wanyu/IteraTeR_v2 huggingface dataset:
Original:  The DBaS-based DDP (DBaS-DDP) is compared to the penalty method used in constrained DDP problems where it is shown that the DBaS-DDP consistently outperforms the penalty method .
Revised:  The DBaS-based DDP (DBaS-DDP) is compared to the penalty method used in constrained DDP problems .
Edit intent: coherence
Original: Diffusion is a fundamental graph process and has been a basic building block in the study of graph clustering and graph learning tasks such as node classification .
Revised: Diffusion is a fundamental graph procedure and has been a basic building block in the study of graph clustering and graph learning tasks such as node classification .
Edit intent: clarity
Original: Diffusion is a fundamental graph process and has been a basic building block in the study of graph clustering and graph learning tasks such as node classification .
Revised: Diffusion is a fundamental graph process and has been a basic building block in a wide range of theoretical and empirical applications such as graph partitioning and semi-supervised learning on graphs .
Edit intent: clarity
Original:  In this paper, we initiate the study of computationally efficient diffusion primitives beyond random walk.
Revised:  In this paper, we study computationally efficient diffusion primitives beyond random walk.
Edit intent: coherence
Original:  We provide an O(m)-time randomized algorithm for the \ell_2-norm flow diffusion problem, obtaining the approximation factor of 1+1/poly(n).
Revised:  We design an O(m)-time randomized algorithm for the \ell_2-norm flow diffusion problem, obtaining the approximation factor of 1+1/poly(n).
Edit intent: clarity
Original:  Using the connection between its dual solution and local cut structure, we give an alternative approach for finding locally-biased low conductance cuts .
Revised:  Using the connection between its dual solution and local cut structure, our algorithm gives an alternative approach for finding locally-biased low conductance cuts .
Edit intent: clarity
Original: A Spiking Neural Network (SNN)  trained with Spike Time Dependent Plasticity (STDP)  is a neuro-inspired unsupervised learning method for various machine learning applications.
Revised: A Spiking Neural Network (SNN) trained with Spike Timing Dependent Plasticity (STDP) is a neuro-inspired unsupervised learning method for various machine learning applications.
Edit intent: fluency
Original: A Spiking Neural Network (SNN)  trained with Spike Time Dependent Plasticity (STDP)  is a neuro-inspired unsupervised learning method for various machine learning applications.
Revised: A Spiking Neural Network (SNN) trained with Spike Time Dependent Plasticity (STDP) , which is a neuro-inspired unsupervised learning method for various machine learning applications.
Edit intent: coherence
Original:  The paper analyzes the effects of STDP learning models and associated hyper-parameters on the generalizability properties of an SNN and characterizes the generalizability vs learnability trade-off in an SNN . The analysis is used to develop a Bayesian optimization approach to optimize the hyper-parameters for an STDP model to improve the generalizability properties of an SNN.
Revised:  The paper analyzes the effects of STDP learning models and associated hyper-parameters on the generalizability properties of an SNN . The analysis is used to develop a Bayesian optimization approach to optimize the hyper-parameters for an STDP model to improve the generalizability properties of an SNN.
Edit intent: coherence
Original:  The paper analyzes the effects of STDP learning models and associated hyper-parameters on the generalizability properties of an SNN and characterizes the generalizability vs learnability trade-off in an SNN . The analysis is used to develop a Bayesian optimization approach to optimize the hyper-parameters for an STDP model to improve the generalizability properties of an SNN.
Revised:  The paper analyzes the effects of STDP learning models and associated hyper-parameters on the generalizability properties of an SNN and characterizes the generalizability vs learnability trade-off in an SNN . The analysis is used to develop a Bayesian optimization approach to optimize the hyper-parameters for an STDP model for improving the generalizability properties of an SNN.
Edit intent: fluency
Original:  for %DIFDELCMD < \lq\lq %%% optimal%DIFDELCMD < \rq %%%  parameter \delta = 1 which ensures the best output quality, no polynomial bounds are known, and except for LLL algorithm, it is even not formally proved that the algorithm always halts within finitely many steps.
Revised:  for %DIFDELCMD < \lq\lq %%% %DIFDELCMD < \rq %%% parameter \delta = 1 which ensures the best output quality, no polynomial bounds are known, and except for LLL algorithm, it is even not formally proved that the algorithm always halts within finitely many steps.
