wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Assuming the grid cells form a vector representation of self-position, we elucidate a minimally simple recurrent model for path integral, which models the change of the vector representation given the self-motion, and we discern two matrix Lie algebras and their Lie groups that are naturally coupled together. This enables us to connect the path integral model to the dimension reduction model for place cells via group representation theory of harmonic analysis. By reconstructing the kernel functions for place cells, our model learns hexagon grid patterns that characterize the grid cells.
Revised:  Assuming the grid cells form a vector representation of self-position, we elucidate a minimally simple recurrent model for path integral, which models the change of the vector representation given the self-motion, and we discern two matrix Lie algebras that underlie two coupled rotation systems that mirror the agent's self-motion: (1) When the agent moves along a certain direction, the vector is rotated by a generator matrix. (2) When the agent changes direction, the generator matrix is rotated by another generator matrix. Our experiments show that our model learns hexagon grid patterns that characterize the grid cells.
Edit intent: clarity
Original:  By reconstructing the kernel functions for place cells, our model learns hexagon grid patterns that characterize the grid cells. The learned model is capable of near perfect path integral , and it is also capable of error correction  .
Revised:  By reconstructing the kernel functions for place cells, our model learns hexagonal grid response patterns that resemble the firing patterns observed from the grid cells in the brain. Furthermore, the learned model is capable of near perfect path integral , and it is also capable of error correction .
Edit intent: meaning-changed
Original: The grid cells in the mammalian medial entorhinal cortex exhibit striking hexagon firing patterns when the agent navigates in the open field. It is hypothesized that the grid cells are involved in path integration so that the agent is aware of its self-position by accumulating its self-motion.
Revised: The purpose of this paper is to understand how the grid cells may perform path integration calculations. We study a general representational model in which the self-position is represented by a vector formed by the activities of a population of grid cells, and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration. We identify an isotropic condition so that the agent is aware of its self-position by accumulating its self-motion.
Edit intent: meaning-changed
Original:  Assuming the grid cells form a vector representation of self-position, we elucidate a minimally simple recurrent model for grid cells' path integration based on two coupled matrix Lie algebras that underlie two coupled rotation systems that mirror the agent's self-motion : (1) When the agent moves along a certain direction, the vectoris rotated by a generator matrix.
Revised:  We then study a minimally simple prototype model where the local change is a linear transformation of the vector. This linear model gives rise to explicit algebraic structure in terms of matrix Lie algebra and matrix Lie group, as well as explicit geometric structure where the self-motion : (1) When the agent moves along a certain direction, the vectoris rotated by a generator matrix.
Edit intent: meaning-changed
Original:  Assuming the grid cells form a vector representation of self-position, we elucidate a minimally simple recurrent model for grid cells' path integration based on two coupled matrix Lie algebras that underlie two coupled rotation systems that mirror the agent's self-motion : (1) When the agent moves along a certain direction, the vectoris rotated by a generator matrix. (2) When the agent changes direction, the generator matrix is rotated by another generator matrix. Our experiments show that our model learns hexagonal grid response patterns that resemble the firing patterns observed from the grid cells in the  brain.
Revised:  Assuming the grid cells form a vector representation of self-position, we elucidate a minimally simple recurrent model for grid cells' path integration based on two coupled matrix Lie algebras that underlie two coupled rotation systems that mirror the agent's self-motion is represented by the rotation of the vector. We connect the isotropic condition under the linear model to the hexagon grid patterns of the response maps of grid cells. Our numerical experiments demonstrate that our model learns hexagonal grid response patterns that resemble the firing patterns observed from the grid cells in the brain.
Edit intent: meaning-changed
Original:  We study a general representational model  in which the self-position is represented by a vector formed by the activities of a population of grid cells, and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Revised:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells, and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Edit intent: clarity
Original:   We identify an isotropic condition  so that the local change of this vector is a conformal embedding of the  self-motion.
Revised:  For local infinitesimal self-motion, the change of the vector is determined by the directional derivative of the recurrent network, and the norm of the directional derivative captures the metric of the path integration model. We identify an isotropic condition so that the local change of this vector is a conformal embedding of the self-motion.
Edit intent: meaning-changed
Original:  This linear model gives rise to explicit algebraic structure in terms of matrix Lie algebra and matrix Lie group , as well as explicit geometric structure where the self-motion is represented by the rotation of the vector.
Revised:  This linear model gives rise to explicit algebraic structure in terms of matrix Lie group representation of 2D self-motion , as well as explicit geometric structure where the self-motion is represented by the rotation of the vector.
