sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: In order for those methods to perform as well as they did with the smaller version of Frogger, the value for B[s, a] needs to be set higher and decayed more slowly by manually finding new values for b and d. Thus, like r h , the optimal values to b and d are dependent on both the domain and the quality of feedback.
Sentence 2: the estimated feedback consistency, Ĉ, used by Advise only depends on the true feedback consistency, C. For comparison, we next show how sensitive Advise is to a suboptimal estimate of C. Interactions with a real human will mean that in most cases Advise will not have an exact estimate, Ĉ, of the true feedback consistency, C. It is presumably possible to identify a value for Ĉ that is close to the true value.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Traditionally, in the non-private literature, the goal is to minimize the multiplicative error γ, with the current state-of-the-art (non-private) algorithm achieving multiplicative error of γ = 6.357 (with no additive error) [2].
Sentence 2: in spite of the long line of works on private k-means [8,28,14,18,27,33,31,32,17,6,29,21], all of the existing polynomial time private algorithms for the problem obtained only a super constant multiplicative error.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In this paper, we study the rate of ∆ as a function of : We identify a function T : R + → R + such that when ∆ = O(T ( )), we can give an algorithm that outputs a point x such that f (x) ≤ min x f (x) + within time poly d, 1 over a natural class of well-conditioned convex bodies.
Sentence 2: when ∆ = Ω(T ( )) 1 , we also prove an information theoretic lower bound that any algorithm outputs such x must use super polynomial number of evaluations of f . Our result can be summarized as the following two theorems: Theorem (Algorithmic upper bound, informal).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Using a KL-bound for the update of the search distribution is a common approach in the stochastic search.
Sentence 2: such information theoretic bounds could so far only be approximately applied either by using Taylor-expansions of the KL-divergence resulting in natural evolutionary strategies (NES) [2,11], or sample-based approximations, resulting in the relative entropy policy search (REPS) [9] algorithm.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To see this, consider the case where the starting kernel K is a poor fit to the data.
Sentence 2: in this case, a large initial step size η will probably be accepted; even though such a step will likely result in the truncation of many eigenvalues at 0, the resulting matrix will still be an improvement over the poor initial K. with many zero eigenvalues, the new K will be near-diagonal, and, unfortunately, Equation (5) dictates that if the current K is diagonal, then its gradient is as well.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This results in a looser bound in (15) for large α. as a function of the conditional entropy H(G|X n ) and the size of the set of all graphs with p nodes.
Sentence 2: a naïve application of Fano's inequality results in a trivial lower bound as the set of all graphs, which can be realized by G ER (p, c/p) is "too large".
Relationship: contrasting
Domain: NeurIPS
Sentence 1: An important effort to show that fitting the training data exactly can under certain conditions be theoretically justified is the margins theory for boosting [37] and other margin-based methods [6,24,28,29,34].
Sentence 2: this theory lacks explanatory power for the performance of classifiers that perfectly fit noisy labels, when it is known that no margin is present in the data [12,51].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Unlike regression or classification, unsupervised graph learning lacks at present an error function, so it seems difficult to apply the bias-variance framework here.
Sentence 2: we have conducted a wide range of empirical tests to understand the properties of the ensemble MSTs, and to compare them to the other graph construction methods, in terms of the error in the geodesic distances (if known a priori).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Since r ≤ ǫτ /72d, by Lemma 7 kµ by assumption, this ball contains at least k sample points, and hence X i is kept.
Sentence 2: if X i ∈ S σ−r , then the set B M (X i , r) contains mass at most Thus by Lemma 6 B M (X i , r) contains fewer than k sample points, and hence X i is removed.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For test points, the learnt regression function is applied in the reduced space and then standard recovery algorithms from CS literature are used to obtain sparse predicted labels [8,9].
Sentence 2: in this method, learning of the decision functions is independent of the sparse recovery and hence in practice, it requires several measurements to match accuracy of the standard baseline methods such as 1-vs-all SVM.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: One can note that all the quantities entering in the right-hand side of ( 6) are known, so that it is not hard to choose µ and γ in such a way that they satisfy the conditions of Theorem 2.1.
Sentence 2: in practice, this theoretical choice may be too conservative in which case it could be a better idea to rely on cross validation.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This makes the applicability of this approach for large real life problems rather limited.
Sentence 2: if we would know a subspace (spanned by the d columns of a matrix V ∈ ℜ (nt+nw)×d ) in which (or close to which) the label vector lies, we can restrict the feasible region for Γ, leading to a much more efficient algorithm.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Although our sample-based approach is intuitively straightforward, its implementation has two drawbacks: (1) One has to be cautious of samples that are close together, because they lead to unbounded gradients; and (2) all samples must be considered when computing the force on a data point, which makes the approach computation intensive.