Edit intent: fluency
Original:  Then we make use of the discrete gradient method and  Pad\'e approximation and propose efficient fully-discrete schemes.
Revised:  Then we make use of the discrete gradient method and the Pad\'e approximation and propose efficient fully-discrete schemes.
Edit intent: fluency
Original:  Then we make use of the discrete gradient method and  Pad\'e approximation and propose efficient fully-discrete schemes.
Revised:  Then we make use of the discrete gradient method and Pad\'e approximation to propose efficient fully-discrete schemes.
Edit intent: coherence
Original:  We prove the unique recovery of the spatially-dependent potential coefficient and the order \alpha of the derivation simultaneously from the measured trace data at one end point, when the model is equipped with a boundary excitation with compact supports away from t=0.
Revised:  We prove the unique recovery of the spatially-dependent potential coefficient and the order \alpha of the derivation simultaneously from the measured trace data at one end point, when the model is equipped with a boundary excitation with a compact support away from t=0.
Edit intent: fluency
Original: We present a novel verification technique to prove interesting properties of a class of array programs with a symbolic parameter N denoting the size of the array .
Revised: We present a novel verification technique to prove interesting properties of a class of array programs with a symbolic parameter N denoting the size of arrays .
Edit intent: fluency
Original:  The technique relies on constructing two slightly different versions of the  program.
Revised:  The technique relies on constructing two slightly different versions of the same program.
Edit intent: clarity
Original:  We formulate a new technique to prove the desired post-condition  by inducting on the program parameter N, in which the difference invariants are crucially used in the key inductive step.
Revised:  We formulate a new technique to prove the desired post-condition by inducting on the program parameter N, wherein the difference invariants are crucially used in the key inductive step.
Edit intent: clarity
Original:  We formulate a new technique to prove the desired post-condition  by inducting on the program parameter N, in which the difference invariants are crucially used in the key inductive step.
Revised:  We formulate a new technique to prove the desired post-condition by inducting on the program parameter N, in which the difference invariants are crucially used in the inductive step.
Edit intent: clarity
Original:  We show the results on a set of benchmarks and compare its performance vis-a-vis state-of-the-art tools for verifying array programs .
Revised:  We present results comparing the performance of diffy with that of state-of-the-art tools for verifying array programs .
Edit intent: clarity
Original:  We show the results on a set of benchmarks and compare its performance vis-a-vis state-of-the-art tools for verifying array programs .
Revised:  We show the results on a set of benchmarks and compare its performance vis-a-vis state-of-the-art tools .
Edit intent: clarity
Original:  Specifically, we are able to delay or advance a given bifurcation point to a given parameter value, often to within machine precision .
Revised:  Specifically, we are able to delay or advance a given branch point to a given parameter value, often to within machine precision .
Edit intent: clarity
Original:  Specifically, we are able to delay or advance a given bifurcation point to a given parameter value, often to within machine precision .
Revised:  Specifically, we are able to delay or advance a given bifurcation point to a target parameter value .
Edit intent: clarity
Original:  The algorithm consists of solving a shape optimization problem constrained by an augmented system of equations, the Moore--Spence system, that characterize the location of the bifurcation points.
Revised:  The algorithm consists of solving a shape optimization problem constrained by an augmented system of equations, the Moore--Spence system, that characterize the location of the branch points.
Edit intent: clarity
Original: Sensing and measurement systems are a quintessential piece to the safe and reliable operation of electric power grids.
Revised: Sensing and measurement systems are quintessential to the safe and reliable operation of electric power grids.
Edit intent: clarity
Original:  Besides , large-scale, long-term deployments pose additional challenges because the boundary conditions change as technologies evolve.
Revised:  Further , large-scale, long-term deployments pose additional challenges because the boundary conditions change as technologies evolve.
Edit intent: fluency
Original:  Also, the placement strategies developed for transmission grids might not be suitable for distribution grids, and vice versa, due to unique characteristics.
Revised:  Also, the placement strategies developed for transmission grids might not be suitable for distribution grids, and vice versa, because of unique characteristics.
