wanyu/IteraTeR_v2 huggingface dataset:
Original:  Tested on four datasets, our novel results demonstrate that deep learning methods can be applied directly also to high dimensional non-grid like data, while learning from a small amount of labeled examples with imbalanced classes and achieving better accuracy than the traditional two phases approach . Moreover, we have been able to create sparse MLP models with over one million neurons and to train them on a typical laptop without GPU .
Revised:  Tested on four datasets, our novel results demonstrate that deep learning methods can be applied directly also to high dimensional non-grid like data, while learning from a small amount of labeled examples with imbalanced classes and achieving better accuracy than the traditional two phases approaches . Moreover, we have been able to create sparse MLP models with over one million neurons and to train them on a typical laptop without GPU .
Edit intent: fluency
Original:  Tested on four datasets, our novel results demonstrate that deep learning methods can be applied directly also to high dimensional non-grid like data, while learning from a small amount of labeled examples with imbalanced classes and achieving better accuracy than the traditional two phases approach . Moreover, we have been able to create sparse MLP models with over one million neurons and to train them on a typical laptop without GPU .
Revised:  Tested on four datasets, our novel results demonstrate that deep learning methods can be applied directly also to high dimensional non-grid like data, while learning from a small amount of labeled examples with imbalanced classes and achieving better accuracy than the traditional two phases approach . Moreover, we have been able to create truly sparse MultiLayer Perceptrons (MLPs) models with over one million neurons and to train them on a typical laptop without GPU .
Edit intent: clarity
Original:  We also discuss how to introduce various constraints on the investor's portfolio and  temporary quadratic transaction costs in both discrete and continuous time, provide Monte Carlo simulations of the previous strategies  , and describe further  extensions of our work.
Revised:  We also discuss how to introduce various constraints on the investor's portfolio and temporary quadratic transaction costs , provide extensive Monte Carlo simulations of the previous strategies , and describe further extensions of our work.
Edit intent: clarity
Original:  Previous modeling of one such two-component system - the pyrenoid, an organelle found in algae and plants - surprisingly revealed that phase separation is suppressed for certain combinations of numbers of binding sites.
Revised:  Previous biologically-motivated modeling of such a two-component system - the pyrenoid, an organelle found in algae and plants - surprisingly revealed that phase separation is suppressed for certain combinations of numbers of binding sites.
Edit intent: clarity
Original:  Previous modeling of one such two-component system - the pyrenoid, an organelle found in algae and plants - surprisingly revealed that phase separation is suppressed for certain combinations of numbers of binding sites.
Revised:  Previous modeling of one such two-component system surprisingly revealed that phase separation is suppressed for certain combinations of numbers of binding sites.
Edit intent: clarity
Original: We present criteria on the existence of telescopers for trivariate rational functions in four mixed cases, in which discrete and continuous variables appear simultaneously .
Revised: We present criteria on the existence of telescopers for rational functions in four mixed cases, in which discrete and continuous variables appear simultaneously .
Edit intent: clarity
Original:  We reduce the existence problem in the trivariate case to the exactness testing problem, the separation problem and the existence problem in the bivariate case .
Revised:  We reduce the existence problem from the trivariate case to the exactness testing problem, the separation problem and the existence problem in the bivariate case .
Edit intent: fluency
Original:  We reduce the existence problem in the trivariate case to the exactness testing problem, the separation problem and the existence problem in the bivariate case .
Revised:  We reduce the existence problem in the trivariate case to the bivariate case and some related problems .
Edit intent: clarity
Original:  The existence criteria we present help us determine the termination of Zeilberger's algorithm for the input functions studied in this paper .
Revised:  The existence criteria given in this paper enable us to determine the termination of Zeilberger's algorithm for the input functions studied in this paper .
Edit intent: clarity
Original:  In this paper, a new queuing model for the Tactile Internet is proposed for the cloud radio access network ( C-RAN ) architecture of the next generation wireless networks, e.g., fifth generation wireless networks (5G), assisted via power domain non-orthogonal multiple access (PD-NOMA) technology.
