sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: We randomly generate n = 50 warping functions {γ i } such that {γ −1 i } are i.i.d with mean γ id .
Sentence 2: using Lemma 1, the Fisher-Rao distance between any two warping functions is found to be d F R (γ 1 , γ 2 ) = cos −1 ( 1 0 γ1 (t) γ2 (t)dt).
Relationship: neutral
Domain: NeurIPS
Sentence 1: At this stage, the generative models do not perform well, as the number of available examples is low compared to the number of parameters in the model.
Sentence 2: in the classical supervised learning classification framework, a decision rule is to be learned from a learning set L n = {x i , y i } n i=1 , where each example is described by a pattern x i ∈ X and by the supervisor's response y i ∈ Ω = {ω 1 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For comparison, all models have three-block layers (selected after a pilot test), using VGG-19 features and 1k answers, then, the number of learning blocks is explored to confirm the pilot test.
Sentence 2: we carefully select alternative models (a)-(c) for the importance of embeddings in multimodal learning [18,24], (d) for the effectiveness of identity mapping as reported by [6], and (e) for the confirmation of using question-only shortcuts in the multiple blocks as in [29].
Relationship: neutral
Domain: NeurIPS
Sentence 1: For single-round data collection, the mechanism 1BitMean in (1) preserves -LDP for each user.
Sentence 2: [8] sends a 0-1 random response for each bucket: send 1 with probability e ε/2 /(e ε/2 + 1) if the value is in this bucket, and with probability 1/(e ε/2 + 1) if not.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let d A t,k denotes a size-n vector taking value in d * for j ∈ A t,k and taking value 0 for j / ∈ A t,k .
Sentence 2: some dual or primal (stochastic) sub-gradient descent methods have cheap cost for each iteration, but require O(1/ 2 ) iterations to find a solution of precision, which in practice can even hardly find a feasible solution satisfying all constraints [14].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our approach is related to the Multiple Kernel Learning framework (Lanckriet et al., 2004), although we do not aim here at learning linear combinations of the kernels k T , but rather start from an hierarchical belief on them to propose an algebraic combination.
Sentence 2: in the kernel literature, structured objects are usually represented as histograms of components, e.g., images as histograms of colors and/or features, texts as bags of words and sequences as histograms of letters or n-grams.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, in the semi-supervised classification problem, one usually strives to make sure that labels are equally distributed among the labeled dataset.
Sentence 2: when the discriminator is optimal, the objective of ∆-GAN becomes the Jensen-Shannon divergence (JSD) among three distributions, which is symmetric; the objective of Triple GAN consists of a JSD term plus a Kullback-Leibler (KL) divergence term.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Part 2 of this figure a volume holographic grating (VHG) is employed to diffract the photons in a wavelength-dependent manner, and therefore photons are distributed spatially across a digital mirror microdevice (DMD); distinct wavelengths are associated with each micromirror.
Sentence 2: the elements of the rate vector of λ 0 vary from .07 to 1.5 per bin, and the cumulative dark current Φλ 0 can provide in excess of 50% of the signal energy, depending on the measurement (very noisy measurements).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Specifically, we set F 0 = ∅, N = 0, and λ = σ 2 log m−s η 1 in the multi-stage method, and set p = 2, l = s, η 1 = m−s m η, and η 2 = s m η for a convenient of comparison with Theorem 1.
Sentence 2: an approximate equivalence between the LASSO estimator and the Dantzig selector was shown in [1].
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this regime, the marginal distribution at a node is asymptotically independent of the configuration of a growing boundary.
Sentence 2: we propose an efficient method for graph estimation, and establish its structural consistency when the number of samples n scales as n = Ω(θ −δη(η+1)−2 min log p), where θ min is the minimum edge potential, δ is the depth (i.e., distance from a hidden node to the nearest observed nodes), and η is a parameter which depends on the minimum and maximum node and edge potentials in the Ising model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As seen in figure 1(b)-(c), our intuition is that easy examples should be resolved by the network, that is, classified correctly with high confidence at lower layer probes themselves, while hard examples would either not be resolved at all or be resolved only at or close to the final layer probes.
