wanyu/IteraTeR_full_sent huggingface dataset:
Original:  With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed  frame, respectively, the corresponding extending Kalman filter (EKF) , terms as SE_2(3) -EKF has also been derived.
Revised:  With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed (ECEF) frame, respectively, the corresponding extending Kalman filter (EKF) , terms as SE_2(3) -EKF has also been derived.
Edit intent: clarity
Original:  With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed  frame, respectively, the corresponding extending Kalman filter (EKF) , terms as SE_2(3) -EKF has also been derived.
Revised:  With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed frame, respectively, the corresponding EKF , terms as SE_2(3) -EKF has also been derived.
Edit intent: meaning-changed
Original:  With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed  frame, respectively, the corresponding extending Kalman filter (EKF) , terms as SE_2(3) -EKF has also been derived.
Revised:  With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed frame, respectively, the corresponding extending Kalman filter (EKF) , terms as SE_2(3) based EKF has also been derived.
Edit intent: coherence
Original:  Furthermore, we propose a SE_2(3)-based smoothing algorithm based on the SE_2(3)-based EKF .
Revised:  Furthermore, we design two new modified error dynamics on the NED frame and the ECEF frame respectively by introducing new auxiliary vectors. Finally the equivalence of the left-invariant EKF and left SE_2(3) based EKF have been shown in navigation frame and ECEF frame .
Edit intent: meaning-changed
Original:  In this paper, we propose Multi-step Hindsight Experience Replay (MHER) based on n-step relabeling , incorporating multi-step relabeled returns  to improve sample efficiency.
Revised:  In this paper, we propose Multi-step Hindsight Experience Replay (MHER) based on n-step relabeling , incorporating multi-step relabeled returns to improve sample efficiency.
Edit intent: fluency
Original:  In this paper, we propose Multi-step Hindsight Experience Replay (MHER) based on n-step relabeling , incorporating multi-step relabeled returns  to improve sample efficiency.
Revised:  In this paper, we propose Multi-step Hindsight Experience Replay (MHER) based on n-step relabeling , incorporating multi-step relabeled returns based on n-step relabeling to improve sample efficiency.
Edit intent: meaning-changed
Original:  In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales  .
Revised:  In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales . Regional positions relative to density scaling laws were remarkably persistent after the first 5-9 days of the available data set. The determinants of this persistent behaviour probably precede the pandemic and remain unchanged .
Edit intent: meaning-changed
Original:  We prove that, starting from a warm start, it mixes in, where f is L-smooth and m-strongly-convex, within accuracy \varepsilon after } \widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon)) steps for a well-rounded polytope, ignoring logarithmic factors where \kappa is the condition number of the negative log-density, d is the dimension, \ell is an upper bound on the number of reflections, and \varepsilon is the accuracy parameter.
Revised:  We prove that, starting from a warm start, the walk mixes to a log-concave target distribution \pi(x) \propto e^{-f(x), where f is L-smooth and m-strongly-convex, within accuracy \varepsilon after } \widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon)) steps for a well-rounded polytope, ignoring logarithmic factors where \kappa is the condition number of the negative log-density, d is the dimension, \ell is an upper bound on the number of reflections, and \varepsilon is the accuracy parameter.
Edit intent: meaning-changed
Original:  We prove that, starting from a warm start, it mixes in, where f is L-smooth and m-strongly-convex, within accuracy \varepsilon after } \widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon)) steps for a well-rounded polytope, ignoring logarithmic factors where \kappa is the condition number of the negative log-density, d is the dimension, \ell is an upper bound on the number of reflections, and \varepsilon is the accuracy parameter.
Revised:  We prove that, starting from a warm start, it mixes in, where f is L-smooth and m-strongly-convex, within accuracy \varepsilon after } \widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon)) steps for a well-rounded convex body where \kappa = L / m is the condition number of the negative log-density, d is the dimension, \ell is an upper bound on the number of reflections, and \varepsilon is the accuracy parameter.
Edit intent: meaning-changed
Original:  For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics  , as well as their potential application to future epidemics.
Revised:  For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics , such as Covid-19 , as well as their potential application to future epidemics.
