sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: In other words, we must spend at least this many time steps in order to acquire a sample from a distribution close to P L . Our next result states that the chain in Algorithm 1 mixes rapidly:  One advantage of having a rapidly-mixing Markov chain as means of sampling from a DPP is that it is robust to addition/deletion of elements.
Sentence 2: when a new element is introduced to or removed from S, we may simply continue the current chain until it is mixed again to obtain a sample from the new distribution.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We have evaluated seven nowcasting algorithms, including the simplest model which always predicts the last frame, two optical flow based methods (ROVER and its nonlinear variant), and four deep learning methods (TrajGRU, ConvGRU, 2D CNN, and 3D CNN).
Sentence 2: we have evaluated the performance of deep learning models in the online setting by fine-tuning the algorithms using AdaGrad [4] with learning rate equal to 10 −4 .
Relationship: entailment
Domain: NeurIPS
Sentence 1: The generalization power of compression was recognized by [17] and [22].
Sentence 2: it was shown in [21,Theorem 8] that if the mapping S n → S n is a compression scheme, then with probability at least 1 − δ, for any S n which is an (α, m)-compression of S n ∼ μn , we have (omitting the constants, explicitly provided therein, which do not affect our analysis) Defining Q(n, α, m, δ) as the RHS of Eq.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In this paper, we carefully analyze the AllReduce based setup, propose timing models which include network latency, bandwidth, cluster size and compute time, and demonstrate that a pipelined training with a width of two combines the best of both synchronous and asynchronous training.
Sentence 2: for a setup consisting of a four-node GPU cluster we show wall-clock time training improvements of up to 5.4× compared to conventional approaches.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In order to fit the "orthogonal" rank-k X * , we need a weighted trace-norm of X * tr(p,q) = tc pq (X) = √ k. How large a sample S ∩ A can we now shatter using such a weighted trace-norm?
Sentence 2: we can shatter a sample if Y S∩A tr ≤ √ k. We can calculate: we can shatter a sample of size up to |S| = 8kn A < 8kn.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The only difference is the set K, specialized in various ways, over which the minimum, min K∈K ω(K), is computed.
Sentence 2: it also is important to note, that with the generalization of the theta function comes an implicit generalization of the geometric representation of G. for any feasible K in (11), there is an embedding U = [u 1 , .
Relationship: entailment
Domain: NeurIPS
Sentence 1: The space of possible hyperparameters to explore in GC-LDA is vast, so we restrict our comparison to the aspects of the model which are novel relative to the original Correspondence-LDA model.
Sentence 2: for all three model variants, we compared the log-likelihood of the test data across different values of γ, where γ ∈ 0, 0.001, 0.01, 0.1, 1 .
Relationship: entailment
Domain: NeurIPS
Sentence 1: In this case the dissimilarities can be transformed into a set of values more suitable for embedding through the use of an appropriate transformation: Metric MDS can be formulated as a continuous optimisation problem through the definition of an appropriate error function.
Sentence 2: least squares scaling algorithms directly seek to minimise the sum-of-squares error between the disparities and the inter-point distances.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In the remainder of this section, we show theoretically that choosing d > 0 does not hurt in the sense that it does not reduce the space of policies available to the policy gradient method.
Sentence 2: we show that when using an expressive enough reward parameterization, PGRD's space of policies is not restricted relative to OLPOMDP's space of policies.
Relationship: entailment
Domain: NeurIPS
Sentence 1: For Algorithm 1 running on (1) where f is L-smooth and g i is µ-strongly convex with µ > 0 for all i ∈ [n], it holds that where σ := A [P] 2 op and η P := min t θ E P [ρ t,P | α (t) ].
Sentence 2: expectations are over the choice of P. for strongly convex g i , Algorithm 1 has a linear convergence rate.
Relationship: entailment
Domain: NeurIPS
Sentence 1: For example, in the case of the urban sound detection problem [5], the training data contains the relevant sound somewhere in the given 1-2 secs clip, while the actual vehicle noise itself might last only for few hundreds of milliseconds.
Sentence 2: the sliding window length should be greater than 1 sec while ideally we should restrict ourselves to 100ms window lengths.