Edit intent: coherence
Original:  Despite the extensive literature on the present topic, the focus of published works tends to be on a specific subject, such as  optimal placement of measurements to assure observability in transmission grids.
Revised:  Despite the extensive literature on the present topic, the focus of published works tends to be on a specific subject, such as the optimal placement of measurements to assure observability in transmission grids.
Edit intent: fluency
Original:  Despite the extensive literature on the present topic, the focus of published works tends to be on a specific subject, such as  optimal placement of measurements to assure observability in transmission grids.
Revised:  Despite the extensive literature on the present topic, the focus of published works tends to be on a specific subject, such as optimal placement of measurements to ensure observability in transmission grids.
Edit intent: fluency
Original: We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic safe differentiable framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of both immediate and long-term constraint satisfaction at any stage of the learning and control progress.
Revised: We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of both immediate and long-term constraint satisfaction at any stage of the learning and control progress.
Edit intent: clarity
Original: We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic safe differentiable framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of both immediate and long-term constraint satisfaction at any stage of the learning and control progress.
Revised: We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic safe differentiable framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of safety constraint satisfaction at any stage of the learning and control progress.
Edit intent: clarity
Original:  In the spirit of interior-point methods, Safe PDP handles different types of state and input constraints by incorporating them into the cost and loss through barrier functions.
Revised:  In the spirit of interior-point methods, Safe PDP handles different types of system constraints on states and inputs by incorporating them into the cost and loss through barrier functions.
Edit intent: clarity
Original:  In the spirit of interior-point methods, Safe PDP handles different types of state and input constraints by incorporating them into the cost and loss through barrier functions.
Revised:  In the spirit of interior-point methods, Safe PDP handles different types of state and input constraints by incorporating them into the cost or loss through barrier functions.
Edit intent: fluency
Original:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in  backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Revised:  We prove three fundamentals of the proposed Safe PDP: first, both the constrained solution and its gradient in backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Edit intent: clarity
Original:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in  backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Revised:  We prove the following fundamental features of Safe PDP: first, both the solution and its gradient in backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Edit intent: clarity
Original:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in  backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Revised:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in the backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Edit intent: fluency
Original:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in  backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Revised:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in backward pass can be approximated by solving their more efficient unconstrained counterpart ;
Edit intent: clarity
Original:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in  backward pass can be approximated by solving a more efficient unconstrained counterpart ;
Revised:  We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in backward pass can be approximated by solving a more efficient unconstrained counterparts ;
Edit intent: fluency
Original:  second, the approximation for both the solution and its gradient can be controlled for arbitrary accuracy using a barrier parameter;
Revised:  second, the approximation for both the solution and its gradient can be controlled for arbitrary accuracy by a barrier parameter;
Edit intent: fluency
Original:  and third, importantly, any intermediate results throughout the approximation and optimization are strictly respecting all constraints, thus guaranteeing safety throughout the entire learning and control process.
Revised:  and third, importantly, all intermediate results throughout the approximation and optimization are strictly respecting all constraints, thus guaranteeing safety throughout the entire learning and control process.
Edit intent: fluency
Original:  and third, importantly, any intermediate results throughout the approximation and optimization are strictly respecting all constraints, thus guaranteeing safety throughout the entire learning and control process.
Revised:  and third, importantly, any intermediate results throughout the approximation and optimization strictly respect the constraints, thus guaranteeing safety throughout the entire learning and control process.
Edit intent: clarity
Original:  We demonstrate the capabilities of Safe PDP in solving various safe learning and control tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging control systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.
Revised:  We demonstrate the capabilities of Safe PDP in solving various safety-critical tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging control systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.
Edit intent: clarity
Original:  We demonstrate the capabilities of Safe PDP in solving various safe learning and control tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging control systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.
Revised:  We demonstrate the capabilities of Safe PDP in solving various safe learning and control tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.
Edit intent: clarity
Original: In this paper, we apply the self-attention from the state-of-art Transformer in Attention Is All You Need the first time to a data-driven operator learning problem related to partial differential equations.
Revised: In this paper, we apply the self-attention from the state-of-the-art Transformer in Attention Is All You Need the first time to a data-driven operator learning problem related to partial differential equations.
