sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Initially, the network starts with some random connectivity, and obeys the dynamical equations, We then apply the following modified learning rules for D and Ω, (20) We note that in both cases, the learning remains local.
Sentence 2: similar to the rate dynamics, the dynamics of learning now requires a slower synaptic process that computes the averaged signal inputs and presynaptic firing rates.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In contrast, if samples are allocated uniformly to the alternatives under the same conditions, then the most natural procedures require K max i =i ∆ −2 i log(K/δ) samples before returning i with probability at least 1 − δ.
Sentence 2: standard best-arm bandit algorithms do not incorporate asymmetry as induced by nullhypotheses as in definition (1) by default.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Specifically, the distribution of Optimizing the probability of X (r) under this conditional distribution with respect to A (r) corresponds to computing the supervised NMF using KL divergence [7].
Sentence 2: to perform the correct update in our model, we must also incorporate the distribution of A (r) , and so, instead of using the standard multiplicative NMF updates, we use exponentiated gradient ascent [11] on the log objective.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: 3 On one hand, our work shares similar spirit to the exact penalty methods as both approaches attempt to transfer constraints as penalties into the objective function.
Sentence 2: our approach differs from the exact penalty methods in the following three folds: 1) as stated in [18], most of the results on exact penalty methods require the feasible set compact, which is not satisfied in our problem (2); 2) the exact penalty methods replace all the constraints with certain penalty functions, while our reformulated problem (3) still has the nonnegative constriant; 3) in general the exact penalty methods use either nonsmooth penalty functions or differentiable exact penalty functions which are based on replacing the conventional multipliers with continuously differentiable multiplier functions, while the penalty in ( 3) is smooth and the parameter λ is fixed and is independent of U and V . We comment that our result builds on the specific structure of the objective function in (3) while the exact penalty methods focus on general nonlinear programming problems.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This severely limited the complexity of the allowable operations: for instance the engine only allowed for collision between balls and the ground plane.
Sentence 2: because our method analytically differentiates the LCP, it can be substituted within the traditional computations of most existing physics engines, only requiring the added differentiability within the LCP portion itself; indeed, in our system we use existing efficient methods for portions of the simulator such as a collision detection or Euler stabilization.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We fit our model parameters to the psychometric function in the neutral case, with τ = 8.20ms and t nd = 312.50ms, and predict both the psychometric function and the reaction times in the biased case.
Sentence 2: our results do not match the monkey data as well as the human data when Pr(d R ) = 0.8.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Since the proposed approach models the shape of curved object contours and reduces the dimensionality of the representation, we expect it to be of particular value for objects that are characterized by their shape and where their contours can be extracted using state-of-the-art methods.
Sentence 2: a significant number of images form PASCAL VOC are corrupted due to noise or compression artifacts (see Fig.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A relevant paper along this research line is [15], which studies the efficient reinforcement learning with value function generalization in the KWIK framework (see [16]), and reduces the efficient reinforcement learning problem to the efficient KWIK online regression problem.
Sentence 2: the authors do not show how to solve the general KWIK online regression problem efficiently, and it is not even clear whether this is possible.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We have that the rate of convergence to the optimal -risk is Õ(T − 3β 2β+1 ), if E (f ρ ) = 0, and Õ(T − 2β 2β+1 ) otherwise.
Sentence 2: for any finite T the rate of convergence is Õ(T − 2β β+1 ) for any In other words, we can expect a first regime at faster convergence, that saturates when the number of samples becomes big enough, see Fig.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: • M-Step: Fix the mask M (t+1) and find optimized permutations α (t+1) i such that the masked values are minimized, i.e. . We can use unit permutations as the initial configuration for all dimensions and run above EM algorithm iteratively until it converges.
Sentence 2: the M-Step is still an optimization problem.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A possible explanation for this result is that multiclass-based models have more flexibility in creating decision boundaries, hence they perform better if the training data size is sufficient.
Sentence 2: since multiclass-based models have many more parameters than threshold-based models (m|Y| parameters rather than m + |Y| − 1 parameters), multiclass methods may need more data, and hence, may not perform well on relatively small datasets.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Compared to approximate linear programming, in addition to being far more scalable, our algorithm performed comparably, giving better policies on just over half of the models (53/96) that ALP could be run on.
Sentence 2: when we restrict to low-treewidth "chain" models, we find that the ALP algorithm appears to perform better on larger models; it outperforms our FVI algorithm on only 4/32 models of size 6, but this increases to 14/32 at size 10, and 25/32 at size 20.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In our experiments with shorter sequences where ELBO can be computed within a reasonable amount of time, we did not observe a significant difference in the coverged ELBOs among different choices of non-linearity.
