sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Naively computing δ tar would involve explicitly enumerating all 2 p − 1 feature subsets and evaluating their respective minimum attainable p-values, something unfeasible even for moderate p. Existing work in significant discriminative pattern mining solves that limitation by exploiting specific properties of certain test statistics, such as Fisher's Exact Test or Pearson's χ 2 test, that allow to apply branch-andbound algorithms to evaluate δ tar .
Sentence 2: the properties those algorithms rely on do not apply to conditional statistical association tests, such as the CMH test.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The expression in (1) provides a variational bound for matching p θ (x) to samples of q(x), thus one may naively think to simultaneously set a similar variational expression for q φ (z), with these two variational expressions optimized jointly.
Sentence 2: to compute this additional variational expression we require an analytic expression for q φ (x, z) = q φ (z|x)q(x), which also means we need an analytic expression for q(x), which we do not have.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This is due to the fact that the Gamma band LFP is a filtered version of the wide band LFP, making these signals highly correlated in the Gamma band.
Sentence 2: in addition to this obvious linear dependency, we observe significant interactions in the lowest frequencies (0.5-2Hz) which can not be explained by linear interaction (and is thus not detected by the linear kernel).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The aggregate Markov model (AMM) of Saul and Pereira [13] (also discussed by Hofmann and Puzicha [10] as a special case of the aspect model) factors the conditional probability table of a word given its context by a latent variable representing context "classes".
Sentence 2: this latent variable approach is difficult to generalize to multiword contexts, as the size of the conditional probability table for class given context grows exponentially with the context length.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It should also be noted that, because hypercubes are all k-regular graphs (in particular, the hypercube Q n is n-regular), the form of the normalized Laplacian becomes simple.
Sentence 2: the usual formula for the normalized Laplacian is: since the graph is regular, we have D = kI, and so Also note that, because the formula for the combinatorial Laplacian is L = D − A, we also have L = 1 k L. The Laplacian also distributes over graph products, as shown in the following theorem.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Electrophysiological studies performed in primary visual cortex agree in reporting high sparseness values for neural activity [7,8,9,10,11,12].
Sentence 2: it is contested whether the high degree of sparseness is due to a neural representation which is optimally sparse, or is an epiphenomenon due to neural selectivity [10,12].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: So, T iterations will take To achieve -accuracy, ignoring again the logarithmic factor, we need T = From the last expression, for a fixed number of processors n, there exists an optimal value for h that depends on the network size and communication graph G: If the network is a complete graph, using h opt yields τ ( ) = O(n); i.e., using more processors hurts performance when not communicating every iteration.
Sentence 2: if the network is a k-regular expander then τ ( ) = c1 √ n + c 2 for constants c 1 , c 2 , and we obtain a diminishing speedup.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Following a standard procedure [11], we introduce a variational distribution q(Θ) and compute the Jensen's lower bound F v on the logarithm of ( 9), where θ denotes the model's parameters.
Sentence 2: the above form of the lower bound is problematic because X (in the GP term p(F |X)) appears non-linearly inside the covariance matrix K N N making the integration over X difficult.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: r t denotes the rewarding value of the outcome the animal receives at time t, which is a often set to a "fixed" value that can be either positive or negative, depending on whether the corresponding stimulus is appetitive or aversive, respectively.
Sentence 2: animals motivation for outcomes is not fixed, but a function of their internal state: a food pellet is more rewarding to a hungry, than a sated rat.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Compared to the baseline model, the linear-combination cache model (ResNet32-Cache3; green) significantly reduces the first singular value but slightly increases the lower-order singular values.
Sentence 2: although the cache-only model does not reduce the first singular value as much as the linear-combination cache model does, it produces a more consistent reduction in the singular values (ResNet32-CacheOnly; black).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Additionally, under certain assumptions, "unrolling" the model in time effectively removes the cycles, which is used in methods such as vector auto-regressive models, which are popular in econometrics, or more generally, Dynamic Bayesian Networks [5] and ordinary differential equation models.
Sentence 2: all these methods need time series data where the temporal resolution of the measurements is high relative to the characteristic time scale of the feedback loops in order to rule out instantaneous cyclic relationships.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This way we keep the same invariant (η is never larger than the right-hand side of (9), with equality when the budget is depleted), and the frequency of doubling remains logarithmic in L * T with a constant determined by φ, so both approaches are equally valid.
Sentence 2: controlling the sequence of values of η allows for easier comparison to AdaHedge.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Besides, our relaxation algorithm has O(n) parameters in the SDP cone and O(n) linear equality constraints, which involves a worst-case computational complexity of O(n 4.5 ).