Relationship: entailment
Domain: NeurIPS
Sentence 1: For b ∈ {1, . . . , k}, (1) (applied under the conditional distribution given V b−1 , combined with the law of total probability) implies that ∀m > 0, letting By a union bound, this holds for all m ∈ N, with probability at least 1 − δ/(2k).
Sentence 2: this means it holds for m = i bM − i (b−1)M . But note that for this value of m, any h, g m (since for every (x, y) ∈ Z b,m \ Q b , either both h and g make a mistake, or neither do).
Relationship: entailment
Domain: NeurIPS
Sentence 1: Formally, for any x i , x j ∈ X , it assumes that where f X denotes ((L i f )(x i )) M i=1 and ⊥ denotes probabilistic independence between two random variables.
Sentence 2: the original empirical covariance matrix K X is replaced by a rank-M approximation , where K X is the covariance of f X and K X, X ∈ R N ×M is the cross-covariance between f X and f X .
Relationship: entailment
Domain: NeurIPS
Sentence 1: We start from the combined hypothesis that 1) bottom-up saliency is based on centersurround processing, and 2) this processing is optimal in a decision theoretic sense.
Sentence 2: it is hypothesized that, in the absence of high-level goals, the most salient locations of the visual field are those that enable the discrimination between center and surround with smallest expected probability of error.
Relationship: entailment
Domain: NeurIPS
Sentence 1: As shown in [13], every stochastic policy can be represented by a convex combination of deterministic policies and every convex combination of deterministic policies corresponds to a stochastic policy.
Sentence 2: for any stochastic policy π s ∈ Π s , we can represent π s = i p i π d i using some set of {π d 1 , .
Relationship: entailment
Domain: NeurIPS
Sentence 1: We now derive efficient updates that avoids an explicit computation of V. Our derivation involves two key steps.
Sentence 2: the first step is to show that V k+1 can be parameterized by γ k . if we initialize V 0 = Σ, then we can show that: , where with γ 0 = γ 0 .
Relationship: entailment
Domain: NeurIPS
Sentence 1: In particular, we will choose the confidence function g(x) so that is a potential function, which serves as a repository for guarding our loss (we will chose g(x) to be an odd function, and hence will always have Φ t ≥ 0).
Sentence 2: we will choose g(x) so that the change of Φ t lower bounds the payoff of the algorithm.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We can decompose the approximation ratio as follows: 1 ))] As k increases from 1, the tightening ratio T (k) increases towards 1 and the rounding ratio R(k) decreases from 1.
Sentence 2: in this section, we lower bound T and R each in turn, thus lower-bounding the approximation ratio as a function of k. we show that T (k) reaches 1 at small k and that R(k) falls as 2 ⇡ + ⇥( 1 k ).
Relationship: entailment
Domain: NeurIPS
Sentence 1: Approximate Learning: Exact maximum likelihood learning in this model is intractable, but efficient approximate learning of DBMs can be carried out by using a mean-field inference to estimate data-dependent expectations, and an MCMC based stochastic approximation procedure to approximate the model's expected sufficient statistics [14].
Sentence 2: consider approximating the true posterior P (h|v; ψ) with a fully factorized approximating distribution over the three sets of hidden units: where µ = {µ 1 , µ 2 , µ 3 } are the mean-field parameters with q(h l i = 1) = µ l i for l = 1, 2, 3.
Relationship: entailment
Domain: NeurIPS
Sentence 1: While there are many ways in which prediction tasks may be related [20], most of the existing approaches to transfer or lifelong learning are exploiting possible similarities between the optimal predictors for the considered tasks.
Sentence 2: one widely used relatedness assumption is that these predictors can be described as linear or sparse combinations of some common metafeatures and the corresponding methods aim at learning this representations [10,2,15,3].
Relationship: entailment
Domain: NeurIPS
Sentence 1: The key idea of this paper is to introduce an object bounding box B as an abstracted interface to manipulate the semantic label map.
Sentence 2: we define a controllable bounding box B = {b, c} as a combination of box corners b ∈ R 4 and a class label c = {0, . . . , C}, which represents the location, size and category of an object.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Figure 5: Test set accuracy on full and limited training sets To test the ability of our pretrained features to generalize across rotations and lighting conditions given only a weak supervised signal, we limited the labeled training set to comprise only examples with a particular set of viewing angles and lighting conditions.
