wanyu/IteraTeR_v2 huggingface dataset:
Original:  This family -- exponential family RBM (Exp-RBM) -- is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearities for neurons . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBMs can learn useful representations using novel stochastic units.
Revised:  This family -- exponential family RBM (Exp-RBM) , is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearities for neurons . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBMs can learn useful representations using novel stochastic units.
Edit intent: fluency
Original:  This family -- exponential family RBM (Exp-RBM) -- is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearities for neurons . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBMs can learn useful representations using novel stochastic units.
Revised:  This family -- exponential family RBM (Exp-RBM) -- is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearity for each neuron . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBMs can learn useful representations using novel stochastic units.
Edit intent: clarity
Original:  This family -- exponential family RBM (Exp-RBM) -- is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearities for neurons . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBMs can learn useful representations using novel stochastic units.
Revised:  This family -- exponential family RBM (Exp-RBM) -- is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearities for neurons . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBM can learn useful representations using novel stochastic units.
Edit intent: clarity
Original:  In their simplest version, a fire spreads from one fixed vertex step by step from burning to adjacent non-burning vertices, and at each time step B-many non-burning vertices can be protected from catching fire.
Revised:  In their simplest version, a fire spreads from one fixed vertex step by step from burning to adjacent non-burning vertices, and at each time step , B many non-burning vertices can be protected from catching fire.
Edit intent: fluency
Original:  The Firefighter problem asks, for a given B, to maximize the number of vertices that will not catch fire, whereas RMFC (on a tree) asks to find the smallest B which allows for saving all leaves of the tree.
Revised:  The Firefighter problem asks, for a given B, to maximize the number of vertices that will not catch fire, whereas RMFC (on a tree) asks to find the smallest B that allows for saving all leaves of the tree.
Edit intent: fluency
Original:  Prior to this work, the best known approximation ratios were an O(1)-approximation for the Firefighter problem and an O(\log^* n)-approximation for RMFC, both being LP-based and  matching the integrality gaps of two natural LP relaxations.
Revised:  Prior to this work, the best known approximation ratios were an O(1)-approximation for the Firefighter problem and an O(\log^* n)-approximation for RMFC, both being LP-based and essentially matching the integrality gaps of two natural LP relaxations.
Edit intent: clarity
Original:  Our results are obtained through a combination of the LP with several new techniques, which allow for efficiently enumerating subsets of super-constant size of a good solution to reduce the integrality gap of the LPs.
Revised:  Our results are obtained through a combination of the known LPs with several new techniques, which allow for efficiently enumerating subsets of super-constant size of a good solution to reduce the integrality gap of the LPs.
Edit intent: clarity
Original:  Our results are obtained through a combination of the LP with several new techniques, which allow for efficiently enumerating subsets of super-constant size of a good solution to reduce the integrality gap of the LPs.
Revised:  Our results are obtained through a combination of the LP with several new techniques, which allow for efficiently enumerating subsets of super-constant size of a good solution to obtain stronger LPs.
Edit intent: clarity
Original:  This is a continuation of a recent work in which it is introduced and studied a natural discrete version of m by considering the existence of\emph{complete Kneser transversals (i.e., (d- \lambda) -transversals L to the convex hulls of all k-sets and L containing (d-\lambda)+1 points of the given set of points) .
Revised:  This is a continuation of a recent work in which it is introduced and studied a natural discrete version of m by considering the existence of\emph{complete Kneser transversals \lambda) -transversals L to the convex hulls of all k-sets and L containing (d-\lambda)+1 points of the given set of points) .
Edit intent: coherence
Original:  This is a continuation of a recent work in which it is introduced and studied a natural discrete version of m by considering the existence of\emph{complete Kneser transversals (i.e., (d- \lambda) -transversals L to the convex hulls of all k-sets and L containing (d-\lambda)+1 points of the given set of points) .
Revised:  This is a continuation of a recent work in which it is introduced and studied a natural discrete version of m by considering the existence of\emph{complete Kneser transversals (i.e., (d- \lambda) -transversals L to the convex hull of all k-sets and L containing (d-\lambda)+1 points of the given set of points) .