Sentence 2: suppose, training the simple model on training dataset D train results in classifier M . We view this training procedure of simple models through a different lens: It is equivalent to the optimal classification algorithm trained on the following class distribution mixtures: P M (x|y = 1) and P M (x|y = 0).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The parameter λ > 0 controls the trade-off between the closeness of σ(Φ(X, Θ)) and σ(Φ(X, Θ given )), and the computational cost.
Sentence 2: consider a classification problem, of learning a mapping from an input space X ⊆ R d (e.g., images) to an output space Y ⊆ R (e.g., labels), given training points x 1 , x 2 , ...x n , and corresponding labels y 1 , y 2 , ...y n . We consider a neural network as our prediction model, which takes the form ŷi is the last intermediate layer feature in the neural network for input x i .
Relationship: neutral
Domain: NeurIPS
Sentence 1: In order to evaluate our strategies, a simple problem is considered in which K = 5, L = 3, κ = (0.9, 0.6, 0.3) and θ = (0.45, 0.35, 0.25, 0.15, 0.05).
Sentence 2: we propose to analyze multiple-play bandits in the Position-based model (PBM) [5].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Due to the optimal matching's complexity, researchers have developed approximation algorithms to compute close solutions for a fraction of the computational cost [4,8,1,7].
Sentence 2: we call our algorithm the vocabulary-guided (VG) pyramid match, since the histogram pyramids are defined by the "vocabulary" or structure of the feature space, and the pyramids are used to count implicit matches.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Discriminative visual dialog models produce a distribution over the candidate answer list A t and maximize the log-likelihood of the correct option a gt t . The loss function for D needs to be conducive for knowledge transfer.
Sentence 2: ', besides the ground-truth answer 'No, I do not', D can also assign high scores to other options that are valid responses to the question, including the one generated by G: 'Not that I can see'.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This will produce a graph G ∈ G s . In such a situation, the value of Ĝ is recovered by a general unipartite b-matching algorithm rather than a bipartite b-matching program.
Sentence 2: furthermore, we warm-started the symmetric algorithm with the star-pattern solution of the asymmetric algorithm to make it converge more quickly.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The excellent survey by Guyon, Janzing and Schölkopf [GJS10] on causality from a machine learning perspective underlines the issue as one of the "ten open problems" in the area.
Sentence 2: proof of Theorem 4. to pa(S), then using Lemma 1 and the obtained samples, test (with error probability at most 1/(3K d 2 n)): d+1) n . Output "∆(X , Y) > " if the latter.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The proof of Theorem 1 follows by applying Lemma 1 to Theorem 2.
Sentence 2: we say the sparse vectors h \ and m \ have comparable effective sparsity if there exist an ↵ 2 R such that with ↵ satisfying 1 C  ↵  C for some C 2 R + .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Taking traffic signs as an example, an adversary performing perturbation-based attacks can draw graffiti [4] or place stickers [18] on an existing stop sign in order to exploit a classifier.
Sentence 2: this enables them to assume adversarial examples have the same ground-truth labels as unperturbed images, while we use human evaluation to ensure the labels for our evaluation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since the seminal work of Angluin [2] and Littlestone [14], the paradigmatic application of (noisy) interactive learning has been online learning of a binary classifier when the algorithm is provided with feedback on samples it had previously classified incorrectly.
Sentence 2: if feedback is not noisy (i.e., p = 1), all the non-zero node weights are equal.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our decoupled formulations generalize those in supervised binary code discovery [23] and semi-supervised learning [24], respectively; and more crucially, we propose a novel combined optimization to jointly estimate HDQC and learn LDS in large-scale unsupervised scenarios, from the labeled ImageNet 1.2M [25] to the unlabeled Flickr 100M dataset [26].
Sentence 2: we want samples belonging to the same quasi-classes to be close to each other in the activation spaces, while samples from different quasi-classes should be far from each other in the activation spaces.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let G j denote the 5 × 5 payoff matrix of game j and let the term strategy denote a distribution over all actions.
