sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Such environments are widely used, both as benchmark tasks for RL agents [Brockman et al., 2016], and as "cheap" simulation environments that can (ideally) allow for transfer to real domains.
Sentence 2: despite their ubiquity, these simulation environments are in some sense poorly suited for deep learning settings: the environments are not natively differentiable, and so gradients (e.g., policy gradients for control tasks, physical property gradients for modeling fitting, or dynamics Jacobians for model-based control) must all be evaluated via finite differencing, with some attendant issues of speed and numerical stability.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We report ν in Figure 2. l 1 init + refine achieves nearly the global maximum on both datasets and outperforms random init + refine, showing the effectiveness of the proposed initialization and that the iterative update ( 6) can get stuck in a bad local minimum if initialized badly.
Sentence 2: l 1 init + refine outperforms l 1 init alone, showing the importance of iteratively refining the solution.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: COCO tends to find functions with large variance for f (X) and g(Y ), which may not be the most correlated features.
Sentence 2: kernel CCA may encounter situations where it finds functions with moderately large covariance but very small variance for f (X) or g(Y ), since Σ XX and Σ Y Y can have arbitrarily small eigenvalues.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Due to the properties of the L 1 score, in this solution, many features will have weight 0, generally leading to a sparse network structure.
Sentence 2: it is generally impractical to simply initialize the model to include all possible features: exact inference in such a model is almost invariably intractable, and approximate inference methods such as loopy belief propagation [17] are likely to give highly inaccurate estimates of the gradient, leading to poorly learned models.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In this setting, it would be desirable to obtain zero TE between both electrodes, since there is no interaction between the sources giving rise to the EEG.
Sentence 2: some rather tedious algebraic manipulations reveal that in this case Note that ( 4) is zero if and only if γ = 0, i.e., if s 3 represents white noise.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The latter may explain why dendrites can have a tuning different from the whole neuron as has been observed in Layer 2/3 pyramidal cells of the visual cortex [6].
Sentence 2: saturating dendritic units can enhance single neuron computation through implementing all positive Boolean functions (Proposition 3), while reducing the energetic costs associated with the active ion channels required for dendritic spikes [4,13].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Here we show that they provide natural priors for Bayesian entropy estimation, due to the analytic tractability of the moments of the induced posterior distribution over entropy H. We derive formulas for the posterior mean and variance of H given data.
Sentence 2: we show that a fixed Dirichlet or Pitman-Yor process prior implies a narrow prior on H, meaning the prior strongly determines the estimate in the under-sampled regime.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The myopic most uncertain selection method, MostUncertain, shows an overall inferior performance to Discriminative on Australian, Cleve, Crx, Heart and Hepatitis, and achieves a tie on Flare and Vote.
Sentence 2: discriminative demonstrates weak perfor-  These empirical results suggest that selecting unlabeled instances through optimizing the classification model directly would obtain more relevant and informative instances, comparing with using heuristic scores to guide the selection.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Kernel density plug-in estimators are simple, easy to implement and widely used for estimation of entropy.
Sentence 2: for large feature dimension d, kernel plug-in estimators suffer from the curse of dimensionality: the MSE rate of convergence is glacially slow -of order O(T −γ/d ), where T is the number of samples, and γ > 0 is a rate parameter.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Equivalently, this can be seen as letting the player use a refined partition with P + n cells.
Sentence 2: instead of sampling one point in R p,k , the algorithm is only allowed to sample all the K points in region in the chosen R p at the same time, one uniformly in each sub-region R p,k , still using of course the same total budget of n points (and not nK).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Xu and Jordan [34] examine several aspects of EM for GMMs and counter the claims of Redner and Walker [24], who claimed EM to be inferior to generic secondorder nonlinear programming techniques.
Sentence 2: it is now well-known (e.g., [34]) that EM can attain good likelihood values rapidly, and scales to much larger problems than amenable to secondorder methods.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This intersection framework provides several advantages with respect to earlier approaches based on computing the correlations between trial-averaged psychometric performance and trial-averaged neurometric performance [13,14,18], because it quantifies associations between sensory information coding and choices within the same trial, instead of considering the similarity of trial-averaged neural stimulus coding and trial-averaged behavioral performance.
Sentence 2: the intersection information measure proposed in Ref.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As this parameter is effectively a variance, natural estimators exist by assessing the problem in hyperparameter (variance) space, transitioning natural ideas from Type II to solve what is much less intuitive for Type I.
