wanyu/IteraTeR_v2 huggingface dataset:
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: multiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: clarity
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: We propose a novel variant of the with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: clarity
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence zero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: fluency
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence for with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: clarity
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games Nash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: clarity
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueto an equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: fluency
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the algorithm reaches first an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: clarity
Original: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by a rate of at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Revised: We propose a novel variant of themultiplicative weights update method with forward-looking best-response strategies , that guarantees last-iterate convergence forzero-sum games with a uniqueNash equilibrium . Particularly, we show that the proposed algorithm converges to an \eta^{1/\rho}-approximate Nash equilibrium, with \rho > 1, by decreasing the Kullback-Leibler divergence of each iterate by at least \Omega(\eta^{1+1{\rho}}), for sufficiently small learning rate \eta.
Edit intent: clarity
Original:  When our method enters a sufficiently small neighborhood of the solution, it becomes a contraction and converges to the Nash equilibriumof the game .
Revised:  When our method enters a sufficiently small neighborhood of the solution, it becomes a contraction and converges to the exact equilibrium .
Edit intent: clarity
Original:  Furthermore, we perform an experimental comparison with the recently proposed optimistic variant of the multiplicative weights update method, by \cite{Daskalakis2019LastIterateCZ} , which has also been proved to attain last-iterate convergence.
Revised:  Furthermore, we perform experimental comparisons with the optimistic variant of the multiplicative weights update method, by \cite{Daskalakis2019LastIterateCZ} , which has also been proved to attain last-iterate convergence.
Edit intent: clarity
Original:  Our findings reveal that our algorithm  offers substantial gains both in terms of the convergencerate and the region of contraction relative to the previous approach .
Revised:  Our findings reveal that our algorithm offers substantial gains in terms of the convergencerate and the region of contraction relative to the previous approach .
Edit intent: clarity
Original:  Results show that it reliably estimates player objectives from single short sequences of noisy, partially observed interactions .
Revised:  Results show that it reliably estimates player objectives from a short sequence of noise-corrupted partial state observations .
Edit intent: clarity
Original: We address the detection of material defects, which are inside a layered material structure using compressive sensing based  multiple-output (MIMO) wireless radar.
Revised: We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-input and multiple-output (MIMO) wireless radar.
Edit intent: clarity
Original: We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces that preserve full approximation power . Roughly speaking, these optimal subspaces are obtained from the full spline space defined on certain uniform knot sequences by imposing specific additional boundary conditions.
Revised: We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces . Roughly speaking, these optimal subspaces are obtained from the full spline space defined on certain uniform knot sequences by imposing specific additional boundary conditions.
Edit intent: clarity
Original:  Here , we complete the analysis of the approximation properties of these optimal spline subspaces.
Revised:  Here we complete the analysis of the approximation properties of these optimal spline subspaces.
Edit intent: fluency
Original:  Thus , there are no spurious numerical values in the approximated spectrum.
Revised:  Thus , there are no spurious values in the approximated spectrum.
Edit intent: clarity
Original:  In other words, the considered subspaces provide fully accurate outlier-free discretizations in the univariate and in the multivariate tensor-product case.
Revised:  In other words, the considered subspaces provide accurate outlier-free discretizations in the univariate and in the multivariate tensor-product case.
Edit intent: clarity
Original:  Their role as discretization spaces for addressing general problems with non-homogeneous boundary behavior is discussed as well.
Revised:  The role of such spaces as accurate discretization spaces for addressing general problems with non-homogeneous boundary behavior is discussed as well.
Edit intent: clarity
Original:  Prior to our work, producing rewards from self-supervised embeddings has typically required alignment with a reference trajectory, which may be difficult to acquire  .
Revised:  Prior to our work, producing rewards from self-supervised embeddings typically required alignment with a reference trajectory, which may be difficult to acquire .
Edit intent: clarity
Original:  We show empirically that if the embeddings are aware of task-progress , simply taking the negative distance between the current state and goal state in the learned embedding space is useful as a reward for training policies with reinforcement learning.
Revised:  We show empirically that if the embeddings are aware of task progress , simply taking the negative distance between the current state and goal state in the learned embedding space is useful as a reward for training policies with reinforcement learning.
Edit intent: clarity
Original:  We also find that XIRL policies are more sample efficient than baselines, and in some cases exceed the sample efficiency of the same agent trained with ground truth sparse rewards.
Revised:  We also find that XIRL is more sample efficient than baselines, and in some cases exceed the sample efficiency of the same agent trained with ground truth sparse rewards.
