sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: If we restrict f V to have zero mean ( v∈V f (v) = 0), then the criterion (1) can be rewritten as follows: The obvious minimum of R(f ) under the constraint v∈V f (v) = 0 is reached for any function f such that f V is equal to the second largest eigenvector of L (the largest eigenvector of L begin the constant vector).
Sentence 2: this only defines the values of f on the points V , but leaves indeterminacy on the values of f outside of V . Moreover, any arbitrary choice of f under a single constraint on f V is likely to be a mapping that overfits the known graph at the expense of the capacity to infer the unknown edges.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As common practice of standard zero-shot learning, we can apply the trained model f c in Eq.
Sentence 2: ( 3) to classify the unseen data over only target classes T . in generalized zero-shot learning, things become more difficult as we have to make predictions over both source and target classes S ∪ T . Due to the huge gap between the disjoint source and target classes, a deep network trained on the source classes may still be under-confident for the target classes.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Given a set of positive (relevant) and negative (non-relevant) samples, the parameters of a retrieval system can be estimated using the AP-SVM framework, which minimizes a regularized convex upper bound on the empirical AP loss.
Sentence 2: the high computational complexity of loss-augmented inference, which is required for learning an AP-SVM, prohibits its use with large training datasets.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Any node with degree strictly greater than |C| must be in C. The observation follows simply from the fact that if a node is omitted from C, then all of its neighbors must belong to C. Thus, if S is the set of all nodes in G with degree greater than k, then S is contained in every vertex cover of size at most k. We can compute U (k) in time exponential in k but polynomial in the number of nodes n for fixed k [18], but these algorithms remain impractical for our datasets.
Sentence 2: the results motivate our algorithm in Section 3, which is based on taking the union of several minimal vertex covers.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ¢ is the length of the suffix fq F6 § @9 A9 A9 !
Sentence 2: § 3 of the training sequence that the on-line algorithm had not seen yet when D G was generated, is the cumulative loss of D R on that suffix, and §¦ 0 G$ S k For the sake of simplicity, we will restrict to losses X with range V t % § @k e . it should be clear that losses taking values in arbitrary bounded real interval can be handled using techniques similar to those shown in Section 3.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: While the original DDPG hyperparameters were set to achieve robust performance on a large set of benchmarks (and out-of-the-box DDPG performed remarkably well on the considered problems) our experiments indicate that the number of samples required to achieve good performance can be substantially reduced for individual tasks by hyperparameter optimization with BOHAMIANN.
Sentence 2: dNGO did not perform as well on this specific task, getting stuck during optimization, see Figure 2 (right).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For some tasks, it may also be useful to feed the output of the localisation network, θ, forward to the rest of the network, as it explicitly encodes the transformation, and hence the pose, of a region or object.
Sentence 2: it is also possible to use spatial transformers to downsample or oversample a feature map, as one can define the output dimensions H and W to be different to the input dimensions H and W . with sampling kernels with a fixed, small spatial support (such as the bilinear kernel), downsampling with a spatial transformer can cause aliasing effects.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As discussed when presenting results, one may also learn the CS dictionary in advance, off-line, with appropriate training images (using the model in ( 2)).
Sentence 2: the unique opportunity for joint CS inversion and learning of an appropriate parsimonious dictionary is deemed to be a significant advantage, as it does not presuppose that one would know an appropriate training set in advance.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We gather the parameters into a n Then, for image x, the "classeme" descriptor h(x) is computed as the concatenation of the outputs of the classifiers learned for the training categories: The PICODE descriptor is also of this form.
Sentence 2: the key-difference with respect to [27] lies in our training procedure, and the fact that the dimensionality C is no longer restricted to be the same as the number of training classes.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Since the O(1/k) convergence rate of the testing cost, achieved by SG methods with decreasing step sizes (and a single pass through the data), is provably optimal when the algorithm only accesses the function through unbiased measurements of the objective and its gradient, it is unlikely that one can obtain a linear convergence rate for the testing cost with the SAG iterations.
Sentence 2: as shown in our experiments, the testing cost of the SAG iterates often reaches its minimum quicker than existing SG methods, and we could expect to improve the constant in the O(1/k) convergence rate, as is the case with online second-order methods [32].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the case of contacts, the boundary might have a complex shape that is not well modeled by a GMM.
Sentence 2: if we use the GMM to obtain a prior for linear regression, it is easy to determine the correct linear mode from the covariance of (x ti , u ti ) with x t+1i in the current samples at time step t. The time-varying linear dynamics can then capture different linear modes at different time steps depending on the actual observed transitions, even if the states are very similar.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Recent efforts have focused on developing statistical techniques to post-process the noisy labels in order to improve its quality (e.g., [RYZ + 10, ZLP + 15, KOS11, IPSW14]).
