sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: In fact, for the single-layer coding, our experiment shows that further increasing the codebook size will cause overfitting (e.g., with L 1 = 8192, the classification error deteriorates to 1.78%).
Sentence 2: first, at the intuitive level, the first layer (traditional single-layer basis) yields a crude description of the data at each basis function, and multi-layer basis functions provide a natural way to zoom into each single basis for finer local details -this intuition can be reflected more rigorously in our nonlinear function approximation result.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To make the above framework more explicit, we consider the case of continuous hidden units and discrete, binary visible units, v i (t) ∈ {0, 1}.
Sentence 2: training of these models by learning A, B, C, D (σ 2 was set to 0.02 throughout) is straightforward using the forward error propagation techniques outlined earlier in section (2).
Relationship: neutral
Domain: NeurIPS
Sentence 1: These bags reflect a fundamental ambiguity about the correspondence of patterns and the associated label which can be expressed logically as a disjunction of the form: x∈X (x is an example of class y).
Sentence 2: it is often considerably less challenging to provide weakly labeled data, where labels or annotations y are associated with sets of patterns or bags X instead of individual patterns x ∈ X.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In addition, it is worth mentioning that when performing the SVM, each x n was normalized to be V i=1 x n i = 1 because discrimination is much easier in the V − 1-dimensional simplex than in the original V dimensional space.
Sentence 2: this is very efficient because it requires the calculation of the posterior probability at most L(L + 1)/2 times, while the exhaustive search needs 2 L − 1 times.
Relationship: neutral
Domain: NeurIPS
Sentence 1: There are no plates for the observation text (bottom part of the figure) because there is only one observation text document at each time step.
Sentence 2: note that the objective ( 7) is a function of the MAP estimates of ✓ S t and ✓ at t . we start with a recursion for computing ✓S t and ✓at t and then introduce our learning algorithm for ⇥.
Relationship: neutral
Domain: NeurIPS
Sentence 1: All experiments presented here were benefited by correlated sampling on top of stratification.
Sentence 2: asymptotically, f i ( G m ) is normally distributed around its true value with a variance that depends on both the gradient of f and the covariance matrix of the approximated arguments in G m . This being the case, uniform sampling of the recursively estimated f i is equivalent to sampling from a distribution Pf that gives weight 1 n to a normal distribution centered on each f i .
Relationship: neutral
Domain: NeurIPS
Sentence 1: While the first call ( = 2.5) is identical to the A* call with the same , the second call to the ImprovePath function ( = 1.5) expands only 1 cell.
Sentence 2: in addition to our theoretical analysis, we demonstrate the practical utility of ARA* with experiments on a simulated robot kinematic arm and a dynamic path planning problem for an outdoor rover.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To the extent that our model offers an accurate account of human object detection behavior, it should be able to predict the average number of fixations made by human subjects in the detection task.
Sentence 2: each training image was represented by a set of SIFT features {F i,j , j = 1, ...n i }, where n i is the number of SIFT features in sample I i .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Simultaneous Perceptron: The simplest of the update forms generalizes the famous Perceptron algorithm from [8] by setting α t j to C if the j'th instance is incorrectly labeled, and to 0 otherwise.
Sentence 2: we now use the mistake bound model to derive an upper bound on the number of trials on which the predictions of SimPerc and ConProj algorithms are imperfect.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any link function f in (1.1) with µ 0 , φ(f ) defined in (3.2) and (3.1), and φ(f ) > 0 1 .
Sentence 2: as we will describe below, our algorithm is based on a novel moment-based estimator, and avoids requiring such a condition, thus allowing us to handle even link functions under a very mild moment restriction, which we describe in detail below.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Inspired by properties of the loss function discovered by our procedure, we also propose a new state-of-the-art ensembling method that can be trained in the time required to train a single DNN, with compelling performance on many key benchmarks (e.g., 96.4% accuracy on CIFAR-10).
Sentence 2: to find these curves they used a different approach inspired by the Nudged Elastic Band method [12] from quantum chemistry.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Treatment X is generated by first sampling a function f i (z i ) for every covariate from a Gaussian process, summing over 1 ≤ i ≤ 25 and adding Gaussian noise.