Edit intent: meaning-changed
Original:  Our GNN policies are trained using very few expert demonstrations on simple tasks, and exhibits generalization over number and configurations of objects in the environment and even to new, more complex tasks, and provide interpretable explanations for their decision-making.
Revised:  Our GNN policies are trained using very few expert demonstrations on simple tasks, and exhibit generalization over number and configurations of objects in the environment and even to new, more complex tasks, and provide interpretable explanations for their decision-making.
Edit intent: fluency
Original:  Our GNN policies are trained using very few expert demonstrations on simple tasks, and exhibits generalization over number and configurations of objects in the environment and even to new, more complex tasks, and provide interpretable explanations for their decision-making.
Revised:  Our GNN policies are trained using very few expert demonstrations on simple tasks, and exhibits generalization over number and configurations of objects in the environment and even to new, more complex tasks, while providing interpretable explanations for their decision-making.
Edit intent: coherence
Original:  To address this problem, we introduce a robust representation learning approach for RL . We introduce an auxiliary objective based on the multi-view information bottleneck (MIB) principle which  encourages learning representations that are both predictive of the future and less sensitive to task-irrelevant distractions.
Revised:  To address this problem, we leverage the sequential nature of RL to learn robust representations that encode only task-relevant information from observations based on the unsupervised multi-view setting. Specifically, we introduce an auxiliary objective based on the multi-view information bottleneck (MIB) principle which encourages learning representations that are both predictive of the future and less sensitive to task-irrelevant distractions.
Edit intent: meaning-changed
Original:  To address this problem, we introduce a robust representation learning approach for RL . We introduce an auxiliary objective based on the multi-view information bottleneck (MIB) principle which  encourages learning representations that are both predictive of the future and less sensitive to task-irrelevant distractions.
Revised:  To address this problem, we introduce a robust representation learning approach for RL . We introduce an auxiliary objective based on the multi-view in-formation bottleneck (MIB) principle which encourages learning representations that are both predictive of the future and less sensitive to task-irrelevant distractions.
Edit intent: meaning-changed
Original:  To address this problem, we introduce a robust representation learning approach for RL . We introduce an auxiliary objective based on the multi-view information bottleneck (MIB) principle which  encourages learning representations that are both predictive of the future and less sensitive to task-irrelevant distractions.
Revised:  To address this problem, we introduce a robust representation learning approach for RL . We introduce an auxiliary objective based on the multi-view information bottleneck (MIB) principle which quantifies the amount of task-irrelevant information and encourages learning representations that are both predictive of the future and less sensitive to task-irrelevant distractions.
Edit intent: meaning-changed
Original:  This leads firstly, to a new perspective of the algebraic and logical structure of desirability and  secondly, it connects desirability, hence imprecise probabilities , to other formalism in computer science sharing the same underlying structure.
Revised:  This leads firstly, to a new perspective of the algebraic and logical structure of desirability and imprecise probabilities and secondly, it connects desirability, hence imprecise probabilities , to other formalism in computer science sharing the same underlying structure.
Edit intent: coherence
Original:  This leads firstly, to a new perspective of the algebraic and logical structure of desirability and  secondly, it connects desirability, hence imprecise probabilities , to other formalism in computer science sharing the same underlying structure.
Revised:  This leads firstly, to a new perspective of the algebraic and logical structure of desirability and secondly, it connects imprecise probabilities to other formalism in computer science sharing the same underlying structure.
Edit intent: coherence
Original:  In this paper, we first provide our definition of emotion-driven services, and then we propose a novel methodological framework, referred to as the Virtual-Reality-Based Emotion-Elicitation-Emotion-Recognition loop (VEE-loop), that can be exploited to realize it.
Revised:  In this paper, we first provide our definition of emotion-driven services, and then we propose a novel methodological framework, referred to as the Virtual-Reality-Based Emotion-Elicitation-and-Recognition loop (VEE-loop), that can be exploited to realize it.
Edit intent: clarity
Original:  We derive the benefits of a discovery on decision making. A researcher maximizes the benefits of discovery net the cost of research. We characterize the researcher's optimal choice of research question and research effort. Benefits and cost of research crucially depend on the structure of pre-existing knowledge.
