Second, we reduce 1/\gamma from exponential in d to roughly d^{3/2}/\varepsilon^2 (where d is the maximum size of the matrices M_i ), and to nearly linear (roughly d/\varepsilon^2) for matrices M_i of sizes within a constant factor of each other.
Edit intent: fluency
Original:  For the case of matrices of equal size, our bound matches the bound given by Dvir and Liu (\textit{Theory of Computing, 2020 ) for the rigidity of generalized Walsh--Hadamard matrices (Kronecker powers of DFT matrices ), and improves their bounds for DFT matrices of abelian groups that are direct products of small groups .
Revised:  \textit{Theory of Computing, 2020 ) for the rigidity of generalized Walsh--Hadamard matrices (Kronecker powers of DFT matrices ), and improves their bounds for DFT matrices of abelian groups that are direct products of small groups .
Edit intent: clarity
Original:  For the case of matrices of equal size, our bound matches the bound given by Dvir and Liu (\textit{Theory of Computing, 2020 ) for the rigidity of generalized Walsh--Hadamard matrices (Kronecker powers of DFT matrices ), and improves their bounds for DFT matrices of abelian groups that are direct products of small groups .
Revised:  For the case of matrices of equal size, our bound matches the bound given by Dvir and Liu (\textit{ ) for the rigidity of generalized Walsh--Hadamard matrices (Kronecker powers of DFT matrices ), and improves their bounds for DFT matrices of abelian groups that are direct products of small groups .
Edit intent: clarity
Original:  For the case of matrices of equal size, our bound matches the bound given by Dvir and Liu (\textit{Theory of Computing, 2020 ) for the rigidity of generalized Walsh--Hadamard matrices (Kronecker powers of DFT matrices ), and improves their bounds for DFT matrices of abelian groups that are direct products of small groups .
Revised:  For the case of matrices of equal size, our bound matches the bound given by Dvir and Liu (\textit{Theory of Computing, 2020 As an application of our results we significantly expand the class of Hadamard matrices that are known not to be Valiant-rigid; these now include the Kronecker products of Paley-Hadamard matrices and Hadamard matrices of bounded size .
Edit intent: meaning-changed
Original:  In this paper, we present CANINE, a neural encoder that operates directly on character sequences--without explicit tokenization or vocabulary--and a pre-training strategy with soft inductive biases in place of hard token boundaries.
Revised:  In this paper, we present CANINE, a neural encoder that operates directly on character sequences, without explicit tokenization or vocabulary--and a pre-training strategy with soft inductive biases in place of hard token boundaries.
Edit intent: fluency
Original:  In this paper, we present CANINE, a neural encoder that operates directly on character sequences--without explicit tokenization or vocabulary--and a pre-training strategy with soft inductive biases in place of hard token boundaries.
Revised:  In this paper, we present CANINE, a neural encoder that operates directly on character sequences--without explicit tokenization or vocabulary, and a pre-training strategy with soft inductive biases in place of hard token boundaries.
Edit intent: fluency
Original:  Current mainstream methods, such as functionality decomposition or end-to-end reinforcement learning (RL), either suffer high time complexity or poor interpretability and limited safety performance in real-world complex autonomous driving tasks.
Revised:  Current mainstream methods, such as functionality decomposition and end-to-end reinforcement learning (RL), either suffer high time complexity or poor interpretability and limited safety performance in real-world complex autonomous driving tasks.
Edit intent: fluency
Original:  In this paper, we present an interpretable and efficient decision and control framework for automated vehicles, which decomposes the driving task into multi-path planning and optimal tracking that are structured hierarchically.
Revised:  In this paper, we present an interpretable and computationally efficient framework called integrated decision and control framework for automated vehicles, which decomposes the driving task into multi-path planning and optimal tracking that are structured hierarchically.
Edit intent: meaning-changed
Original:  To that end, in theory, we formulate a constrained optimal control problem (OCP) for each candidate path, optimize them separately and choose the one with the best tracking performance to follow. More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Revised:  To that end, in theory, we formulate a constrained optimal control problem (OCP) for each candidate path, optimize them separately and choose the one with the best tracking performance . To unload the heavy online computation , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Edit intent: clarity
Original:  More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Revised:  More importantly , we propose a model-based reinforcement learning (RL) algorithm that can be served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Edit intent: clarity
Original:  More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Revised:  More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Edit intent: coherence
Original:  More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Revised:  More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a single complete RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Edit intent: meaning-changed
Original:  More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline by our algorithm into value and policy networks, for real-time online path selecting and tracking respectively.
Revised:  More importantly , we propose a model-based reinforcement learning (RL) algorithm , which is served as an approximate constrained OCP solver , to unload the heavy computation by the paradigm of offline training and online application . Specifically, the OCPs for all paths are considered together to construct a multi-task RL problem and then solved offline in the form of value and policy networks, for real-time online path selecting and tracking respectively.