Edit intent: meaning-changed
Original: The purpose of this paper is to understand how the grid cells may perform path integration calculations . We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the  self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Revised: The purpose of this paper is to understand how the grid cells may perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Edit intent: meaning-changed
Original:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the  self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Revised:  We study a general representational model of path integration by grid cells, where the 2D self-position is represented by a vector formed by the activities of a population of grid cells , and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Edit intent: meaning-changed
Original:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the  self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Revised:  We study a general representational model of path integration in which the self-position is encoded as a higher dimensional vector , and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Edit intent: meaning-changed
Original:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the  self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Revised:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the 2D self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
Edit intent: meaning-changed
Original:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the  self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration. For local infinitesimal self-motion, the change of the vector is determined by the directional derivative of the recurrent network, and the norm of the directional derivative captures the metric of the path integrationmodel.
Revised:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the self-motion is represented by a general transformation of the vector is determined by the directional derivative of the recurrent network, and the norm of the directional derivative captures the metric of the path integrationmodel.
Edit intent: clarity
Original:  For local infinitesimal self-motion, the change of the vector is determined by the directional derivative of the recurrent network, and the norm of the directional derivative captures the metric of the path integrationmodel. We identify an isotropic condition on the norm of the directional derivative of the recurrent network , so that the local change of this vector is a conformal embedding of the local self-motion.
Revised:  For local infinitesimal self-motion, the change of the vector . We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration. The other is an isotropic scaling condition that ensures locally conformal embedding , so that the local change of this vector is a conformal embedding of the local self-motion.
Edit intent: clarity
Original:  We identify an isotropic condition on the norm of the directional derivative of the recurrent network , so that the local change of this vector is a conformal embedding of the local self-motion. We then study a minimally simple prototype model where the local change is a linear transformationof the vector.This linear model gives rise to explicit algebraic structure in terms of matrix Lie group representation of 2D self-motion, as well as explicit geometric structure where the self-motion is represented by the rotation of the vector.
Revised:  We identify an isotropic condition on the norm of the directional derivative of the recurrent network , so that the error in the vector representation translates proportionally to the error in the 2D self-position. Then we investigate the simplest transformation, i.e., the linear transformation, uncover its explicit algebraic and geometric structure as matrix Lie group representation of 2D self-motion, as well as explicit geometric structure where the self-motion is represented by the rotation of the vector.
Edit intent: clarity
Original: This linear model gives rise to explicit algebraic structure in terms of matrix Lie group representation of 2D self-motion, as well as explicit geometric structure where the self-motion is represented by the rotation of the vector. We connect the isotropic condition under the linear model to the hexagon grid patterns of the response maps of grid cells .
Revised: This linear model gives rise to explicit algebraic structure in terms of matrix Lie group of rotation, and establish the connection between the isotropic scaling condition and hexagon grid patterns of the response maps of grid cells .
Edit intent: clarity
Original:  We connect the isotropic condition under the linear model to the hexagon grid patterns of the response maps of grid cells . Our numerical experiments demonstrate that our model learns hexagon grid patterns which share various observed properties of the grid cells in the rodent brain.
Revised:  We connect the isotropic condition under the linear model to the hexagon grid patterns of grid cells under the linear transformation. Finally, with our optimization-based approach, we manage to learn hexagon grid patterns which share various observed properties of the grid cells in the rodent brain.
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Original: In the first part of this work , we uncover a connection between polynomial-reproducing bases of simplex splines and certain single-element liftings of oriented matroids associated to point configurations. We use this correspondence to construct a broad family of spline bases on generic point multisets, generalizing a known result on Delaunay configurations .
Revised: In the first part of this work , we uncover a connection between polynomial-reproducing spline spaces over subsets of conv(A) and fine zonotopal tilings of the zonotope Z(V) associated to the corresponding vector configuration. This link directly generalizes a known result on Delaunay configurations .
Edit intent: meaning-changed
Original:  We use this correspondence to construct a broad family of spline bases on generic point multisets, generalizing a known result on Delaunay configurations . Our spline bases are naturally defined on finite knot sets with affine dependencies and higher multiplicities, without need for special treatment of degenerate cases. We reformulate our bases in the language of zonotopal tilings, via the Bohne-Dress theorem, obtaining a link to a known construction algorithm for bivariate spline bases based on centroid triangulations. In the second part of this work, we restrict again our attention to weighted Delaunay configurations and the associated spline bases, and we capitalize on our combinatorial viewpoint to extend, in this restricted case, the well-known bivariate construction algorithm to higher dimensions and generic point multisets.
Revised:  We use this correspondence to construct a broad family of spline bases on generic point multisets, generalizing a known result on Delaunay configurations and naturally encompasses, due to its combinatorial character, the case of repeated and affinely dependent points in A. We prove the existence of a general iterative construction process for such spaces. Finally, we turn our attention to weighted Delaunay configurations and the associated spline bases, and we capitalize on our combinatorial viewpoint to extend, in this restricted case, the well-known bivariate construction algorithm to higher dimensions and generic point multisets.
Edit intent: meaning-changed
Original:  In the second part of this work, we restrict again our attention to weighted Delaunay configurations and the associated spline bases, and we capitalize on our combinatorial viewpoint to extend, in this restricted case, the well-known bivariate construction algorithm to higher dimensions and generic point multisets. Finally, we employ this machinery to propose algorithms for the determination and evaluation of all multivariate basis spline functionssupported on a given point .