Revised:  We derive the benefits of discoveries are non-monotone in novelty. Nevertheless, due to a dynamic externality, it can be optimal to incentivize research on distant discoveries to improve the evolution of knowledge. One reason is that the probability of a discovery and the novelty of the question are endogenously linked. They can be complements or substitutes depending on existing knowledge.
Edit intent: meaning-changed
Original: Designing agents that acquire knowledge autonomously and use it to solve new tasks efficiently is an important challenge in reinforcement learning , and unsupervised learning provides a useful paradigm for autonomous acquisition of task-agnostic knowledge. In supervised settings, representations discovered through unsupervised pre-training offer important benefits when transferred to downstream tasks . Given the nature of the reinforcement learning problem, we argue that representation alone is not enough for efficient transfer in challenging domains and explore how to transfer knowledge through behavior.
Revised: Designing agents that acquire knowledge autonomously and use it to solve new tasks efficiently is an important challenge in reinforcement learning . Knowledge acquired during an unsupervised pre-training offer important benefits when transferred to downstream tasks . Given the nature of the reinforcement learning problem, we argue that representation alone is not enough for efficient transfer in challenging domains and explore how to transfer knowledge through behavior.
Edit intent: clarity
Original:  In supervised settings, representations discovered through unsupervised pre-training offer important benefits when transferred to downstream tasks . Given the nature of the reinforcement learning problem, we argue that representation alone is not enough for efficient transfer in challenging domains and explore how to transfer knowledge through behavior.
Revised:  In supervised settings, representations discovered through unsupervised pre-training phase is often transferred by fine-tuning neural network weights once rewards are exposed, as is common practice in supervised domains . Given the nature of the reinforcement learning problem, we argue that representation alone is not enough for efficient transfer in challenging domains and explore how to transfer knowledge through behavior.
Edit intent: meaning-changed
Original:  In supervised settings, representations discovered through unsupervised pre-training offer important benefits when transferred to downstream tasks . Given the nature of the reinforcement learning problem, we argue that representation alone is not enough for efficient transfer in challenging domains and explore how to transfer knowledge through behavior.
Revised:  In supervised settings, representations discovered through unsupervised pre-training offer important benefits when transferred to downstream tasks . Given the nature of the reinforcement learning problem, we argue that standard fine-tuning strategies alone are not enough for efficient transfer in challenging domains and explore how to transfer knowledge through behavior.
Edit intent: meaning-changed
Original:  In supervised settings, representations discovered through unsupervised pre-training offer important benefits when transferred to downstream tasks . Given the nature of the reinforcement learning problem, we argue that representation alone is not enough for efficient transfer in challenging domains and explore how to transfer knowledge through behavior. The behavior of pre-trained policies may be used for solving the task at hand (exploitation), as well as for collecting useful data to solve the problem (exploration ).
Revised:  In supervised settings, representations discovered through unsupervised pre-training offer important benefits when transferred to downstream tasks . Given the nature of the reinforcement learning problem, we argue that representation alone is not enough for efficient transfer in challenging domains . We introduce Behavior Transfer (BT), a technique that leverages pre-trained policies may be used for solving the task at hand (exploitation), as well as for collecting useful data to solve the problem (exploration ).
Edit intent: coherence
Original:  The behavior of pre-trained policies may be used for solving the task at hand (exploitation), as well as for collecting useful data to solve the problem (exploration ). We argue that policies pre-trained to maximize coverage will produce behavior thatis useful for both strategies. When using these policies for both exploitation and exploration, our agents discover better solutions  .
Revised:  The behavior of pre-trained policies for exploration and that is complementary to transferring neural network weights. Our experiments show that, when combined with large-scale pre-training in the absence of rewards, existing intrinsic motivation objectives can lead to the emergence of complex behaviors. These pre-trained policies can then be leveraged by BT to discover better solutions .
Edit intent: meaning-changed
Original: We introduce a new approach for capturing model uncertainty for neural networks (NNs) in regression , which we call Neural Optimization-based Model Uncertainty (NOMU).