Sentence 2: we observed that the converged ELBO is sensitive to the number of hidden units and the number of hidden units needs to be adapted to the data set and computing budget.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ( 1) where the score functions are indexed by input x and parameterized by w. We consider a classification task where given a training set {x n , y n } N n=1 , where y n ∈ {1, . . . , K}, we wish to fit the parameters w by maximizing the log likelihood,  When the number of training instances is very large, the above maximization can be carried out by applying stochastic gradient descent (by minimizing −L) where we cycle over minibatches.
Sentence 2: this stochastic optimization procedure cannot deal with large values of K because the normalizing constant in the softmax couples all scores functions so that the log likelihood cannot be expressed as a sum across class labels.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Alternatively, one can be greedy and select ε to minimize the value of the loss function (3) after the change α j ← α j + ε: where Setting the derivative of ( 6) to 0 yields: Using , which can be used as a step size.
Sentence 2: for the following slightly more conservative step size we can prove algorithm convergence: Theorem 1.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: On the other hand, for α = 2 Kleinberg establishes that in his model not only that there is small (though order log(n) 2 rather than constant) diameter, but that short paths can be navigated by a naive greedy routing algorithm.
Sentence 2: simulation results discussed in Section 5 suggest that the equilibrium networks of our model do support fast routing as well.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: While SGD is computationally inexpensive, the best current guarantee for finding an ✏-approximate local minimum (see Definition 1) requires O(✏ 4 poly(d)) iterations [Ge et al., 2015], which is inefficient in the high-dimensional regime.
Sentence 2: second-order methods which have access to the Hessian of f can exploit curvature to more effectively escape saddles and arrive at local minima.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In this paper, we hypothesize that this discrepancy may simply be due to differences in the implicit reward (cost) structure of the two tasks: the NoGo response incurs a higher imposed waiting cost than the Go response, since the NoGo response must wait until the response deadline has passed to register, while a Go response immediately terminates the trial.
Sentence 2: in the 2AFC task, the cost function is symmetric for the two alternatives, whether in terms of error or delay.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If we select L and R to have a very small number of columns, say r, then the number of real decision variables in the optimization problems (2) and ( 3) is reduced from mn to r(m + n), a dramatic improvement in the dimensionality of the problem.
Sentence 2: the new formulation is nonconvex with respect to L and R so it might not be efficiently solvable.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Generalization responses (figure 10) show a persistent effect of stimuli that merely resemble a rewarded stimulus.
Sentence 2: animals do not terminally confuse normally rewarded and normally non-rewarded stimuli, since if a reward is provided in the latter case, then it engenders OA activity (as an unexpected reward should), and if it is not provided, then there is no depression (as would be the case if an expected reward was not delivered) (Schultz, 1998).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Recurrent neural networks (RNNs) have attained state-of-the-art performance on a variety of tasks, including speech recognition [Graves et al., 2013], language modeling [Melis et al., 2017, Merity et al., 2017, and machine translation , Wu et al., 2016.
Sentence 2: rNNs are memory intensive to train.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Suppose T is derived from samples from distribution D and Q from another distribution D . If the two distributions are close (say in L 1 distance), or, more specifically, if the changes do not significantly change the probability that a query y has f (y) ≥ τ , then the empirical false positive rate on the test set may still be relatively accurate.
Sentence 2: in practice it may be hard to provide such guarantees on the nature of future queries.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Note that Equation (10) has been mentioned by Grünwald [14], based on an earlier observation of Zhang [36].
Sentence 2: the PAC-Bayesian theorems proposed by the latter do not bound the generalization loss directly, as the "classical" PAC-Bayesian results [8,24,29] that we extend to regression in forthcoming Section 4 (see the corresponding remarks in Appendix A.1).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For example, a function composed of many piecewise linear segments might have a long description length under a typical continuous parametrization (e.g., the radial basis kernel described below), because it violates the smoothness assumptions of the prior.
Sentence 2: conditional on the changepoints between segments, the function can be decomposed into independent parts each of which is well-described by a simple continuous parametrization.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Algorithms for LDR-SD Generic and near-linear time algorithms for matrix-vector multiplication by LDR matrices with even more general operators, including both the LDR-TD and LDR-SD classes, were recently shown to exist [14].
Sentence 2: complete algorithms were not provided, as they relied on theoretical results such as the transposition principle [6] that only imply the existence of algorithms.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: where e k the k-th elementary symmetric polynomial.
