sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: no outliers), all methods perform well; their RMSEs are close to optimal (1/2, the standard deviation of i ).
Sentence 2: when outliers start to appear, the result of least squares is significantly skewed, while the results of classic robust statistics methods, Huber, L1 and LTS, indeed turn out to be more robust than the least squares, but nevertheless are still affected significantly.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: An MDP is defined as the 5-tuple (S, A, P, R, γ) [18], where S is a finite state space, A is a finite action space, The use of the 1-step policy improvement in Reinforcement Learning (RL) was theoretically investigated under several frameworks, e.g., Policy Iteration (PI) [18], approximate PI [2,9,13], and Actor-Critic [10]; its practical uses are abundant [22,12,25].
Sentence 2: single-step based improvement is not necessarily the optimal choice.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Quasiorthogonalization makes use of evaluations of Hessians of the fourth cumulant function to construct a matrix of the form C = ADA T where D has all positive diagonal entries-a task which is complicated by the possibility that the latent signals S i may have fourth order cumulants of differing signs-and requires taking the matrix square root of a positive definite matrix of this form.
Sentence 2: the algorithm used for constructing C under sampling error is not always positive definite in practice, which can make the preprocessing step fail.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: However, these studies do not attempt to infer functional connections between non-simultaneously observed neurons.
Sentence 2: a few studies have presented statistical methods for dealing with sub-sampled observations of neural activity or connectivity, but these approaches are not applicable to our problem: A recent study [12] presented a method for predicting noise correlations between non-simultaneously recorded neurons, but this method requires the strong assumption that noise correlations are monotonically related to stimulus correlations.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: New data-local quadratic subproblems.
Sentence 2: during a computation step, node k locally solves the following minimization problem min where (2) Crucially, this subproblem only depends on the local data A [k] , and local vectors v l from the neighborhood of the current node k. in COCOA [Smith et al., 2018] the subproblem is defined in terms of a global aggregated shared vector v c := Ax 2 R d , which is not available in the decentralized setting.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This was done in both [19] (in which messages are approximated using a using a mixture of delta functions, which in practice results in retaining the K largest message components) and [20] (which uses an additional uniform distribution in the approximating distribution to ensure non-zero weights for all states in the discretization).
Sentence 2: these approaches appear to suffer when multiplying messages with disjoint peaks whose tails have been truncated to enforce sparsity: such peaks are unable to fuse their evidence correctly.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Inspection of the right-hand side of (13) suggests that the usual Ω(log N ) lower bounds [14,27,24] can be obtained if φ(u) behaves like u log u for large u.
Sentence 2: if φ(u) behaves like − log u for small u, then the lower bounds will be of the form Ω log 1 δ .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Most past work in neural programs induction assumes that a very large amount of training data is available to train a particular task, and ignores data sparsity issues entirely.
Sentence 2: in a practical scenario such as the FlashFill domain described in Section 1 or the real-world Karel analogue , the approach we take is to randomly sample a number of k-sized sets and performing ensembling of the softmax log probabilities for each output token.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To take a more attainable view, we also computed a standard ensemble Ensemble(Ours, SAN) and compared to an Ensemble(SAN, SAN) model, outperforming it by 1.24% for VQA v2 but falling short by 0.15% for VQA v1.
Sentence 2: ensemble(GVQA, SAN) improves VQA v2 performance by only 0.54%.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Equation ( 6), in turn, leads to an optimal rule for finding the features h b to merge with the current optimal solution h a : the set which minimizes The equation also leads to a straightforward procedure for updating the optimal cost once this set is determined.
Sentence 2: when the cost function is BE, the equivalent expression is Note that the non-linearity introduced by the !
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Notice that in the statement of Theorem 3, the approximation guarantee of ESC-Streaming is given with respect to a memory only large enough to fit the offline greedy algorithm's solution.
Sentence 2: if we allow our memory M to be as large as k ⇤ /✏, then Theorem 1 follows immediately for ✏ = 1/ ln(1/✏).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Initially, tree-based methods Gray, 2012, Koenigstein et al., 2012] were proposed for MIPS, which use the idea of branch and bound similar to k-d tree [Friedman and Tukey, 1974].
Sentence 2: these methods suffer from the curse of dimensionality and their performance can be even worse than linear scan when feature dimension is as low as 20 [Weber et al., 1998].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Compared with GD, which achieves -stationarity using O( N i=1 L i / ) gradient evaluations in the worse case (in the sense that N i=1 L i /N = L), the rate in [21] is O(N 1/3 ) times better.
