wanyu/IteraTeR_full_sent huggingface dataset:
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SL imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SSH imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SA imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% Slgorithm for imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% SS imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: clarity
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: meaning-changed
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{H ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: coherence
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ PC ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Edit intent: meaning-changed
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computation.
Edit intent: fluency
Original: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{  ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computation. Our system is an auspicious illustration of the power of randomized algorithms carefully tailored for high-performance computing platforms.
Revised: We present FLASH ( %DIFDELCMD < {\bf %%% F ast%DIFDELCMD < {\bf %%% L SH%DIFDELCMD < {\bf %%% A lgorithm for%DIFDELCMD < {\bf %%% S imilarity search accelerated with %DIFDELCMD < {\bf %%% H PC(High-Performance Computing) \textbf{ ), a similarity search system for ultra-high dimensional datasets on a single machine, which does not require similarity computations and is tailored for high-performance computing platforms.
Edit intent: clarity
Original:  We leverage LSH style randomized indexing procedure and combine it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations . The combination, while retaining sound theoretical guarantees , reduces the computational as well as parallelization overhead of our proposal.
Revised:  We leverage LSH style randomized indexing procedure and combine it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations , we reduce the computational and parallelization costs of similarity search, while retaining sound theoretical guarantees , reduces the computational as well as parallelization overhead of our proposal.
Edit intent: meaning-changed
Original:  The combination, while retaining sound theoretical guarantees , reduces the computational as well as parallelization overhead of our proposal. We provide CPU and hybrid CPU-GPU implementations of FLASH for replicability of our results URL We evaluate FLASH on several real high dimensional datasets coming from different domains  including text, malicious URL, click-through prediction, social networks, etc.
Revised:  The combination, while retaining sound theoretical guarantees . We evaluate FLASH on several real high dimensional datasets coming from different domains including text, malicious URL, click-through prediction, social networks, etc.
Edit intent: coherence
Original:  We provide CPU and hybrid CPU-GPU implementations of FLASH for replicability of our results URL We evaluate FLASH on several real high dimensional datasets coming from different domains  including text, malicious URL, click-through prediction, social networks, etc.
Revised:  We provide CPU and hybrid CPU-GPU implementations of FLASH for replicability of our results URL We evaluate FLASH on several real , high-dimensional datasets from different domains including text, malicious URL, click-through prediction, social networks, etc.
Edit intent: clarity
Original:  We provide CPU and hybrid CPU-GPU implementations of FLASH for replicability of our results URL We evaluate FLASH on several real high dimensional datasets coming from different domains  including text, malicious URL, click-through prediction, social networks, etc.
Revised:  We provide CPU and hybrid CPU-GPU implementations of FLASH for replicability of our results URL We evaluate FLASH on several real high dimensional datasets coming from different domains , including text, malicious URL, click-through prediction, social networks, etc.
Edit intent: fluency
Original:  Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than our system . FLASH is capable of computing an approximate k-NN graph, from scratch, over  full webspam dataset (1.3 billion nonzeros) in less than 10 seconds.
Revised:  Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than FLASH . FLASH is capable of computing an approximate k-NN graph, from scratch, over full webspam dataset (1.3 billion nonzeros) in less than 10 seconds.
Edit intent: clarity
Original:  Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than our system . FLASH is capable of computing an approximate k-NN graph, from scratch, over  full webspam dataset (1.3 billion nonzeros) in less than 10 seconds.
Revised:  Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than our system . FLASH is capable of computing an approximate k-NN graph, from scratch, over the full webspam dataset (1.3 billion nonzeros) in less than 10 seconds.
Edit intent: fluency
Original:  Computing  full k-NN graph in less than 10 seconds on  webspam dataset, using brute-force (n^2D), will require at least 20 TFLOPS.
Revised:  Computing a full k-NN graph in less than 10 seconds on webspam dataset, using brute-force (n^2D), will require at least 20 TFLOPS.
Edit intent: fluency
Original:  Computing  full k-NN graph in less than 10 seconds on  webspam dataset, using brute-force (n^2D), will require at least 20 TFLOPS.
Revised:  Computing full k-NN graph in less than 10 seconds on the webspam dataset, using brute-force (n^2D), will require at least 20 TFLOPS.
Edit intent: clarity
Original:  Computing  full k-NN graph in less than 10 seconds on  webspam dataset, using brute-force (n^2D), will require at least 20 TFLOPS. We hope that FLASH gets adopted in practice .
Revised:  Computing full k-NN graph in less than 10 seconds on webspam dataset, using brute-force (n^2D), will require at least 20 teraflops. We provide CPU and GPU implementations of FLASH for replicability of our results .
Edit intent: meaning-changed
Original:  The classical formula by Dupire, despite being heavily used by industry practitioners , can potentially produce unstable or even singular volatility surfaces ] . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.