Sentence 2: in the previous relaxation algorithms [1,14], there are approximately O(n 2 ) parameters in the SDP cone, which involve a worst-case computational complexity in the scale of O(n 6.5 ).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A deterministic apprentice policy π A that closely imitates the expert will either set π A (s) = a s 1 or π A (s) = a s 2 , but in either case the classification error will not be less than 1 2 .
Sentence 2: since π E is optimal, both actions a s 1 and a s 2 must be optimal actions for state s, and so the apprentice policy π A will be optimal as well.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We say the stochastic gradient has second moment at most Observe that any stochastic gradient with second moment bound B is automatically also a stochastic gradient with variance bound Second, in convex optimization, one often assumes a second moment bound Data: Local copy of the parameter vector x 1 for each iteration t do 2 Let g i t be an independent stochastic gradient ; )) //encode gradients ;  when dealing with non-smooth convex optimization, and a variance bound when dealing with smooth convex optimization.
Sentence 2: for us it will be convenient to consistently assume a second moment bound.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In particular, note that the regret does not depend on n. This seemingly contradicts the result of Lai and Robbins (1985) who showed that the expected regret of any algorithm is at least 1)) log n where p i⇤ and p i are the reward distributions of the optimal arm and arm i respectively and D is the Kullback-Leibler divergence.
Sentence 2: our algorithm receives as an input, and thus its expected regret depends on .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: When we sample from the global policy π θ (u t |x t ), our method resembles policy gradient methods with KL-divergence constraints [14,13,17].
Sentence 2: policy gradient methods update the policy π θ (u t |x t ) at each iteration by linearizing with respect to the policy parameters, which often requires small steps for complex, nonlinear policies, such as neural networks.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For a fixed empirical distribution p(x F , x T ), we define d(F ), a set function of the FVS F as the minimum value of (1), i.e., When the FVS is unknown, the ML estimate can be computed exactly by enumerating all possible n k FVSs of size k to find the F that minimizes d(F ).
Sentence 2: hence, the exact solution can be obtained with complexity O(n k+2 k), which is polynomial in n for fixed k. as our empirical results suggest, choosing k = O(log(n)) works well, leading to quasi-polynomial complexity even for this exact algorithm.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The most dominant step is estimating W; when doing Gibbs sampling, if done naïvely, it would O(DK 3 ) time if sampling W row-wise, and O(KD 3 ) time if sampling column-wise.
Sentence 2: if using the EM algorithm, estimating W can be done much more efficiently, e.g., using Conjugate Gradient updates because, it is not even required to solved for W exactly in each iteration of the EM algorithm [20].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For tanh and ↵-ReLU with ↵ < 1, they are still subexponential and polynomial (Thm B.21).
Sentence 2: while (0) = exp(⇥(l)) (l) for a ReLU resnet, its weight gradients have size independent of layer, within O(1) (Thm B.21)!
Relationship: contrasting
Domain: NeurIPS
Sentence 1: With these assumptions, the probability of an assignment ι C,k,m that maps k named instances to m distinct objects, when C contains n objects, is given by When n > m, the world contains objects unreferenced by any of the terms.
Sentence 2: these filler objects are obviously irrelevant (if they affected the attributes of some named term, they would have been named as functions of that term.)
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The goal of the classification task is to find a good hypothesis f with small excess risk R 0−1 And to find the good hypothesis based on the samples, one minimizes the empirical risk.
Sentence 2: using 0-1 loss, it is hard to find the global minimizer of the empirical risk because the loss function is discontinuous and non-convex.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: [8] for monotone submodular objective functions are quite efficient, requiring only O(k) memory (k is the size of the largest feasible set) and using only O(km) value and independence oracle queries for processing a single element of the stream (m is the number of matroids used to define the p-matchoid constraint).
Sentence 2: the algorithms developed for non-monotone submodular objectives are much less efficient (see Table 1 for their exact parameters).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Similar to the fast bipartiteness/K-colorability test, there is a loss in the power of the fast max clique test due to both the estimation and the sketching procedures.
Sentence 2: unlike the fast bipartiteness/K-colorability test, the sampling procedure also contributes to partial of the type-I error in the fast max clique test which implies a more stringent requirement on the sampling percentage.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Figure 2 (bottom) shows that both VASE and CCI-VAE learn progressively more informative latent representations when exposed to each dataset s, as evidenced by the increasing classification accuracy and decreasing mean squared error (MSE) measures within each stage of training.
Sentence 2: with CCI-VAE, the accuracy and MSE measures degrade sharply once a domain shift occurs.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In (4), τ (k) > 0 is a "global" scaling parameter for all the elements of {ω (k) ij |i = 1, ..., n, j < i} and generally fixed to be one [18], and γ With the Laplacian prior (4), many off-diagonal elements of Ω (k) are encouraged to be close to zero.