Sentence 2: in [10,7] approximations are proposed that reduce the computational complexity of the approach.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Specifically, Q(s) and the divergence between Q(s o ) and P (s o ) are parameterized with two neural networks, i.e., one generator and one discriminator, and then play an adversarial game [12].
Sentence 2: different from the original GANs, our model has one extra discriminator (called as reconstructor), since the first term in Eq.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: From Section 2.4, assume r(•) is three times continuously differentiable on [0, 1], at the boundary, the asymptotic order of the bias is , which is smaller than the interior points.
Sentence 2: the asymptotic order of the variance is O p {(3σ 2 e (n + 1) 2 )/(k(i)(k(i) + 1)(2k(i) + 1)} and attains O p (n 2 ), as i is close to either 2 or n − 1.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Kalai and Servedio [7] showed that, if data is corrupted with noise at a rate η, it is possible to boost the accuracy of any noise-tolerant weak learner arbitrarily close to 1 − η, and they showed that it is impossible to boost beyond 1 − η.
Sentence 2: we show that, in the presence of noise at a rate arbitrarily close to 1/2, the AUC can be boosted arbitrarily close to 1.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If the robot succeeds at achieving the goal configuration when the visual statistics of the pair of initial and goal image is similar to before and after image in the training set, then this would not be a convincing demonstration of generalization.
Sentence 2: if the robot is able to displace objects into goal positions that are much farther apart as compared to position of objects before and after a single poke then it might suggest that our model has not simply overfit but has learnt something about the underlying physics of how objects move when poked.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Some learning algorithms are generic, e.g., working on arbitrary unstructured vectors in d , such as ordinary SVMs, decision trees, neural networks, and boosting applied to generic learning algorithms.
Sentence 2: other learning algorithms successfully exploit the specific topology of their input, e.g., SIFT-based machine vision [10], convolutional neural networks [6,7], time-delay neural networks [5,16].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Since its early beginning [24,34], the PAC-Bayesian theory claims to provide "PAC guarantees to Bayesian algorithms" (McAllester [24]).
Sentence 2: despite the amount of work dedicated to this statistical learning theory-many authors improved the initial results [8,21,25,30,35] and/or generalized them for various machine learning setups [4,12,15,20,28,31,32,33]-it is mostly used as a frequentist method.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To be explicit, if is defined by an edge set © £ ¦ ¤£ © , then e £ n must have zeros in all elements corresponding to edges not in © £ ¦ .
Sentence 2: given an edge ¥ belonging to two trees H and §¦ , the quantity e ©£ n H can be different than e £ n ¦ $ .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Another key feature of cortical circuits is the detailed and tight balance of excitation and inhibition, which has received growing support both at the experimental (Froemke et al., 2007;Xue et al., 2014;Froemke, 2015) and theoretical level (van Vreeswijk and Sompolinsky, 1996;Brunel, 2000;Vogels and Abbott, 2009;Hennequin et al., 2014Hennequin et al., , 2017.
Sentence 2: the computational processes that are facilitated by these architectures and dynamics are still elusive.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For example, orientation selective neurons in superficial layers in ferret visual cortex receive more than 50% of their cortico-cortical excitatory inputs from neurons with orientation preference which is less than 30 o apart.
Sentence 2: this input structure is rather broad in terms of stimulus-specificity: cortico-cortical connections between neurons tuned to dissimilar stimulus orientation also exist [4].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For instance, indoor spaces, pictures containing people, particularly if their face is visible, close up views on objects, animals, are more memorable than buildings, pictures of natural landscapes, and natural surfaces in general (like mountains, grass, field).
Sentence 2: to date, there is no work which has attempted to predict which local information from an image is memorable or forgettable, in an automatic manner.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As in the latent dynamical system, the resulting model enforces a "bottleneck", whereby predictions of y t based on y 1 . . . y t−1 must be carried by the low-dimensional x t . State prediction in the RLM is related to the Kalman filter [7] and we show in the next section a formal equivalence between the likelihoods of the RLM and the latent dynamical model when observation noise is Gaussian distributed.
Sentence 2: spiking data is not well modelled as Gaussian, and the generalisation of our approach to Poisson noise leads to a departure from the latent dynamical approach.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We note that while the top methods from the literature also achieve accuracies above 92% and compression factors above 20×, they employ a considerable amount of hand-designed steps, such as pruning, retraining, various types of weight clustering, special encoding of the sparse weight matrices into an index-difference based format and then finally use entropy coding.
Sentence 2: we directly minimize the entropy of the weights in the training, obtaining a highly compressible representation using standard entropy coding.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In DPI and CBMPI, we managed to obtain results similar to CE, only after multiplying the per iteration budget B used in the D-T experiments by 10.