Sentence 2: the algorithm in [21] is different from NESTT-G in two aspects: 1) it does not generalize to the nonsmooth constrained problem (1.1); 2) it samples two component functions at each iteration, while NESTT-G only samples once.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This map moves N points of mass 1/N each a distance at most 2✏ n (K), so we may bound Combining these two bounds, we see that For each n, we choose to set N = n, which yields W 2 (⌫ n,n , ⌫ ⇤ )  2✏ n (K) + Cn 1/d .
Sentence 2: applying Lemma 4.1, and recalling that ⌫ ⇤ is the minimizer of J, we have we must have , because both are measures on the same n point 2✏ n (K)cover, but ⌫ ⇤ n has weights chosen to minimize J.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the first, non-stochastic setting [7,11], the reward is generated by an adversary instead of a stationary, stochastic process.
Sentence 2: the reward observed by the learner is still a real reward, in that the learner is still interested in maximizing it, or more precisely, minimizing some notion of regret in reference to some reference policy [8].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In general, an RKHS is usually smaller than the L 2 space defined on the same input domain.
Sentence 2: so, it is not always true that fλ,G * achieves f . one can choose to use universal kernels K uj so that their corresponding RKHSs are dense in the L 2 spaces (see [3], [15]).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Our second contribution is another algorithm, PEGE2, which combines gap estimation with a PEGE algorithm, to achieve an O(log T ) regret bound, matching the GCB guarantee but removing the dependence on size of the learner's action space.
Sentence 2: like GCB, PEGE2 requires access to both offline oracles and the existence of a unique optimal action.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In particular, the joint peristimulus time histogram (JPSTH) and its integral, the shuffle-corrected correlogram [1,2,3] have become widely used tools to analyze such data.
Sentence 2: the JPSTH and correlogram cannot distinguish correlations induced by connections between the two measured neurons (direct connection correlations) from correlations induced by common connections from a third, unmeasured neuron (common input correlations).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Such a conditional independence property is essential for the guarantees that we will present in this work to extend to a BAYES-CCE and hence do not seem to extend to the notion given in [4].
Sentence 2: as we will show in Section 5, the no-regret dynamics that we analyze, which are mathematically equivalent to the dynamics in [4], do converge to this smaller set of BAYES-CCE that we define and for which our efficiency guarantees will extend.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Secondly, for different values of α, MST and TSP need to be recomputed since the distance between two points is the p-th power of their Euclidean distance where p = d(1 − α).
Sentence 2: the k-NN graph does not change for different values of p, since p-th power is a monotone transformation, and hence the estimates for multiple values of α can be calculated without the extra penalty incurred by the recomputation of the graph.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This phenomenon is closely linked to the graph connectivity issues associated with SSC, mentioned before.
Sentence 2: in particular, under a random-sample model, the true positive rate for SSC will go to zero as N t /d t grows, where N t is the number of samples from S t with dim(S t ) = d t . the true positive behavior for CSC has several favorable characteristics.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We remark that the same multi-stage scheme (especially the setting of m and n 0 ) Algorithm 1 is due to [8], which was also used in several stochastic optimization algorithms for solving different problems [11,12].
Sentence 2: the difference from these studies is that ∂ Q t (θ) is not an unbiased stochastic gradient of Q(θ).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Figure 4 (Right) shows that AQM nearly always chooses the true target image from 10K candidates in six turns if the PropAcc λ is 1.0.
Sentence 2: aQM also chooses correctly with a probability of 51% and 39% (accuracy of goal-oriented dialog) in six turns, when the PropAcc λ is 0.95 and 0.90, respectively.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This form of coding was loosely inspired by the idea of "energy landscape" coding proposed by Hinton and Brown [2].
Sentence 2: contrary to [2] and other theories using rate-based representation of probabilities, this model is self-consistent and does not require different models for encoding and decoding: As output spikes provide new, unpredictable, temporally independent evidence, they can be used directly as an input to other Bayesian neurons.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: More importantly, in BayesSCDC the variational posterior gathers information from L through message passing in the relational model.
Sentence 2: the amortized form q(z|o)q(x, z|o) used in SCDC ignores the effect of observed annotations L. Another advantage of the inference algorithm in BayesSCDC is in the computational cost.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For large values of ρ the following holds: where Setting the derivatives ( 9) and ( 10) to zero and inserting equations (8) yields the following necessary conditions for a maximum of the free energy that hold in the limit ρ → ∞: Note that equations (11) are not straight-forward update rules.
Sentence 2: we can use them in the fixed-point sense and approximate the parameters which appear on the right-hand-side of the equations using the values from the previous iteration.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The motion of a simulated whisker in reaction to external forces from a collision is constrained only by the fixed spatial location of the follicle, and by the damped dynamics of the springs at each node of the whisker.
