wanyu/IteraTeR_v2 huggingface dataset:
Original:  We prove that the  branch-depth of the matroid defined by the columns of the constraint matrixis equal to the minimum tree-depth of a row-equivalent matrix, and we strengthen the fixed parameter algorithm for integer programs with bounded tree-depth by showing that integer programs whose matrix has branch-depth d and largest entry D are solvable in time h(d ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Revised:  We prove that the branch-depth of the matroid defined by the columns of the constraint matrixis equal to the minimum tree-depth of a row-equivalent matrix, and we strengthen the fixed parameter algorithm for integer programs with bounded tree-depth . Finally, we use these results to obtain an algorithm for integer programming running in time g(d* ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Edit intent: clarity
Original:  most other proofs involve formulating approximate degree as a linear program and exhibiting an explicit dual witness .
Revised:  most other proofs involve the more complicated formulation of approximate degree as a linear program and exhibiting an explicit dual witness .
Edit intent: clarity
Original:  Our proof relies on a symmetrization technique involving Laurent polynomials (polynomials with negative exponents) that was previously introduced by Aaronson, Kothari, Kretschmer, and Thaler [AKKT19].
Revised:  Our proof also demonstrates the power of a symmetrization technique involving Laurent polynomials (polynomials with negative exponents) that was previously introduced by Aaronson, Kothari, Kretschmer, and Thaler [AKKT19].
Edit intent: clarity
Original:  most other proofs involve the more complicated formulation of approximate degree as a linear program [BT13, She13, BDBGK18].
Revised:  most other proofs that involve formulating approximate degree as a linear program [BT13, She13, BDBGK18].
Edit intent: clarity
Original:  However, deciding on the best activation is non-trivial  and the choice depends on the architecture, hyper-parameters, and even on the dataset.
Revised:  However, deciding on the best activation is non-trivial , and the choice depends on the architecture, hyper-parameters, and even on the dataset.
Edit intent: fluency
Original:  Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance and reduce the training time of common deep architectures .
Revised:  Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance .
Edit intent: clarity
Original:  The source code can be found at URL
Revised:  URL
Edit intent: clarity
Original:  This tree can in turn be represented in a maximally compact form as a direct acyclic graph (dag ) where common subtrees are factored and shared, keeping only one copy of each unique subtree.
Revised:  This tree can in turn be represented in a maximally compact form as a direct acyclic graph dag ) where common subtrees are factored and shared, keeping only one copy of each unique subtree.
Edit intent: clarity
Original:  This tree can in turn be represented in a maximally compact form as a direct acyclic graph (dag ) where common subtrees are factored and shared, keeping only one copy of each unique subtree.
Revised:  This tree can in turn be represented in a maximally compact form as a direct acyclic graph ( ) where common subtrees are factored and shared, keeping only one copy of each unique subtree.
Edit intent: clarity
Original:  This tree can in turn be represented in a maximally compact form as a direct acyclic graph (dag ) where common subtrees are factored and shared, keeping only one copy of each unique subtree.
Revised:  This tree can in turn be represented in a maximally compact form as a direct acyclic graph (dag where common subtrees are factored and shared, keeping only one copy of each unique subtree.
Edit intent: fluency
Original:  This yields the celebrated and widely used structure called reduced ordered binary decision diagram ( robdd ).
Revised:  This yields the celebrated and widely used structure called reduced ordered binary decision diagram ( ROBDD ).
Edit intent: fluency
Original:  We propose to revisit the classical compaction process to give a new way of enumerating robdd s of a given size without considering fully expanded trees and the compaction step.
Revised:  We propose to revisit the classical compaction process to give a new way of enumerating s of a given size without considering fully expanded trees and the compaction step.
Edit intent: fluency
Original:  Our method also provides an unranking procedure for the set of robdd s . As a by-product we get a random uniform and exhaustive sampler for robdd s for a given number of variables and size .
Revised:  Our method also provides an unranking procedure for the set of s . As a by-product we get a random uniform and exhaustive sampler for robdd s for a given number of variables and size .
