wanyu/IteraTeR_v2 huggingface dataset:
Original:  We solve the resulting non-convex problem by incorporating block coordinate descent (BCD) and alternating projection (AP) methods in a single algorithmic framework called BCD-AP MRMC. We achieve this by exploiting the relationship between mutual information and weighted minimum mean-squared-error (WMMSE), which allows  use of the Lagrange dual problem in finding closed-form solutions for precoders and radar waveform.
Revised:  We solve the resulting non-convex problem by incorporating block coordinate descent (BCD) and alternating projection (AP) methods in a single algorithmic framework called BCD-AP MRMC. We achieve this by exploiting the relationship between mutual information and weighted minimum mean-squared-error (WMMSE), which allows the use of the Lagrange dual problem in finding closed-form solutions for precoders and radar waveform.
Edit intent: fluency
Original:  Numerical experiments show that our proposed WMMSE-based method quickly achieves monotonic convergence, improves target detection by 6-13 \% compared to conventional radar coding, and provides  8.3-30\% higher  rate in IBFD MU-MIMO system than other precoding strategies.
Revised:  Numerical experiments show that our proposed WMMSE-based method quickly achieves monotonic convergence, improves target detection by 6-13 \% compared to conventional radar coding, and provides an 8.3-30\% higher rate in IBFD MU-MIMO system than other precoding strategies.
Edit intent: fluency
Original: We study training of Convolutional Neural Networks (CNNs) with ReLU activations and introduce exact convex optimization formulations with a polynomial complexity with respect to the number of data samples, the number of neurons  and data dimension.
Revised: We study training of Convolutional Neural Networks (CNNs) with ReLU activations and introduce exact convex optimization formulations with a polynomial complexity with respect to the number of data samples, the number of neurons , and data dimension.
Edit intent: fluency
Original:  Particularly , we develop a convex analytic framework utilizing semi-infinite duality to obtain equivalent convex optimization problems for several  CNN architectures.
Revised:  More specifically , we develop a convex analytic framework utilizing semi-infinite duality to obtain equivalent convex optimization problems for several CNN architectures.
Edit intent: coherence
Original:  We then show that certain three-layer CNN training problems are equivalent to an \ell_1 regularized convex program  .
Revised:  We then show that three-layer CNN training problems are equivalent to an \ell_1 regularized convex program .
Edit intent: clarity
Original:  We also extend these results to multi-layer CNN architectures including three-layer networks with two ReLU layers and deeper circular convolutions with a single ReLU layer .
Revised:  We also extend these results to three-layer networks with two ReLU layers and deeper circular convolutions with a single ReLU layer .
Edit intent: clarity
Original:  We also extend these results to multi-layer CNN architectures including three-layer networks with two ReLU layers and deeper circular convolutions with a single ReLU layer .
Revised:  We also extend these results to multi-layer CNN architectures including three-layer CNNs with two ReLU layers and deeper circular convolutions with a single ReLU layer .
Edit intent: clarity
Original:  We also extend these results to multi-layer CNN architectures including three-layer networks with two ReLU layers and deeper circular convolutions with a single ReLU layer .
Revised:  We also extend these results to multi-layer CNN architectures including three-layer networks with two ReLU layers .
Edit intent: clarity
Original: How does the human brain learn new concepts from raw sensory experience , without explicit instruction ?
Revised: How do humans learn from raw sensory experience , without explicit instruction ?
Edit intent: clarity
Original:  The spatial semidiscretizations are built using the unifying framework of summation by parts operators and include finite difference, spectral collocation, and both discontinuous and continuous finite element methods.
Revised:  The spatial semidiscretizations include finite difference, spectral collocation, and both discontinuous and continuous finite element methods.
Edit intent: clarity
Original:  However, existing work generally relies on heavily-engineered task specific features and model architectures.
Revised:  However, existing work generally relies on heavily-engineered task-specific features and model architectures.
Edit intent: fluency
Original:  In this paper, we present TURL, a novel framework that introduces the pre-training/ finetuning paradigm to relational Web tables.
Revised:  In this paper, we present TURL, a novel framework that introduces the pre-training/ fine-tuning paradigm to relational Web tables.