Sentence 2: when the inputs to these algorithms are erroneous, it is difficult to guarantee that the processed labels will be reliable enough for subsequent use by machine learning or other applications.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For generative models, the recent Wasserstein GAN [11] improved the training stability of GANs by reformulating the optimization problem as a minimization of the Wasserstein distance between the real and generated distributions [12].
Sentence 2: this method relies on an efficient way of constraining the Lipschitz constant of the critic, which was only partially addressed in the original paper, and the object of several follow-up works [13,14].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This is an adversarial communication environment, where a speaker agent ('Alice') must communicate a message to a listener agent ('Bob'), who must reconstruct the message at the other end.
Sentence 2: an adversarial agent ('Eve') is also observing the channel, and wants to reconstruct the message -Alice and Bob are penalized based on Eve's reconstruction, and thus Alice must encode her message using a randomly generated key, known only to Alice and Bob.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Although we have introduced RBM units with continuous values to better deal with the representation of input variables, they could also be considered for use in the hidden layers, in replacement or complementing the binomial units which have been used in the past.
Sentence 2: gaussian and exponential hidden units have a weakness: the mean-field propagation through a Gaussian unit gives rise to a purely linear transformation.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Given our assumptions, we obtain equations linear in W j 12 , W j 21 , and W j p1 For each delay k, we obtain three equations: one from E{R 1 }, and one from the projection of E{XR At first glance, it appears that the unknowns greatly outnumber the equations.
Sentence 2: the system of equations is well-posed because the W j p1 W  q2 appear in the same combination for each of the three equations at a given delay.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For example, if the actions are placed as the elements in {0, 1/2, 1} n , we use the l ∞ metric, and r ∈ (1/2, 1), it is easily seen that the sphere packing number is just 1.
Sentence 2: the sphere covering number is at least 2 n = k log 3 (2) ≈ k 0.63 , since we need a separate sphere to cover every element in {0, 1} n . Third, consider the random Erdös -Rényi graph G = G(k, p), which is formed by linking every action i to every action j with probability p independently.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In that case we would directly represent Pr(Y t |X t , Y t−1 ), hence we could implement a sequential Monte Carlo algorithm simply directly sampling s t ∼ Pr(Y t |X t = x t , Y t−1 = s t−1 ) from slice to slice.
Sentence 2: in [9], it was pointed out that MEMMs suffer from the label-bias problem to which as a solution CRFs were invented.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: And, by definition of πk , λk is the gain of the chosen policy πk for MDP Mk .
Sentence 2: the algorithm executes this policy on the true MDP M. The only difference between the two is the transition model: on taking an action a j := πk (s) in state s in MDP Mk , the next state follows the sampled distribution where as on taking the corresponding action a in MDP M, the next state follows the distribution P s,a .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the case that the hidden unit dynamics is known to be highly stochastic, this class of models is arguably less appropriate.
Sentence 2: stochastic hidden dynamics is often used in cases where one believes that the true hidden dynamics is too complex to model effectively (or, rather, deal with computationally) and one uses noise to 'cover' for the lack of complexity in the assumed hidden dynamics.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We can query a pair of nodes (u, v) to test whether s(u, v) = +1 indicating u and v belong to the same cluster or s(u, v) = −1 indicating they are not.
Sentence 2: the query fails to return the correct answer with probability 0 < p < 1/2, and we want to query the minimal possible pairs.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Unfortunately, Proposition 1 only holds for polynomials in one variable.
Sentence 2: its first statement may be generalised to polynomials of more than one variable: for every psd matrix P 0 the polynomial p (ρ) = θ ρ P θ ρ is non-negative everywhere, even if θ i is any monomial in ρ 1 , .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For this reason, Bayesian nonparametric models, such as Gaussian processes (GPs), are often the model of choice in MBRL, especially in low-dimensional problems where data efficiency is critical [Kocijan et al., 2004, Ko et al., 2007, Nguyen-Tuong et al., 2008, Grancharova et al., 2008, Deisenroth et al., 2014, Kamthe and Deisenroth, 2018.
Sentence 2: such models introduce additional assumptions on the system, such as the smoothness assumption inherent in GPs with squared-exponential kernels [Rasmussen and Kuss, 2003].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As expected, the results at γ ≈ 0 validate x loc as a true local minimum.
Sentence 2: even with γ = 1 yielding a random initialization, 59 of the 1,000 trials still result in an error of > 50%, thereby yielding a failure rate of 5.90 ± 2.24% up to three standard deviations.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For linear-Gaussian p i (u t |x t ) and (nonlinear) conditionally Gaussian π θ (u t |x t ) = N (µ π (x t ), Σ π (x t )), where µ π and Σ π can be any function (such as a deep neural network), the KL-divergence D KL (π θ (u t |x t,i,j ) p i (u t |x t,i,j )) can easily be evaluated and differentiated in closed form [6].