Edit intent: fluency
Original: In this paper, we apply the self-attention from the state-of-the-art Transformer in Attention Is All You Need  the first time to a data-driven operator learning problem related to partial differential equations.
Revised: In this paper, we apply the self-attention from the state-of-the-art Transformer in Attention Is All You Need for the first time to a data-driven operator learning problem related to partial differential equations.
Edit intent: coherence
Original:  We put together an effort to explain the heuristics of, and  improve the efficacy of the self-attention by demonstrating that the softmax normalization in the scaled dot-product attention is sufficient but not necessary , and have proved the approximation capacity of a linear variant as a Petrov-Galerkin projection  .
Revised:  An effort is put together to explain the heuristics of, and improve the efficacy of the self-attention by demonstrating that the softmax normalization in the scaled dot-product attention is sufficient but not necessary , and have proved the approximation capacity of a linear variant as a Petrov-Galerkin projection .
Edit intent: clarity
Original:  We put together an effort to explain the heuristics of, and  improve the efficacy of the self-attention by demonstrating that the softmax normalization in the scaled dot-product attention is sufficient but not necessary , and have proved the approximation capacity of a linear variant as a Petrov-Galerkin projection  .
Revised:  We put together an effort to explain the heuristics of, and to improve the efficacy of the self-attention by demonstrating that the softmax normalization in the scaled dot-product attention is sufficient but not necessary , and have proved the approximation capacity of a linear variant as a Petrov-Galerkin projection .
Edit intent: fluency
Original:  All experiments validate the improvements of the newly proposed simple attention-based operator learner over their softmax-normalized counterparts.
Revised:  The newly proposed simple attention-based operator learner over their softmax-normalized counterparts.
Edit intent: clarity
Original: Value factorisation proves to be a very useful technique in multi-agent reinforcement learning (MARL), but the underlying mechanism is not yet fully understood.
Revised: Value factorisation proves to be a useful technique in multi-agent reinforcement learning (MARL), but the underlying mechanism is not yet fully understood.
Edit intent: coherence
Original:  This paper explores a theoretic basis for value factorisation  .
Revised:  This paper explores a theoretical framework for value factorisation .
Edit intent: clarity
Original:  We generalise the Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL.
Revised:  We generalise Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL.
Edit intent: fluency
Original:  We generalise the Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL.
Revised:  We generalise the Shapley value in coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL.
Edit intent: fluency
Original:  We generalise the Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL.
Revised:  We generalise the Shapley value in the coalitional game theory to Markov convex game (MCG) and use it to guide value factorisation in MARL.
Edit intent: fluency
Original:  We generalise the Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL.
Revised:  We generalise the Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it as a value factorisation method for MARL.
Edit intent: clarity
Original:  We show that the generalised Shapley value possesses several features such as (1) accurate estimation of the maximum global value, (2) fairness in the factorisation of the global value, and (3) being sensitive to dummy agents.
Revised:  We show that the generalised Shapley value possesses several features such as (1) accurate estimation of the maximum global value, (2) fairness in factorisation of the global value, and (3) being sensitive to dummy agents.
Edit intent: fluency
Original:  We show that the generalised Shapley value possesses several features such as (1) accurate estimation of the maximum global value, (2) fairness in the factorisation of the global value, and (3) being sensitive to dummy agents.
Revised:  We show that the generalised Shapley value possesses several features such as (1) accurate estimation of the maximum global value, (2) fairness in the factorisation of the global value, and (3) sensitiveness to dummy agents.
Edit intent: clarity
Original: The optimal fusion of estimates in a Distributed Kalman Filter (DKF) requires tracking of the complete network error covariance, which is a problem in terms of memory and communication bandwidth .
Revised: The optimal fusion of estimates in a Distributed Kalman Filter (DKF) requires tracking of the complete network error covariance, problematic in terms of memory and communication bandwidth .
Edit intent: clarity
Original: The optimal fusion of estimates in a Distributed Kalman Filter (DKF) requires tracking of the complete network error covariance, which is a problem in terms of memory and communication bandwidth .
Revised: The optimal fusion of estimates in a Distributed Kalman Filter (DKF) requires tracking of the complete network error covariance, which is a problem in terms of memory and communication .
Edit intent: clarity