Sentence 2: although the spring equilibrium displacements are determined by static measurements as described above, the damping factors and spring stiffnesses cannot be fully determined from these data.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Over the last decade multiple authors have introduced explicit reductions showing how stochastic planning can be solved using probabilistic inference (for example, [4,25,5,17,23,12,8,19,26,10,18]) with applications in robotics, scheduling and environmental problems.
Sentence 2: heuristic methods and search are still the best performing approaches for planning in large combinatorial state and action spaces [9,7,2].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In particular, it has been shown that a slow-and-smooth prior, and related models, can qualitatively account for a range of experimental results [17,15,16] and can quantitatively account for others [7,12].
Sentence 2: the integration strategy modeled by the slow-and-smooth prior may not generalize to more complex motion types, such as circular and radial motion, which are critically important for estimating ego motion.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Each time interval provides evidence as to the value ρ it .
Sentence 2: given prior distribution ρ it ∼ Beta(α it , β it ), the posterior is to limit the evidence provided from each item, we scale it by a factor of n. When all locations are considered, the resulting posterior is: where F i is feature map i and χ t is the set of locations containing elements of type t. With the approach we've described, evidence concerning the value of ρ it accumulates over a sequence of trials.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Consequently, many researchers are now working on developing semi-supervised learning techniques for a variety of approaches, including generative models [14], self-learning [5], co-training [3], information-theoretic regularization [6,8], and graph-based transduction [22,23,24].
Sentence 2: most of these techniques have been developed for univariate classification problems, or class label classification with a structured input [22,23,24].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The methods relying on a whitening step [2][3][4], will perform the whitening using the matrix E † l obtained from the low-rank SVD truncated at rank l: TPM will use E l to whiten the tensor M 3 to a tensor T l 2 R l⇥l⇥l .
Sentence 2: when k > l, T l may not admit a symmetric orthogonal decomposition 4 .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The experimental design consists of randomized stimuli, thus all runs of repetitions or alternations are spurious, and any behavioral tendencies driven by such patterns are useless.
Sentence 2: compared to artificial experimental settings, truly random sequential events may be rare in the natural environment, where the laws of physics and biology dictate that both external entities and the observer's viewpoint undergo continuous transformations for the most part, leading to statistical regularities that persist over time on characteristic timescales.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The quality of f is measured by its excess risk, which is the expectation of its loss `(Y, f (X)) minus the expected loss of the best prediction function f ⇤ in a given class of functions F. Analysis in this setting usually involves giving guarantees about the performance of f in the worst case over the choice of the distribution of the data.
Sentence 2: the setting of sequential prediction (also called online learning) [2] makes no probabilistic assumptions about the source of the data.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It is worth noting that, since the gain function g(v i ) defined in Eq (1) has no upper saturation, recurrent interactions can easily result in runaway excitation and firing rates growing unbounded.
Sentence 2: our optimization algorithm will naturally seek stable solutions, in which firing rates are kept within a limited range due to a fine dynamic balance of excitation and inhibition [14].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Now from all x ∈ D which result in the same truncated representation, we select a single representative to be included in D This results in a set D of size at most (4nT ) n/2 which is a 1/ √ T -net for D. That is, every x ∈ D is at distance at most 1/ √ T from its nearest neighbor in D. Since an admissible loss vector has norm at most √ n, summing over the T rounds of the game, we see that the optimal loss for D is within an additive √ nT of the optimal loss for D. For implementation purposes, it may be impractical to store the decision set (or the covering net of the decision set) explicitly as a list of points.
Sentence 2: our algorithms only require the ability to sample from a specific distribution over the decision set.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Empirically, it is shown that the proposed GHN benefits from a fast and robust learning process that is on par with that of the batch-normalization approach, yet without resorting to sophisticated learning process of additional parameters (see Section 4 for experimental results).
Sentence 2: gHN also benefits from the rapid developments of neural computing techniques, in particular, those employing parallel computing on GPUs.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Let C ⊂ R D be a convex set and let x ∈ C. Then for all z, we have where y ≡ argmin y∈C d f (y, z) is the projection of z onto C. At first glance, the Pythagorean theorem may appear to be a triangle inequality for Bregman divergences.
Sentence 2: the inequality is actually the reverse of the standard triangle inequality and only applies to the very special case when y is the projection of z onto a convex set containing x.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Furthermore, given any point x = (x 1 , ..., x d ) generated from the distribution Λ, calculating ŷ the regression model output (5), involves finding a ŷ that solves equation ( 12), where z = (ŷ, x 1 , ..., x d ), and, recalling from above, for ŷ is in general a nonlinear single variable optimization problem, which can be solved using a root finding algorithm (for example the Newton-Raphson Method outlined in [4]).