Sentence 2: cBMPI and CE use the same number of samples, 150, 000, 000, when they converge after 2 and 60 iterations, respectively (see Figure 5).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Given a distribution p over permutations, the matrix M k of k'th order marginals is where S j1...j k i1...i k is the two-sided coset µ j1... Clearly, these matrices satisfy a number of linear equations, and therefore are redundant.
Sentence 2: it can be shown that for for some appropriate basis transformation matrix T k , i.e., the Fourier matrices { p(λ)} λ : λi=n−k capture exactly the "pure k'th order effects" in the distribution p. In the spectral analysis of rankings, as advocated, e.g., in [7], there is a lot of emphasis on projecting data to this space, Marg k , but using an FFT this takes around O(n 2 n!)
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We further demonstrated how this computed reward can be used by different learning mechanisms to form appropriate Pavlovian or instrumental associations.
Sentence 2: it should be noted that concerning food (and other ingestible) outcomes, the basic form of the drive-reduction definition of reward (equation 2) has four interrelated problems, some of them used traditionally to criticize the drive reduction theory: (1) Post-digestive nutritive feedback of food, defined by the drive reduction equation, might occur hours after ingestion.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Their approach was later signficantly extended [Ruttor et al., 2013, Ruttor and Opper, 2010, Vrettas et al., 2015.
Sentence 2: similiar to [Lyons et al., 2012] they study parameter estimation in stochastic dynamical systems while our work focuses on deterministic systems.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: However, the state-of-the-art alternating based algorithms (such as ANLS and HALS) for nonsymmetric NMF utilize the splitting property of (1) and thus can not be used for (2).
Sentence 2: first-order method such as projected gradient descent (PGD) for solving (2) suffers from very slow convergence.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To apply Theorem 1, we need to learn distribution in C and find a q that is O(" 2)-close in 2 -distance to p. For the class of monotone distributions, we are able to efficiently obtain such a q, which immediately implies sample-optimal learning algorithms for this class.
Sentence 2: for some classes, we may not be able to learn a q with such strong guarantees, and we must consider modifications to our base testing algorithm.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We have The regret of the game with early stopping can be written as R T = T t=1 t s=1 e s (y t − ŷt ) 2 − ∆ * t . One might notice that δ * t = 0 for the choice y t = θ * t−1 x t , where θ * t−1 is the ordinary least squares solution on data through time t − 1, and the regret always increases.
Sentence 2: this choice of y t may violate the label constraints, in particular, for B t = 1 and x t ∈ R increasing.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This illustrates a basic tension in the resulting bounds: in its primal form 2 (combination of trees), TRW is inefficient: it maintains a weight and O(|V |) parameters for each tree, and a large number of trees may be required to obtain a tight bound; this uses memory and makes optimization slow.
Sentence 2: the dual, or free energy, form uses only O(|E|) parameters (the TRW messages) to optimize over the set of all possible spanning trees -but, the resulting optimization is only guaranteed to be a bound at convergence, 3 making it difficult to use in an anytime fashion.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: With such definitions, the optimization problem may be interpreted as an upper-bound on the classification risk defined from ℓ FN and ℓ FP .
Sentence 2: the machinery of Section 3.2 unveils a major problem: the SVM decision function provided by sign(f (x i ) + b) is not consistent with the probabilistic interpretation of SVM scores.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It may result in some accuracy loss when simply replacing the floating gradients with ternary gradients while keeping other hyper-parameters unchanged.
Sentence 2: we are able to train large-scale DNNs by TernGrad successfully after making some or all of the following changes: (1) decreasing dropout ratio to keep more neurons; (2) using smaller weight decay; and (3) disabling ternarizing in the last classification layer.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Linear signal in 3d  optimal over both the bigger and smaller classes.
Sentence 2: as soon as we enter the 3d world, it is no longer clear whether TV denoising can adapt to the smaller, inscribed Sobolev ball, whose minimax rate is faster, n −2/5 versus n −1/3 (ignoring log factors).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Many practical problems modeled by multi-agent MDPs use centralized policies to achieve fairness, e.g., network bandwidth allocation by telecommunication companies, traffic congestion control, public service allocation, and, more generally, fair resource allocation under uncertainty.
Sentence 2: we can derive decentralized policies for individual agents from a maximin fairness policy π * by marginalizing it over the actions of all other agents.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: [3] showed that if ρ(M −1 Hog N Hog ) < 1, the Markov chain admits N (µ, Σ) as stationary distribution where The above approach can be generalized to blocks of larger sizes.