Sentence 2: in the nonlinear setting, minimizing this objective no longer minimizes the KL-divergence between trajectory distributions D KL (π θ (τ ) p i (τ )) exactly, which means that MDGPS does not correspond exactly to mirror descent: although the C-step can still be evaluated exactly, the S-step now corresponds to an approximate projection onto the constraint manifold.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: These studies show that frequency and AoA are highly correlated (typically r = -.6) explaining the confound of older studies on frequency.
Sentence 2: still more recent studies question this finding and find that both AoA and frequency are significant and contribute independently to naming latency (Ellis & Morrison, 1998;Gerhand & Barry, 1998,1999.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Thus, we can prune D(I, a) from iteration T 0 until iteration T 1 so long as In the worst case, this allows us to skip only R(I,a) U (I,a)−L(I) iterations.
Sentence 2: in practice it performs significantly better, though we cannot know on iteration T 0 how many iterations it will skip because it depends on what is played in T 0 ≤ t ≤ T 1 .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Influence functions study how the model or prediction would change if a training point was up-weighted infinitesimally, but require model differentiability and convexity to work.
Sentence 2: it was recently shown that these assumptions can be relaxed and that influence functions can be used for understanding model behavior, model debugging, detecting dataset errors, and creating visually indistinguishable adversarial training examples [12].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A very recent result of Wang and Chen [32] removes the 1/p * factor in [8] for the tabular case and presents a worst-case bound of O(L|E| √ n), which in the tabular complete graph case improves over our result by O(L).
Sentence 2: their analysis does not give structural guarantees that we provide with maximum observed relevance C * obtaining potentially much better results for the case in hand and giving insights for the complexity of IM bandits.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In a parametric approach, we consider a parameterized function f (x; θ), with θ being distributed according to some prior.
Sentence 2: the nonparametric GP approach directly puts the GP prior over f as For a finite set of points, the GP model is simply a joint Gaussian: f (x 1:N ) ∼ N (m(x 1:N ), K), where K i,j = κ(x i , x j ) and N is the number of data points.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Running WSAT on 100 formulas with N = 10000 required 27771 seconds on the same servers, and would have taken even longer if about half of the runs had not been stopped by a cutoff without producing a satisfying con£guration.
Sentence 2: the same 100 formulas were solved by SP followed with WSAT in 10,420 sec, of which only 300 seconds were spent in WSAT.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Given a joint probability distribution p(y, x) where y are observations and x are latent variables (possibly including model parameters that consist of random variables) and a variational distribution q v (x), the objective is to maximize the lower bound with respect to the variational parameters v. Ideally, in order to tune v we would like to have a closed-form expression for the lower bound so that we could subsequently maximize it by using standard optimization routines such as gradient-based algorithms.
Sentence 2: for many probabilistic models and forms of the variational distribution at least one of the two expectations in (2) is intractable.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The relative pose is then 6 , where ⊕ denotes concatenation.
Sentence 2: with relative pose P i of consecutive joints in hand, the encoding vector v h to represent the robot can be explicitly constructed as follows 3 : In the above section, we discussed how kinematic structure of the hardware can be explicitly encoded as v h . in most cases, we need to not only encode kinematic structure but also the underlying dynamic factors.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For any λ, σ 2 > 0 there exists a unique α > α min such that λ(α) = λ (with the function α → λ(α) defined by λ(α The assumption of a converging problem-sequence is important for the result to hold, while the hypothesis of gaussian measurement matrices A(N ) is necessary for the proof technique to be correct.
Sentence 2: the restrictions λ, σ 2 > 0, and P{X 0 = 0} > 0 (whence τ * = 0 using λ ) are made in order to avoid technical complications due to degenerate cases.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This means that data programming achieves the same learning rate as methods that use labeled data, while requiring asymptotically less work from its users, who need to specify O(1) labeling functions rather than manually label Õ( −2 ) examples.
Sentence 2: in the crowdsourcing setting [17], the number of workers m tends to infinity while here it is constant while the dataset grows.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Recall that Exp and Poly have parameters set with respect to the number of actions N . We see from the figures that NormalHedge is completely unaffected by the replication of actions; no matter how many times the actions may be replicated, the performance of NormalHedge stays exactly the same.
Sentence 2: increasing the replication factor affects the performance of Exp and Poly: Exp and Poly become more sensitive to the changes in the total losses of the actions (e.g.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The numerical procedures presented in section 2.1 provide a general and computationally efficient means for inference in non-Gaussian densities whose application could be useful for a range of probabilistic models.