Sentence 2: hence, the full likelihood for observed actions in game j in Steps 10 and 11 of Algorithm 1 is given by the product Multi(|I| • α j (t; j1); ᾱj (t; j1)).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For each frequency, q , and shift amount, d (where B ¦ @ rU Rd is an integer), we define the Gaussian-Fourier basis functions, 9 ¦ F s , by 9 ¦ F s 5 87 69 B ¦ d 5 87 ¨7 H d B e ut s v 3 Zweck and Williams [13] showed that the Gaussian-Fourier basis is shiftable-twistable.
Sentence 2: 5 87 S 9 IT P d7 49 B ¡ 5 87 bB £ ¥ ¦ 5 87 69 B (11) § ¢ !
Relationship: neutral
Domain: NeurIPS
Sentence 1: number of parameters) to some small number would not usually fit in with our prior beliefs about the true data generating process, it makes sense to use large models (no matter how much data you have) and pursue the infinite limit if you can 2 • For example, we ought not to limit the number of basis functions in function approximation a priori since we don't really believe that the data was actually generated from a small number of fixed basis functions.
Sentence 2: example: Should we use Occam's Razor to determine the optimal number of hidden units in a neural network or should we simply use as many hidden units as possible computationally?
Relationship: neutral
Domain: NeurIPS
Sentence 1: While existing solutions to this problem require some prior knowledge of the parameters ✓ 0 , ✓ 1 , ↵, we propose an adaptive algorithm that requires no such knowledge yet still obtains near-optimal sample complexity guarantees.
Sentence 2: the player can flip any coin she picks from the bag as many times as she wants, and the goal is to identify a heavy coin using as few total flips as possible.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Following the spirit of a margin-based structured predictor such as M 3 N, we employ only the unnormalized energy function F (x, y, z; w) (which usually consists of linear combinations of feature functions or potentials) as the cost function for structured prediction, and we adopt a prediction rule directly extended from the MaxEnDNet-average over all the possible models defined by different w, and at the same time marginalized over all hidden variables z.
Sentence 2: while likelihood-based methods have been extensively explored, to our knowledge, learning structured prediction models with latent variables based on the max-margin principle remains largely an open problem.
Relationship: neutral
Domain: NeurIPS
Sentence 1: All experiments were conducted on workstations with Xeon(R) CPU (W5590@3.33GHz) and 48GB RAM, under Windows 7 System.
Sentence 2: the efficiency of testing may be very important in practice, for example, when the classifier is deployed in a user-facing application (such as search), while the cost of training or preprocessing may be less critical and can be conducted off-line.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We combine the results of the two attention vectors and the equation ( 11) becomes: where W p , W q and b p are all trainable parameters.
Sentence 2: for the formula form, the most popular objective is the maximum log likelihood estimation [Bahdanau et al., 2015;Xia et al., 2017]:  this results in the high frequency of some commonly used expressions such as "I don't know" in the output sentences because of the nature of the class imbalance in the corpus.
Relationship: neutral
Domain: NeurIPS
Sentence 1: DCD-PSGD admits a slightly better convergence rate than ECD-PSGD when the data variation among nodes is very large.
Sentence 2: comparison between DCD-PSGD and ECD-PSGD On one side, in term of the convergence rate, ECD-PSGD is slightly worse than DCD-PSGD due to additional terms that suggests that if σ is relatively large than σ, the additional terms dominate the convergence rate.
Relationship: neutral
Domain: NeurIPS
Sentence 1: However it is clear that (0, 0) is not a local min-max.
Sentence 2: assume f is twice differentiable and ∇f is Lipschitz with constant L. The set of initial vectors (x 0 , y 0 ) so that GDA converges to (linearly) GDA-unstable fixed points (critical points) is of measure zero.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Instead of comparing absolute running times, we observe that all four solvers are based on the Z3 theorem prover [6] and rely on the counterexamples from Z3 to adjust their search strategy.
Sentence 2: using predicate (x < 0 ∨ y > 0) as the loop invariant I suffices to prove the assertion, as shown in Figure 1(b).
Relationship: neutral
Domain: NeurIPS
Sentence 1: There also has been some recent work which examines the complexity of lifted inference independent of the specific algorithm used [13,2,8].
Sentence 2: then, since constraints are in canonical form, for any other variable x ∈ x i involved in (in)equality constraint with x with V as the support, we have V = V every pair of values v i , v j ∈ V behave identically with respect to the constraint tuple T xi and hence, are symmetric to each other.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If in addition to r1 also q1 is known, the two local minimia of F ∞ (p 1 = 0 and p2 = 0) allow to recover t0 = t 0 only.
