sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Sketching is a powerful dimensionality reduction tool for accelerating statistical learning algorithms.
Sentence 2: its applicability has been limited to a certain extent since the crucial ingredient, the so-called oblivious subspace embedding, can only be applied to data spaces with an explicit representation as the column span or row span of a matrix, while in many settings learning is done in a high-dimensional space implicitly defined by the data matrix via a kernel transformation.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Method Average Score DQN [66] 343 ± 18 A3C (continuous) [36] 591 ± 45 A3C (discrete) [41] 652 ± 10 Gym Leader [44] 838  Full World Model (V and M) The representation z t provided by V only captures a representation at a moment in time and does not have much predictive power.
Sentence 2: m is trained to do one thing, and to do it really well, which is to predict z t+1 .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Over the past twenty years or so, the attention of cognitive neuroscientists and computationally minded psychologists has tended to focus on habit-based control, due in large part to interest in potential links between dopaminergic function and temporal-difference algorithms for reinforcement learning.
Sentence 2: a resurgence of interest in purposive action selection is now being driven by innovations in animal behavior research, which have yielded powerful new behavioral assays [3], and revealed specific effects of focal neural damage on goaldirected behavior [4].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: 6: end for Return: x k . Algorithm 4: ReLU pxq Input: x x 1 1: Branch: Algorithm 5: ReLU pxq Input: x x 1 1: Branch: Figure 1: Two programs that implement ReLU pxq: Both programs are correct and return the same value.
Sentence 2: the program on the right violates Assumption 3.1 since the gradient of the constraint function at x 0, ∇px 3 1 q 3x 2 1 0. where each p z is a polynomial; I Sz is the indicator function on the set S ; and S z consists of all x where the program executes branch z when given x as input.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The effects of stress, strain, and NA on future reward discounting indicate that stress, high anxiety, and elevated noradrenaline are all detrimental for learning delayed future rewards.
Sentence 2: since the effects of NA and stress on reward discount factors are more pronounced for DBA/2 mice, γ-s might be sensitive to noradrenaline at higher levels than β-s are.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: . . y [r,I] ): Input variables, such as "feature vectors" in a purely discriminative model.
Sentence 2: a CGPM is required to satisfy the following conditional independence constraint: (1) Eq (1) formalizes the notion that all dependencies across members r ∈ N are completely mediated by the population parameters θ and member-specific variables z r . elements x [r,i] and x [r,j] within a member are generally free to assume any dependence structure.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Belief propagation (BP), originally proposed by Pearl [1], has gained in popularity as a method of approximate inference, and in the last decade has led to a number of more sophisticated algorithms based on conjugate dual formulations and free energy approximations [4,5,6].
Sentence 2: the progress on approximate inference in systems with continuous random variables has not kept pace with that for discrete random variables.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We have only considered classification tasks in this paper, but a continuous key-value cache component can be added to models performing other image-based tasks, such as object detection or segmentation, as well.
Sentence 2: different tasks might require different similarity measures (Equation 1) and different ways of combining the predictions of the cache component with the predictions of the underlying model (Equation 3).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For function F and any U ∈ {U|σ min (X U) ≥ γ}, we have: Lemma 4.2 tells function f is smooth if spectral norm of U is not very large.
Sentence 2: σ min (X U) not too small requires both σ min (U U) and σ min (X W) are not too small, where W is top-k eigenspace of UU .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the three plots involving feature y 1 it can be seen that the directions of the response vector (i.e., the vector composed of the slow feature values at a particular point in time) cluster at class-specific angles, which is characteristic for What-information.
Sentence 2: these phase plots tend to form loops in phase space (instead of just straight lines from the origin), where each point on this loop corresponds to a position within the trajectory.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Due to the low-rank constraint in our optimization framework, we seek a small value of eigengap(C) for a good optimal value.
Sentence 2: we can set a stopping criterion for our method using eigengap(C) < T for a small threshold, T . due to the noise reaching a small threshold cannot be guaranteed, therefore, a practical stopping criterion adopted by our method is when eigengap(C) has stoped decreasing.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For the more general setting where p may not be uniform, Foygel and Srebro [4] show that the max norm is still an effective regularizer (in particular, bounds on error for the max norm are not affected by p).
Sentence 2: salakhutdinov and Srebro [5] show that the trace norm is not robust to non-uniform sampling-regularizing with the trace norm may yield large error due to over-fitting on the rows and columns with high marginals.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This "Ugliness-in-Averageness" (UiA) effect has previously been explained via a qualitative disfluency account, which posits that the negative affect associated with the difficult race or gender categorization is inadvertently interpreted by the brain as a dislike for the face itself.