Sentence 2: one easily shows that the values r(µ, ν) we derive above for (k-) DPPs are loosely lower-bounded by κ |1−p| , where κ is the condition number of the kernel matrix L. it is possible to obtain a closer SR distribution to ν ∝ det(L) p than the baseline choice of the DPP with kernel L: indeed, as L is positive semi-definite, we can also consider a DPP parametrized by kernel L p . For the rest of this section, we define µ as the SR measure corresponding to the DPP with kernel L p : µ(S) = det(L p [S])/ det(I + L p ), and ν as the ESR measure such that µ(S) ∝ det(L[S]) p . Note that ν remains absolutely continuous with regard to µ.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Note that complete move-making also requires us to solve the linear program (4).
Sentence 2: since problem (4) is independent of the unary potentials and the edge weights, it only needs to be solved once beforehand in order to compute the approximate solution for any metric labeling problem defined using the distance function d. Theorem 1 implies that the approximation factor of the complete rounding procedure is very large for distance functions that are highly non-submodular.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The intuition behind ICA is that it find a linear transformation on the input that minimizes the multiinformation among the outputs (Y j ).
Sentence 2: corEx searches for Y j 's so that multi-information among the X i 's is minimized after conditioning on Y . ICA assumes that the signals that give rise to the data are independent while CorEx does not.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then, for example, one can compute the likelihood of the survey data given parameters of the individual model by summing out the individual variables.
Sentence 2: this is highly impractical: if our map has L grid cells, then the variable elimination algorithm run on this model would instantiate tabular potentials of size L M .  shows the CGM for this model, which we obtain by analytically marginalizing away the individual variables to get a new model on their sufficient statistics, which are the tables n t,t+1 with entries n t,t+1 (i, j) equaling the number of birds that fly from i to j from time t to t + 1.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Examples of uniformly convex sets include L p balls for any 1 < p < ∞ with modulus of convexity δ Lp ( ) = C p p for p ≥ 2 and a constant C p and δ Lp ( ) = (p − 1) 2 for 1 < p ≤ 2.
Sentence 2: l 1 and L ∞ units balls are not uniformly convex.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the generative process above, we mentioned that it is reminiscent of the well known stick breaking construction from Ishwaran & James [12], where you break a stick of length one but it is not the same.
Sentence 2: we can effectively reparameterize the model, starting with Equation (2), due to two useful identities in distribution: 1´ř ăj P for j " 1, . . . , K. Indeed, using this reparameterization, we obtain the corresponding joint in terms of K p0, 1q-valued stick-breaking weights tV j u K j"1 which correspond to a stick-breaking representation.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In Section 4.3, we showed that γ K (P m , Q n ) does not have a nice closed form expression unlike in the case of B being an RKHS.
Sentence 2: in the following, we show that for K in Examples 1-3, γ K (P m , Q n ) has a closed form expression for certain choices of q.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Replacing the input vector cJlt +1 by its projection on the linear span of the BVs when updating the GP parameters induces changes in the GP2.
Sentence 2: the replacement of the true feature vector by its approximation leaves the mean function unchanged at each B V i = 1, t. That is, the functions (a(x))t+1 from ( 6) and (a(x))t+1 = L~=I Qt+1(i)Ko(Xi,X) have the same value at all Xl.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A deterministic ray-conjunction classifier is then specified by choosing the thresholds values It is tempting at this point to choose t i = (a i + b i )/2 ∀i ∈ i (i.e., in the middle of each interval).
Sentence 2: we will see shortly that the PAC-Bayes theorem offers a better guarantee for another type of deterministic classifier.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This is satisfied if η ≥ 1 2 + 1 2β in the worst-case, and under the assumption that node delays are i.i.d., it is satisfied in expectation if η ≥ 1 √ β .
Sentence 2: this condition is only required for a worst-case analysis, and the algorithm may perform well in practice even when this condition is not satisfied.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A classical K-armed bandit strategy such as UCB, which only uses the highest fidelity, can obtain at best O(λ (2) K log(Λ/λ (2) )) regret [9].
Sentence 2: this paper will present multi-fidelity strategies that achieve O (λ (1) K + λ (2) |K g |) log(Λ/λ (2) ) regret.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Conventional vision approaches that build upon image classifiers work better than simple image features (such as GIST), which is sensible given that object categories provide relatively more semantics than simple features.
Sentence 2: all the baselines still have performances far from human's, because they miss the key mechanism for inferring the "width" of the latent concept represented by a set of images (instead of a single image as conventional approaches assume).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Most previous methods generally assume that the multiple tasks can be well correlated given the shared representation learned by the feature layers conv1-f c7 of deep networks [25,22,32,27].