Edit intent: fluency
Original: In this paper ,  we introduce and study the notions of stability andunstability .
Revised: In this paper , we introduce the notions of stability andunstability .
Edit intent: clarity
Original: In this paper ,  we introduce and study the notions of stability andunstability .
Revised: In this paper , we introduce and study the notions of andunstability .
Edit intent: fluency
Original: In this paper ,  we introduce and study the notions of stability andunstability .
Revised: In this paper , we introduce and study the notions of stability unstability .
Edit intent: fluency
Original: In this paper ,  we introduce and study the notions of stability andunstability .
Revised: In this paper , we introduce and study the notions of stability and .
Edit intent: fluency
Original: Let k,d,\lambda \geqslant 1 be integers with d\geqslant \lambda and let X \subset\mathbb{R be a finite set  . A (d-\lambda)-plane L transversal to the convex hull of all k-sets of X is called Kneser transversal.
Revised: Let k,d,\lambda \geqslant 1 be integers with d\geqslant \lambda and let X be a finite set . A (d-\lambda)-plane L transversal to the convex hull of all k-sets of X is called Kneser transversal.
Edit intent: coherence
Original: Let k,d,\lambda \geqslant 1 be integers with d\geqslant \lambda and let X \subset\mathbb{R be a finite set  . A (d-\lambda)-plane L transversal to the convex hull of all k-sets of X is called Kneser transversal.
Revised: Let k,d,\lambda \geqslant 1 be integers with d\geqslant \lambda and let X \subset\mathbb{R be a finite set . A (d-\lambda)-plane L transversal to the convex hulls of all k-sets of X is called Kneser transversal.
Edit intent: fluency
Original:  The latter leads to new upper and lower bounds (in the case when \lambda =2 and 3) for m(k,d,\lambda) defined as the maximum positive integer n such that every set of n points (not necessarily in general position) in R^{d} admitting a Kneser transversal.
Revised:  The latter leads to new upper and lower bounds (in the case when \lambda =2 and 3) for m(k,d,\lambda) defined as the maximum positive integer n such that every set of n points (not necessarily in general position) in R^{d} admit a Kneser transversal.
Edit intent: fluency
Original:  We survey five types of coresets and sketches: shape-fitting, density estimation, high-dimensional vectors, high- dimensional point sets / matrices, and clustering.
Revised:  We survey five types of coresets and sketches: shape-fitting, density estimation, high-dimensional vectors, high-dimensional point sets / matrices, and clustering.
Edit intent: fluency
Original: We study the L1 median for locationally uncertain points with discrete distributions.
Revised: Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions.
Edit intent: clarity
Original:  However given the probabilistic nature of this data , there is a distribution describing the L1 median, not a single location .
Revised:  However given the probabilistic nature of uncertain data makes it challenging to compute such estimators, since the true value of the estimator is now described by a distribution rather than a single point .
Edit intent: clarity
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised:  1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: clarity
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised: Given n integers x %DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: clarity
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised: Given n integers x 1%DIFDELCMD < ]%%% n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: coherence
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised: Given n integers x 1%DIFDELCMD < ]%%% ,...,x %DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: fluency
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: coherence
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x %DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: fluency
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: coherence
Original: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x k%DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Revised: Given n integers x 1%DIFDELCMD < ]%%% ,...,x n%DIFDELCMD < ]%%% , it is obvious that calculating the n LSB bits of the integer part of prod(2^(n*x k%DIFDELCMD < ]%%% )+2^(-n*x %DIFDELCMD < ]%%% )) has polynomial time complexity if the integers are supplied in unary radix.
Edit intent: fluency
Original: Infectious diseases are notorious for their complex dynamics, which make it difficult to fit models and test hypotheses.
Revised: Infectious diseases are notorious for their complex dynamics, which make it difficult to fit models to test hypotheses.
Edit intent: fluency
Original:  Methods based on state-space reconstruction have been claimed to infer causal interactions in noisy, nonlinear dynamical systems without the need for an underlying model .