Sentence 2: we hypothesize that human preference for an object is increased when it incurs lower encoding cost, in particular when its perceived statistical typicality is high, in consonance with Barlow's seminal "efficient coding hypothesis."
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Using ( 13), (18), and (11), we can further write Since t > 1, it is easy to see that r j (θ) > 0 is a convex function of θ.
Sentence 2: since g t is convex and t > 1 it follows that l i (θ) > 0 is also a convex function of θ.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Many planning problems in robotics are best phrased as MDPs, defined over world states or-in case of partial observability-belief states [7].
Sentence 2: existing MDP planning techniques generally scale poorly to multirobot systems because of the curse of dimensionality: in general, it is exponentially harder to solve an MDP for N agents than it is to solve a single-agent MDP, because the state and action space for N robots can be exponentially larger than for a single-robot system.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: First, we have purposely incorporated the self-attention module into all of our baselines models-indeed having self-attention in the architecture could potentially induce a supervisedly-trained graph, because of which one may argue that this graph could replace its unsupervised counterpart.
Sentence 2: as is shown in Table 1, augmenting training with unsupervisedly-learned graphs has further improved performance.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Submodular optimization is an important problem that arises across many settings, including sensor placements [16,15], summarization [26,17,23], inferring latent influence networks [8], diversified recommender systems [5,4,25,21], and multiple solution prediction [1,3,22,19].
Sentence 2: the majority of previous work has focused on offline submodular optimization whereby the submodular function to be optimized is fixed a priori (i.e., does not vary depending on feedback).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: By Lemma 9, the long-run average payoff to Player 1 from time T onward is within the interval val(G ij ) ± O(κ) ± O(ε).
Sentence 2: by Lemma 9 again, the long-run average payoff to Player 1 from time 0 onward is within the interval val(G) ± O(ε).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As pointed out in [52], KDEs seldom do a good job of capturing the underlying density, since they do not scale well with data.
Sentence 2: when the underlying data distribution is discrete, count-based non-parametric models such as smoothed n-gram language models [20] are extremely it is therefore quite impossible to separate the various provisions of the single market with regard to quotas .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Previous analyses of EM only established such results for specific methods of initializing EM (e.g., Dasgupta and Schulman, 2007;Balakrishnan et al., 2014); our results show that they are not really necessary in the large sample limit.
Sentence 2: in any real scenario, the large sample limit may not accurately characterize the behavior of EM.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To achieve better numerical efficiency and convergence behavior compared to the dual ascent method, it is favorable to set ρ > 0 in the augmented Lagrangian (2) which we call the method of multipliers.
Sentence 2: ( 2) is no longer separable and solving entire augmented Lagrangian (2) exactly is computationally expensive.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In a deterministic optimization setting and for general smooth convex functions, these methods enjoy a rate of O(1/n 2 ) (where n is the number of iterations) as opposed to O(1/n) using standard methods.
Sentence 2: in a stochastic setting (which is the relevant one for learning problems), the rate of both approaches have an O(1/ √ n) dominant term in general, so the benefit of using accelerated methods for learning problems is not obvious.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: There is a series of on-going works on this direction [29,34,32,13,2,11,31,33].
Sentence 2: among all these networks designed for image classification, the features of high resolution are extracted by the shallow layers with small receptive field, which lack the high-level semantic meaning that can only be obtained on Design in combining features from different layers.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This is because in our scheme the training size is not the number of instances, but rather the number of observed features (See Table 1).
Sentence 2: in the next theorem we obtain an upper bound that is independent of m, and hence is tighter for large m. Pr sup {t1,...,tm} where |X j | denotes the alphabet size of X j (i.e.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ( 2)) factorizes over a graph, we can, in theory, use local messages to propagate beliefs about statistics t[p ✓ ✓ ✓(x) (y)] along its edges (BP; [20]).
Sentence 2: special care must be taken to handle intractable operations caused by non-parametric local potentials and to allow an end-to-end integration.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This is because the scene classification model is influenced by the latent object modeling through the term ∆L ⋆ d (s), which can improve the decision boundary of a standard linear SVM for those images that have negative scores of ∆L ⋆ d (s), as we have discussed in the online loss-augmented SVM.
Sentence 2: object modeling does not improve the classification accuracy and sometimes it can even be harmful when the scene model is learned with the standard MLE.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Hierarchical clustering models aim to fit hierarchies to data, and enjoy the property that clusterings of varying size can be obtained by "pruning" the tree at particular levels.