Edit intent: clarity
Original: Person names are essential entities in the Named Entity Recognition (NER) task. Traditional NER models have good performance in recognising well-formed person names from text with consistent and complete syntax, such as news articles.
Revised: In this paper, we introduce the NameRec* task, which aims to do highly accurate and fine-grained person name recognition. Traditional Named Entity Recognition models have good performance in recognising well-formed person names from text with consistent and complete syntax, such as news articles.
Edit intent: meaning-changed
Original:  However, the inter-sentence context and implicit relations, which are extremely essential for recognizing person names in long documents, are not captured. To address this issue, we propose a Multi-inference Overlapped BERT Model ( NameRec*)through an overlapped input processor, and an inter-sentence encoder with bidirectional overlapped contextual embedding learning and multiple inference mechanisms.
Revised:  However, the inter-sentence context and implicit relations, which are extremely essential for recognizing person names in long documents, we further propose an Inter-sentence BERT Model ( NameRec*)through an overlapped input processor, and an inter-sentence encoder with bidirectional overlapped contextual embedding learning and multiple inference mechanisms.
Edit intent: clarity
Original:  To address this issue, we propose a Multi-inference Overlapped BERT Model ( NameRec*)through an overlapped input processor, and an inter-sentence encoder with bidirectional overlapped contextual embedding learning and multiple inference mechanisms.
Revised:  To address this issue, we propose a Multi-inference Overlapped BERT Model ( IsBERT). IsBERT has an overlapped input processor, and an inter-sentence encoder with bidirectional overlapped contextual embedding learning and multiple inference mechanisms.
Edit intent: clarity
Original:  To address this issue, we propose a Multi-inference Overlapped BERT Model ( NameRec*)through an overlapped input processor, and an inter-sentence encoder with bidirectional overlapped contextual embedding learning and multiple inference mechanisms.
Revised:  To address this issue, we propose a Multi-inference Overlapped BERT Model ( NameRec*)through an overlapped input processor, and an inter-sentence encoder with bidirectional overlapped contextual embedding learning and multi-hop inference mechanisms.
Edit intent: clarity
Original:  To derive benefit from different documents with  diverse abundance of context, we further propose an advanced Adaptive Multi-inference Overlapping BERT Model ( Ada-NameRec* ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Revised:  To derive benefit from different documents with a diverse abundance of context, we further propose an advanced Adaptive Multi-inference Overlapping BERT Model ( Ada-NameRec* ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Edit intent: fluency
Original:  To derive benefit from different documents with  diverse abundance of context, we further propose an advanced Adaptive Multi-inference Overlapping BERT Model ( Ada-NameRec* ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Revised:  To derive benefit from different documents with diverse abundance of context, we propose an advanced Adaptive Multi-inference Overlapping BERT Model ( Ada-NameRec* ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Edit intent: coherence
Original:  To derive benefit from different documents with  diverse abundance of context, we further propose an advanced Adaptive Multi-inference Overlapping BERT Model ( Ada-NameRec* ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Revised:  To derive benefit from different documents with diverse abundance of context, we further propose an advanced Adaptive Inter-sentence BERT Model ( Ada-NameRec* ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Edit intent: meaning-changed
Original:  To derive benefit from different documents with  diverse abundance of context, we further propose an advanced Adaptive Multi-inference Overlapping BERT Model ( Ada-NameRec* ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Revised:  To derive benefit from different documents with diverse abundance of context, we further propose an advanced Adaptive Multi-inference Overlapping BERT Model ( Ada-IsBERT ) to dynamically adjust the inter-sentence overlapping ratio to different documents.
Edit intent: meaning-changed
Original: FoF1-ATP synthases are the ubiquitous membrane enzymes which catalyze ATP synthesis or ATP hydrolysisin reverse, respectively. Enzyme kinetics are controlled by internal subunit rotation, by substrate and product concentrations, by mechanical inhibitory mechanisms, but also by the electrochemical potential of protons across the membrane.
Revised: FoF1-ATP synthases are the ubiquitous membrane enzymes which catalyze ATP synthesis and hydrolysis. Their enzyme kinetics are controlled by internal subunit rotation, by substrate and product concentrations, by mechanical inhibitory mechanisms, but also by the electrochemical potential of protons across the membrane.
Edit intent: clarity
Original:  By utilizing an Anti-Brownian electrokinetic trap (ABEL trap), single-molecule F\"orster resonance energy transfer (smFRET) -based subunit rotation monitoring was prolonged from milliseconds to seconds .
Revised:  By utilizing an Anti-Brownian electrokinetic trap (ABEL trap), single-molecule F\"orster resonance energy transfer (smFRET) has been used to detect subunit rotation within FoF1-ATP synthases embedded in freely diffusing liposomes. We now report that kinetic monitoring of functional rotation can be prolonged from milliseconds to seconds .
Edit intent: meaning-changed