Sentence 2: since global optimization is generally intractable, in practice it is implemented through an expectationmaximization (EM) procedure known as Baum-Welch algorithm [20,9].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Fig 4 shows examples where hierarchical constraints between layers improves segmentation quality relative to independent clustering at each threshold.
Sentence 2: pairs (u, v) that do not correspond to an edge in the original graph can still be assigned a unique distance based on the coarsest level l at which they lie in different connected components of the cut specified by X l . To compute the quality of an ultrametric d with respect to an input set of edge weights θ, we measure the squared L 2 difference between the edge weights and the ultrametric distance θ − d 2 2 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: It turns out that Σ * can be well approximated by Σ r , r = 50, where Σ r is the best rank r approximation to Σ * obtained from computing its eigendecomposition and setting to zero all but the top r eigenvalues.
Sentence 2: the approach of [7] treats (5) as an instance of (1) and uses nuclear norm regularization to enforce rank-one solutions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For a M × N matrix X, the matrix-variate normal distribution is given by [10] N (X|M, Σ, Ω) = (2π) where M is the mean, and Σ, Ω are M × M row and N × N column covariances, respectively.
Sentence 2: when σ 2 y = 0, q cannot directly be set and a trial-and-error procedure is required to find it.
Relationship: neutral
Domain: NeurIPS
Sentence 1: From the training set, we produce coresets and uniformly sampled subsets of sizes between 70 and 1000, using the parameters k = 33 (as in [11]), β = 66, and δ = 0.1, and fit GMMs.
Sentence 2: one major advantage of coresets is that they can be constructed in parallel, as well as in a streaming setting where data points arrive one by one, and it is impossible to remember the entire data set due to memory constraints.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Moreover, doing so would be difficult as the unconfounded sample is not expected to cover the confounded one.
Sentence 2: the observational data are iid draws from the population given by conditioning on the event E Conf : Using potential outcome notation, assuming the standard Stable Unit Treatment Value Assumption (SUTVA), which posits no interference and consistency between observed and potential outcomes, we let Y (0), Y (1) be the potential outcomes of administering each of the two treatments and Y = Y (T ) = T Y (1) + (1 − T )Y (0).
Relationship: neutral
Domain: NeurIPS
Sentence 1: First, unlike other approximation schemes, KBRL always converges to a unique solution.
Sentence 2: the first set was a 3 × 3 grid over [0.1, 0.3] × [0.3, 0.5] and the second one was composed of four states: {0.1, 0.3} × {0.9, 1.0}.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then we show how this bound can be customized into a surrogate objective function in order to either search in the space of policies (Action-based POIS) or to search in the space of parameters (Parameter-bases POIS).
Sentence 2: with little abuse of notation, we will replace D α (P Q) with D α (p q) whenever possible within the context.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Defining p = rp + 1 − r and q = rq + 1 − r, the number of constraints in (1.6) becomes statistically equivalent to those of a fully observed graph where p and q are replaced by p and q. Consequently, for a fixed r > 0, from (2.3), we require p ≥ p − q O( 1 √ n ) for success.
Sentence 2: our analysis is helpful in understanding the phase transition from failure to success for the simple approach.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A natural choice in this context is to measure the log-likelihood difference between the positive and negative models, normalized by the length of the sequence.
Sentence 2: input: HMM λ = {q j } j=n j=1 , M, π, A, B , heavy state q i , O 1: Draw random HMM, λ i = {q j } j=n+N j=n+1 , M, {π j } j=n+N j=n+1 , {a jk } j,k=n+N j,k=n+1 , {b jm } j=n+N,m=M j=n+1,m=1 2: For each 1 ≤ j ≤ n, j = i, replace transition q j q i with q j q n+1 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is easy to verify that adding εU i,j to J amounts to introducing a vortex of direction i → j → S → i, and any vortex of N states (N ≥ 3) N −1 n=1 U sn,sn+1 in the case of state S being in the vortex and assuming s N = S without loss of generality, or U s N ,s1 + N −1 n=1 U sn,sn+1 if S is not in the vortex, as demonstrated in Figure 1.