Sentence 2: standard clustering models must specify the number of clusters beforehand, while Nonparametric Bayesian (NPB) clustering models such as the Dirichlet Process Mixture (DPM) [5,13] directly infer the (effective) number of clusters.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The sufficient statistics of the model are the visible activations v, the hidden activations h, and the products vh T . Therefore, γ M A is defined by: For many models of interest, including RBMs, it is infeasible to determine γ M A exactly, as it requires solving two often intractable problems: (1) computing the moments of p b , and (2) solving for model parameters which match the averaged moments s(β).
Sentence 2: much work has been devoted to practical approximations [19,20], some of which we use in our experiments with intractable models.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For instance, to the best of our knowledge, there is no result explaining how to sample the space so that the corresponding sensing matrix Φ satisfies the nice recovery properties needed by the previous theorems, for a general family of features {ϕ k } k≤K .
Sentence 2: it is proven in [12] that under some hypotheses on the functional basis, we are able to recover the strong RIP property for the matrix Φ with high probability.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ( 8), allows us to create an optimization problem that minimizes an upper bound on the average loss in eq.
Sentence 2: ( 5) with maximum-margin constraints: ξ iα subject to: Note that if we have a very large number of classes, it might be beneficial to choose P ∈ R r×c with r < c. the convex formulation described in the next paragraph requires P to be square.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For practical and computational reasons we choose to work with the space of trigonometric polynomials H nm defined below, where each element of the space is a function in n m variables (n m ∈ N, m = 1, 2, ..., M ).
Sentence 2: we note that the results obtained in this paper are not limited to this particular choice of RKHS (see, e.g., [24]).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We verify that the solutions to MF-IIM undergo a shift from focusing on high-degree nodes at low interaction strengths to focusing on low-degree nodes at high interaction strengths.
Sentence 2: we also find that for sufficiently high and low interaction strengths, the MF optimal external field achieves the maximum exact magnetization, while admitting performance losses near β c . even at β c , we demonstrate that solutions to MF-IIM significantly outperform common node-selection heuristics based on node degree and centrality.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The hierarchical regression parameters are just like topics' regression parameters in SLDA: each topic k (here, a tree node) has a parameter η k , and the model uses the empirical distribution over the nodes that generated a document as the regressors.
Sentence 2: the hierarchy in SHLDA makes it possible to discover relationships between topics and the response variable that SLDA's simple latent space obscures.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The pre-image of the projection is the z ∈ X that satisfies ϕ(z) = Pϕ(x); z is also referred to as the KPCA reconstruction of x.
Sentence 2: the pre-image of Pϕ(x) usually does not exist, so finding the KPCA reconstruction of x means finding z such that ϕ(z) is as close to Pϕ(x) as possible.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The standard approach to characterizing symmetries in objects is to look not at their images, but at their 3D shape; if the latter is available, then symmetries can be recovered by analysing the intrinsic geometry of the shape.
Sentence 2: often only images of the objects are available, and reconstructing an accurate 3D shape from them can be very challenging, especially if the object is deformable.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Supposing that σ is sufficiently small, it is a straightforward argument that even when n = 1, β * is recoverable from Y = X, β * + W by a brute-force method with probability tending to one as p goes to infinity (whp).
Sentence 2: for sparse and binary-valued β * , the Basis Pursuit method in the noiseless case Donoho and Tanner (2006) and the Basis Pursuit Denoising Scheme in the noisy case Gamarnik and Zadik (2017b) have been proven to fail to recover a binary β * with n = o(k log p k ) samples.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: An alternative approach towards scalability is to restrict the size of the subsets, as done in k-DPP [16] or when using rank-k DPP kernels [9] (where k ≪ N ).
Sentence 2: without further assumptions, both approaches still require O(N 3 ) preprocessing for exact sampling; another caveat is that they limit the DPP model by assigning zero probabilities to sets of cardinality greater than k. KRONDPP uses a kernel matrix of the form L = L 1 ⊗ .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In particular, it gives a low probability to the coincidence that, while "dax" meant BALL the entire time, the model happened never to hear dax when there was a ball around.
Sentence 2: a lexicon learning no new words scores best on the corpus (because of the prior on smaller lexicons) but has no explanation for why it heard the word "dax" in the new situation.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This visual similarity is reflected in the rank correlation with absolute value (Figure 3-Top), SSIM, and the HOGs metric (Figure 4).
Sentence 2: re-initialization disrupts the sign of the map, so that the Spearman rank correlation without absolute values goes to zero (Figure 3-Bottom) almost as soon as the top layers are randomized.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The classifier resulting from minimising the unhinged loss is not new [Devroye et al., 1996, Chapter 10], [Schölkopf and Smola, 2002, Section 1.2], [Shawe-Taylor and Cristianini, 2004, Section 5.1].