Edit intent: fluency
Original:  Our method also provides an unranking procedure for the set of robdd s . As a by-product we get a random uniform and exhaustive sampler for robdd s for a given number of variables and size .
Revised:  Our method also provides an unranking procedure for the set of robdd s . As a by-product we get a random uniform and exhaustive sampler for s for a given number of variables and size .
Edit intent: fluency
Original:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{zbdd s) .
Revised:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants of s (namelyqbdd s and\textsc{zbdd s) .
Edit intent: fluency
Original:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{zbdd s) .
Revised:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd qbdd s and\textsc{zbdd s) .
Edit intent: coherence
Original:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{zbdd s) .
Revised:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namely s and\textsc{zbdd s) .
Edit intent: fluency
Original:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{zbdd s) .
Revised:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd \textsc{zbdd s) .
Edit intent: coherence
Original:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{zbdd s) .
Revised:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{ s) .
Edit intent: fluency
Original:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{zbdd s) .
Revised:  Finally, we give some key ideas to extend the approach to other strategies of compaction, in relation with variants ofbdd s (namelyqbdd s and\textsc{zbdd .
Edit intent: fluency
Original:  The paper argues that this requirement is captured by supervenience , hereby further identified as a property necessary for compression.
Revised:  The paper argues that this requirement is captured by supervenience , hereby further identified as a property necessary for compression.
Edit intent: fluency
Original:  One challenge limiting the utilization of adaptive sampling by domain experts is the relatively high complexity to efficiently running it on HPC systems.
Revised:  One challenge limiting the utilization of adaptive sampling by domain experts is the relatively high complexity of efficiently running adaptive sampling on HPC systems.
Edit intent: clarity
Original:  \% to learn to do each Alice and Bob and jobs.
Edit intent: coherence
Original: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Revised: Repertoire-based learning is a data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Edit intent: coherence
Original: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Revised: Among the data-efficient adaptation approach based on a two-step process in which ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Edit intent: clarity
Original: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Revised: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Edit intent: clarity
Original: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Revised: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set of policies is learned in simulation, and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Edit intent: clarity
Original: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) learns to pick online the best working policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Revised: Among the data-efficient approaches for online adaptation in robotics (meta-learning, model-based reinforcement learning, etc.), repertoire-based learning ( 1) generates a large and diverse set policies in simulation that acts as a "reservoir" for future adaptations and (2) a planning or learning algorithm chooses the most appropriate policies according to the current situation (e.g., a damaged robot, a new object, etc.).
Edit intent: clarity
Original:  Instead, we generate repertoires for many different situations (e.g., with a missing leg, on different floors, etc.) in simulation that act as priors for adaptation .
Revised:  Instead, we generate repertoires for many different situations (e.g., with a missing leg, on different floors, etc.) and let our algorithm selects the most useful prior .
Edit intent: clarity
Original:  We evaluate APROL on two simulated tasks: (1) pushing unknown objects of various shapes and sizes with a kuka arm and (2) a goal reaching task with a damaged hexapod robot.
Revised:  We evaluate APROL on two simulated tasks: (1) pushing unknown objects of various shapes and sizes with a robotic arm and (2) a goal reaching task with a damaged hexapod robot.
Edit intent: clarity
Original:  The results show that APROL solves both  tasks in less interaction time than the baselines.
Revised:  The results show that APROL solves both the tasks in less interaction time than the baselines.
Edit intent: fluency
Original:  Additionally, we demonstrate APROL on a real, damaged hexapod that quickly learns  compensatory policies to reach a goal by avoiding obstacle in the path.
Revised:  Additionally, we demonstrate APROL on a real, damaged hexapod that quickly learns compensatory policies to reach a goal by avoiding obstacles in the path.
Edit intent: fluency
Original:  These scalar fields are evaluated at each node within a discretized computational domain.
Revised:  These scalar fields are evaluated at each node within a discretised computational domain.