Edit intent: fluency
Original:  For an optimal value of p_c^*~(=0.029), individual GR cells exhibit diverse spiking patterns which are well- or ill-matched with the unconditioned stimulus.
Revised:  For an optimal value of p_c^*~(=0.029), individual granule cells show various well- or ill-matched with the unconditioned stimulus.
Edit intent: clarity
Original:  For an optimal value of p_c^*~(=0.029), individual GR cells exhibit diverse spiking patterns which are well- or ill-matched with the unconditioned stimulus.
Revised:  For an optimal value of p_c^*~(=0.029), individual GR cells exhibit diverse spiking patterns which are well- and ill-matched with the unconditioned stimulus.
Edit intent: fluency
Original:  For an optimal value of p_c^*~(=0.029), individual GR cells exhibit diverse spiking patterns which are well- or ill-matched with the unconditioned stimulus.
Revised:  For an optimal value of p_c^*~(=0.029), individual GR cells exhibit diverse spiking patterns which are well- or ill-matched firing patterns relative to the unconditioned stimulus.
Edit intent: clarity
Original:  In this case, the timing degree {\cal T}_d of CR becomes good due to presence of  ill-matched spiking group which plays a role of protection barrier for the timing.
Revised:  In this case, the timing degree {\cal T}_d of CR becomes good due to presence of the ill-matched spiking group which plays a role of protection barrier for the timing.
Edit intent: fluency
Original:  Thus, the learning efficiency degree {\cal L}_e (taking into consideration both timing and strength of CR) for the CR increases with learning trial , and eventually it becomes saturated.
Revised:  Thus, with increasing the learning trial, the (overall) learning efficiency degree {\cal L}_e (taking into consideration both timing and strength of CR) for the CR increases with learning trial , and eventually it becomes saturated.
Edit intent: clarity
Original:  Thus, the learning efficiency degree {\cal L}_e (taking into consideration both timing and strength of CR) for the CR increases with learning trial , and eventually it becomes saturated.
Revised:  Thus, the learning efficiency degree {\cal L}_e (taking into consideration both timing and strength of CR) for the CR is increased , and eventually it becomes saturated.
Edit intent: clarity
Original:  It is this found that, the more diverse in temporal recoding of GR cells , the more effective in motor learning for the Pavlovian EBC.
Revised:  It is thus found that, the more diverse in temporal recoding of GR cells , the more effective in motor learning for the Pavlovian EBC.
Edit intent: fluency
Original:  It is this found that, the more diverse in temporal recoding of GR cells , the more effective in motor learning for the Pavlovian EBC.
Revised:  It is this found that, the more various in temporal recoding of GR cells , the more effective in motor learning for the Pavlovian EBC.
Edit intent: fluency
Original:  It is this found that, the more diverse in temporal recoding of GR cells , the more effective in motor learning for the Pavlovian EBC.
Revised:  It is this found that, the more diverse in temporal recoding , the more effective in motor learning for the Pavlovian EBC.
Edit intent: clarity
Original:  It is this found that, the more diverse in temporal recoding of GR cells , the more effective in motor learning for the Pavlovian EBC.
Revised:  It is this found that, the more diverse in temporal recoding of GR cells , the more effective in learning for the Pavlovian EBC.
Edit intent: clarity
Original:  Building on that work, we show in this paper that every graph with no K_t minor is O(t (\log \log t)^{ 24 })-colorable.
Revised:  In combination with that work, we show in this paper that every graph with no K_t minor is O(t (\log \log t)^{ 24 })-colorable.
Edit intent: clarity
Original: We propose a new regularisation strategy within the classical ensemble Kalman inversion (EKI) framework for estimating parameters in PDEs.
Revised: We propose a new regularisation strategy for the classical ensemble Kalman inversion (EKI) framework for estimating parameters in PDEs.
Edit intent: clarity
Original:  The regularisation strategy consists of: (i) an adaptive choice for the regularisation /inflation parameter in the update formula in EKI, and (ii) criteria for the early stopping of the scheme.
Revised:  The regularisation strategy consists of: (i) an adaptive choice for the regularisation parameter in the update formula in EKI, and (ii) criteria for the early stopping of the scheme.
Edit intent: clarity
Original:  Our main contribution is the selection of the regularisation parameter which, in contrast to existing approaches, it does not rely on further parameters which often have severe effects on the efficiency of EKI.
