sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Because M is a left-stochastic linear map between finite-dimensional spaces, it is a continuous map from the convex and compact S to a convex and compact subset of S that we denote S M . The shadow Dirichlet has two parameters: the generating Dirichlet's parameter α ∈ R d + , and the d × d matrix M . Both α and M can be estimated from data.
Sentence 2: as we show in the following subsections, the matrix M can be profitably used as a design parameter that is chosen based on application-specific knowledge or side-information to specify the restricted domain S M , and in that way impose dependency between the components of the random pmfs.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: . . = r N = r. Let the recovered tensor A = G ×1 U 1× .
Sentence 2: . . ×N U N , the root mean square error (RMSE) is a frequently used measure of the difference between the recovered tensor and the true one: RMSE := 1 √ I N ∥D − A∥ F . [25] analyzes the statistical performance of the convex tensor Schatten 1-norm minimization problem with the general linear operator X : R I1×...×IN → R m . our model ( 6) is non-convex for the LRTC problem with the operator P Ω .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This motivates the idea of using dimensionality reduction methods to identify the features that affect the neural response [1][2][3][4][5][6][7][8][9].
Sentence 2: many neurons in the early visual pathway pool signals from a small population of upstream neurons, each of which integrates and nolinearly transforms the light from a small region of visual space.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Like VEEGAN, all of these methods also use a discriminator D ω (z, x) on the joint (z, x) space.
Sentence 2: the VEEGAN objective function O(θ, γ) provides significant benefits over the logistic regression loss over θ and γ that is used in ALI/BiGAN, or the KL-divergence used in LFVI.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Lion 5 Jaguar Cat Whale 0.8 0.6 Input 1 Input 2 Cat Jaguar Lion Whale Cat Jaguar Cat Lion sampled subset sampled subset sampled subset target Deep learning models have shown impressive performances on classification tasks [17,10,11].
Sentence 2: most of the efforts thus far have been made on improving the network architecture, while the predominant choice of the final classification function remained to be the basic softmax regression.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Figure 3 (supplement) also further emphasizes the utility of Bayesian marginalization versus optimization, even with vague priors.
Sentence 2: we do not necessarily expect high fidelity images from any arbitrary generator sampled from the posterior over generators; in fact, such a generator would probably have less posterior probability than the DCGAN, which we show in Section 2 can be viewed as a maximum likelihood analogue of our approach.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then Note that for fixed , δ, when α → 0 the above bound approaches the familiar O ln( 1 /δ) 2 bound by DKW [12] and Massart [17] for α = 0.
Sentence 2: when α → 1 the above bound tends to ∞, reflecting the fact that the multiplicative variant of Glivenko-Cantelli (α = 1) does not hold.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We note that it is possible to ensure that under some conditions that the dual support method will correctly recover each of the individual signed supports, without any incorrect exclusions.
Sentence 2: as illustrated by Theorem 2, doing so requires additional assumptions on the size of the gap Our results thus far show under standard mutual incoherence or irrepresentability conditions, the block 1 / ∞ method produces consistent estimators for n = Ω(s log(p − s)).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Note that conditioned on {Y d } D d=1 , both the latent matrix Z and the weighting matrices {B d } D d=1 are independent of the observation matrix Gibbs sampler and, in consequence, is the standard method of choice in the context of the standard linear-Gaussian IBP [8].
Sentence 2: this algorithm suffers from a high computational cost (being complexity per iteration cubic with the number of data points N ), which is prohibitive when dealing with large databases.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As we can see, ZO-SVRG-Ave requires more queries than ZO-SGD to achieve the first significant drop in attack loss.
Sentence 2: by fixing the total number of queries (10 7 ), ZO-SVRG-Ave eventually converges to a lower loss than ZO-SGD: the former reaches the average loss 4.81 with std 0.32 (computed from the last 100 attack losses), while the latter reaches 6.74 ± 0.46.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Alongside components such as residual blocks and long-short term memory networks, soft attention provides a rich neural network building block for controlling gradient flow and encoding inductive biases.
Sentence 2: more so than these other components, which are often treated as black-boxes, researchers use intermediate attention decisions directly as a tool for model interpretability [43,1] or as a factor in final predictions [25,68].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: These results were further boosted by recent work on extra-gradient variants of the algorithm [11,17], and the ergodic relaxation of [8] where the independence assumption on the gradient samples is relaxed and is replaced by a mixing distribution that converges in probability to a well-defined limit.
Sentence 2: all these works focus exclusively on the algorithm's ergodic average (also known as timeaverage), a mode of convergence which is strictly weaker than the convergence of the algorithm's last iterate.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This operation is difficult to implement efficiently for large-scale data with many features even if all features are sparse, although important progress was made recently so the complexity is logarithmic in the number of features [5].
