sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Although gradient descent (GD) almost always escapes saddle points asymptotically , this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape.
Sentence 2: gradient descent with perturbations [Ge et al., 2015 is not slowed down by saddle points-it can find an approximate local minimizer in polynomial time.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The most natural metric for evaluating disaggregation performance is the disaggregation error in (4).
Sentence 2: average disaggregation error is not a particularly intuitive metric, and so we also evaluate a total-week accuracy of the prediction system, defined formally as  Despite the complex definition, this quantity simply captures the average amount of energy predicted correctly over the week (i.e., the overlap between the true and predicted energy pie charts).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It is known that a good binary CPE model can be used to obtain a good binary classification model (by thresholding at 0.5), and also to obtain a good bipartite ranking model (by using the CPE model directly as a ranking model); it is also known that a binary classification model does not necessarily yield a CPE model.
Sentence 2: not much is known about other directions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In particular, even though the optimization problem has an exponentially large number of constraints (one constraint per policy), the optimum can be found efficiently (i.e., in polynomial time) using, for example, the ellipsoid method, since we can efficiently identify a constraint that is violated.
Sentence 2: 5 in practice we found the following constraint generation method more efficient:  1.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It consists of building a strong classifier as a linear combination of weaklearners, by adding them one after another in a greedy manner.
Sentence 2: while textbook AdaBoost repeatedly selects each of them using all the training examples and all the features for a predetermined number of rounds, one is not obligated to do so and can instead choose only to look at a subset of examples and features.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In CartPole, it is not immediately clear that Φ guess is better than Φ net , since both should be very close to V * .
Sentence 2: φ net is both a biased estimate of V * and noisy (due the inexactness of gradient descent), whereas the simple expert Φ guess is highly related to the goal (keeping the pole centered).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: natural images in the case of the retina, therefore this type of stimulus should be relatively quickly cancelled out.
Sentence 2: non-natural stimuli, like white noise patterns, will be less well captured by interneuron receptive fields and their activation will occur after a longer Accordingly, it will take longer to cancel out nonnatural stimuli, leading to longer principal neuron transients.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: One widely adopted method is multitask Gaussian process (MTGP) [4], which assumes a Gaussian process prior over latent functions to directly induce correlations between tasks.
Sentence 2: for a cokriging task with M variables of P locations for T time stamps, the time complexity of MTGP is O(M 3 P 3 T ) [4].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For instance, the shape of the action potential is intimately related to the dynamics of sodium and potassium channels in the Hodgkin-Huxley model.
Sentence 2: the space of possible features is immense, and given the highly non-linear nature of many of the neural models in question, it can sometimes be of interest to simply perform statistical inference without having to hand-design features.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Except in some special cases [12], it is not known whether any of the approaches used within the Learning community lead to optimality in either of the above senses of the word.
Sentence 2: it is known that under certain regularity conditions, Bayesian estimators lead to either minimax or admissible estimators, and thus to well-defined optimality in the classical (frequentist) sense.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This has the potential to automate a range of applications, such as autonomous vehicles and interactive conversational agents.
Sentence 2: current model-free reinforcement learning algorithms are quite data-expensive to train, which often limits their application to simulated domains [Mnih et al., 2015, with a few exceptions [Kober andPeters, 2009, Levine et al., 2016].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This model is related to latent-variable GP models (GP-LVM) [21], in that we infer the latent {w i } that reside within a GP kernel.
Sentence 2: here {w i } are also factor scores in a factor model, and the GP is used within the context of a Bayesian SVM classifier; neither of latter two have been considered previously.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: (2015) develops a primal-dual gradient method solving (1-2), which achieves a convergence time of O(1/" 1+⌫ 1+3⌫ ), where ⌫ is the modulus of Hölder continuity on the gradient of the dual function of the formulation (1-2).
Sentence 2: 2 the work Yu and Neely (2018) shows that when the dual function has Lipschitz continuous gradient and satisfies a locally quadratic property (i.e.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For small p, collecting additional data is more valuable than decontaminating the existing data, but once we have roughly p = 4 samples, the benefit of decontamination is comparable to the benefit obtained from collecting an additional round of ratings.
Sentence 2: the cost of collecting additional ratings can be quite high if you consider large data sets, e.g., music and movies.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: So in the computation of nearest neighbor distances, each of the p 1 dimensions of {x 1i } receive the same weight, as shown in (1).