Revised:  In the second part of this work, we restrict again our attention to regular fine zonotopal tilings, specializing our previous results and exploiting the adjacency graph of the tiling to propose a set of practical algorithms for the determination and evaluation of all multivariate basis spline functionssupported on a given point .
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Original:  We present a deterministic O(n \log n)-time algorithm for the case that the centers of the two optimal disks are close together , that is, the overlap of the two optimal disks is a constant fraction of the disk area.
Revised:  We present a deterministic O(n \log n)-time algorithm for the case that the centers of the two optimal disks are close to each other , that is, the overlap of the two optimal disks is a constant fraction of the disk area.
Edit intent: clarity
Original: State-of-the-art neural machine translation models generate outputs autoregressively, where every step conditions on the previously generated tokens. This sequentialnature causes inherent decoding latency.
Revised: State-of-the-art neural machine translation , which appears to be an efficient alternative to state-of-the-art autoregressive machine translation on modern GPUs. In contrast to the latter where generation is sequential, the former allows generation to be parallelized across target token positions.
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Original:  Non-autoregressive translation techniques, on the other hand, parallelize generation across positions and speed up inference at the expense of translation quality. Much recent effort has been devoted to non-autoregressive methods, aiming for a better balance between speed and quality .
Revised:  Non-autoregressive machine translation provides a tradeoff between translation quality and inference speed, but some of the latest models have achieved impressive tradeoffs compared to autoregressive baselines .
Edit intent: clarity
Original:  Our extensive experiments show that given a sufficiently deep encoder, a one-layer autoregressive decoder yields state-of-the-art accuracy with comparable latency to strong non-autoregressive models . Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Revised:  Our extensive experiments show that given a sufficiently deep encoder, a one-layer autoregressive decoder yields state-of-the-art accuracy with comparable latency to strong non-autoregressive models with comparable inference speed. We show that the speed disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Edit intent: clarity
Original:  Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Revised:  Our findings suggest that the latency disadvantage for autoregressive baselines compared to non-autoregressive methods has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Edit intent: meaning-changed
Original:  Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Revised:  Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated in three aspects: suboptimal layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Edit intent: meaning-changed
Original:  Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Revised:  Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, insufficient speed measurement, and lack of knowledge distillation. Our results establish a new protocol for future research toward fast, accurate translation.
Edit intent: meaning-changed
Original:  Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate translation.
Revised:  Our findings suggest that the latency disadvantage for autoregressive translation has been overestimated due to a suboptimal choice of layer allocation, and we provide a new speed-quality baseline for future research toward fast, accurate machine translation. Our code is available at URL
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Original:  First , making use the Schwarz ODE, we develop an analytic method to determine a conformal mapping the unit disk onto a given circular quadrilateral. We devise a numerical method to find  the accessory parameters , solve the equation and to compute the modulus of the quadrilateral.
Revised:  First , making use the Schwarz ODE, we develop an analytic approach which reduces this problem to ODEs and devise a numeric method to find the accessory parameters , solve the equation and to compute the modulus of the quadrilateral.
Edit intent: meaning-changed
Original:  Prior work has attempted to quantify the number of facts PLMs learn, but we present, using synthetic data, the first study that establishes a causal relation between facts present in training and facts learned by the PLM.
Revised:  Prior work has attempted to quantify the number of facts PLMs learn, but we present, using synthetic data, the first study that investigates the causal relation between facts present in training and facts learned by the PLM.
Edit intent: clarity
Original:  Further, subgraph prediction tasks present several unique challenges , because subgraphs can have non-trivial internal topology, but also carry a notion of position and external connectivity information relative to the underlying graph in which they exist.
Revised:  Further, subgraph prediction tasks present several unique challenges : subgraphs can have non-trivial internal topology, but also carry a notion of position and external connectivity information relative to the underlying graph in which they exist.
Edit intent: coherence
Original:  Empirical results for subgraph classification on eight datasets show that SUB-GNN achieves considerable performance gains, outperforming strong baseline methods, including node-level and graph-level GNNs, by 12.4 \% over the strongest baseline.
Revised:  Empirical results for subgraph classification on eight datasets show that SubGNN achieves considerable performance gains, outperforming strong baseline methods, including node-level and graph-level GNNs, by 12.4 \% over the strongest baseline.
Edit intent: clarity
Original:  Empirical results for subgraph classification on eight datasets show that SUB-GNN achieves considerable performance gains, outperforming strong baseline methods, including node-level and graph-level GNNs, by 12.4 \% over the strongest baseline.
Revised:  Empirical results for subgraph classification on eight datasets show that SUB-GNN achieves considerable performance gains, outperforming strong baseline methods, including node-level and graph-level GNNs, by 19.8 \% over the strongest baseline.
Edit intent: meaning-changed