Revised:  In contrast to existing approaches, it does not rely on further parameters which often have severe effects on the efficiency of EKI.
Edit intent: coherence
Original:  Our main contribution is the selection of the regularisation parameter which, in contrast to existing approaches, it does not rely on further parameters which often have severe effects on the efficiency of EKI.
Revised:  Our main contribution is the selection of the regularisation parameter which, in contrast to existing approaches, our parameter choice does not rely on further parameters which often have severe effects on the efficiency of EKI.
Edit intent: clarity
Original:  Our main contribution is the selection of the regularisation parameter which, in contrast to existing approaches, it does not rely on further parameters which often have severe effects on the efficiency of EKI.
Revised:  Our main contribution is the selection of the regularisation parameter which, in contrast to existing approaches, it does not rely on additional tuning parameters which often have severe effects on the efficiency of EKI.
Edit intent: clarity
Original:  We provide comparisons against a standard method  and demonstrate that the proposed method is  viable choice to address computational efficiency of EKI in practical/operational settings.
Revised:  We provide comparisons against a standard method of choice and demonstrate that the proposed method is viable choice to address computational efficiency of EKI in practical/operational settings.
Edit intent: clarity
Original:  We provide comparisons against a standard method  and demonstrate that the proposed method is  viable choice to address computational efficiency of EKI in practical/operational settings.
Revised:  We provide comparisons against a standard method and demonstrate that the proposed method is a viable choice to address computational efficiency of EKI in practical/operational settings.
Edit intent: fluency
Original: The anisotropic and heterogeneous N-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system.
Revised: The anisotropic and heterogeneous -dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system.
Edit intent: clarity
Original:  An investor competes with a benchmark of market and peer investors, expecting to outperform the benchmark and minimizing the \%proportion of initial capital.
Revised:  An investor competes with a benchmark of market and peer investors, expecting to outperform the benchmark and minimizing the initial capital.
Edit intent: clarity
Original:  It can be characterized as the smallest nonnegative continuous solution of a Cauchy problem.
Revised:  It can be characterized by the smallest nonnegative continuous solution of a Cauchy problem.
Edit intent: fluency
Original:  If L\subseteq\Delta_n^* is an infinite language such that for each u\in L there is v\in L with \vert \vert\vert v\vert\leq \exp^{k,\alpha}\vert u\vert then we call L a language with the \emph{growth bounded by} (k,\alpha)-tetration.
Revised:  If L\subseteq\Delta_n^* is an infinite language such that for each u\in L there is v\in L with \vert u\vert\vert v\vert\leq \exp^{k,\alpha}\vert u\vert then we call L a language with the \emph{growth bounded by} (k,\alpha)-tetration.
Edit intent: fluency
Original:  We show that there are 3k-3 context free languages L_1,L_2,\dots, L_{3k-3} over the alphabet \Sigma_{2k-1 with 2k-1 letters, an erasing alphabetical homomorphism \upsilon: 2k-1^*\rightarrow \Delta_1^*, a nonerasing alphabetical homomorphism \pi: }  \Delta_n^* \rightarrow \Delta_1^* such that the homomorphic image \upsilon(\left( i=1^{3k-3}L_i ) dissects the homomorphic image \pi(L ) \right)  .
Revised:  We show that there are context free languages L_1,L_2,\dots, L_{3k-3} over the alphabet \Sigma_{2k-1 with 2k-1 letters, an erasing alphabetical homomorphism \upsilon: 2k-1^*\rightarrow \Delta_1^*, a nonerasing alphabetical homomorphism \pi: } \Delta_n^* \rightarrow \Delta_1^* such that the homomorphic image \upsilon(\left( i=1^{3k-3}L_i ) dissects the homomorphic image \pi(L ) \right) .
Edit intent: clarity
Original:  We show that there are 3k-3 context free languages L_1,L_2,\dots, L_{3k-3} over the alphabet \Sigma_{2k-1 with 2k-1 letters, an erasing alphabetical homomorphism \upsilon: 2k-1^*\rightarrow \Delta_1^*, a nonerasing alphabetical homomorphism \pi: }  \Delta_n^* \rightarrow \Delta_1^* such that the homomorphic image \upsilon(\left( i=1^{3k-3}L_i ) dissects the homomorphic image \pi(L ) \right)  .