Sentence 2: inspired by the recently proposed ideas in metric learning [22], we use a more general distance metric by applying a linear transformation T 1 of size p 1 × p 1 in the space, and then perform MCU using the transformed points, T 1 x i .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As before, we will use the EM-algorithm to maximize the model evidence p(Y) with respect to the parameters Λ, W, σ.
Sentence 2: we additionally impose that each column Λ i of Λ shall be sparse, thereby ensuring that the diversity of parameter dependencies of the latent variables z i = φ z φ,i is reduced.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The drop in TD NSS scores likely reflects the players' shift of attention away from the usual relevant locations (horizon line, focus of expansion) and toward other regions relevant to the crash-recovery task.
Sentence 2: the lack of change in BU NSS scores indicates that the locations attended during crash recovery where neither more nor less salient than locations attended in general; together, these results suggest that during crash recovery players' attention is more strongly driven by some influence that is not captured well by either of the current BU and TD models.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In summary then, the general methods of [4,8,11] and [12,13,17] as well as the variational method of [15] are all identical with respect to their ARD-based cost functions; they differ only in which covariance components (and possibly hyperpriors) are used and in how optimization is performed as will be discussed below.
Sentence 2: the variational model from [14] introduces an additional hierarchy to the ARD framework to explicitly model temporal correlations between sources which may be spatially separated.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: 2 (a) respectively, beyond which the L → ∞ scenario outperforms the L = R scenario, while the R = 1 case does not have such a threshold.
Sentence 2: if the bandwidth is wide enough, the difference of the expected bit error probabilities in decibel, P (p, R), is proved to have similar qualitative characteristics as shown in Fig.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Our analysis can be modified to establish similar positive results for other formulations of the large-margin learning problem, including ones (see [28]) that have been tied closely to weak learnability (these modifications are not presented due to space constraints).
Sentence 2: our main negative result is an information-theoretic argument that suggests that such positive parallel learning results cannot be obtained by boosting alone.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Finally, as in [5], an application of nonlinear radial-basis kernels did not produce significan t improvement in the number of correct classifications when compared to linear kernels and this was the case for type Rt classifiers for which the improvement never exceeded 2% (results not shown).
Sentence 2: the performance of type R int classifiers increased considerably (~8 % ) when they were trai ned with nonli near as opposed to linear kernels (time interval t = [150, 450] ms, res ults not shown).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Although polynomial, it is not clear whether the algorithm given in Lovasz and Vempala [2006], based on random walks, is of practical interest (e.g., the running time bound has a constant of 10 30 ).
Sentence 2: we believe our observation provides insight into the complexity of sampling when ↵ is not too small, and may be a starting point towards explaining the empirical success of using Markov chain Monte Carlo to do inference in LDA.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Initial ideas to multi-task learning exploited supervised data from related tasks to define a form of regularization in the target problem [2,12].
Sentence 2: in this setting, related tasks, also sometimes referred to our DA approach learns a single linear boundary β in a common feature space Z, and task-specific mappings φ 1 (x), φ 2 (x) : X → Z.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The SICS problem where f (X) = − log det(X) + ⟨ Σ, X⟩ and g(X) = ρ∥X∥ 1 , is of the same form as (4).
Sentence 2: in this case neither f (X) nor g(X) have Lipschitz continuous gradients.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If 0 ∈ ∂ q(λ) then the direction d * = argmin d subject to d ∈ ∂ q(λ) is a descent direction and inf α>0 q(λ − αd) < q(λ) − .
Sentence 2: if 0 ∈ ∂ q(λ) then q(λ) ≤ inf λ q(λ) + .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This can be problematic since the chance of producing an assignment of values to Y that has high probability under the likelihood can be quite low, in effect wasting many particles.
Sentence 2: if we can analytically marginalize out the new rows of Y, we can avoid sampling those values from the prior and instead sample them from the posterior, in end for 7: normalize particle weights 8: resample particles according to weight CDF 9: for ℓ = 1, . . . , L do 10: sample end for 12: end for Figure 4: Infinite binary matrix factorization results.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: However, we do not have any assumptions on the form of the expected reward function other than the Lipschitz continuity and that it depends on a single type for each action.
Sentence 2: in [12] graphical bandits are proposed where the learner takes an action vector a which includes actions from several types that consitute a type set T . The expected reward of a for context vector x can be decomposed into sum of reward functions each of which only depends on a subset of D ∪ T . it is assumed that the form of decomposition is known but the functions are not known.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A scale invariant local measure of curvature is the cosine distance between the two vectors formed by three temporally adjacent samples.