Revised:  The most common approach among industry practitioners is based on the celebrated Dupire's formula ] . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.
Edit intent: clarity
Original:  The classical formula by Dupire, despite being heavily used by industry practitioners , can potentially produce unstable or even singular volatility surfaces ] . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.
Revised:  The classical formula by Dupire, despite being heavily used by industry practitioners , can potentially produce unstable or even singular volatility surfaces 6] . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.
Edit intent: meaning-changed
Original:  The classical formula by Dupire, despite being heavily used by industry practitioners , can potentially produce unstable or even singular volatility surfaces ] . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.
Revised:  The classical formula by Dupire, despite being heavily used by industry practitioners , can potentially produce unstable or even singular volatility surfaces ], which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that can only be obtained via some form of price interpolation . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.
Edit intent: meaning-changed
Original:  Inspired by the work of Benamou and Brenier, we formulate a martingale optimal transport problem  which seeks a  diffusion process that matches the known densities of an asset price at two different dates and minimizes a chosen cost function.
Revised:  We formulate a time continuous martingale optimal transport problem which seeks a diffusion process that matches the known densities of an asset price at two different dates and minimizes a chosen cost function.
Edit intent: meaning-changed
Original:  Inspired by the work of Benamou and Brenier, we formulate a martingale optimal transport problem  which seeks a  diffusion process that matches the known densities of an asset price at two different dates and minimizes a chosen cost function.
Revised:  Inspired by the work of Benamou and Brenier, we formulate a martingale optimal transport problem , which seeks a diffusion process that matches the known densities of an asset price at two different dates and minimizes a chosen cost function.
Edit intent: fluency
Original:  Inspired by the work of Benamou and Brenier, we formulate a martingale optimal transport problem  which seeks a  diffusion process that matches the known densities of an asset price at two different dates and minimizes a chosen cost function.
Revised:  Inspired by the work of Benamou and Brenier, we formulate a martingale optimal transport problem which seeks a martingale diffusion process that matches the known densities of an asset price at two different dates and minimizes a chosen cost function.
Edit intent: fluency
Original:  Inspired by the work of Benamou and Brenier, we formulate a martingale optimal transport problem  which seeks a  diffusion process that matches the known densities of an asset price at two different dates and minimizes a chosen cost function.
Revised:  Inspired by the work of Benamou and Brenier, we formulate a martingale optimal transport problem which seeks a diffusion process that matches the known densities of an asset price at two different dates , while minimizing a chosen cost function.
Edit intent: coherence
Original:  The process effectively interpolates the dynamic of the asset price between the two dates while recovering the local volatility function. This approach leads to a convex optimisation problemand it is numerically solved ] via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm  .
Revised:  Inspired by the seminal work of Benamou and Brenier ] via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm .
Edit intent: meaning-changed
Original:  This approach leads to a convex optimisation problemand it is numerically solved ] via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm  .
Revised:  This approach leads to a convex optimisation problemand it is numerically solved ], we formulate the problem as a convex optimization problem, derive its dual formulation, and solve it numerically via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm .
Edit intent: meaning-changed
Original:  This approach leads to a convex optimisation problemand it is numerically solved ] via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm  .
Revised:  This approach leads to a convex optimisation problemand it is numerically solved ] via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm . The solution effectively reconstructs the dynamic of the asset price between the two dates by recovering the optimal local volatility function, without requiring any time interpolation of the option prices .
Edit intent: meaning-changed
Original:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Edit intent: fluency
Original:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0, where \|.\| is the unform norm. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Edit intent: meaning-changed
Original:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings has recently been found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Edit intent: fluency
Original:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , which reduces to solving a system of linear equations over Z_2.
Edit intent: clarity
Original:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 , which reduces to solving a system of linear equations over Z_2.
Revised:  A map \varphi:G\rightarrow M is a weak embedding if it can be perturbed into an embedding \psi_\varepsilon:G\rightarrow M with \|\varphi-\psi_\varepsilon\|<\varepsilon for every \varepsilon> 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl , 2017 . It reduces the problem to solving a system of linear equations over Z_2.
Edit intent: clarity
Original:  It runs in O(n^{2\omega})\leq O(n^{4.75}) time, where \omega \approx  2.373  is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n\log n).
Revised:  It runs in O(n^{2\omega})\leq O(n^{4.75}) time, where \omega \in 2.373 is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n\log n).
Edit intent: clarity
Original:  It runs in O(n^{2\omega})\leq O(n^{4.75}) time, where \omega \approx  2.373  is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n\log n).
Revised:  It runs in O(n^{2\omega})\leq O(n^{4.75}) time, where \omega \approx 2, 2.373 is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n\log n).
Edit intent: meaning-changed