Revised:  We show that there are 3k-3 context free languages L_1,L_2,\dots, L_{3k-3} with 2k-1 letters, an erasing alphabetical homomorphism \upsilon: 2k-1^*\rightarrow \Delta_1^*, a nonerasing alphabetical homomorphism \pi: } \Delta_n^* \rightarrow \Delta_1^* such that the homomorphic image \upsilon(\left( i=1^{3k-3}L_i ) dissects the homomorphic image \pi(L ) \right) .
Edit intent: clarity
Original:  Such markets abstract online matching platforms ( for e.g. UpWork, TaskRabbit) and falls within the purview of matching bandit models introduced in Liu et al.
Revised:  Such markets abstract online matching platforms ( e.g. UpWork, TaskRabbit) and falls within the purview of matching bandit models introduced in Liu et al.
Edit intent: clarity
Original:  We design the first decentralized algorithm -%DIFDELCMD < \fullname%%% \;
Revised:  We design the first decentralized algorithm %DIFDELCMD < \fullname%%% \;
Edit intent: fluency
Original:  (%DIFDELCMD < \name%%%  ), for matching bandits under uniform valuation that does not require any knowledge of reward gaps or time horizon , and thus partially resolves an open question in \mbox{ matching_bandits0pt . }%DIFDELCMD < \name%%% \;
Revised:  (%DIFDELCMD < \name%%% ), for the agents, that does not require any knowledge of reward gaps or time horizon , and thus partially resolves an open question in \mbox{ matching_bandits0pt . }%DIFDELCMD < \name%%% \;
Edit intent: clarity
Original:  (%DIFDELCMD < \name%%%  ), for matching bandits under uniform valuation that does not require any knowledge of reward gaps or time horizon , and thus partially resolves an open question in \mbox{ matching_bandits0pt . }%DIFDELCMD < \name%%% \;
Revised:  (%DIFDELCMD < \name%%% ), for matching bandits under uniform valuation that does not require any knowledge of reward gaps or time horizon 0pt . }%DIFDELCMD < \name%%% \;
Edit intent: coherence
Original:  In each phasei, an agent first deletes dominated arms -- the arms preferred by agents ranked higher than itself.
Revised:  In each phasei, an agent first deletes dominated armsdominated arms -- the arms preferred by agents ranked higher than itself.
Edit intent: clarity
Original:  Finally, the preferred arm is broadcast in a decentralized fashion to other agents through {\em pure exploitation} in (N-1)K rounds with N agents and K arms.
Revised:  Finally, the preferred arm is broadcast in a decentralized fashion to other agents through {\em pure exploitation} 
Edit intent: clarity
Original:  Comparing the obtained reward with respect to the unique stable matching, we show that%DIFDELCMD < \name%%% \;
Revised:  %DIFDELCMD < \name%%% \;
Edit intent: coherence
Original:  For example, with NASGD , on CIFAR-10, our method designs and trains networks with an error rate of 4.06 in only 12 hours on a single GPU.
Revised:  For example, using NASGD on CIFAR-10, our method designs and trains networks with an error rate of 4.06 in only 12 hours on a single GPU.
Edit intent: fluency
Original: The inverse design of metamaterials is difficult due to a high-dimensional topological design space and presence of multiple local optima . Computational cost is even more demanding for design of multiscale metamaterial systems with aperiodic microstructures and spatially-varying or functionally gradient properties.
Revised: The inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space and presence of multiple local optima . Computational cost is even more demanding for design of multiscale metamaterial systems with aperiodic microstructures and spatially-varying or functionally gradient properties.
Edit intent: clarity
Original: The inverse design of metamaterials is difficult due to a high-dimensional topological design space and presence of multiple local optima . Computational cost is even more demanding for design of multiscale metamaterial systems with aperiodic microstructures and spatially-varying or functionally gradient properties.
Revised: The inverse design of metamaterials is difficult due to a high-dimensional topological design space , multiple local optima . Computational cost is even more demanding for design of multiscale metamaterial systems with aperiodic microstructures and spatially-varying or functionally gradient properties.