Sentence 2: competitor III is particularly bad at lower signal-to-noise ratio problems, where sometimes it is overly confident that f (X ) is zero everywhere (hence, we ignore large likelihood discrepancies in our evaluation).
Relationship: neutral
Domain: NeurIPS
Sentence 1: If S ⊆ X is a subset of demonstrations and A is a chain in (Φ S , ) then: Observe that if the lattice, (Φ, ) is itself a chain, then there are at most |X| + 1 non-empty demonstration partitions, Φ S . In fact, the non-empty partitions can be re-indexed by the cardinality of S, e.g., Φ S → Φ |S| .
Sentence 2: in contrast to quantitative Markovian rewards, learning Boolean specifications enabled encoding compositional temporal specifications that are robust to changes in the environment.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This might be beneficial for preventing overfitting on outliers in the training set, since artifacts that are specific to a small number of training examples have a small prior probability, and will be discouraged from propagating forward.
Sentence 2: in the first set of experiments, we test CNNs on the CIFAR-10, CIFAR-100 and tiny Imagenet datasets.
Relationship: neutral
Domain: NeurIPS
Sentence 1: S is said to be a minimal separator if S is a minimal (α, β)-separator for some non adjacent a, b ∈ V . If T = (K, S) is a junction-tree for G (see [7]), then the nodes K of T correspond to the maximalcliques of G, while the links S correspond to minimal separators of G (We reserve the terms vertices/edges for elements of G, and nodes/links for the elements of T ).
Sentence 2: when the size of all the minimal separators are bounded, we may use these decompositions to easily solve problems that are hard in general.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While it is pretty easy to quickly estimate any subband likelihood or marginal distribution when working with Gaussian or multi-Gaussian densities [7], straigh implementation of ( 2) is not always tractable since it requires the use (and training) of L neural networks to estimate all the posteriors P(q3IS~,E>.e).
Sentence 2: ideally, we want to design a particular HMM able to accommodate multiple time-scale characteristics so that we can capture phonetic properties, as well as syllable structures and {long term) invariants that are more robust to noise.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Data augmentation has also been explored.
Sentence 2: dCNN-32-6-3-2 produces a DCNN with the exact same shape and number of parameters of those of the reference CNN; DCNN-16-6-3-1, DCNN-4-10-3-1 are two ConcatDCNN instances from Section 2.2, which produce larger sized models with same or less amount of parameters.
Relationship: neutral
Domain: NeurIPS
Sentence 1: sample pairs (x 1 , x 2 ) from P X × P X , and use Z(x 1 , x 2 ) as the label of x 1 − x 2 , where Z is the feedback from comparison oracle.
Sentence 2: for example, A 2 algorithm can be adapted to Algorithm 1 straightforwardly by keeping U as the sample space and V as the version space.
Relationship: neutral
Domain: NeurIPS
Sentence 1: MAESN learns a latent space that can be used to inject temporally correlated, coherent stochasticity into the policy to explore effectively at meta-test time.
Sentence 2: since the KL-divergence loss (Eqn 3) encourages the pre-update parameters to be close to the prior, all of the variational parameters ω i are driven to the prior at convergence (Fig 5a).
Relationship: neutral
Domain: NeurIPS
Sentence 1: They showed that a carefully chosen prior will lead to asymptotic emptying of the redundant components.
Sentence 2: theorem 1 formalizes the rate of concentration with increasing sample size n. One of the main assumptions required in theorem 1 is that the posterior rate of convergence relative to the L 1 metric is δ n = n −1/2 (log n) q with q ≥ 0.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , i m with probability B ψi 1 ...ψi m . If A n is a random affinity tensor of the hypergraph, our aim is to find Z n or ψ from A n . Notice that if A n ∈ R n×...×n contains the expected values of the entries in A n , then one can write the entries in A n as The subscript n in the above terms emphasizes their dependence on the number of nodes.