Edit intent: fluency
Original:  We exploit this notion of localized scalar-field influence for approximating global qois, which often are integrals of certain field quantities.
Revised:  We exploit this notion of localised scalar-field influence for approximating global qois, which often are integrals of certain field quantities.
Edit intent: fluency
Original:  We formalize our ideas by assigning ridge approximations for the field at select nodes.
Revised:  We formalise our ideas by assigning ridge approximations for the field at select nodes.
Edit intent: fluency
Original:  To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schr\"{o}dinger equation, called Gross--Pitaevskii equation, as one or two physical parameters are varied.
Revised:  To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schr\"{o}dinger equation, called Gross-Pitaevskii equation, as one or two physical parameters are varied.
Edit intent: fluency
Original:  We show that the class of k-volume regular graphs is the largest class of undirected (possibly weighted) graphs whose transition matrix admits k stepwise eigenvectors (i.e., vectors that are constant over each set of the hidden partition).
Revised:  We show that the class of k-volume-regular graphs is the largest class of undirected (possibly weighted) graphs whose transition matrix admits k stepwise eigenvectors (i.e., vectors that are constant over each set of the hidden partition).
Edit intent: fluency
Original:  We show that the class of k-volume regular graphs is the largest class of undirected (possibly weighted) graphs whose transition matrix admits k stepwise eigenvectors (i.e., vectors that are constant over each set of the hidden partition).
Revised:  We show that the class of k-volume regular graphs is the largest class of undirected (possibly weighted) graphs whose transition matrix admits k "stepwise" eigenvectors (i.e., vectors that are constant over each set of the hidden partition).
Edit intent: clarity
Original:  Moreover, we prove that if the stepwise eigenvectors are those associated to the first k eigenvalues and the gap between the k-th and the (k+1)-th eigenvalues is sufficiently large, the Averaging dynamics of Becchetti et al. recovers the underlying community structure of the graph in logarithmic time, with high probability.
Revised:  Moreover, we prove that if the stepwise eigenvectors are those associated to the first k eigenvalues and the gap between the k-th and the (k+1)-th eigenvalues is sufficiently large, the averaging dynamics of Becchetti et al. recovers the underlying community structure of the graph in logarithmic time, with high probability.
Edit intent: fluency
Original: The state-of-the-art approaches employ approximate computing to improve the energy consumption of DNN hardware.
Revised: The state-of-the-art approaches employ approximate computing to reduce the energy consumption of DNN hardware.
Edit intent: clarity
Original:  Approximate DNNs then require "extensive retraining " afterwards to recover from the accuracy loss caused by the use of approximate operations.
Revised:  Approximate DNNs then require extensive retraining afterwards to recover from the accuracy loss caused by the use of approximate operations.
Edit intent: fluency
Original:  In this paper, we demonstrate that efficient approximations can be introduced into the computational path of DNN accelerators " while retraining can completely be avoided " . ALWANN provides highly optimized implementations of DNNs for custom low-power accelerators in which the number of computing units is lower than the number of DNN layers.
Revised:  In this paper, we demonstrate that efficient approximations can be introduced into the computational path of DNN accelerators while retraining can completely be avoided " . ALWANN provides highly optimized implementations of DNNs for custom low-power accelerators in which the number of computing units is lower than the number of DNN layers.
Edit intent: fluency
Original:  In this paper, we demonstrate that efficient approximations can be introduced into the computational path of DNN accelerators " while retraining can completely be avoided " . ALWANN provides highly optimized implementations of DNNs for custom low-power accelerators in which the number of computing units is lower than the number of DNN layers.
Revised:  In this paper, we demonstrate that efficient approximations can be introduced into the computational path of DNN accelerators " while retraining can completely be avoided . ALWANN provides highly optimized implementations of DNNs for custom low-power accelerators in which the number of computing units is lower than the number of DNN layers.
Edit intent: fluency
Original:  First, a fully trained DNN (e.g. in TensorFlow) is converted to operate with 8-bit weights and 8-bit multipliers in convolutional layers.