Revised:  In this paper, a new queuing model for the TI is proposed for the cloud radio access network ( C-RAN ) architecture of the next generation wireless networks, e.g., fifth generation wireless networks (5G), assisted via power domain non-orthogonal multiple access (PD-NOMA) technology.
Edit intent: clarity
Original:  In this paper, a new queuing model for the Tactile Internet is proposed for the cloud radio access network ( C-RAN ) architecture of the next generation wireless networks, e.g., fifth generation wireless networks (5G), assisted via power domain non-orthogonal multiple access (PD-NOMA) technology.
Revised:  In this paper, a new queuing model for the Tactile Internet is proposed for the cloud radio access network ( CRAN ) architecture of the next generation wireless networks, e.g., fifth generation wireless networks (5G), assisted via power domain non-orthogonal multiple access (PD-NOMA) technology.
Edit intent: clarity
Original:  In this paper, a new queuing model for the Tactile Internet is proposed for the cloud radio access network ( C-RAN ) architecture of the next generation wireless networks, e.g., fifth generation wireless networks (5G), assisted via power domain non-orthogonal multiple access (PD-NOMA) technology.
Revised:  In this paper, a new queuing model for the Tactile Internet is proposed for the cloud radio access network ( C-RAN ) architecture of the NGWN by applying power domain non-orthogonal multiple access (PD-NOMA) technology.
Edit intent: clarity
Original:  This modelincludes both the radio remote head (RRH) and baseband processing unit (BBU) queuing delays for each end to end (E2E) connection between a pair of tactile users.
Revised:  In this model, we consider both the radio remote head (RRH) and baseband processing unit (BBU) queuing delays for each end to end (E2E) connection between a pair of tactile users.
Edit intent: clarity
Original:  This modelincludes both the radio remote head (RRH) and baseband processing unit (BBU) queuing delays for each end to end (E2E) connection between a pair of tactile users.
Revised:  This modelincludes both the radio remote head (RRH) and baseband processing unit (BBU) queuing delays for each end-to-end (E2E) connection between a pair of tactile users.
Edit intent: fluency
Original:  For this setup, with the aim to minimize the transmit power of users subject to guaranteeing tolerable delay of users, and fronthaul and access limitations , we formulate a resource allocation  problem .
Revised:  In our setup, to minimize the transmit power of users subject to guaranteeing tolerable delay of users, and fronthaul and access limitations , we formulate a resource allocation problem .
Edit intent: clarity
Original:  For this setup, with the aim to minimize the transmit power of users subject to guaranteeing tolerable delay of users, and fronthaul and access limitations , we formulate a resource allocation  problem .
Revised:  For this setup, with the aim to minimize the transmit power of users subject to guaranteeing an acceptable delay of users, and fronthaul and access limitations , we formulate a resource allocation problem .
Edit intent: fluency
Original:  For this setup, with the aim to minimize the transmit power of users subject to guaranteeing tolerable delay of users, and fronthaul and access limitations , we formulate a resource allocation  problem .
Revised:  For this setup, with the aim to minimize the transmit power of users subject to guaranteeing tolerable delay of users, and fronthaul and access constraints , we formulate a resource allocation problem .
Edit intent: fluency
Original:  Since the proposed optimization problem is highly non-convex,  to solve it in an efficient manner , we utilize diverse transformation techniques such as successive convex approximation (SCA) and difference of two convex functions (DC).
Revised:  Since the proposed optimization problem is highly non-convex, in order to solve it in an efficient manner , we utilize diverse transformation techniques such as successive convex approximation (SCA) and difference of two convex functions (DC).
Edit intent: coherence
Original:  Since the proposed optimization problem is highly non-convex,  to solve it in an efficient manner , we utilize diverse transformation techniques such as successive convex approximation (SCA) and difference of two convex functions (DC).
Revised:  Since the proposed optimization problem is highly non-convex, to solve it , we utilize diverse transformation techniques such as successive convex approximation (SCA) and difference of two convex functions (DC).
Edit intent: clarity
Original:  Simulation results reveal that by dynamic adjustment of the access and fronthaul delays, transmit power can be saved compared to the case of fixed approach per each transmission session .