Revised:  Methods based on state-space reconstruction have been proposed to infer causal interactions in noisy, nonlinear dynamical systems without the need for an underlying model .
Edit intent: clarity
Original:  Methods based on state-space reconstruction have been claimed to infer causal interactions in noisy, nonlinear dynamical systems without the need for an underlying model .
Revised:  Methods based on state-space reconstruction have been claimed to infer causal interactions in noisy, nonlinear dynamical systems .
Edit intent: clarity
Original:  Traditional CCM is extremely sensitive to periodic fluctuations, often inferring interactions between independent strains that oscillate with similar frequencies.
Revised:  Traditional CCM is extremely sensitive to periodic fluctuations, inferring interactions between independent strains that oscillate with similar frequencies.
Edit intent: clarity
Original:  This sensitivity vanishes with alternative criteria for inferring causality , which can identify the correct direction of interactions between strains that are nearly identical .
Revised:  This sensitivity vanishes with alternative criteria for inferring causality .
Edit intent: clarity
Original:  This sensitivity is problematic because methods to gauge noise and non-steady-state behavior in natural systems, including the quality of reconstructed attractors that underlie cross-mapping , are not well developed .
Revised:  This sensitivity is problematic because it remains challenging to measure (and even define) noise and nonequilibrium behavior in natural systems, including the quality of reconstructed attractors that underlie cross-mapping , are not well developed .
Edit intent: clarity
Original:  This sensitivity is problematic because methods to gauge noise and non-steady-state behavior in natural systems, including the quality of reconstructed attractors that underlie cross-mapping , are not well developed .
Revised:  This sensitivity is problematic because methods to gauge noise and non-steady-state behavior in natural systems, including the quality of reconstructed attractors that underlie cross-mapping .
Edit intent: clarity
Original:  We illustrate these challenges by analyzing time series of six reportable childhood infections in New York City and Chicago during the pre-vaccine era.
Revised:  We illustrate these challenges by analyzing time series of reportable childhood infections in New York City and Chicago during the pre-vaccine era.
Edit intent: clarity
Original:  The inconsistent results suggest that noise and nonequilibrium behavior may be pervasive obstacles to the application of causal inference based on state-space reconstruction in natural systems .
Revised:  We comment on the statistical and conceptual challenges that limit the use of state-space reconstruction in natural systems .
Edit intent: clarity
Original:  The inconsistent results suggest that noise and nonequilibrium behavior may be pervasive obstacles to the application of causal inference based on state-space reconstruction in natural systems .
Revised:  The inconsistent results suggest that noise and nonequilibrium behavior may be pervasive obstacles to the application of causal inference based on state-space reconstruction in causal inference .
Edit intent: clarity
Original:  Traditional CCM is extremely sensitive to periodic fluctuations, inferring interactions between independent strains that oscillate with similar frequencies.
Revised:  The original method of CCM is extremely sensitive to periodic fluctuations, inferring interactions between independent strains that oscillate with similar frequencies.
Edit intent: clarity
Original:  However, CCM in general is sensitive to high levels of process noise and deviations from steady-state dynamics .
Revised:  However, CCM remains sensitive to high levels of process noise and deviations from steady-state dynamics .
Edit intent: clarity
Original:  This sensitivity is problematic because it remains challenging to measure (and even define) noise and nonequilibrium behavior in natural systems, including the quality of reconstructed attractors that underlie cross-mapping.
Revised:  This sensitivity is problematic because it remains challenging to gauge noise and dynamical changes in natural systems, including the quality of reconstructed attractors that underlie cross-mapping.
Edit intent: clarity
Original:  We describe simulation results that provide overall insight into sparse representations as well as two primary results.
Revised:  We describe simulation results that provide further insight into sparse representations as well as two primary results.
Edit intent: clarity
Original:  Our model neuron matches many of the known properties of pyramidal neurons.
Revised:  Our model matches many of the known properties of pyramidal neurons.
Edit intent: clarity
Original:  As such the theory provides a unified and practical mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.
Revised:  As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.