Sentence 2: for analyses of update rules and sparsity properties of local and global solutions, as well as extensions to more general likelihood models, we can leverage coefficient-space techniques developed for Type I and apply them to Type II.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The k nonnegative components W ∈ W k returned by our Low Rank NNPCA algorithm on the sketch M are used as a surrogate for the desired components of the original input M. Intuitively, the performance of the extracted nonnegative components depends on how well M is approximated by the low rank sketch M; a higher rank approximation leads to better results.
Sentence 2: the complexity of our low rank solver depends exponentially in the rank of its input.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The expectation (1) cannot be computed since the distribution P(x, y) is unknown.
Sentence 2: given a training set {(Xi, Yi) h <i<n, it is common to minimize instead the empirical ri~: -- Empirical Risk Minimization (ERM) is therefore equivalent to minimizing the expectation of the loss function with respect to an empirical distribution Pemp(x,y) formed by assembling delta functions located on each example: It is quite natural to consider improved density estimates by replacing the delta functions ox, (x) by some estimate of the density in the vicinity of the point Xi, PXi (X).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Permanently small ¡ corresponds to over-confidence in estimates of `¡ , thus making adaptation of that estimate slow, similar to NE depletion.
Sentence 2: because the NE system is still intact, the system is able to detect when ) ¡ dramatically differs from the prediction (which is often, since `is slow to adapt and leaves little room for variance), and thus to base inference of ) ¡ directly on the bottom-up information ¥ ) ¡ 0 ¡ .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: However, in PLDSID, only the cost O(N T pq 2 ) of calculating the Hankel-matrix scales with the data set size (assuming k is of order p).
Sentence 2: this simple covariance calculation was much cheaper in our experiments than the moment conversion with cost O(pq 2 ) or the SVD with cost O(p 3 q 3 ), both of which are independent of the data set size N T . each iteration of EM requires at least O(N T (p 3 + pq)) time.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We investigated several simple methods to defend against these attacks, including (i) evaluating the validation accuracy for each class label, instead of a global value, to find the contaminated label, (ii) running independence tests on the distribution of attributes between each party, and (iii) performing leave-one-party-out cross validation techniques.
Sentence 2: simple methods such as these were insufficient as a general defense.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Ignoring terms independent of the weighting parameters, its log is given by: (5) Computing ( 5) requires the quantities ICI and (VC-1rP, which for infinite dimensionality feature spaces might appear problematic.
Sentence 2: by judicious re-writing of the terms of interest, we are able to both compute the log-likelihood (to within a constant) and optimise it with respect to the weights.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Theorem 8 is proved via an inductive argument, given in Appendix C. Roughly, consider in Step 6 of Algorithm 2, setting Ŝ := S instead of S • S. By Lemma 5 and the formula in Lemma 6, the leverage score approximations l i computed in Step 7 would be good approximations to the true leverage scores, and S would satisfy Theorem 8 by a standard matrix Bernstein bound (see Lemma 9).
Sentence 2: if we set Ŝ := S, it will have n/2 columns in expectation, and the computation in Step 7 will be expensive -requiring roughly O(n 3 ) time.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In these applications there is a natural place where one might divide data into episodes: for type 1 diabetes treatment, one might treat each day as an independent episode, and for digital marketing, one might treat each user interaction as an independent episode.
Sentence 2: each day is not actually independent in diabetes treatment-a person's blood sugar in the morning depends on their blood sugar at the end of the previous day.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For each of these trends the flP model outperforms the causal power model, with overall R 2 values of 0.95 and 0.35 respectively.
Sentence 2: it is important to note that the responses of the human subjects in columns 8-10 (contingencies {l.00 , 0.50} , {0 .80 , 0.40} , {0 .40, O.OO}) are not quite consistent with the predictions of flP : they show a slight V-shaped non-linearity, with P( C -+E) judged to be smaller for 0.80 , 0.40 than for either of the extreme cases.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: From (7) we see that λ n appears in the conditional posterior p(f |y, K, λ, γ) as first order terms, thus we can write where n and γ (i) are the estimates of f n and γ at the i-th iteration, and u n . From (7) and (8) we can obtain the EM updates: In the ECM setting, learning the parameters of the covariance function is not as straightforward as in MCMC.
Sentence 2: we can borrow from the GP literature [7] and use the fact that we can marginalize f while conditioning on λ and γ: Note that K is a function of X and θ. Estimation of θ is done by maximizing log Z(y, X, λ, γ, θ).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Technically, BMC leverages the regularized Bayesian inference (RegBayes) principle [15], which has shown promise on supervised learning tasks, such as classification [16,17], link prediction [18], and matrix factorisation [19], where max-margin constraints are introduced to improve the discriminative power of a Bayesian model.