Revised:  Simulation results reveal that by dynamic adjustment of the access and fronthaul delays, transmit power reduces in comparison with the fixed approach per each transmission session .
Edit intent: clarity
Original:  Simulation results reveal that by dynamic adjustment of the access and fronthaul delays, transmit power can be saved compared to the case of fixed approach per each transmission session .
Revised:  Simulation results reveal that by dynamic adjustment of the access and fronthaul delays, transmit power can be saved compared to the case of fixed approach per each connection .
Edit intent: clarity
Original:  Also, the energy efficiency of orthogonal frequency division multiple access ( OFDM) and NOMA are compared for our setup.
Revised:  Also, energy efficiency of orthogonal frequency division multiple access ( OFDM) and NOMA are compared for our setup.
Edit intent: fluency
Original: We consider a double-auction mechanism, which was recently proposed in the context of a mobile data-offloading market.
Revised: We consider a double-auction mechanism, which was recently proposed in the context of rate allocation in mobile data-offloading market.
Edit intent: clarity
Original:  A system-designer decomposes the problem into a network problem and agent problems.
Revised:  A network-manager decomposes the problem into a network problem and agent problems.
Edit intent: clarity
Original:  Agents' payoffs and costs are then determined by the allocations and prices set by the system designer . Under this design, so long as the agents do not anticipate the effect of their actions , a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the system utility .
Revised:  Agents' payoffs and costs are then determined by the allocations and prices set by the network-manager . Under this design, so long as the agents do not anticipate the effect of their actions , a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the system utility .
Edit intent: clarity
Original:  Agents' payoffs and costs are then determined by the allocations and prices set by the system designer . Under this design, so long as the agents do not anticipate the effect of their actions , a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the system utility .
Revised:  Agents' payoffs and costs are then determined by the allocations and prices set by the system designer . Under this design, so long as the agents do not anticipate the effect of their actions , a competitive equilibrium exists as a solution to the network and agent problems, and this equilibrium optimizes the sum utility of all agents .
Edit intent: clarity
Original:  However, this design fails when the agents are  strategic (price-anticipating).
Revised:  However, this design fails when the agents are all strategic (price-anticipating).
Edit intent: coherence
Original:  The presence of strategic supplying agents drives the system to an undesirable equilibrium with zero participation resulting in an efficiency loss of 100\%.
Revised:  Specifically, the presence of a strategic link-supplier drives the system to an undesirable equilibrium with zero participation resulting in an efficiency loss of 100\%.
Edit intent: clarity
Original:  This is in stark contrast to the setting when link-suppliers are not strategic : the efficiency loss is  at most 34\% when the users alone are strategic .
Revised:  This is in stark contrast to the setting when link-suppliers are not strategic : the efficiency loss is known to be at most 34\% when the users alone are strategic .
Edit intent: clarity
Original:  This is in stark contrast to the setting when link-suppliers are not strategic : the efficiency loss is  at most 34\% when the users alone are strategic .
Revised:  This is in stark contrast to the setting when link-suppliers are not strategic : the efficiency loss is at most 34\% .
Edit intent: clarity
Original:  The paper then proposes a Stackelberg game modification with asymmetric information structures for suppliers and users in order to alleviate the efficiency loss problem.
Revised:  The paper then proposes a Stackelberg game modification where the efficiency loss problem.
Edit intent: clarity
Original:  In particular, we study how stiffness varies with 1) class membership, 2) distance between data points ( in the input space as well as in latent spaces) , 3) training iteration, and 4) learning rate.
Revised:  In particular, we study how stiffness depends on 1) class membership, 2) distance between data points ( in the input space as well as in latent spaces) , 3) training iteration, and 4) learning rate.
Edit intent: clarity
Original:  In particular, we study how stiffness varies with 1) class membership, 2) distance between data points ( in the input space as well as in latent spaces) , 3) training iteration, and 4) learning rate.
Revised:  In particular, we study how stiffness varies with 1) class membership, 2) distance between data points in the input space as well as in latent spaces) , 3) training iteration, and 4) learning rate.