Sentence 2: establishing this classifier's (strong) SLN-robustness, uniqueness thereof, and its equivalence to a highly regularised SVM solution, to our knowledge is novel.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For margins γ γ, which are prone to over-fitting, Q n (α(γ), m(γ)) is not a reliable estimate for h S n (γ) since compression may not yet taken place for samples of size n. Nevertheless, these margins are discarded by KSU due to the penalty term in Q.
Sentence 2: for γ-nets with margin γ γ, which are prone to under-fitting, the true error is well estimated by As one can see, the assumption that X is finite-dimensional plays a major role in the proof.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The above theorem suggests that ψ-regularized multi-agent inverse reinforcement learning is seeking, for each agent i, a policy whose occupancy measure is close to one where we replace policy π i with expert π Ei , as measured by the convex function ψ i .
Sentence 2: we do not assume access to the expert policy π E during training, so it is not possible to obtain ρ π i,E −i .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In this asymptotic setting the local MICL criterion behaves like k-Nearest Neighbor (k-NN).
Sentence 2: the finitesample behavior of the local MICL criterion can differ drastically from that of k-NN, especially   , local MICL effectively approximates the local shape of the distribution p j (x) by a (regularized) Gaussian, exploiting structure in the distribution of the nearest neighbors (see figure 3).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ( 1) can be reformulated as a maximization for θ using max θ f (θ, w * (θ)).
Sentence 2: typical GAN training only alternates two gradient updates w ← w − η w ∇ w f (θ, w) and θ ← θ + η θ ∇ θ f (θ, w), and usually just one step for each of θ and w in each round.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The heart data involves 6 variables giving rise to 2 6 = 64 clique candidates in total and a search space of 2 This illustrates the power of branch-and-bound type algorithms behind the solvers and their ability to prune the search space.
Sentence 2: the econ dataset is based on 8 variables giving rise to a much larger search space 2 28 .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Here, we consider polynomial combinations of higher degree d ≥ 1 of the base kernels with non-negative coefficients of the form: Any kernel function K µ of this form is PDS since products and sums of PDS kernels are PDS [4].
Sentence 2: note that K µ is in fact a linear combination of the PDS kernels the number of coefficients µ k1•••kp is in O(p d ), which may be too large for a reliable estimation from a sample of size m. Instead, we can assume that for some subset I of all p-tuples (k 1 , .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We find that object recognition performance of models B1 to B9 is improved compared to models A1 to A9, both on the distortions they were actually trained on (diagonal entries with red rectangles in Figure 4) as well as on a few of the distortions that were not part of the training data.
Sentence 2: this improvement may be largely due to the fact that models B1 to B9 were trained on 200 epochs instead of 100 epochs as for models A1 to A9, since the accuracy of model B9 (trained & tested on uniform noise, 200 epochs) also shows an improvement towards model A9 (trained & tested on uniform noise, 100 epochs).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: While other features such as "athlete" or "musician" might indicate that one person could be a friend of another, the geographic features could have extremely negative weights so that people who live far from each other are less likely to be friends.
Sentence 2: the parameters for the non-geographic features would still be tied for all people, allowing us to make stronger inferences about how they influence the relations.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It has been shown that when using a characteristic kernel for the mapping [9], the properties of RKHS operators are related to statistical independence between input variables and allow testing for it in a principled way with the Hilbert-Schmidt Independence Criterion (HSIC) test [11].
Sentence 2: the suitability of this test relies heavily on the assumption that i.i.d.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A deep understanding of the value of control items may provide useful guidance for crowdsourcing practitioners.
Sentence 2: a line of research has studied more advanced consensus methods that are able to simultaneously estimate the workers' performance and items' answers without any ground truth on the items, by building joint statistical models of the workers and labels (e.g., Dawid and Skene, 1979, Whitehill et al., 2009, Karger et al., 2011, Liu et al., 2012, Zhou et al., 2012.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: BrownBoost is designed for noise tolerance, and it does well in the case of l = 5, but it also cannot handle the case of l = 20 and η > 0%.
Sentence 2: directBoost order performs very well for all cases, showing DirectBoost order 's impressive noise tolerance property since the most difficult examples are given up without any penalty.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then, for any bidding policy µ, R µ T (f ) ≥ (1/16 The proof of Theorem 2 is obtained by showing that, every time the bid is cleared, an incremental regret greater than /2 is incurred under the distribution with π = (1/2− ); otherwise, an incremental regret greater than /2 is incurred under the distribution with π = (1/2 + ).
Sentence 2: to distinguish between these two distributions, one needs Ω(T ) samples, which results in a regret lower bound of Ω( √ T ).
Relationship: contrasting