Sentence 2: nORB contains images spanning 9 elevations, 18 azimuths and 6 lighting conditions, and we trained our linear classifier only on data with elevations {2, 4, 6}, azimuths {10, 18, 24} and These results demonstrate that Tiled CNNs perform well even with limited labeled data.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In the restricted-information scheme, we make a much milder assumption that the learner is informed about the losses of the available actions.
Sentence 2: we define the set of available components as and assume that the learner can observe the i-th component of the loss vector t if and only if i ∈ D t . This is a sensible assumption in a number of practical applications, e.g., in sequential routing problems where components are associated with links in a network.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In fact, we note that Diag(w) * = w 1 and p −1/2 1 Diag(w) * = w * = w 2 .
Sentence 2: we can express the 1 and 2 -norms of w using the trace norm of a given matrix times the matrix Diag(w).
Relationship: entailment
Domain: NeurIPS
Sentence 1: We evaluated the learned causal DAGs based on their accuracy in predicting the true effects of each of the interventions (shown in Figure 5(a)) when leaving out the data for that intervention.
Sentence 2: if the predicted DAG indicates an arrow from gene A to gene B, we count this as a true positive if knocking out gene A caused a significant change 2 in the distribution of gene B, and a false positive otherwise.
Relationship: entailment
Domain: NeurIPS
Sentence 1: As recent work has highlighted the possibility that neurons encode fractional derivatives, it is noteworthy that the non-local nature of fractional calculus offers a natural framework for predictive coding.
Sentence 2: as we will show, when we assume that the predictive information about the future signal is fully contained in the current set of spikes, a signal approximated as a sum of powerlaw kernels corresponds to a fractional derivative in the form of a sum of Dirac-δ functions, which the neuron can obviously communicate through timed spikes.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In what follows, we will assume that the m th fidelity mean of an arm is within ζ (m) , a known quantity, of its highest fidelity mean, where ζ (m) , decreasing with m, characterise the successive approximations.
Sentence 2: |µ for all k ∈ K and m = 1, . . . , M , where = 0 and the ζ (m) 's are known.
Relationship: entailment
Domain: NeurIPS
Sentence 1: To eliminate such preprocessing step from the equation, one has to develop a class of new statistical estimators that admit strong performance guarantees, such as exponentially tight concentration around the unknown parameter of interest, under weak assumptions on the underlying distribution, such as existence of moments of only low order.
Sentence 2: such heavytailed distributions serve as a viable model for data corrupted with outliers -an almost inevitable scenario for applications.
Relationship: entailment
Domain: NeurIPS
Sentence 1: As with the usual definition of differential privacy, we guarantee that the output of our algorithm is similarly distributed on neighboring databases, only our notion of neighboring databases depends on the hypothesized distributions.
Sentence 2: the a single entry in X drawn from either P 0 or P 1 may be replaced without detection by another entry drawn from either P 0 or P 1 , even if the rest of the database is arbitrary.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Consider the normalized likelihood, where clearly (θ) may be replaced by (θ)/N , Finally, while we have chosen to present our methodology as applied to topic models, we expect the same techniques to be useful in a notably broader context.
Sentence 2: our methodology is directly applicable to problems solved through Nonnegative Matrix Factorization (NMF), a close relative of PLSA where matrix columns or rows are often similarly constrained in their L 1 norm.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Suppose we run Algorithm 1 in the realizable case with inputs example oracle U , labelling oracle O, hypothesis class H, confidence-rated predictor P , target excess error � and target confidence δ.
Sentence 2: then with probability 1 − δ, for all k = 1, 2, . . . , k 0 + 1, and for all h ∈ V k , err D (h) ≤ � k . the ĥ returned at the end of the algorithm satisfies err D ( ĥ) ≤ �.
Relationship: entailment
Domain: NeurIPS
Sentence 1: To minimize (3), we propose to leverage the fact that, as discussed below, C can be thought of as the parameters of an additional network layer, which lets us solve for Θ and C jointly using backpropagation.
Sentence 2: 1 consider the self-expressiveness term in (3), Z Θe − Z Θe C 2 F . Since each data point z i (in the latent space) is approximated by a weighted linear combination of other points {z j } j=1,••• ,N (optionally, j = i) with weights c ij , this linear operation corresponds exactly to a set of linear neurons without non-linear activations.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Secondly, this notion helps clarify how our assumptions are much less restrictive than those considered previously.