Edit intent: fluency
Original:  In particular, we study how stiffness varies with 1) class membership, 2) distance between data points ( in the input space as well as in latent spaces) , 3) training iteration, and 4) learning rate.
Revised:  In particular, we study how stiffness varies with 1) class membership, 2) distance between data points ( in the input space , 3) training iteration, and 4) learning rate.
Edit intent: clarity
Original:  We empirically study the evolution of stiffness on MNIST, FASHION MNIST, CIFAR-10 and CIFAR-100 using fully-connected and convolutional neural networks.
Revised:  We experiment on MNIST, FASHION MNIST, CIFAR-10 and CIFAR-100 using fully-connected and convolutional neural networks.
Edit intent: clarity
Original:  We empirically study the evolution of stiffness on MNIST, FASHION MNIST, CIFAR-10 and CIFAR-100 using fully-connected and convolutional neural networks.
Revised:  We empirically study the evolution of stiffness on MNIST, FASHION MNIST, and CIFAR-10 using fully-connected and convolutional neural networks.
Edit intent: clarity
Original: We investigate neural network training and generalization using the concept of  stiffness.
Revised: In this paper we develop a new perspective on generalization of neural networks by proposing and investigating the concept of stiffness.
Edit intent: clarity
Original:  We experiment on MNIST, FASHION MNIST, and CIFAR-10  using fully-connected and convolutional neural networks  .
Revised:  We present experiments on MNIST, FASHION MNIST, and CIFAR-10 using fully-connected and convolutional neural networks .
Edit intent: clarity
Original:  In addition, we measure how stiffness between two data points depends on their mutual input space distance, and establish the concept of a dynamical critical length that characterizes the distance over which data points react similarly to gradient updates.
Revised:  In addition, we measure how stiffness between two data points depends on their mutual input-space distance, and establish the concept of a dynamical critical length that characterizes the distance over which data points react similarly to gradient updates.
Edit intent: fluency
Original: Bipartite Envy-Free Matching (BEFM) is a relaxation of perfect matching.
Revised: Envy-free matching is a relaxation of perfect matching.
Edit intent: coherence
Original:  In a bipartite graph with parts X and Y, a BEFM is a matching of some vertices in X to some vertices in Y, such that each unmatched vertex in X is not adjacent to any matched vertex in Y (so the unmatched vertices do not "envy" the matched ones).
Revised:  In a bipartite graph with parts X and Y, a BEFM is a matching of some vertices in X to some vertices in Y, such that each unmatched vertex in X is not adjacent to any matched vertex in Y (so the unmatched vertices do not `envy' the matched ones).
Edit intent: fluency
Original:  In a bipartite graph with parts X and Y,an envy-free matching is a matching of some vertices in X to some vertices in Y, such that each unmatched vertex in X is not adjacent to any matched vertex in Y (so the unmatched vertices do not `envy' the matched ones).
Revised:  In a bipartite graph with parts X and Y,an envy-free if no unmatched vertex in X is not adjacent to any matched vertex in Y (so the unmatched vertices do not `envy' the matched ones).
Edit intent: clarity
Original:  In a bipartite graph with parts X and Y,an envy-free matching is a matching of some vertices in X to some vertices in Y, such that each unmatched vertex in X is not adjacent to any matched vertex in Y (so the unmatched vertices do not `envy' the matched ones).
Revised:  In a bipartite graph with parts X and Y,an envy-free matching is a matching of some vertices in X to some vertices in Y, such that each unmatched vertex in X is adjacent to a mathced vertex in Y (so the unmatched vertices do not `envy' the matched ones).
Edit intent: clarity
Original:  We show how envy-free matchings can be used in various fair division problems with either continuous resources ( ``cakes'' ) or discrete ones.
Revised:  We show how envy-free matchings can be used in various fair division problems with either continuous resources ( "cakes" ) or discrete ones.
Edit intent: fluency
Original:  In particular, we show a symmetric algorithm for proportional cake-cutting, and an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete objects\lfloor \rfloor  among n agents.