Sentence 2: minimizing the curvature directly can result in the trivial solutions: z t = ct ∀ t and z t = c ∀ t. These solutions are trivial because they are virtually uninformative with respect to the input x t and therefore cannot be a meaningful representation of the input.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As in [7], we handle cost functions that are multivariate, in the sense that the number of documents returned for a given query can itself vary, but the key challenge we address in this paper is how to work with costs that are everywhere either flat or non-differentiable.
Sentence 2: we emphasize that the method also handles the case of multivariate costs that cannot be represented as a sum of terms, each depending on the output for a single feature vector and its label.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: On the power of gradient vs prox oracles For non-smooth functions, we show that having access to prox oracles for the components can reduce the polynomial dependence on ✏ from 1/✏ 2 to 1/✏, or from 1/( ✏) to 1/ p ✏ for -strongly convex functions.
Sentence 2: all of the optimal complexities for smooth functions can be attained with only component gradient access using accelerated gradient descent (AGD) or accelerated SVRG.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This approach does not require the rank of the decomposition to be specified beforehand, and due to the low-rank inducing property of the Schatten 1-norm, the rank of the decomposition is automatically determined.
Sentence 2: it has been noticed that the above overlapped approach has a limitation that it performs poorly for a tensor that is only low-rank in a certain mode.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Applied to (1), RCD performs the iteration 1 Many of our results can be extended to convex functions of the form f (x) = φ(Ax) − b x, where φ is a smooth and strongly convex function.
Sentence 2: due to space limitations, and the fact that we already have a lot to say in the special case φ(y) = 1 2 y 2 , we leave these more general developments to a follow-up paper.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Comparison with [16] on combinatorial cascading bandits By Lemma 1, we can apply Theorem 1 to combinatorial conjunctive and disjunctive cascading bandits with bounded smoothness constant B = 1, achieving O( √ mKT log T ) distribution-independent regret.
Sentence 2: besides having exactly these terms, the results in [16] have an extra factor of 1/f * , where f * = i∈S * p(i) for conjunctive cascades, and f * = i∈S * (1 − p(i)) for disjunctive cascades, with S * being the optimal solution and p(i) being the probability of success for item (arm) i.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: On the face of things at least, feature vectors for overlapping frames are treated as independent and feature vectors must be augmented with derivative information in order to enable successful modeling with mixtures of diagonal-covariance Gaussians (see [2,3] for a more in-depth discussion of the exact consequences of the delta features).
Sentence 2: perhaps even more disturbing than the frame-independence assumption are the compromises required to deal with two competing pressures in Gaussian mixture model training: the need for expressive models capable of representing the variability present in real speech data and the need to combat the resulting data sparsity and statistical efficiency issues.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Clearly if the algorithm is asked (as above) to output the full partition of the network, it will require a memory scaling linearly with n, the size of the output.
Sentence 2: in the streaming model, we can remove this requirement and the algorithm can output the full partition sequentially similarly to an online algorithm (however our algorithm is not required to take an irrevocable action after the arrival of each column but will classify nodes after a group of columns arrives).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If indeed P 2 were to always play Rock, Paper, and Scissors with probability 0.4, 0.4, 0.2 , then P 1 could choose any arbitrary strategy and receive an expected value of 0.
Sentence 2: by assuming P 2 is playing a fixed strategy, P 1 may not find a strategy that is robust to P 2 adapting.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Prior work on 3D urban scene analysis is mostly limited to simple ground plane estimation [4,29] or models for which the objects and the scene are inferred separately [6,7].
Sentence 2: in this paper we propose a novel generative model that is able to reason jointly about the 3D scene layout as well as the 3D location and orientation of objects in the scene.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In practice, we typically discard the value of V * 0 once the optimization is converged since we are only interested in the fitted variational parameters λ * .
Sentence 2: during the optimization process, V 0 is an important auxiliary quantity and the inference algorithm would be inconsistent without an optimization over V 0 : if we were to extend the model p(x, z) by an additional observed variable x which is statistically independent of the latent variables z, then the log joint (as a function of z alone) changes by a constant positive prefactor.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: When the combined error of the ideal hypothesis is large, there is no classifier that performs well on both the source and target domains, so we cannot hope to find a good target hypothesis by training only on the source domain.
Sentence 2: for small λ (the most relevant case for domain adaptation), Theorem 1 shows that source error and unlabeled H∆H-distance are important quantities for computing target error.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The logistic upper bound is obtained using 100 logistic samples: the logistic upper-bound A logistic is close to the superdifferential lower bound from [5] and is indeed significantly lower than the bound A L-field .