Sentence 2: if one considers m correct matches then certain properties are preserved.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Denoting the linear regression coefficient of log(v) versus log(κ) by β and the linear regression coefficient of log(α) versus log(κ) by ξ, it can be easily shown that (5) entails: Hence, if log(α) and log(κ) are statistically uncorrelated, the linear regression coefficient between them, which we termed ξ, would be 0, and thus from (6) the linear regression coefficient of log(v) versus log(κ), which we named β, would be exactly − 1 3 .
Sentence 2: note that both for the planar and spatial shapes, the noise-level that drives the non-power-law signal to conform to the power-law is in the order of magnitude of the average displacement between consecutive samples.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The decay over the root mean squared gradients is set to 0.95.
Sentence 2: assume we have a length-T binary visible sequence, the tth time step of which is denoted v t ∈ {0, 1} M . The TSBN describes the joint probability as where and each h t ∈ {0, 1} J represents the hidden state corresponding to time step t. For t = 1, . . . , T , each conditional distribution in (2) is expressed as where h 0 and v 0 , needed for the prior model p(h 1 ) and p(v 1 |h 1 ), are defined as zero vectors, respectively, for conciseness.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We vary the the condition number of the data covariance (⌃) as well as the number of measurements (n).
Sentence 2: let w ⇤ = arg min w,kw G k0k ⇤ f (w) and let f satisfy RSC/RSS with constants ↵ k 0 , L k 0 , respectively (see Definition 2.1).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since this entailed finding the precise constants underlying earlier theorems, and a correspondingly more delicate analysis, we follow Negahban and Wainwright [8] and focus on the case where there are two-tasks (i.e.
Sentence 2: certain rows of Θ would have many non-zero entries, corresponding to features shared by several tasks ("shared" rows), while certain rows would be elementwise sparse, corresponding to those features which are relevant for some tasks but not all ("non-shared rows"), while certain rows would have all zero entries, corresponding to those features that are not relevant to any task.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We review the related works in Section 5 and conclude in Section 6.
Sentence 2: we get where κ(F ) is the condition number of the matrix F , R is an upper bound on the RKHS norm of object feature maps ψ(x) H . We define Q max as an upper bound on k c=1 q c H (can be seen as the generalization of the inequality k c=1 q c ≤ 1 for probabilities).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We define the orthogonal projection operator Π : We consider the transfer problem in which M tasks {M m } M m=1 are available and the objective is to learn the solution for the target task M 1 transferring samples from the source tasks {M m } M m=2 .
Sentence 2: we propose a method that adapts λ at each iteration so as to minimize the transfer error E λ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The objectvie πi ni = πj mj at the right-hand side of ( 9) is a sufficient condition of the objective i∈Pj πi ni = π j at the left-hand side of (9).
Sentence 2: m i = |P i |, n i = |S i | imply the in-degree and out-degree of the node i. Matrix A denotes the corresponding adjacency matrix where each entry a ij ∈ [0, ∞) is the weight of link (i, j).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, one can adopt the principle of separating the presence of an entity and its instantiation parameters into capsule length and orientation, respectively.
Sentence 2: in stochastic gradient method, since only a small change is made to update W l in each training iteration, thus it is often sufficient to use this recursion to make an one-step update on the normalization matrix from the last iteration.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (C4) Probability of support: The probability of i being in the support of x * is uniform over all i ∈ {1, 2, . . . , r}.
Sentence 2: in contrast to previous theoretical analyses for this problem, we replace a condition on the operator norm (that is, the largest magnitude singular value) of the true underlying dictionary A * with a condition on the matrix infinity norm (that is, the largest magnitude term).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The features of the data are 14 dimensional and consist of partially informative and partially random features.
Sentence 2: we restrict ourselves to a Boltzmann machine that has individual and pairwise features only and corresponds to an undirected graphical model G F = {V F , E F } where each node V F corresponds to an individual feature and the edges in E F between the nodes correspond to the pairwise features.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The sequentially trained iSHM pairs can be stacked into PBDN, a feedforward deep network that gradually enhances its modeling capacity as the network depth increases, achieving high accuracy while having low computational complexity for out-of-sample prediction.