Revised:  In particular, we show a symmetric algorithm for proportional cake-cutting, an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete objects\lfloor \rfloor among n agents.
Edit intent: coherence
Original:  In particular, we show a symmetric algorithm for proportional cake-cutting, and an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete objects\lfloor \rfloor  among n agents.
Revised:  In particular, we show a symmetric algorithm for proportional cake-cutting, and an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete goods, and an algorithm for 1-out-of-\lfloor \rfloor among n agents.
Edit intent: clarity
Original: A matching in a bipartite graph G:=(X + Y ,E) is said to be envy-free if no unmatched vertex in X is  adjacent to a mathced vertex in Y. Every perfect matching is envy-free, but envy-free matchings may exist even when perfect matchings do not.
Revised: A matching in a bipartite graph with parts X and Y is called *envy-free* if no unmatched vertex in X is adjacent to a mathced vertex in Y. Every perfect matching is envy-free, but envy-free matchings may exist even when perfect matchings do not.
Edit intent: clarity
Original: A matching in a bipartite graph G:=(X + Y ,E) is said to be envy-free if no unmatched vertex in X is  adjacent to a mathced vertex in Y. Every perfect matching is envy-free, but envy-free matchings may exist even when perfect matchings do not.
Revised: A matching in a bipartite graph G:=(X + Y ,E) is said to be envy-free if no unmatched vertex in X is a adjacent to a mathced vertex in Y. Every perfect matching is envy-free, but envy-free matchings may exist even when perfect matchings do not.
Edit intent: fluency
Original: A matching in a bipartite graph G:=(X + Y ,E) is said to be envy-free if no unmatched vertex in X is  adjacent to a mathced vertex in Y. Every perfect matching is envy-free, but envy-free matchings may exist even when perfect matchings do not.
Revised: A matching in a bipartite graph G:=(X + Y ,E) is said to be envy-free if no unmatched vertex in X is adjacent to a matched vertex in Y. Every perfect matching is envy-free, but envy-free matchings may exist even when perfect matchings do not.
Edit intent: fluency
Original: A matching in a bipartite graph G:=(X + Y ,E) is said to be envy-free if no unmatched vertex in X is  adjacent to a mathced vertex in Y. Every perfect matching is envy-free, but envy-free matchings may exist even when perfect matchings do not.
Revised: A matching in a bipartite graph G:=(X + Y ,E) is said to be envy-free if no unmatched vertex in X is adjacent to a mathced vertex in Y. Every perfect matching is envy-free, but envy-free matchings exist even when perfect matchings do not.
Edit intent: clarity
Original:  We show how envy-free matchings can be used in various fair division problems with either continuous resources ( "cakes" ) or discrete ones.
Revised:  We show how envy-free matchings can be used in various fair division problems with either continuous resources ( ``cakes'' ) or discrete ones.
Edit intent: fluency
Original:  In particular, we show a symmetric algorithm for proportional cake-cutting, an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete goods, and an algorithm for 1-out-of-%DIFDELCMD < \lfloor %%%  2n/3 %DIFDELCMD < \rfloor %%%  maximin-share allocation of discrete bads (chores) among n agents.
Revised:  In particular, we propose a symmetric algorithm for proportional cake-cutting, an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete goods, and an algorithm for 1-out-of-%DIFDELCMD < \lfloor %%% 2n/3 %DIFDELCMD < \rfloor %%% maximin-share allocation of discrete bads (chores) among n agents.
Edit intent: clarity
Original:  In particular, we show a symmetric algorithm for proportional cake-cutting, an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete goods, and an algorithm for 1-out-of-%DIFDELCMD < \lfloor %%%  2n/3 %DIFDELCMD < \rfloor %%%  maximin-share allocation of discrete bads (chores) among n agents.
Revised:  In particular, we show a symmetric algorithm for proportional cake-cutting, an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete goods, and an algorithm for %DIFDELCMD < \lfloor %%% 2n/3 %DIFDELCMD < \rfloor %%% maximin-share allocation of discrete bads (chores) among n agents.
Edit intent: fluency