Sentence 2: the soft-regularization formulation ( 2) is efficient for a batch setting [8] so we pursue it here in an online setting where it has complexity independent of the number of features.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Figure 4a  STC model performs significantly better than the subunit model (Figure 4a; < r Rust >= 0.81, < r subunit >= 0.33; p ⌧ 0.005).
Sentence 2: this is primarily due to over-fitting: Visual inspection of the STC kernels for most cells reveals very little structure.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It is important to note that c ∞ ≥ c 2 , which implies then that as long as c ∞ → 0, then c 2 → 0, so that the conditions of Theorem 3(a) and (b) are equivalent.
Sentence 2: note that if c 2 does not go to 0, then in fact, the method could fail to recover the correct support even if θ 1,∞ > 1 + δ.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the update steps used by ARS V1 and V2 each perturbation direction k is weighted by the difference of the rewards r(⇡ j,k,+ ) and r(⇡ j,k, ).
Sentence 2: if r(⇡ j,k,+ ) > r(⇡ j,k, ), ARS pushes the policy weights M j in the direction of k . If r(⇡ j,k,+ ) < r(⇡ j,k, ), ARS pushes the policy weights M j in the direction of k . since r(⇡ j,k,+ ) and r(⇡ j,k, ) are noisy evaluations of the performance of the policies parametrized by M j + ⌫ k and M j ⌫ k , ARS V1 and V2 might push the weights M j in the direction k even when k is better, or vice versa.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To improve the speed of learning decoupled models, we consider the use of natural gradient descent [2].
Sentence 2: in particular, we are interested in the update rule for natural parameters, which has empirically demonstrated impressive convergence performance over other choices of parametrizations [29] it is unclear what the natural parameters (5) for the general decoupled basis in (5) are and whether finite-dimensional natural parameters even exist for such a model.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Since the classification result is determined by the majority vote from 3 nearest instances, the classification loss is defined using the distance to the 2nd nearest instance in each class (which is referred to as a TN; see Section 2 for details).
Sentence 2: since 'nearest' instances are generally changed when feature metric/weights are updated, TNs must also be updated to be kept consistent with the learned feature metric/weights during the learning process.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Sparse learning with convex regularization has been successfully applied to a wide range of applications including marker genes identification [19], face recognition [22], image restoration [2], text corpora understanding [9] and radar imaging [20].
Sentence 2: it has been shown recently that many convex sparse learning formulations are inferior to their non-convex counterparts in both theory and practice [27,12,23,25,16,26,24,11].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: From this low-rank approximation to H the model parameters A, C as well as the covariances Q and R can be found by linear regression and by solving an algebraic Riccati equation; d is given simply by the empirical mean of the data.
Sentence 2: this specific procedure works only for linear systems with Gaussian observations and innovations, and not for models which feature non-linear transformations or non-Gaussian observation models.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We then have: is the Gibbs error rate (by definition), we see that the expected margin is just one minus twice the Gibbs error rate.
Sentence 2: the error for the Q-weighted majority vote is given by Hence, for large enough β, the sigmoid loss (or tanh loss) of f Q should be very close to the error rate of the Q-weighted majority vote.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Our proposed log partition function tracking strategy is applicable to any Gibbs distribution model that is undergoing relatively smooth changes in the partition function.
Sentence 2: we concentrate on its application to the RBM since it has become a model of choice for learning unsupervised features for use in deep feed-forward architectures [9,1] as well as for modeling complex, high-dimensional distributions [27,24,12].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It is also interesting to note that the NN3-30K initial model in panel (b), which is trained with more data, presents robustness to a larger level of noise compared to NN2-10K in panel (a).
Sentence 2: the retrained models behave rather similarly (blue curves) indicating the saving that can be achieved in the number of training samples via Net-Trim.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Current text generation approaches [16] often fail to capture the diversity of such small portion of descriptions, and pure generation pipelines are biased towards generating plausible sentences that look natural by the language model but poor at finding visual groundings [17].
Sentence 2: a desirable medical report usually has to not only describe normal and abnormal findings, but also support itself by visual evidences such as location and attributes of the detected findings appearing in the image.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In FWBQ, we first select design points {x FW i } n i=1 using the FW algorithm.
Sentence 2: when computing the quadrature approximation, instead of using the usual FW weights {w FW i } n i=1 we use instead the weights {w BQ i } n i=1 provided by BQ.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Positive coefficients for sender outdegree, reciprocity, and transitivity in these plots imply that users with a high numbers of friends tend to make more friends, tend to reciprocate their relations, and tend to make friends with their friends' friends, respectively.