Sentence 2: independence given the label: Independence given the label implies that for any S 1 ⊆ X + 1 and S 2 ⊆ X + 2 we have Pr(S 2 |S 1 ) = Pr(S 2 ).
Relationship: entailment
Domain: NeurIPS
Sentence 1: As an extreme example, if all columns of Z ⊤ B ⊤ are discretized to take values from a set of n vectors, PCSA degenerates to Mixture of PPCA [7,20] with n components, whose subspace loadings are the same.
Sentence 2: learning such a PCSA model actually implements the group PPCA [24] throughout different components.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Problem (1) can be solved by alternately updating W k and T k through the stochastic gradient descent (SGD) method, which will be introduced in the following paragraphs.
Sentence 2: since binary matrix T k can be determined with the constraints in (1), we only need to investigate the update scheme of W k . Inspired by the method of Lagrange Multipliers and gradient descent, we give the following scheme for updating W k . in which β indicates a positive learning rate.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Such methods may achieve quadratic convergence rates with O(np 2 + p 3 ) per-iteration cost [Bis95,Nes04].
Sentence 2: for t large enough, Newton's method yields k ✓t+1 ✓ ⇤ k 2  ⇠ 2,NM k ✓t ✓ ⇤ k 2 2 , and it is insensitive to the condition number of the Hessian.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In the prediction phase, all we have to do is to keep the trained β fixed, and turn the optimization problem ( 5) into an analogous one that optimizes over the response y.
Sentence 2: given a new sample x t of unknown response, our sample matrix X grows by one column X → [X, x t ], which means all our feature vectors gets one more dimension.
Relationship: entailment
Domain: NeurIPS
Sentence 1: SVP is a simple projected gradient descent method where the projection is onto the set of low-rank matrices.
Sentence 2: the t-th step update for SVP is given by: where M t is the t-th step iterate, η > 0 is the step-size, and P L (M ) is the projection of M onto the set of rank-L positive semi-definite definite (PSD) matrices.
Relationship: entailment
Domain: NeurIPS
Sentence 1: For the image classification branch, we choose φ α enc as the rest of the original VGG-M network for image classification.
Sentence 2: the decoder function ψ cls dec for the image-level labels is initialized to be the same as the fully-connected layers of the original VGG-M, such that φ VGG-M enc = ψ cls dec • φ img enc .
Relationship: entailment
Domain: NeurIPS
Sentence 1: 2, that iteratively expands a buffer q old → q new around a given subchain y S . Growbuf terminates when all belief residuals satisfy The GrowBuf sub-routine can be computed efficiently due to (1) monotonicity of the forward and backward messages so that only residuals at endpoints, q(x S 1 ) and q(x S L ), need be considered, and (2) the reuse of computations.
Sentence 2: the forward-backward pass can be rooted at the midpoint of y S so that messages to the endpoints can be efficiently propagated, and vice versa [22].
Relationship: entailment
Domain: NeurIPS
Sentence 1: Setup To show this quantitatively, we the ✏ value for a traditional perturbation-based attack (a 100-step PGD) until the attack success rates on the certified defenses are similar to those for our technique.
Sentence 2: we used an ✏ of 0.31 and 0.2 to attack [16] and [17] respectively, resulting in success rates of 86.0% and 83.5%.
Relationship: entailment
Domain: NeurIPS
Sentence 1: However, we argue that it's actually rather unrestrictive.
Sentence 2: in fact the individual valuations v k,t can be generated arbitrarily so long as v k,t  w ⇤> t x t and equality holds for some k. we can imagine that nature first computes the market valuation v + t , then arbitrarily (even adversarialy) selects which buyer gets this valuation, and the other buyer valuations.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Their approach breaks down the concept of similarity into one-to-one mappings, one-to-many mappings and many-to-many mappings, and probes each kind of mappings by ad-hoc techniques.
Sentence 2: they applied linear correlation and mutual information analysis to study one-to-one mappings, and found that some core representations are shared by differently-initialized networks, but some rare ones are not; they applied a sparse weighted LASSO model to study one-to-many mappings and found that the whole correspondence can be decoupled to a series of correspondences between smaller neuron clusters; and finally they applied a spectral clustering algorithm to find many-to-many mappings.