Edit intent: clarity
Original: This paper focuses on the coordinate update method, which is useful for solving large-sized problems involving linear and nonlinear mappings, and smooth and nonsmooth functions.
Revised: This paper focuses on coordinate update methods, which are useful for solving large-sized problems involving linear and nonlinear mappings, and smooth and nonsmooth functions.
Edit intent: fluency
Original:  It decomposes a problem into simple subproblems, where each subproblem updates one, or a small block of, variables .
Revised:  It decomposes a problem into simple subproblems, where each updates one, or a small block of, variables .
Edit intent: fluency
Original:   The obtained algorithms are scalable to very large instances through parallel and even asynchronous computing.
Revised:  The obtained algorithms are scalable to large instances through parallel and even asynchronous computing.
Edit intent: clarity
Original:  The great performance of coordinate update methods depends on solving simple subproblems .
Revised:  The great performance of coordinate update methods depends on solving simple sub-problems .
Edit intent: fluency
Original:  To derive simple subproblems for several new classes of applications, this paper systematically studies coordinate friendly operators that perform low-cost coordinate updates.
Revised:  To derive simple subproblems for several new classes of applications, this paper systematically studies coordinate-friendly operators that perform low-cost coordinate updates.
Edit intent: fluency
Original: The performance of deep neural networks is  sensitive to the setting of their hyperparameters (e. g. L2-norm panelties).
Revised: The performance of deep neural networks is well known to be sensitive to the setting of their hyperparameters (e. g. L2-norm panelties).
Edit intent: clarity
Original: The performance of deep neural networks is  sensitive to the setting of their hyperparameters (e. g. L2-norm panelties).
Revised: The performance of deep neural networks is sensitive to the setting of their hyperparameters .
Edit intent: coherence
Original:  Recent advances in reverse-mode automatic differentiation have made it possible to optimize hyperparameters with gradients.
Revised:  Recent advances in reverse-mode automatic differentiation allow for optimizing hyperparameters with gradients.
Edit intent: clarity
Original:  The standard way of computing these gradients involves a forward and backward pass , which is similar to its cousin, back-propagation, used for training weights of neural networks .
Revised:  The standard way of computing these gradients involves a forward and backward pass of computations .
Edit intent: clarity
Original:  Experiments carried out on MNIST dataset show that our approach reduces memory consumption by  orders of magnitude  without sacrificing its effectiveness.
Revised:  Experiments on MNIST dataset show that our approach reduces memory consumption by orders of magnitude without sacrificing its effectiveness.
Edit intent: clarity
Original: The performance of deep neural networks is well known to be sensitive to the setting of their hyperparameters.
Revised: The performance of deep neural networks is well-known to be sensitive to the setting of their hyperparameters.
Edit intent: fluency
Original:  In this work we propose a new method, DrMAD, to distill the knowledge of the forward pass into an shortcut path, through which we approximately reverse the training trajectory.
Revised:  In this work we propose a new method, DrMAD, to distill the knowledge of the forward pass into a shortcut path, through which we approximately reverse the training trajectory.
Edit intent: fluency
Original:  Experiments on MNIST dataset show that DrMAD reduces memory consumption by 4 orders of magnitude for optimizing hyperparameters without sacrificing its effectiveness.
Revised:  Experiments on MNIST dataset show that DrMAD reduces memory consumption by 4 orders of magnitude for optimizing hyperparameters with minimal compromise to its effectiveness.
Edit intent: clarity
Original:  To the best of our knowledge, DrMAD is the first research attempt to automatically tune hundreds of thousands of hyperparameters of deep neural networks in practice.
Revised:  To the best of our knowledge, DrMAD is the first research attempt to automatically tune thousands of hyperparameters of deep neural networks in practice.
Edit intent: clarity
Original:  To the best of our knowledge, DrMAD is the first research attempt to  automatically tune thousands of hyperparameters of deep neural networks in practice .
Revised:  To the best of our knowledge, DrMAD is the first research attempt to automatically tune thousands of hyperparameters of deep neural networks .
Edit intent: clarity