Sentence 2: from Lemma 1, it follows immediately that in the discrete case, the comparison of MCMC estimators based on two Markov chains with the same stationary distribution can be cast as a different problem of matrix comparison, as stated in the following proposition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then the error rate of the form n −b , b ≥ 1, which is much faster than the rates of Monte Carlo methods, will be guaranteed with b being a constant representing the degree of smoothness of the RKHS (e.g., the order of differentiability).
Sentence 2: one can incorporate one's knowledge or belief on f into the construction of weighted points {(w i , X i )} via the choice of α.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Here we drew 30 samples from the posterior and set H � = H, but investigation of a range of sample number and H � values yields the same results, suggesting that our approximation parameters do not have an effect on our results (see Supp.
Sentence 2: the studies [28,30,12] suggest that globular fields are a consequence of occlusion nonlinearities.
Relationship: neutral
Domain: NeurIPS
Sentence 1: That is why the impact of the noisy set on training must be reduced by oversampling clean instances [14,3].
Sentence 2: 11 for each clean instance Do Gibbs sweeps to sample from the current p θ θ θ (y y y, ŷ y y, h h h|x x x (•) ) for each clean/noisy instance (m n , m c ) ← (# noisy instances in minibatch, # clean instances in minibatch) , y y y (c) , ŷ y y (c) ) by Eq.12 and 13 end end 4  In this section, we examine the proposed robust CNN-CRF model for the image labeling problem.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Retrieval is finally based on the Hamming distance between these hash codes.
Sentence 2: since ( 7) and ( 10) are special cases of ( 2) and ( 3), respectively, the MC-SVM is a special case of the formulation of Section 2, with predictor f (x) = Φ(x) and codewords y l = w l . This leads to the duality of Figure 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper, we introduce two strategies for conducting convolutions on the sphere, using either a spherical-polar grid or a grid based on the cubed-sphere representation.
Sentence 2: we can apply the conventional 3D convolutions in equation ( 1) to features on the concentric cubedsphere and the concentric spherical-polar grids, and denote these as concentric cubed-sphere convolution (CCSconv) and concentric spherical-polar convolution (CSPconv).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For inference, we assume Rayleigh-fading channels and, therefore, we place a circularly symmetric complex Gaussian prior distribution over the channel coefficients, h m |σ 2 ∼ CN (0, σ 2 I, 0), and over the noise term, n t ∼ CN (0, σ 2 y I, 0).
Sentence 2: we artificially mix the data 10 times (corresponding to 10 microphones) with mixing weights sampled from Uniform(0, 1), such that each microphone receives a linear combination of all the considered signals, corrupted by Gaussian noise with standard deviation 0.3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The conditional intensity can thus be derived given by: where δ ap = t ap − t ap−1 with p being defined by arg max{p : t ai < t}.
Sentence 2: given that datasets are sparse -as shown by the fraction of non-zeros in the ground truth, or %NZ, in Table 1 -the Kendall Correlations and Relative Errors are unreliable metrics for large networks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given the training data points {(x i , ŷi )} N i=1 , a natural candidate for the center of the Wasserstein ball is the empirical distribution PN = 1 N N i=1 δ (xi,ŷi) , where δ (xi,ŷi) denotes the Dirac point measure at (x i , ŷi ).
Sentence 2: similarly, in each trial related to the MNIST dataset, we randomly select 10 shows that DRLR wins by a large margin (outperforming RLR by 4%-43%).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In order to get a partition of the input data into coherent groups, a simple approach is to iteratively finding a dominant set and then removing it from the graph, until all vertices have been grouped (see [9] for a hierarchical extension of this framework).
Sentence 2: now, let n = | V | be the cardinality of V and let xS be the (n-dimensional) characteristic vector of S in Ĝ, which is obtained by padding x S with zeros.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Boosting algorithms are an important recent development in classification.
Sentence 2: if for some m we have Q(f m ) ≤ Q( f ), then theorem is trivially true for all m ≥ m. we are going to consider only the case when Let f m − f = αi hi , where αi and hi correspond to the best representation (with the smallest l * -norm).
Relationship: neutral