Relationship: entailment
Domain: NeurIPS
Sentence 1: To address this more challenging situation, we study informationbased learning strategies of agents in unbounded state spaces using non-parametric Bayesian models.
Sentence 2: we demonstrate that the Chinese Restaurant Process (CRP) model is able to solve this problem and that an Empirical Bayes version is able to efficiently explore bounded and unbounded worlds by relying on little prior information.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Since it has been shown [13] that the empirical estimate of the mean, µ X = 1 /m i k x i , is a good proxy for µ P , the injectivity of µ can be used to define distances between distributions P and Q, observed via samples X = {x i } m i=1 and Y = {y i } n i=1 .
Sentence 2: this can be done via the maximum mean discrepancy where F denotes a suitable class of functions X → R, and E x∼P [ f (x)] denotes the expectation of f (x) w.r.t.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We show that the player can benefit from such a hint if the set of feasible actions is sufficiently round.
Sentence 2: if the set is strongly convex, the hint can be used to guarantee a regret of O(log(T )), and if the set is q-uniformly convex for q ∈ (2, 3), the hint can be used to guarantee a regret of o( √ T ).
Relationship: entailment
Domain: NeurIPS
Sentence 1: By selecting different values for the total number of arcs, we can obtain models representing the brain connectivity at different levels of strength.
Sentence 2: given a small value for the total number of arcs, only strong arcs will show up in the resulting connectivity model, so the model is a model of strong brain connectivity; when increasing the total number of arcs, mild arcs will also show up in the resulting connectivity model, so the model is a model of mild and strong brain connectivity.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Attending to memory is formalized as the problem of computing w. A content addressable memory, proposed in [7,21,2,17], is an external memory with an addressing scheme which selects w based upon the similarity of memory words to a given query q.
Sentence 2: for the ith read weight w(i) we define, where d is a similarity measure, typically Euclidean distance or cosine similarity, and f is a differentiable monotonic transformation, typically a softmax.
Relationship: entailment
Domain: NeurIPS
Sentence 1: This is motivated by the fact that there exist unseen/seen classes that fall into the same superclass, i.e., the unseen class samples become 'seen' at the superclass level and thus easier to recognize.
Sentence 2: our DIPL model is employed for ZSL with superclasses as follows: 1) Group all unseen and seen class prototypes  Datasets.
Relationship: entailment
Domain: NeurIPS
Sentence 1: This algorithm also requires a suitable choice of T to guarantee that OFFLINEPCPD is called for a window of data that actually contains k ⇤ .
Sentence 2: t should be large enough that the algorithm is unlikely to call OFFLINEPCPD when j < k ⇤ but small enough so that it is likely to call OFFLINEPCPD by time j = k ⇤ + n/2.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We now provide lower bounds on the number of learners and sample complexity for arbitrary online boosting algorithms to evaluate the optimality of OnlineMBBM under 0-1 loss.
Sentence 2: we construct weak learners that satisfy the online weak learning condition (1) and have almost matching asymptotic error rate and excess loss compared to those of OnlineMBBM as in (7).
Relationship: entailment
Domain: NeurIPS
Sentence 1: The only exceptions are object root particles for which we predict the global dynamics.
Sentence 2: the state prediction module (g, p i , e i ) predicts the local future delta position t+1 i,`= t+1 i t+1 par(i) using the particle state p i , the total effect e i on p i , and the gravity g as input.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Theorem 5 suggests an asymptotic test, which is computationally preferable to a permutation test.
Sentence 2: for a desired Type I error rate α ∈ (0, 1) our test rejects the null hypothesis p = q if and only if When s = 0, this approach is closely related to several two-sample tests in the literature based on comparing empirical characteristic functions (CFs).
Relationship: entailment
Domain: NeurIPS
Sentence 1: In other words, after the recognition by a parent-node classifier, we may use classifiers trained to discriminate between its children to implement a discriminative novelty detection algorithm.
Sentence 2: we used the approach described in [8] to build a unified representation for all objects in the sub-class level, which is the representation computed for the parent object whose classifier had accepted (positively recognized) the object.
Relationship: entailment