Sentence 2: the tree-reweighted belief propagation bound behaves a bit better in the second case, but its calculation takes more time, and it cannot be applied for general submodular functions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: An important difference between Imax and the IB setting, is that in the Imax setting, I(Y a ; Y b ) is invariant to scaling and translation of the Y 's since the compression achieved in the mapping X a → Y a is not modeled explicitly.
Sentence 2: the IB framework aims to characterize the dependence of the solution on the explicit compression term I(T ; X), which is a scale sensitive measure when the transformation is noisy.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This condition entails the following: first, for any i ∈ U, adding a single individual to any dataset D can either keep f (i, D) constant, or increase it by 1/n; and second, f (i, D) can only increase in this case for at most items i ∈ U.
Sentence 2: the utility of this algorithm depends only on log , rather than log K. our algorithm does not require the first condition.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The sublinear O(1/k 2 ) convergence rate is known to be optimal if f is simply given by a first-order oracle [12].
Sentence 2: if f is strongly convex, then the convergence rate can be improved to O(c k ) for some c ∈ (0, 1) (i.e., a linear convergence rate) [16].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Since we can replay an execution trace with the interpreter to obtain detailed information about the program state at each step, a trace-based synthesis model can rely upon the interpreter to handle the semantics of the DSL's operations, and focus more on how to infer control flow constructs by reconciling different paths taken in different inputs.
Sentence 2: execution traces are difficult to obtain as they are much more challenging for the end user to specify, so it is hard to reap their benefits.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Together with the transformation U , this implies that there exists a weight matrix Although A k a is indeed sparse, any attempt to learn W k a using GL would fail, since W k a may have a very low level of sparsity.
Sentence 2: an algorithm able to learn a suitable transformation U , it may be able to recover the representation Φ * (and the corresponding space F * ) and exploit the high level of sparsity of A k a .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This includes simulated environments, such as playing Atari games (Mnih et al., 2015), and defeating the best human player at the game of Go (Silver et al., 2016), as well as robotic tasks such as helicopter control (Ng et al., 2006), hitting a baseball (Peters and Schaal, 2008), screwing a cap onto a bottle (Levine et al., 2015), or door opening (Chebotar et al., 2016).
Sentence 2: a common challenge, especially for robotics, is the need to engineer a reward function that not only reflects the task at hand but is also carefully shaped (Ng et al., 1999) to guide the policy optimization.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: When the underlying graph is a tree, the log partition function may be computed exactly via the sum product algorithm in time linear in the number of nodes [15].
Sentence 2: when the graph contains cycles, a generalized version of the sum product algorithm known as loopy belief propagation may either fail to converge or terminate in local optima of a nonconvex objective function [26,20,8,13].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The action a * in line 6 is the maximal valued action in state s ′ , according to the value function Q A .
Sentence 2: instead of using the value Q A (s ′ , a * ) = max a Q A (s ′ , a) to update Q A , as Q-learning would do, we use the value Q B (s ′ , a * ).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The intracellular recording therefore can be used to obtain a ground truth labeling for the spikes originating from one neuron that can be used to evaluate the performance of human sorters and automatic spike sorting algorithms that sort extracellular recordings [13].
Sentence 2: by this method ground truth can only be determined for one of the neurons whose spikes are present in the extracellular recording, and this should be kept in mind when evaluating the performance of spike sorting algorithms on such a data set.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We found that if the true model is in the model class, the (downward) bias in a maximum entropy estimate from finite observations is proportional to the ratio of the number of parameters to the number of observations, a relationship which is identical to that of the (naive) histogram estimators [8,9].
Sentence 2: we also show that if the model is misspecified (i.e.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: With the notation f (x) = x/ x 2 , we define the AMP iteration over vectors v t ∈ R n by v 0 = y, f (v −1 ) = 0, and Our main conclusion is that the behavior of AMP is qualitatively similar to the one of power iteration.
Sentence 2: we can establish stronger results in two respects: 1.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For example, the Dobrushin criterion is that ||R|| 1 < 1, which can be easier to verify in many cases, since ||R|| 1 = max j i |R ij | does not require the computation of singular values.
Sentence 2: for symmetric matrices, it can be shown that ||R|| 2 ≤ ||R|| 1 , meaning the above result is tighter.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Observe that ℓ 1 penalty encourages sparsity of the signal at each time point and enables a selection over the relevant coefficients; whereas the total variation penalty is used to partition the interval [0, 1] so that βk is constant within each segment.
Sentence 2: there are also some drawbacks of the procedure, as shown in Lemma 1 below.
Relationship: contrasting