Revised:  First, a fully trained DNN is converted to operate with 8-bit weights and 8-bit multipliers in convolutional layers.
Edit intent: clarity
Original:  The proposed approach is evaluated for two architectures of DNN accelerators executing three versions of ResNet on CIFAR-10 and with approximate multipliers taken from the open-source EvoApprox library.
Revised:  The proposed approach is evaluated for two architectures of DNN accelerators with approximate multipliers taken from the open-source EvoApprox library.
Edit intent: clarity
Original:  The proposed approach is evaluated for two architectures of DNN accelerators executing three versions of ResNet on CIFAR-10 and with approximate multipliers taken from the open-source EvoApprox library.
Revised:  The proposed approach is evaluated for two architectures of DNN accelerators executing three versions of ResNet on CIFAR-10 and with approximate multipliers from the open-source EvoApprox library.
Edit intent: clarity
Original:  The proposed technique and approximate layers will be made available as an open-source extension of TensorFlow framework.
Revised:  The proposed technique and approximate layers are available as an open-source extension of TensorFlow framework.
Edit intent: clarity
Original:  The proposed technique and approximate layers will be made available as an open-source extension of TensorFlow framework.
Revised:  The proposed technique and approximate layers will be made available as an open-source extension of TensorFlow at URL
Edit intent: clarity
Original: In this paper we introduce a formal method for the derivation of the predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain constant.
Revised: In this paper we introduce a formal method for the derivation of a predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain constant.
Edit intent: fluency
Original: Optimizing caching locations of popular content has received significant research attention over the last few years.
Revised: Caching of popular content has received significant research attention over the last few years.
Edit intent: clarity
Original:  This paper targets the optimization of the caching locations by proposing a novel transformation of the optimization problem to a grey-scale image that is applied to a deep convolutional neural network (CNN) .
Revised:  This paper targets the optimization of the caching locations by proposing a novel transformation of the optimization problem to a grayscale image and train a convolutional neural network (CNN) .
Edit intent: coherence
Original:  The rational for the proposed modeling comes from CNN's superiority to capture features in gray-scale images reaching human level performance in image recognition problems.
Revised:  The rational for the proposed modelling comes from CNN's superiority to capture features in gray-scale images reaching human level performance in image recognition problems.
Edit intent: fluency
Original:  The rational for the proposed modeling comes from CNN's superiority to capture features in gray-scale images reaching human level performance in image recognition problems.
Revised:  The rational for the proposed modeling comes from CNN's superiority to capture features in grayscale images reaching human level performance in image recognition problems.
Edit intent: fluency
Original:  The CNN has been trained with optimal solutions and the numerical investigations and analyses demonstrate the promising performance of the proposed method.
Revised:  The CNN is trained with optimal solutions and the numerical investigations and analyses demonstrate the promising performance of the proposed method.
Edit intent: clarity
Original:  However, location-aware deployment of edge computing infrastructure requires careful placement scheme for edge servers.
Revised:  However, location-aware deployment of edge computing infrastructure requires a careful placement of the edge servers.
Edit intent: clarity
Original:  To address these challenges, we formulate the edge server placement  as a capacitated location-allocation problem , while minimizing the distance between servers and access points of a real city-wide Wi-Fi network deployment.
Revised:  To address these challenges, we formulate the edge server placement as a capacitated location-allocation problem . PACK minimizes the distances between servers and access points of a real city-wide Wi-Fi network deployment.
Edit intent: coherence
Original:  The data set consists of both dense deployment of access points in central areas, but also sparse deployment in suburban areas within the same network infrastructure.
Revised:  The data set consists of both dense and sparse deployments of access points in central areas, but also sparse deployment in suburban areas within the same network infrastructure.
Edit intent: clarity
Original:  The aim is to improve application latencies and reduce data transfer load in the opportunistic Internet of Things systems.
Revised:  The aim is to improve application latencies and reduce data transfer load in opportunistic Internet of Things systems.
Edit intent: fluency