Sentence 2: these coefficients decrease towards zero (the blue line) and enter a second phase where the network is structurally stable.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: (2010) [9] gave an ℓ ∞,∞ -norm error bound ) as well as a sign consistency result between Ŵ and W . A direct comparison between these two bounds is difficult due to the use of different norms.
Sentence 2: the worst-case estimate of the ℓ 2,1 -norm error bound of the algorithm in Jalali et al.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We can see that SVRG HEB with some underestimated values of T 1 (e.g, 1000, 2000) converge very slowly.
Sentence 2: the performance of SVRG QEB-RS is not affected too much by the initial value of T 1 , which is consistent with our theory showing the log dependence on the initial value of c. Moreover, SVRG QEB-RS with different values of T 1 perform always better than their counterparts of SVRG HEB .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In addition, it means that we cannot use standard minimax theory for Holder classes to establish lower bounds for the estimation error over GTF classes.
Sentence 2: as we will see next, we can construct lower bounds for GTF classes via another (more purely geometric) embedding strategy; interestingly, the resulting rates match the Holder rates, suggesting that, while GTF classes do not contain all (discretized) Holder functions, they do contain "enough" of these functions to admit the same lower bound rates.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For instance, nurse is moved to to be equally male and female in the direction g. In addition, we find that gender-specific words have additional biases beyond g. For instance, grandmother and grandfather are both closer to wisdom than gal and guy are, which does not reflect a gender difference.
Sentence 2: the fact that babysit is so much closer to grandmother than grandfather (more than for other gender pairs) is a gender bias specific to grandmother.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The KL-divergence KL(ψ∥θ) := x p(x; ψ) log p(x;ψ) p(x;θ) is arguably the optimal divergence for marginal inference because it strives to preserve the marginals of p(x; θ) and p(x; ψ).
Sentence 2: projection in KL-divergence is intractable here because the evaluation of the gradient ∇ θ KL(ψ∥θ) requires the marginals of distribution ψ.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This result shows that any POMDP can be encoded as an HGMDP with deterministic dynamics, where the stochastic dynamics of the POMDP are captured via the stochastic agent policy in the HGMDP.
Sentence 2: the HGMDPs resulting from the PSPACE-hardness reduction are quite pathological compared to those that are likely to arise in practice.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It is clear from the graph that trajectories sampled from reversible chains spread much slower, with only 1/5 of the states reached in (a) and 1/3 in (b), and the trajectory in (b) does not escape from the current peak.
Sentence 2: with vortices added, trajectories of the same length spread over all the states, and effectively explore both peaks of the stationary distribution in (b).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Hence H satisfies this weak-learning condition.
Sentence 2: it can be shown (supplement) that AdaBoost.MH's weak-learning condition is the pair (C MH , B MH γ ), where C MH has non-(positive)negative entries on (in)correct labels, and where each row of the matrix B MH γ is the vector quick calculation shows that for any h ∈ H, and C ∈ C MH with −1 in the first column and zeroes elsewhere, C • 1 h − B MH γ = 1/2 − 1/k.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Recently, Caron & Fox (2014)  proposed the use of a different notion of exchangeability after Kallenberg (2005) and obtained a network model which permits edge-inhomogeneity, such as a power-law degree-distribution whilst retaining desirable statistical properties.
Sentence 2: this model does not capture latent vertex traits such as block-structure.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Sparse Gaussian process (GP) regression [Titsias, 2009] and the Bayesian Gaussian process latent variable model (GPLVM, Titsias and Lawrence [2010]) have been applied in many tasks, such as regression, density estimation, data imputation, and dimensionality reduction.
Sentence 2: the use of these models with big datasets has been limited by the scalability of the inference.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: With the parametric form of quadratic splines, the total length and the curvature along a real fragment can be computed by summing over each spline its length and its total curvature as where l i is the length and κ i (t) is the curvature function of the ith spline.
Sentence 2: estimating these quantities for a virtual fragment is not trivial, as no information is given on how the virtual fragment should look like.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Both h 1 and h 2 are consistent with examples in Z.
Sentence 2: as H is well-structured, mgh(Z) must also be in the version space M(Z), and consequently in H. mgh(Z) = h 1 ∪ h 2 because it cannot include any element without h 1 ∪ h 2 and must include all elements within.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The LP tightness is an inevitable condition to guarantee the performance of BP and no combinatorial optimization instance has been known where BP would be used to solve problems without the LP tightness.
Sentence 2: in the LP literature, it has been extensively studied how to enforce the LP tightness via solving multiple intermediate LPs that are systematically designed, e.g., via the cutting-plane method [21].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Now by using the classical chaining method (Theorem 1) to upper bound E[X W ] by upper bounding E[sup φ∈[0,2π) X φ ] and ignoring the algorithm, we get On the other hand, for every k ≥ −1 we have Therefore, based on the chained mutual information method (Theorem 4), we have Numerical values of the right side of (36) for different values of are given in Table 1 (CMI bound).