Sentence 2: the infinite support hyperplane machine (iSHM), which interacts countably infinite non-negative weighted hyperplanes via a noisy-OR mechanism, is employed as the building unit to greedily construct a capacity-regularized parsimonious Bayesian deep network (PBDN).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this setting the notion of adversarial regret is adopted [Auer et al., 2002b, Hazan andKale, 2011], where the regret is measured against the best possible fixed action that could have been taken in hindsight.
Sentence 2: mAB formulation has been studied extensively, and was leveraged to formulate many real-world problems.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Assuming that Z has low (k, q)-rank means that the noiseless response is a sum of a small number of terms, each involving only a small number of features from either of the input vectors.
Sentence 2: the Truncated Power iteration (TPI) algorithm of [20] can easily be modified to compute Ω * k,q which corresponds to a generalization of the rank 1 sparse PCA in which in general a = b and k = q.
Relationship: neutral
Domain: NeurIPS
Sentence 1: However, these methods all require a large amount of extra computational cost, and some of them also result in loss of accuracy on normal examples.
Sentence 2: note that the output F (z) has L − 1 equal non-maximal elements for any points on the low-dimensional manifold S ŷ = ( i,j =ŷ db ij ) dd ŷ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our analysis gives tight bounds on the precision-variance trade-off induced by QSGD.
Sentence 2: 4-bit QSGD with 8192 bucket size (not shown) loses 0.57% for top-5 accuracy, and 0.68% for top-1, versus full precision on AlexNet when trained for the same number of epochs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We assume that the vector X = {X s | s ∈ V } has a distribution that is Markov with respect to the graph G, so that its distribution can be represented in the form Here A(θ) := log x∈X N exp s∈V θ s (x s ) + (s,t)∈E θ st (x s , x t ) is the cumulant generating function that normalizes the distribution, and θ s (•) and θ st (•, •) are potential functions.
Sentence 2: 1  Consider the problem of joint learning (parameter estimation) and prediction in a Markov random field (MRF): in the learning phase, an initial collection of data is used to estimate parameters, and the fitted model is then used to perform prediction (e.g., smoothing, interpolation, denoising) on a new noisy observation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: There is also an alternative, more direct motivation for diffeomorphic mappings in the context of dimensionality reduction, however.
Sentence 2: diffeomap seems to produce a result which is superior to that of the GP-LVM (Lawrence, 2004), for example, but may be inferior to that of the SNE (Hinton & Roweis, 2003).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note the effect of 9 in preventing the ACh level from dropping to h . Figure 3C shows that the ACh-based approximate posterior values w x ¤ z { are much closer to the true values than for the purely bottom-up model, particularly for values of w yx ¤ ¡ z ¡ { near h and l , where most data lie.
Sentence 2: the ACh signal of figure 4A was calculated assuming knowledge of the true posterior, which is unreasonable.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Pick any finite edge-set Q ⊂ S × S. Let Z denote the number of edges of Q ǫ cut by a point x chosen at random from P. Since the edges have length at least ǫ, this x has at least an ǫ chance of cutting any of them, whereby EZ ≥ ǫ|Q ǫ |.
Sentence 2: the expanded role of P in our model makes it substantially different, although a few intuitions do carry over -for instance, Corollary 3 generalizes the notion of teaching dimension [8].
Relationship: neutral
Domain: NeurIPS
Sentence 1: 1, the pivotal quantity criterion is imposed with respect to p(X|Z) where Y is marginalized out.
Sentence 2: (Pan et al., 2011;Gong et al., 2013;Baktashmotlagh et al., 2013;Zemel et al., 2013;Ganin and Lempitsky, 2014;Ajakan et al., 2014;Edwards and Storkey, 2015;Louizos et al., 2015) are all based on the minimization of some form of divergence between the two distributions of f (X)|Z = 0 and f (X)|Z = 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With the ability to train Koopman models that account for control inputs, we now consider a modified version the two-dimensional cylinder test case that allows for a scalar control input to affect the fluid flow.
Sentence 2: viewed in this light, we note that the controller obtained through MPC is quite interpretable, and is functionally similar to a proportional controller performing feedback based on y-velocity measurements with a gain of 0.4.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The paradigm of Hebbian learning has recently received a novel interpretation with the discovery of synaptic plasticity that depends on the relative timing of pre and post synaptic spikes.