Sentence 2: our current understanding of the best approach to discretise the base densities is limited and further study of this is required, particularly for application in very large systems D 1.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Namely, only if the "truth proximity" assumption holds, then we have c(x) = c(x ′ ) which together with the condition h(x ′ ) = c(x) we can conclude that x ′ is indeed misclassified.
Sentence 2: if small perturbations can change the ground truth, c(x ′ ) can be different from c(x), in which case, it is no long clear whether x ′ is misclassified or not.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This suggests that the dataset Microarray 2 did not include factors other than the first one as those strongly related to the prognosis.
Sentence 2: wLRMF extracted the identical first factor to HCA-greedy, but extracted much more factors concerning Microarray 2, all of which may not be trustworthy because the number of samples observed in Microarray 2 was as small as 25.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For Lie groups, an implementation of an equivariant Karcher mean would be a sufficient operator for M. It is defined as the point on the manifold that minimizes the sum of all weighted geodesic distances [Nielsen and Bhatia, 2012].
Sentence 2: for each group there is a different number of possible realizations from which only few are applicable in a deep neural network architecture.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The previous literature on DP hypothesis testing has a few characteristics in common: 1) nearly all of these proposed methods first add noise to the data, and perform their test as a post-processing procedure, 2) all of the hypothesis tests use either asymptotic distributions or simulations to derive approximate decision rules, and 3) while each procedure is derived intuitively based on classical theory, none show that they are optimal among all possible DP algorithms.
Sentence 2: in this paper we search over all DP hypothesis tests at level α, deriving the uniformly most powerful (UMP) test for a population proportion.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We first explore distributions that fits such heavy-tailed property.
Sentence 2: a common approach to cope with heavy-tails is to use the L 1 distance, which corresponds to the Laplace distribution the tail of the noise distribution is often still heavier than the Laplace distribution: empirically, we find the kurtosis of the SIFT noise distribution to be larger than 7 for most dimensions, while the kurtosis of the Laplace distribution is only 3.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: . . , Ũk ← the clusters obtained by running k-means on the rows of A 5: Ṽi ← all vertices in V with at least θ|U i | neighbors in U i , where θ is as in Equation 3When developing the algorithm, we also tried using other clustering methods than k-means.
Sentence 2: none of them delivered consistently better results than k-means and the differences in the outputs were mostly minor.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The result is proved by interpreting the incomplete observations as complete observations in a transformed graph, The PAC learnability result implies good sample complexity bounds for the DIC and DLT models.
Sentence 2: the PAC learnability result does not lead to an efficient algorithm, as it involves marginalizing a large number of hidden variables (one for each node not observed to be active).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For the specific case of the squared loss, it is indeed possible to obtain the same rates without regularizing; we defer details to the full version of the paper.
Sentence 2: in practice, regularization has several additional benefits: it renders the ERM optimization problem well-posed (i.e., ensures that the underlying matrix that needs to be inverted is well-conditioned), and guarantees it has a unique minimizer.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Besides, compared with the algorithms adopting 1 -or nuclear-norm convex relaxation (e.g., [16,17,18,19]), directly solving problem (1) via FG-HT often exhibits similar accuracy guarantee but is more computationally efficient.
Sentence 2: despite these desirable properties, FG-HT needs to compute the full gradient at each iteration which can be expensive in large-scale problems.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As shown in Lemma 4, this regularizer also helps improve the robustness of the regression model to noise since maximizing f ld (S) minimizes the entropy of the perturbation error.
Sentence 2: for a multivariate Gaussian distribution, f ld (S) also equivalent (up to an additive |S| factor) to the differential entropy of S. f ld (S) is undefined if S is rank-deficient and might also take negative values; the smoothed version f de (S) overcomes these issues.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If the couch is predicted as clutter and the image evidence from the couch is ignored (Figure 1(c)), multiple room hypotheses can be selected based on the predicted labels of the pixels on the wall (Figure 1(d)) and there is still not enough evidence in the image to select one hypothesis over another in a confident manner.
Sentence 2: if we represent the object by a 3D parametric model, such as a cuboid (Figure 1(e)), then simple volumetric reasoning (the 3D volume occupied by the couch should be contained in the free space of the room) can help us reject physically invalid hypotheses and estimate the correct layout of the room by pushing the walls to completely contain the cuboid (Figure 1(f)).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Rao and Sejnowski [8] show that STDP emerges when a neuron attempts to predict its membrane potential at some time t from the potential at time t − ∆t.
Sentence 2: sTDP emerges only for a narrow range of ∆t values, and the qualitative nature of the modeling makes it unclear whether a quantitative fit can be obtained.
Relationship: contrasting