Sentence 2: note that indeed the slow rate of that convergence and the existence of the 2 −k term makes the sum not only finite, but very small.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Over the past years, Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have emerged as the state-of-the-art learning framework for action recognition [3,6,35,51].
Sentence 2: the success of existing supervised learning methods is primarily driven by significant amount of manually labeled data, which is expensive and time-consuming to collect.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In order to learn the optimal policies in this framework and to facilitate the development of the paper, we follow generalized policy iteration (GPI) (Sutton and Barto [2018]).
Sentence 2: the Bayesian framework developed in this paper is dependent on neither the exploration policy used nor the value function representation, and can be applied with on-policy and off-policy learning, value function approximation, traces, deep RL (Li [2017]), and other approaches.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Compared to the aforementioned ZO algorithms [5,14,24], the convergence performance of ZO-SVRG in (10) has an improved (linear rather than sub-linear) dependence on 1/T .
Sentence 2: it suffers an additional error of order O(δ n /b) inherited from (Sχ m /(T γ)) in (5), which is also a consequence of the last error term in (4).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Note that for an 2 norm bounded adversarial perturbation, the dual norm is also an 2 norm, so we can use traditional random projections [Vempala, 2005].
Sentence 2: experiments for the 2 norm are explored further in Appendix H. for the remainder of this section we focus on the 1 case arising from ∞ perturbations.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The recently emerged parameter server architecture [15,18] has started to pave ways for a unified programming interface for data parallel algorithms, based on various parallellization models such as stale synchroneous parallelism (SSP) [15], eager SSP [5], and value-bound asynchronous parallelism [23], etc.
Sentence 2: in addition to Big Data, modern large-scale ML problems have started to encounter the so-called Big Model challenge [8,1,17], in which models with millions if not billions of parameters and/or variables (such as in deep networks [6] or large-scale topic models [20]) must be estimated from big (or even modestly-sized) datasets.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: the Horn and Schunck model is close to the optimal Gaussian model, robust models are better, intensity discontinuities make motion discontinuities more likely).
Sentence 2: a learned GMM model with 64 components significantly outperforms the standard models used in computer vision, primarily because it explicitly distinguishes between flat patches and boundary patches and then uses a different form of nonlocal smoothness for the different cases.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Forms of these terms are similar to the one defined for the object-reflectance higher order terms; these terms are further explained in the supplementary material.
Sentence 2: given the above model, our optimization problem involves solving following joint energy function to get the most likely solution for (R, Z, L, O, A): this problem is very challenging since it consists of both the continuous variables (R, Z, L) and discrete variables (O, A).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Hence, none of these methods allow for local updates to modular policies, which makes them undesirable from a biological standpoint, and impractical for policies for which this derivative is prohibitively difficult to compute.
Sentence 2: by combining these methods with the CoMDP framework reviewed in Section 2.2 and by taking advantage of Property 1, the updates to the actor can be modified to satisfy the locality constraint.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: -FG vs. SG: Although the performance of SG methods can be catastrophic if the step size is not chosen carefully (e.g., the covertype data), with a carefully-chosen step-size the SG methods do substantially better than FG methods on the first few passes through the data (e.g., the rcv1 data).
Sentence 2: fG methods are not sensitive to the step size and because of their steady progress we also see that FG methods slowly catch up to the SG methods and eventually (or will eventually) pass them (e.g., the protein data).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Similarly, we suggest that the large and variable object set used here may provide a meaningful constraint on network structure, as the specific object geometries may be less important then having a wide spectrum of such geometries.
Sentence 2: a key next priority is systematically building an appropriately large and variable set of objects, textures or other class boundaries that more realistically model the tasks that a rodent faces.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Split-merge MCMC algorithms, e.g., Restricted Gibbs split-merge (RGSM) [13] and Smart-Dumb/Dumb-Smart (SDDS) [36], use handdesigned MCMC moves to solve such issues.
Sentence 2: in our framework, it's possible to deal with such relations with a proposal block including all of z, µ and v. doing so requires significant training and inference time (due to larger proposal network and larger proposal block), and the resulting proposal can not generalize to GMMs of different sizes.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The well-known fact that the Laplace mechanism with b ≥ ∆/ε is (ε, 0)-DP follows from this result by noting that δ M (ε) = 0 for any ε ≥ θ.
Sentence 2: theorem 3 also provides more information: it shows that for ε < ∆/b the Laplace mechanism with noise parameter b satisfies (ε, δ)-DP with δ = δ M (ε).
Relationship: contrasting