Sentence 2: little exploration has been devoted to the unsupervised setting, due in part to the absence of true labels that makes it technically challenging to enforce max-margin constraints.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ( 6) does include a sum over distinct pairs of units, as well as a sum over coupled triplets of units, such triplets are excluded by the bipartite structure of the RBM.
Sentence 2: coupled quadruplets do contribute to the fourth-order term and therefore fourth-and higher-order approximations require much more expensive computations [21], though it is possible to utilize adaptive procedures [19].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: MOHEX is a highly optimised algorithm, utilising a complex, hand-made theorem-proving algorithm which calculates provably suboptimal moves, to be pruned from search, and an improved rollout policy; it also optionally uses a specialised end-game solver, particularly powerful for small board sizes.
Sentence 2: our algorithm learns tabula rasa, without game-specific knowledge beside the rules of the game.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Noting that the only non-vanishing steps are PQ, QR and QP, we obtain We note that the number a 0 accounts for the agents who contribute to both steps in the attractor, and thus can complete the attractor dynamics alone in the extremely diverse limit.
Sentence 2: the number a cum arises from the £rst step PQ arriving at Q.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As discussed, a key difficulty of our setting that prevents us from directly applying well studied algorithms for OLO, is that essentially all standard algorithms require to exactly solve (or up to arbitrarily small error) some linear/convex optimization problem over the convexification of the feasible set CH(K).
Sentence 2: not only that our approximation oracle O K (•) cannot perform exact minimization, even for ↵ = 1 it is applicable only with inputs in R d + , and hence cannot optimize in all directions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: I.e., s(0, 0) = s(1, 1) = 1, s(n, 0) = 0 for n > 0 and s(n, m) = 0 for m > n. Other entries can be computed as s(n + 1, m) = s(n, m − 1) + ns(n, m).
Sentence 2: for large l (k) u. , it is often more efficient to sample ρ k,i by simulating the table assignments of the Chinese restaurant according to Eq.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A reader familiar with the multi-armed bandit literature would expect an adaptive sampling algorithm to have a large advantage over uniform sampling when there is a large diversity in the means of H 1 since larger means can be distinguished from µ 0 with fewer samples.
Sentence 2: one should note that to declare all of H 1 as discoveries, one must sample every arm in H 0 at least as many times as the most sampled arm in H 1 , otherwise they are statistically indistinguishable.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In Line 6, G denotes the space of functions over which risk minimization is performed in the classifier.
Sentence 2: we will show (in Theorem 1) that the variational distance between the distribution of one of the samples in U 0 2 and f CI (x, y, z) is very small for large n. the samples in U 0 2 are not exactly i.i.d but close to i.i.d.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In most of our experiments the size parameter is a twodimensional vector including the covariance of an isotropic Gaussian and a scaling factor.
Sentence 2: in general s i can represent an arbitrary parametric distribution: for instance, in the supplement we We show 2D-to-1D projection for illustration purposes, but in practice we perform 3D-to-2D projection.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It follows that the SD is invariant to coordinate permutations and depends only on the sparsity level, i.e., the number of nonzero elements.
Sentence 2: this result is in general not true for a nonorthogonal sparse basis, indicating that the precise location of the spikes (sparsity pattern) and not just their number has an effect on the SD.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Estimation in continuous parameter spaces in some cases allows for closed-form solutions (such as in least-squares regression), or if not we can resort to computing gradients (for smooth continuous functions) or subgradients (for non-smooth continuous functions) which give us a generic tool for finding a local optimum of an arbitrary continuous function (global optimum if the continuous function is convex).
Sentence 2: unless P=NP there is no general tool to efficiently optimize discrete functions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We say that f is weakly Lipschitz with respect to if for all x, y ∈ X , Note that weak Lipschitzness is satisfied whenever f is 1-Lipschitz, i.e., for all x, y ∈ X , one has |f (x) − f (y)| ≤ (x, y).
Sentence 2: weak Lipschitzness implies local (one-sided) 1-Lipschitzness at any maxima.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As we introduced in Section 1, some DL methods [4,5,7] learn a shared dictionary for all classes and a classifier on the coding coefficients simultaneously, while some DL methods [8,9,10] learn a structured dictionary to promote discrimination between classes.
Sentence 2: they all employ 0 or 1 -norm sparsity regularizer on the coding coefficients, making the training stage and the consequent testing stage inefficient.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In this case the output y w (x) is not a differentiable function of w. As one smoothly changes w the output y w (x) jumps discontinuously between discrete output values.