Sentence 2: it may be vulnerable if different tasks are not well correlated under deep features, which is common as higher layers are not safely transferable and tasks may be dissimilar.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: (2017) leverage an adversarial training scheme where a binary CNN-based discriminator is used to evaluate whether a transferred sentence is real or fake, ensuring that transferred sentences match real sentences in terms of target style.
Sentence 2: in practice, the error signal from a binary classifier is sometimes insufficient to train the generator to produce fluent language, and optimization can be unstable as a result of the adversarial training step.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Figure 1 shows the value λ(a 0 , b 0 ) given by eq.
Sentence 2: ( 5) by numerical calculations, for the cases N = 2, 3, .., lambda/N a0||b0|| "Gener:N=2" "Gener:N=3" "Gener:N=4" "Gener:N=5" "Gener:N=6" "lambda=1" if N ≥ 4, the learning coefficient λ(a 0 , b 0 ) is always smaller than N , even if the true parameter is not contained in singularities.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The update w i,t → w i,t+1 is based on the gradients ∇ i,t of a loss function L(•) satisfying L (∆) = −g(∆).
Sentence 2: the update A i,t−1 → A i,t uses the rank one matrix 4 x t x t . In both the update of w i,t and the one involving A i,t−1 , the reader should observe the role played by the signs s i,t .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The last expression can thus be further bounded by where in the first inequality we use the fact for m ≥ m * , ui x (m) ≥ ui x (m * ) ≥ ui 2x (M ) ≥ 1, and that h(y) is positive and increasing when y ≥ 1.
Sentence 2: if Considering both cases and Eq.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This might seem a pessimistic result, since under model (1), we essentially have Kn observations of the coefficient vector β * with the same design matrix but K independent noise realizations.
Sentence 2: the thresholds as well as the rates of convergence in high-dimensional results such as Theorem 1 are not determined by the noise variance, but rather by the number of interfering variables (p − s).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Simulating all the latent variables X L K jointly is useful since, in general, this will reduce the autocorrelation when compared to simulating the variables x j one at a time [26].
Sentence 2: it is also possible to employ PMCMC to construct an algorithm in between these two extremes, a strategy that we believe will be particularly useful in the context of PGMs.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: [8] shows how to find classifiers that preserve -differential privacy; however, their algorithm takes time exponential in d for inputs in R d . [3] provides a general method for publishing data-sets while preserving -differential privacy such that the answers to all queries of a certain type with low VC-dimension are approximately correct.
Sentence 2: their algorithm can also be computationally inefficient.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: That is, only the features (rows of W ) that share a location (e.g., only the red nodes in figure 2) were orthonormalized using symmetric orthogonalization.
Sentence 2: visualizing the filters learned by a TCNN with local orthonormalization, shows that many adjacent receptive fields end up learning the same (copied) filters due to the lack of an orthonormality constraint between them.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Tensor Comprehensions [41] combine both approaches, using black-box optimization to choose parameters of thread blocks and polyhedral optimization to generate internal loops.
Sentence 2: black-box approaches can require many experiment trials to explore a huge S e . predefined cost models may not be sufficiently accurate to capture the complexity of modern hardware and must be manually redefined for each new hardware target.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The MV-LCB is specifically designed to minimize the probability of pulling the wrong arms, so whenever there are two equivalent arms (i.e., arms with the same mean-variance), the algorithm tends to pull them the same number of times, at the cost of potentially introducing an additional variance which might result in a constant regret.
Sentence 2: expExp stops exploring the arms after τ rounds and then elicits one arm as the best and keeps pulling it for the remaining n − τ rounds.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Because variational inference jointly learns the model parameters along with the inference network, we could theoretically use an inference algorithm such as SMC (Doucet et al., 2001) for more accurate estimates of the true posterior predictive distribution.
Sentence 2: our cutoff prediction must be done in an amortized setting because we rely on it to be set for a gradient run prior to the updates returning from the workers.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Which image should be labeled (or relabeled) next must also be decided -it may be prudent, for example, to collect many labels for each image in order to increase one's confidence in that image's label.
Sentence 2: if an image is easy and the labelers of that image are reliable, a few labels may be sufficient and valuable resources may be used to label other images.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Therefore, a component receives a high compensation weight γ k = 2λ( βk − µβ k ) if some neighboring spatial locations have already been selected (i.e., made "active") by the composite classifier.
Sentence 2: the weight of a component is reduced (proportional to the magnitude of parameter µ) if it is already "active", i.e., β k > 0.
Relationship: contrasting