Sentence 2: below we present a specific form of nonlinear K c (z i , z) that allows (12) to be solved analytically.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To date, almost all techniques of text classification are based on words, in which simple statistics of some ordered word combinations (such as n-grams) usually perform the best [12].
Sentence 2: many researchers have found convolutional networks (ConvNets) [17] [18] are useful in extracting information from raw signals, ranging from computer vision applications to speech recognition and others.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Notice that since f de (S) is not monotone in general [13], we cannot use Theorem 3.
Sentence 2: in the case when δ ≥ 1, a simple application of Lemma 13 shows that f de (S) becomes monotonically increasing and we can then use Theorem 3 to obtain a tighter approximation bound.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: By Chebyshev's inequality, an estimator with finite variance enjoys the tail bound P( At the expense of working with slightly more conservative step-size policies (see below), much of our analysis goes through with this weaker requirement for the tails of ξ.
Sentence 2: the extra control provided by the O(1/z q ) tail bound simplifies the presentation considerably, so we do not consider this relaxation here.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In classification, one seeks a binary-valued function h : X →Y that predicts the class of a new instance in X .
Sentence 2: in ranking, one seeks a real-valued function f : X → R that induces a ranking over X ; an instance that is assigned a higher value by f is ranked higher than one that is assigned a lower value by f . The area under the ROC curve (AUC) has recently gained some attention as an evaluation criterion for the bipartite ranking [3].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The recent resurgence of interest in this task has been driven in part by the development of new and larger benchmark datasets such as Flickr 8K [4], Flickr 30K [5] and COCO Captions [6].
Sentence 2: even the largest of these datasets, COCO Captions, is still based on a relatively small set of 91 underlying object classes.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: More concretely, for sufficiently small we argued that δ 3k [Φ] > 1/ √ 32 for all k, and consequently convergence to the optimal solution may fail.
Sentence 2: it can be shown that δ * 3k [Φ] will remain quite small, satisfying implying that performance will nearly match that of an equivalent recovery problem using A (and as we discussed above, δ 3k [A] is likely to be relatively small per its unique, randomized design).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In any case, if we define µ ij = k w k f ik f jk to be the similarity predicted by a particular choice of F and w, then: where σ 2 is the variance of the Gaussian error distribution.
Sentence 2: self-similarities s ii are not modeled in additive clustering, and are generally fixed to (the same) arbitrary values for both the model and data.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To solve (9), we first take the convex surrogate of the objective function, which corresponds to an 1 / p -norm [29,30], where we drop the indicator function and, for p ∈ {2, ∞}, solve The nonnegative parameter λ is a regularization parameter and the function ρ(•) ∈ {ρ e (•), ρ a (•)} enforces whether the reconstruction of each point should be exact or approximate, where More specifically, when dealing with missing entries from noise-free data, which perfectly lie in multiple subspaces, we enforce exact reconstruction by selecting ρ(•) = ρ e (•).
Sentence 2: when dealing with real data where observed entries are corrupted by noise, exact reconstruction is infeasible or comes at the price of losing the sparsity of the solution, which is undesired.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It is also widely accepted that the function f (•) (or the functionf (•)) is a nuisance function as we do not observe its value and its sole purpose is for a convenient formulation of the model [14].
Sentence 2: in this paper, we show that by using privileged information as the noise term, the latent function f now plays a crucial role.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Another straightforward approach is to employ a majority vote among the players: let each player independently identify an arm, and choose the arm having most of the votes (alternatively, at least half of the votes).
Sentence 2: this approach does not lead to any improvement in performance: for this vote to work, each player has to solve the problem correctly with reasonable probability, which already require Ω(H ε ) pulls of each.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: at iteration i + 1, and n,t,r ✓ i ,s,r ✓i , P (R ✓ n t 1 = r ✓ , S n t = s, R ✓ n t = r✓|s n , a n , ⇤ i ) can be computed efficiently by exploiting the intermediate results from evaluating P (R ✓ n t = r ✓ |s n , a n , ⇤ i ) described previously, as detailed in Appendix B.
Sentence 2: if the feature measurements of ' s can be observed by the agent during the expert's demonstration, then recall that we use a generalized linear model to represent ⌧ !
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Let N 2 N µ,⌫ (n, d) be a random network as in Definition 1.
Sentence 2: for any fixed input to N , we have the fourth moment of Z p,q (x) is exponential in Moreover, there exists a constant C K,µ > 0 depending only on K and the first 2K moments of the measures {µ Remark 2.
Relationship: contrasting