Edit intent: clarity
Original:  We propose an approach to multi-model grasp detection that jointly predicts the probabilities that several types of grasps succeed at a given grasp pose.
Revised:  We propose an approach to multi-modal grasp detection that jointly predicts the probabilities that several types of grasps succeed at a given grasp pose.
Edit intent: clarity
Original:   We examine Leontief analysis as a model, demonstrating commonalities with modern approaches in information theory and nonequilibrium statistical mechanics.
Revised:  We examine Leontief analysis as a model, drawing out similarities with modern nonequilibrium statistical mechanics.
Edit intent: clarity
Original:  Paralleling the physical concept of thermo-majorization, we define the concept of eco-majorization and show it is a sufficient condition to determine the directionality of embodied impact flows.
Revised:  Paralleling the physical concept of thermo-majorization, we define the concept of eco-majorization and show it is a sufficient condition to determine the directionality of embodied emission flows.
Edit intent: clarity
Original:  Our results are bolstered by a statistical analysis of null models of MRIO tables developed by the Global Trade Aggregation Project.
Revised:  Our results are bolstered by a statistical analysis of null models of MRIO tables , based on data provided by the Global Trade Aggregation Project.
Edit intent: clarity
Original:  Our results are bolstered by a statistical analysis of null models of MRIO tables developed by the Global Trade Aggregation Project.
Revised:  Our results are bolstered by a statistical analysis of null models of MRIO tables developed by the Global Trade Aggregation Project9
Edit intent: style
Original: Game theoretic approaches have gained traction as a robust methodology for designing distributed local algorithms that induce a desired overall system configuration in a multi-agent setting .
Revised: Game theoretic approaches have gained traction as robust methodologies for designing distributed local algorithms that induce a desired overall system configuration in a multi-agent setting .
Edit intent: fluency
Original: Game theoretic approaches have gained traction as a robust methodology for designing distributed local algorithms that induce a desired overall system configuration in a multi-agent setting .
Revised: Game theoretic approaches have gained traction as a robust methodology for designing distributed local algorithms that induce a desired overall system configuration in multi-agent setting .
Edit intent: fluency
Original: Game theoretic approaches have gained traction as a robust methodology for designing distributed local algorithms that induce a desired overall system configuration in a multi-agent setting .
Revised: Game theoretic approaches have gained traction as a robust methodology for designing distributed local algorithms that induce a desired overall system configuration in a multi-agent settings .
Edit intent: fluency
Original:  However, much of the emphasis in these approaches is on providing asymptotic guarantees on the performance of  network of agents, and there is a gap in the study of efficiency guarantees along transients of these distributed algorithms.
Revised:  However, much of the emphasis in these approaches is on providing asymptotic guarantees on the performance of a network of agents, and there is a gap in the study of efficiency guarantees along transients of these distributed algorithms.
Edit intent: fluency
Original: Let G be a graph of order n and let u,v be vertices of G. Let \kappa_G(u,v) denote the maximum number of internally disjoint u--v paths in G. Then the average connectivity \kappa(G) of G, is defined as \kappa(G)=\{u,v\\subseteq V(G)} \kappa_G(u,v)/n{2}.
Revised: Let G be a graph of order n and let u,v be vertices of G. Let \kappa_G(u,v) denote the maximum number of internally disjoint u-v paths in G. Then the average connectivity \kappa(G) of G, is defined as \kappa(G)=\{u,v\\subseteq V(G)} \kappa_G(u,v)/n{2}.
Edit intent: fluency
Original:  We conjecture that for every integer k %DIFDELCMD < \ge %%% 3 \ge3 , if G is an optimal minimally k-connected graph of order n\geq 2k+1, then G is bipartite, with the set of vertices of degree k and the set of vertices of degree exceeding k as its partite sets.
Revised:  We conjecture that for every integer k %DIFDELCMD < \ge %%% \ge3 , if G is an optimal minimally k-connected graph of order n\geq 2k+1, then G is bipartite, with the set of vertices of degree k and the set of vertices of degree exceeding k as its partite sets.
Edit intent: clarity
Original:  '' Entropic independence is the natural analog of spectral independence, another recently established notion, if one replaces variance by entropy.
Revised:  '' Entropic independence is the analog of the notion of spectral independence, another recently established notion, if one replaces variance by entropy.
Edit intent: clarity
Original:  '' Entropic independence is the natural analog of spectral independence, another recently established notion, if one replaces variance by entropy.