Sentence 2: beyond the block size, the Hogwild sampler does not have any tunable parameter allowing us to modify its incorrect stationary distribution.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The computational complexity of VDMGP is O(N M 2 K +N DK), just as that of SPGP-DR, which is much smaller than the O(N 3 +N 2 D) required by a full GP.
Sentence 2: since the computation of the variational bound of VDMGP involves more steps than the computation of the evidence of SPGP-DR, VDMGP is slower than SPGP-DR.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: These networks use homogeneous binarization: all parameters in each layer or (more commonly) the whole model have the same low bitwidth (e.g., 2 bits).
Sentence 2: modern hardware allows efficient designs where each arithmetic instruction can have a custom bitwidth, motivating heterogeneous binarization, where every parameter in the network may have a different bitwidth.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Sampling θ x will, nevertheless, be harder since the covariance function hyper-parameters enter the expression in a non-trivial way.
Sentence 2: we note that once the state trajectory is fixed, we are left with a problem analogous to Gaussian process regression where x 0:T −1 are the inputs, x 1:T are the outputs and Q is the likelihood covariance matrix.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: One can show that if k(•, •) is a kernel then the function ϕ(•) and the feature space H exist; furthermore k(x, y) = ϕ(x), ϕ(y) [18].
Sentence 2: directly performing linear PCA in the feature space might not be feasible because the feature space typically has very high dimensionality (including infinity).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The terms P (R H ∩ H R (x A )) and P (R H ∩ H R (x A )) allows us to quantify the progress made on determining region validity.
Sentence 2: naively computing these terms would require computing all hypotheses and assigning them to correct subregions, thus requiring a runtime of O 2 T . for the special case of Bernoulli tests, we can reduce this to O (T ) as we can see from the expression We can further reduce this to O (1) when iteratively updated (see supplementary for derivations).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the past decade, significant progress has been made toward the methodological development [13,8,30,22,7,14,28,19,27] as well as theoretical understanding [12,20,1,24,21,4,6,3,2,18,15] of sparse PCA.
Sentence 2: all the above studies focused on estimating the leading eigenvector u 1 .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Some notable studies have been carried out regarding the behavior of these methods for infinitely large sample size (von Luxburg et al., 2008;Rohe et al., 2011), which provide sufficient confidence to practitioners about the effectiveness of these methods.
Sentence 2: recent developments in computer vision have led to a plethora of applications, where the model deals with multi-way affinity relations and can be posed as uniform hypergraphs.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Previous work learning sparse codes of image sequences has shown that it is possible to recover local, direction-selective components (akin to translating Gabors) [11].
Sentence 2: this type of model does not capture the abstract property of motion because each unit is bound to a specific orientation, spatial-frequency and location within the image-i.e., it still suffers from the aperture problem.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Conceptually, the log-likelihood objective implicitly trades off between model error in different regions of the input/output space, but does so in a manner largely opaque to the modeler, and may ultimately not employ the correct tradeoffs for a given task.
Sentence 2: there is an alternative approach to solving (1) that we describe as the model-free "black-box" policy optimization approach.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Otherwise CLSR may be an interesting alternative although this method does not make any assumption about the sparsity of f + and its goal is not to recover a possible sparse f + but only to make good predictions.
Sentence 2: in some sense our method finds a sparse solution in the fact that the regression function g L lies in a space G M of small dimension M N and can thus be expressed using only M coefficients.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We consider the full eigenfunctions ofO(a, b, aI, bl ) below.
Sentence 2: the case that Piepenbrock & Obermayer (1999) studied of a flat arbor function (u A = 00) turns out to be special, admitting two equilibrium solutions, one flat, one with topography, whose stability depends on (3.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Consider any m < M . The ζ (m) conditions on f (m) constrain the value of f (M ) -the confidence band β is large, it means that we have not constrained f (m) sufficiently well at x t and should query at the m th fidelity.
Sentence 2: querying indefinitely in the same region to reduce β t−1 in that region will not help us much as the ζ (m) elongation caps off how much we can learn about f (M ) from f (m) ; i.e.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the preceding example, the Vapnik-Chervonenkis (VC) dimension, which characterizes the sample complexity of supervised learning, is 1.
Sentence 2: the eluder-dimension, which will we define below, is n. To highlight conceptual differences between the eluder dimension and the VC dimension, we will now define VC dimension in a way analogous to how will define eluder dimension.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The piecewise model performs better, but because the observation covariance is not conditioned on o t , the Kalman filter learns to use a very large observation covariance, which forces it to rely almost entirely on the dynamics model for predictions.
Sentence 2: since the BKF learns to output the observation covariances conditioned on o t that optimize the performance of the filter, it is able to find a compromise between the observations and the dynamics model.
Relationship: contrasting