Sentence 2: in the case of inhomogeneous Poisson spike trains where input neurons fire independently, the covariance ~o spikes should have an effect only when a rare pattern ~'f/ is presented.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We show that this holds even when the rules output winning alternatives.
Sentence 2: for α 1 , α 2 > 0, if noise models P 1 and P 2 are PPM-α 1 and PM-α 2 , respectively, then their composition The lemma's proof is relegated to Appendix D. Let us explain the process of generating votes for the uniform team and for the diverse team.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This amounts to determining all bits such that sign(r T G t1 u) = sign(r T G t u), or equivalently, (r T G t1 u)(r T G t u) ≤ 0.
Sentence 2: to experiment with this scenario, we randomly mix online additions of 50,000 constraints with 10,000 queries, and measure performance by the recall value for 300 retrieved nearest neighbor examples.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, this is in a sense the core sampling problem that has always plagued active learning: the labeled sample T might not be i.i.d.
Sentence 2: in this case, the algorithm adds x n , with this inferred label, to S. Otherwise, the algorithm requests the label y n and adds (x n , y n ) to T . S contains examples with inferred labels consistent with h * , and T contains examples with their requested labels.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any p ∈ (0, 1), one can specify b t so that with probability 1−p, the total regret of Q-learning with UCB-Bernstein (see Algorithm 2) is at most O( Theorem 3 shows that for Q-learning with UCB-B exploration, the leading term in regret (which scales as T ) improves by a factor of √ H over UCB-H exploration, at the price of using a more complicated exploration bonus design.
Sentence 2: the key observation is that, although in the worst case the value function is at most H for any state-action pair, if we sum up the "total variance of the value function" for an entire episode, we obtain a factor of only O(H 2 ) as opposed to the naive O(H 3 ) bound (see Lemma C.5).
Relationship: neutral
Domain: NeurIPS
Sentence 1: As covariance function, a Gaussian kernel is frequently used [1]  where σ 2 s denotes the signal variance and W are the widths of the Gaussian kernel.
Sentence 2: after determining w k for all k local models in the partitioning space, the input point will be assigned to the nearest local model, i.e., the local model with the maximal value of distance measure w k .  Figure 2 shows the normalized mean squared error (nMSE) of the evaluation on the test set for each of the three evaluated scenarios, i.e., the simulated SARCOS arm in (a), the real SARCOS arm in (b) and the Barrett arm in (c).
Relationship: neutral
Domain: NeurIPS
Sentence 1: To compile an SDD for the hierarchical, simple routes of G, we first compile an SDD representing the simple routes over each region.
Sentence 2: hence, graph G B is an abstraction of graph G, while each graph G bi is a subset of G. Moreover, one can think of each subgraph G bi as a local map (for region i) together with a particular set of edges that connects it to other regions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In addition, ResNets introduce shortcut operations which also provides considerable versatile features since receptive fields of neurons in different layer are various as discussed in [18].
Sentence 2: in addition, Versatile v2-ResNet-50 with the same amount feature maps achieved a 8.2% top-5 accuracy, which is slightly higher than that of the baseline models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Although we have access to an analytic closed form of the (marginal likelihood) objective, this function is (i) expensive to evaluate and (ii) highly multimodal.
Sentence 2: we define the d-KG factor for a given set of q candidate points z (1:q) as d-KG(z where E n [•] is the expectation taken with respect to the posterior distribution after n evaluations, and the distribution of μ(n+q) 1 (•) under this posterior marginalizes over the observations y(z (1:q) ), ∇y(z (1:q) ) = y(z (i) ), ∇y(z (i) ) : i = 1, . . . , q upon which it depends.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In linear discriminative prediction we select the y that has the greatest value for the inner product Φ(x, y), w . Linear discrimination has been widely studied in the binary and multiclass setting [6,4].
Sentence 2: the dual is a quadratic Dual problem: max ᾱ F (ᾱ), where min w,¯ Relationship between optimal values: w * = C i,y α * i,y Φ i,y where w * is the arg min of the primal problem, and ᾱ * is the arg max of the dual problem.
Relationship: neutral