Sentence 2: in the inference procedure, the above Laplacian shrinkage prior ( 4) is inconvenient due to the lack of analytic updating expressions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Proposition 1 For A = ab ∈ A k,q with strength γ = γ(a, b), there exist universal constants Our proof, presented in the appendix, follows the scheme proposed in [7] and used for the trace norm and 1 norm.
Sentence 2: ω k,q is not decomposable and requires some work to obtain precise upper bounds on various quantities.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Local-SVRG relies on local smoothness to certify that some ∆ t i = ▽φ i x ⊤ i w t − ▽φ i x ⊤ i w are small.
Sentence 2: empirical Affinity SVRG (Algorithm 4) takes ∆ t i > t to be evidence that a loss is active; when ∆ t i = 0 several times, that is evidence of local affinity of the loss, hence it can be sampled less often.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As a result, it could easily be extended to other domains like speech, or text, where the backpropagation through the decoder can be really challenging because of the non-differentiable text generation process for instance.
Sentence 2: methods commonly used in vision to assess the visual quality of the generated images, like PatchGAN, could totally be applied on top of our model.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The standard objective here is a myopic, backwards looking one -in retrospect, we desire that our performance is not much worse than had we chosen any single expert on the sequence of examples provided by Nature.
Sentence 2: a reinforcement learning setting typically makes the much stronger assumption of a fixed environment, typically a Markov decision process (MDP), and the forward looking objective is to maximize some measure of the future reward with respect to this fixed environment.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: First, it is known that for some hypothesis classes, active learning cannot improve over passive learning for certain distributions (Dasgupta, 2005), and the same is true for auditing.
Sentence 2: exponential speedups are possible for active learning on certain classes of distributions (Balcan et al., 2006;Dasgupta et al., 2008), in particular ones with a small disagreement coefficient (Hanneke, 2007a).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The basic idea is to identify "important" co-ordinates by constructing suitable biased estimators of each signal coefficient, followed by a specific eigendecomposition.
Sentence 2: the initialization in CoPRAM is far simpler than the approaches in [22,23]; requiring no pre-processing of the measurements and or tuning parameters other than the sparsity level s. A drawback of the theoretical results of [23] is that they impose a requirement on signal coefficients: this assumption disobeys the power-law decay observed in real world signals.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ( 2) shows that it is equal to 2/N times the number of £ckle agents at time t, which is Poisson distributed with a mean of N/ √ 2πR = ∆/2, where ∆ ≡ N 2/πR is the average step size.
Sentence 2: since the attractor is formed by steps which reverse the sign of A µ , the average step size in the attractor is larger than that in the transient state, because a long jump in the vicinity of the attractor is more likely to get trapped.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As the " -NN results suggest, other state-of-the-art techniques like support vector machines will probably lead to better numerical categorization results than the HSOM.
Sentence 2: since the main purpose of the HSOM is the visualization of relationships between texts and text categories, we believe that the observed categorization performance of the HSOM compares sufficiently well with the more specialized (non-visualization) techniques to warrant its efficient use for creating insightful maps of large bodies of document data.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Traditionally, meteorological radars, such as the National Weather Service NEXRAD system, are tasked to always scan 360 degrees.
Sentence 2: the Collaborative Adaptive Sensing of the Atmosphere (CASA) Engineering Research Center [5] is developing a new generation of small, low-power but agile radars that can perform sector scanning, targeting sensing when and where the user needs are greatest.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The Deep Voice 2 vocal model is based on a WaveNet architecture (Oord et al., 2016) with a two-layer bidirectional QRNN (Bradbury et al., 2017) conditioning network, similar to Deep Voice 1.
Sentence 2: we remove the 1 ⇥ 1 convolution between the gated tanh nonlinearity and the residual connection.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The SM kernel has been used for GP regression of a scalar output (i.e., single function, or observation "task"), achieving impressive results in extrapolating atmospheric CO 2 concentrations [24]; image inpainting [25]; and feature extraction from electrophysiological signals [21].
Sentence 2: the SM kernel is not defined for multiple outputs (multiple correlated functions).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In our current problem setting, the goal is to train a prediction model f c : x → y for each cluster c of similar treatment sequences, where x denotes the input features and y denotes the label.