Revised: We study methods for estimating model uncertainty for neural networks (NNs). To isolate the effect of model uncertainty, we focus on a noiseless setting with scarce training data. We introduce five important desiderata regarding model uncertainty that any method should satisfy. However, we find that established benchmarks often fail to reliably capture some of these desiderata, even those that are required by Bayesian theory. To address this, we introduce a new approach for capturing model uncertainty for neural networks (NNs) in regression , which we call Neural Optimization-based Model Uncertainty (NOMU).
Edit intent: meaning-changed
Original:  The main idea of NOMU is to design a network architecture consisting of two connected sub-networks , one for the model prediction and one for the model uncertainty, and to train it using a carefully designed loss function.
Revised:  The main idea of NOMU is to design a network architecture consisting of two connected sub-NNs , one for the model prediction and one for the model uncertainty, and to train it using a carefully designed loss function.
Edit intent: clarity
Original:  The main idea of NOMU is to design a network architecture consisting of two connected sub-networks , one for the model prediction and one for the model uncertainty, and to train it using a carefully designed loss function.
Revised:  The main idea of NOMU is to design a network architecture consisting of two connected sub-networks , one for model prediction and one for the model uncertainty, and to train it using a carefully designed loss function.
Edit intent: fluency
Original:  The main idea of NOMU is to design a network architecture consisting of two connected sub-networks , one for the model prediction and one for the model uncertainty, and to train it using a carefully designed loss function.
Revised:  The main idea of NOMU is to design a network architecture consisting of two connected sub-networks , one for the model prediction and one for model uncertainty, and to train it using a carefully designed loss function.
Edit intent: fluency
Original:  The main idea of NOMU is to design a network architecture consisting of two connected sub-networks , one for the model prediction and one for the model uncertainty, and to train it using a carefully designed loss function.
Revised:  The main idea of NOMU is to design a network architecture consisting of two connected sub-networks , one for the model prediction and one for the model uncertainty, and to train it using a carefully-designed loss function.
Edit intent: fluency
Original:  With this design , NOMU can provide model uncertainty for any given (previously trained) NN by plugging it into the framework as the sub-network used for model prediction.
Revised:  Importantly, our design enforces that NOMU satisfies our five desiderata. Due to its modular architecture , NOMU can provide model uncertainty for any given (previously trained) NN by plugging it into the framework as the sub-network used for model prediction.
Edit intent: meaning-changed
Original:  With this design , NOMU can provide model uncertainty for any given (previously trained) NN by plugging it into the framework as the sub-network used for model prediction. NOMU is designed to yield uncertainty bounds (UBs) that satisfy four important desiderata regarding model uncertainty , which established methods often do not satisfy. Furthermore, our UBs are themselves representable as a single NN, which leads to computational cost advantages in applications such as Bayesian optimization. We evaluate NOMU experimentally in multiple settings. For regression, we show that NOMU performs as well as or better than established benchmarks.
Revised:  With this design , NOMU can provide model uncertainty for any given (previously trained) NN if given access to its training data. We first experimentally study noiseless regression with scarce training data to highlight the deficiencies of the established benchmarks. Finally, we study the important task of Bayesian optimization (BO) with costly evaluations, where good model uncertainty estimates are essential. Our results show that NOMU performs as well as or better than established benchmarks.
Edit intent: clarity
Original:  It is motivated by the emerging scenario where large-load customers utilize energy storage to reduce the peak procurement from the grid, which accounts for up to 90 \% of their electric bills. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. In this paper, we develop an optimal online algorithm for the problem that attains the best possible competitive ratio (CR) among all deterministic and randomized algorithms. We show that the optimal CR can be computed in polynomial time, by solving a linear number of linear-fractional problems. We also generalize our approach to develop an anytime-optimal online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and achieves adaptive average-case performance. Simulation results based on real-world traces show that our algorithms improve peak reduction by more than 19\% as compared to baseline alternatives.
Revised:  It is motivated by the emerging scenario where large-load customers utilize energy storage to reduce the peak procurement from the grid, which accounts for up to 90 
Edit intent: meaning-changed
Original:  First, we show that the value of the game exists in stationary strategies, which depend solely on the previous action of the player (and not the entire history ), and we provide a full characterization of the value and the optimal strategies.
Revised:  First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the player (and not the entire history ), and we provide a full characterization of the value and the optimal strategies.
Edit intent: coherence