Sentence 2: so one cannot write when the input space X is continuous the gradient ∇ w E [L(y, y w (x))] can exist even when the output space Y is discrete.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For a matrix with IJ rows in total, e.g., B A, in general, the calculation of statistical leverage score is prohibitively expensive.
Sentence 2: due to the special structure of the KRP B A, the upper bound of statistical leverage score, which is sufficient to obtain the same guarantee by using slightly more samples, can be efficiently estimated, as shown in Theorem 3.2.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the previous example, the algorithm had access to both the complete path demonstrated by the teacher, and the same input data (overhead image) the teacher used while generating the path.
Sentence 2: in this example not only is the input data different (since the teacher generally controls the robot from behind and to the side using their own prior knowledge of the environment and highly capable vision system), but we face the additional challenge of estimating the path planned by the teacher at a particular time step from the vehicle motion we observe in future time steps, when the teacher is using additional data.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If there is a potential for X in a possibly rare regime in X to be fully correlated with Y such that Y = f (X), then the hypercontractivity coefficient is maximum: s(X; Y ) = 1.
Sentence 2: just as HGR correlation is not the only one satisfying Rényi's original axioms, the hypercontractivity coefficient is not the only one satisfying our axioms.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: (2009) characterized the distributions that can be realized by a RBM with k parameters as residing within a manifold inside the entire space of distributions on {0, 1} n whose dimension depends on k. For sub-exponential k this implies the existence of distributions which cannot be represented.
Sentence 2: this kind of result gives us no indication of what these hard-torepresent distributions might look like, leaving the possibility that they might all be structureless or otherwise uninteresting.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The standard CCD method follows the standard cyclic order (1, 2, . . . , n) as described in Section 2.
Sentence 2: we can construct a CCD method that follows an alternative deterministic order by considering a permutation ⇡ of {1, 2, . . . , n}, and choosing the coordinates according to the order (⇡(1), ⇡(2), .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Ideally, we prefer to derive new algorithms that find the posterior distribution ρ that minimizes the PAC-Bayesian bound on the expected loss.
Sentence 2: we can also use PAC-Bayesian bounds in order to estimate the expected loss of posterior distributions ρ that were found by other algorithms, such as empirical risk minimization, regularized empirical risk minimization, Bayesian posteriors, and so forth.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Such algorithms are well adapted to stochastic and adversarial domains, due to their sampling nature and the convergence guarantee to min-max values.
Sentence 2: the sampling procedure used in MCTS algorithms is not well-suited for other kinds of problems [Nakhost, 2013], such as deterministic single-agent problems where the objective is to find any solution at all.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then for > 0 with probability at least 1 the buyer loses a surplus of at least Bounding the number of lies: Although we argued in the previous lemma that lies during the learning phase cause the surplus-maximizing buyer to lose surplus relative to the truthful buyer, those lies may result in lower prices offered during the exploit phase, and thus the overall effect of lying may be beneficial to the buyer.
Sentence 2: we show that there is a limit on how large that benefit can be, and thus we have the following high-probability bound on the number of learning phase lies.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We shall consider an array of K × K Hawkes processes, where K is the number of clusters in a partition drawn from a CRP restricted to the individuals V . As in the IRM, the CRP allows the number of processes to grow in an unconstrained manner as the number of individuals in the graph grows.
Sentence 2: unlike the IRM, these Hawkes processes will be pairwise-dependent: the Hawkes process governing events from cluster p to cluster q, will depend upon the Hawkes process governing events from cluster q to cluster p. Let N pq be the counting measure of the (p, q)th Hawkes process.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: [5] and Hein and Audriushchenko [14] theoretically show that the sensitivity to adversarial examples can be controlled by the Lipschitz constant of DNNs and propose Parseval training and cross-Lipschitz regularization, respectively.
Sentence 2: these methods usually require approximations, making them less effective to defend very strong and advanced adversarial attacks.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The minimization of the upper bound (3) amounts to the equivalent problem 3 min where c k ∈ R n represents the unknown true gradient.
Sentence 2: that is, with respect to the bounds k , u k , we can write 3 we derived the optimal solution for a fixed c k ∈ C k . this is not sufficient to find the optimal solution for an arbitrary c k ∈ C k . Just computing the optimal solution for an arbitrary (but fixed) c k ∈ C k is unlikely to yield a good solution.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The genes known to be frequently mutated across GBM subtypes are somewhat enriched out of those that appear to be perturbed according to the PNJGL estimates (3 out of 10 mutated genes were detected by PNJGL; 37 out of 258 total genes were detected by PNJGL; hypergeometric p-value = 0.1594).
Sentence 2: fGL detects every gene as having node perturbation (Figure 4(a)).
Relationship: contrasting