Sentence 2: the straightforward approach to achieve this is to train a prediction model by using only the samples in cluster c. since the available treatment history for some samples might be incomplete, totally excluding the samples from all other clusters ( = c) ignores relevant information about the model f c . Furthermore, the cluster-specific tasks are related and the samples from the other clusters -especially those close to the cluster boundaries of cluster c -also carry valuable information for the model f c . Therefore, we use a multi-task learning approach where a separate model is trained for each cluster by not only using the training samples from the target cluster, but also the available training samples from the remaining clusters with appropriate sample-specific weights.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The gradients of convolutional layers are 4 dimensional tensors with shape of [x, y, k, k] where x, y are two spatial dimensions and k is the size of the convolutional kernel.
Sentence 2: matrices are required to compute the SVD for spectral-ATOMO, and we choose to reshape each layer into a matrix of size [xy/2, 2k 2 ].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In general, it is not easy to quantify the difference to the lower bound of Lai and Robbins lim inf Even for Gaussian distributions, there is no general closed-form formula for T * (µ) and w * (µ) except when K = 2.
Sentence 2: we conjecture that the worst case is when µ 1 and µ 2 are much larger than the other means: then, the regret is almost the same as in the 2-arm case, and ETC strategies are suboptimal by a factor 2.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If the separation between the trajectory classes is large compared to the temporal correlations (i.e., the first term in (11) dominates for the resulting w) the slowest feature will be similar to the weight vector found by FLD on the corresponding classification problem.
Sentence 2: as the temporal correlations of the trajectories increase, i.e., the trajectories themselves become smoother, the slowest feature will tend to favor exploiting this temporal structure of the trajectories over the separation of different classes (in this case, (11) is dominated by the second term for the resulting w).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Here, we see that the quality of the TAP approximation becomes less good.
Sentence 2: our results provide still a reasonable estimate for the bootstrapped generalization error at sample size S = N . While for practical applications of estimating the "true" generalization error using Efron's 0.632 bootstrap estimator the case S = N is of main importance, it is also interesting to discuss the limit of extreme oversampling S → ∞.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If an observation x i is contaminated with large noise so that p(x i |θ , σ i , x i ) has a flat shape, then we can pick a x i that is very different from x i which predicts y i well.
Sentence 2: if an observation x i is contaminated with very small noise, then (1) and ( 2) penalize a parameter θ such that p(x i , y i |θ) is small.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Furthermore, as expected, the projection matrix inferred by the classical CCA had no exact zero entries and even after thresholding significantly small absolute values to zero, the uncovered sparsity was only about 25%.
Sentence 2: the projection matrix inferred by the infinite CCA model had 57% exact zero entries and 62% zero entries after thresholding very small values, thereby demonstrating its effectiveness in also capturing the sparsity patterns.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: While t depends on p we will assume it does so only via X.
Sentence 2: for example t could depend on p through the marginal p X on X or possible group action on X; it is a manifestation in the data X, possibly over time, of underlying structure in the true joint distribution p 2 P. The representation t captures structure in X induced by p. the regression function itself depends only on the conditional p(y|t(x)).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Ever since, a series of applications such as tracking and action recognition [10], body-joint position estimation [12] and multi-class object detection [22] have been presented.
Sentence 2: hough Forests typically produce non-distinctive object hypotheses in the Hough space and hence there is the need to perform non-maximum suppression (NMS) for obtaining the final results.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In addition, we note that Fisher Information does not provide an accurate account of the performance of box-like tuning functions: it fails as soon as the nonlinearity in the tuning functions becomes effective and overestimates the true minimal discrimination error E. Similarly, the approximate neurometric functions E d (∆θ) obtained from equation 6 do not capture the shape of neurometric functions E(∆θ) but underestimate the minimal discrimination error.
Sentence 2: the deviation between both curves stays rather small for cosine tuning functions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Based on our experimental results on the benchmark problems, DNG-MCTS typically needs about 2 to 4 times (depending on problems and the iterating stage of the algorithms) of computational time more than UCT algorithm for a single iteration.
Sentence 2: if the simulations are expensive (e.g., computational physics in 3D environment where the cost of executing the simulation steps greatly exceeds the time needed by action-selection steps in MCTS), DNG-MCTS can obtain much better performance than UCT in terms of computational complexity because DNG-MCTS is expected to have lower sample complexity.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: While there is certainly some optimal trade off between depth and cell size, with enough data, simply upscaling both has yielded remarkable results in neural machine translation (NMT) [6].
Sentence 2: 1 massive upscaling is impractical in all but the least hardware constrained settings and fails to remedy fundamental architecture issues, such as poor gradient flow inherent in recurrent cells [8].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The entire expression can be multiplied out to give a sum of 2 J product forms, and exact "QuickS core" inference can be performed by combining the results of exact inference in each of the 2 J product forms (Heckerman 1989).
Sentence 2: this exponential time complexity makes large problems, such as QMR-DT, intractable.
Relationship: contrasting