Revised:  '' Entropic independence is the natural analog of spectral independence, if one replaces variance by entropy.
Edit intent: clarity
Original:   In our main  result, we show that \mu is entropically independent exactly when a transformed version of the generating polynomial of \mu can be upper bounded by its linear tangent , a property implied by concavity of the said transformation .
Revised:  In our main result, we show that \mu is entropically independent exactly when a transformed version of the generating polynomial of \mu is upper bounded by its linear tangent , a property implied by concavity of the said transformation .
Edit intent: clarity
Original:   In our main  result, we show that \mu is entropically independent exactly when a transformed version of the generating polynomial of \mu can be upper bounded by its linear tangent , a property implied by concavity of the said transformation .
Revised:  In our main result, we show that \mu is entropically independent exactly when a transformed version of the generating polynomial of \mu can be upper bounded by its linear tangent ; this property is implied by concavity of the said transformation .
Edit intent: coherence
Original:  We leverage our results to derive tight modified log-Sobolev inequalities  for multi-step down-up walks on fractionally log-concave distributions.
Revised:  We leverage our results to obtain tight modified log-Sobolev inequalities for multi-step down-up walks on fractionally log-concave distributions.
Edit intent: fluency
Original:  As our main application, we establish the tight mixing time of O(n\log n) for Glauber dynamics on Ising models with interaction matrix of operator norm smaller than 1, improving upon the prior quadratic dependence on n.
Revised:  As our flagship application, we establish the tight mixing time of O(n\log n) for Glauber dynamics on Ising models with interaction matrix of operator norm smaller than 1, improving upon the prior quadratic dependence on n.
Edit intent: clarity
Original:  In dynamical systems theory, such change points are known as bifurcations and lie on a function of the controlled condition called the bifurcation diagram .
Revised:  In dynamical systems theory, such change points are known as bifurcations and lie on a function of the controlled condition called the bifurcation diagram .
Edit intent: fluency
Original:  In this work, we propose a gradient-based semi-supervised approach for inferring the parameters of differential equations that produce a user-specified bifurcation diagram.
Revised:  In this work, we propose a gradient-based approach for inferring the parameters of differential equations that produce a user-specified bifurcation diagram.
Edit intent: clarity
Original:  The cost function contains a supervised error term that is minimal when the model bifurcations match the specified targets and an unsupervised bifurcation measure which has gradients that push optimisers towards bifurcating parameter regimes.
Revised:  The cost function contains an error term that is minimal when the model bifurcations match the specified targets and an unsupervised bifurcation measure which has gradients that push optimisers towards bifurcating parameter regimes.
Edit intent: fluency
Original:  The cost function contains a supervised error term that is minimal when the model bifurcations match the specified targets and an unsupervised bifurcation measure which has gradients that push optimisers towards bifurcating parameter regimes.
Revised:  The cost function contains a supervised error term that is minimal when the model bifurcations match the specified targets and a bifurcation measure which has gradients that push optimisers towards bifurcating parameter regimes.
Edit intent: clarity
Original:  For portable codes that run across heterogeneous hardware architectures, the choice of the memory layout for data structures is therefore ideally decoupled from the rest of a program.
Revised:  For portable codes that run across heterogeneous hardware architectures, the choice of the memory layout for data structures is ideally decoupled from the rest of a program.
Edit intent: coherence
Original:  We present the  C++ library LLAMA, which provides such a data structure abstraction layer with example implementations for multidimensional arrays of nested, structured data.
Revised:  We present the C++ library that provides such a data structure abstraction layer with example implementations for multidimensional arrays of nested, structured data.
Edit intent: coherence
Original:   Providing two close-to-life examples, we show that the LLAMA-generated AoS (Array of Struct ) and SoA (Struct of Array ) layouts produce identical code with the same performance characteristics as manually written data structures.
Revised:  Providing two close-to-life examples, we show that the LLAMA-generated AoS (Array of Structs ) and SoA (Struct of Array ) layouts produce identical code with the same performance characteristics as manually written data structures.
Edit intent: fluency
Original:   Providing two close-to-life examples, we show that the LLAMA-generated AoS (Array of Struct ) and SoA (Struct of Array ) layouts produce identical code with the same performance characteristics as manually written data structures.
Revised:  Providing two close-to-life examples, we show that the LLAMA-generated AoS (Array of Struct ) and SoA (Struct of Arrays ) layouts produce identical code with the same performance characteristics as manually written data structures.
Edit intent: clarity