Edit intent: coherence
Original:  A deep neural network model consisting of a variational autoencoder (VAE) and a regressor for property prediction is trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous  and organized latent space.
Revised:  A variational autoencoder (VAE) and a regressor for property prediction is trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous and organized latent space.
Edit intent: clarity
Original:  A deep neural network model consisting of a variational autoencoder (VAE) and a regressor for property prediction is trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous  and organized latent space.
Revised:  A deep neural network model consisting of a variational autoencoder (VAE) and a regressor for property prediction are simultaneously trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous and organized latent space.
Edit intent: clarity
Original:  A deep neural network model consisting of a variational autoencoder (VAE) and a regressor for property prediction is trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous  and organized latent space.
Revised:  A deep neural network model consisting of a variational autoencoder (VAE) and a regressor for property prediction is trained on a large metamaterial database to map complex microstructures into a low-dimensional, continuous , and organized latent space.
Edit intent: fluency
Original:  First, the latent space of VAE provides a distance metric to measure shape similarity, enabling interpolation between microstructures and encoding meaningful patterns of variation in geometries and properties.
Revised:  First, the latent space of VAE provides a distance metric to measure shape similarity, enable interpolation between microstructures and encoding meaningful patterns of variation in geometries and properties.
Edit intent: fluency
Original:  First, the latent space of VAE provides a distance metric to measure shape similarity, enabling interpolation between microstructures and encoding meaningful patterns of variation in geometries and properties.
Revised:  First, the latent space of VAE provides a distance metric to measure shape similarity, enabling interpolation between microstructures and encode meaningful patterns of variation in geometries and properties.
Edit intent: fluency
Original:  Second, the vector operation can be further extended to form metamaterial families with  controlled gradation of mechanical properties .
Revised:  The vector operation is further extended to form metamaterial families with controlled gradation of mechanical properties .
Edit intent: coherence
Original:  Second, the vector operation can be further extended to form metamaterial families with  controlled gradation of mechanical properties .
Revised:  Second, the vector operation can be further extended to generate metamaterial families with controlled gradation of mechanical properties .
Edit intent: clarity
Original:  Second, the vector operation can be further extended to form metamaterial families with  controlled gradation of mechanical properties .
Revised:  Second, the vector operation can be further extended to form metamaterial families with a controlled gradation of mechanical properties .
Edit intent: coherence
Original: The 'Cheating Robot' is a simultaneous play, yet deterministic, version of Cops and Robbers  played on a finite, simple, connected graph.
Revised: The 'Cheating Robot' version of Cops and Robbers played on a finite, simple, connected graph.
Edit intent: coherence
Original: The 'Cheating Robot' is a simultaneous play, yet deterministic, version of Cops and Robbers  played on a finite, simple, connected graph.
Revised: The 'Cheating Robot' is a simultaneous play, yet deterministic, version of Cops and Robbers is played on a finite, simple, connected graph.
Edit intent: clarity
Original:  The robot knows where the cops will move on the next round and has the time to react .
Revised:  The players move in the same time period. However, before moving, the robot observes to which vertices the cops are moving and it is fast enough to complete its move in the time period .
Edit intent: coherence
Original:  The cops also know that the robot has inside information.
Revised:  The cops also know that the robot will use this information.
Edit intent: clarity
Original:  We illustrate the performance of the stabilized version of the ensemble Kalman filter by using test inverse problems from the literature and comparing it with the classical  formulation of the method.
Revised:  We illustrate the performance of the stabilized version by using test inverse problems from the literature and comparing it with the classical formulation of the method.
Edit intent: clarity
Original:  Our method is based on MultiAspect Graphs  (MAG) to represent the multidimensional networks and we show that well-known centrality algorithms can be straightforwardly adapted to the MAG environment.
Revised:  Our method is based on MultiAspect Graphs ~ (MAG) to represent the multidimensional networks and we show that well-known centrality algorithms can be straightforwardly adapted to the MAG environment.
Edit intent: fluency
Original:  Our simulations show that Simulated Annealing can outperform QAOA for BLLS at a circuit depth of p\leq3 for the probability of sampling the ground state.
Revised:  Our numerics show that Simulated Annealing can outperform QAOA for BLLS at a circuit depth of p\leq3 for the probability of sampling the ground state.
Edit intent: clarity