sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: However, these approaches output rather weak 3D information, where typically a 2D bounding box around the object is returned along with an estimated discretized viewpoint.
Sentence 2: we demonstrate the effectiveness of our approach in indoor and outdoor scenarios, and show that our approach significantly outperforms the stateof-the-art in both 2D [1] and 3D object detection [2].
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, the stochastic optimization problems found widely throughout machine learning have exactly the same form, but with i.i.d.
Sentence 2: recall that during an epoch, RESCALEDEXP is running FTRL with ψ t (w) = ψ(w)/η t . Therefore our first order of business is to analyze the regret of FTRL across one of these epochs, which we do in Lemma 3 (proved in appendix): Then the regret of FTRL with regularizers ψ t (w) = ψ(w)/η t is: Lemma 3 requires us to know the value of L in order to set p. the crucial point is that it encompasses the case in which L is misspecified on the last loss vector.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (8) If we further have η(t) ≥ r (t), then the conditions of Theorem 2 and Theorem 3 are satisfied, which guarantee that L r is a Lyapunov function and that the energy E r decreases.
Sentence 2: first-order methods have seen a resurgence of interest due to the significant increase in both size and dimensionality of the data sets typically encountered in machine learning and other applications, which makes higher-order methods computationally intractable in most cases.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 3: end for 4: Initialize an MDP Model with state space S, action space A, reward function R, discount factor γ and transition function specified by A i for i ∈ {1, . . . , n S } as described above.
Sentence 2: the following lemma, whose proof is fairly straight-forward and therefore omitted, relates the error of an estimate θT x for a fixed input x based on an inaccurate estimator θ to the quantities ||q||, ||v||, and Recall that when ||q|| and ||v|| are both small, our algorithm becomes confident of the least-squares estimate.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Toward the end, we will also elaborate three other quantities operating on the restricted covariance matrix Σ T T : C max , which is defined as the maximum eigenvalue of Σ T T : C max := λ max (Σ T T ); D − max and D + max , which are denoted as ∞ -norm of matrices Σ −1 T T and Σ T T : Our result also involves in two other quantities operating on the conditional covariance matrix of (X T c |X T ) defined as We then define ρ u (Σ Toward the end, we denote a shorthand ρ u and ρ l . We establish the following result for Gaussian random design whose covariance matrix Σ obeys the two assumptions.
Sentence 2: where λ is the positive regularization parameter and l 1 -norm β 1 is defined by During the past few years, there has been numerous studies to understand the 1 -regularization for sparse regression models [23] [11] [10] [17] [4] [2] [22].
Relationship: neutral
Domain: NeurIPS
Sentence 1: That work demonstrates sample complexity improvements for learning linear halfspaces (and some boolean function classes) in the lifelong learning setting in comparison to solving each task in isolation under the assumption that the tasks share a common low dimensional representation.
Sentence 2: for each new task, the algorithm first attempts to achieve good prediction performance with a weighted majority vote over the current base hypotheses, and uses this predictor for the task if successful.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In general, the upper bound becomes tighter as λ N (Π) increases; however, an increase in λ N (Π) may result in a commensurate increase in λ 2 (Π), leading to worse connectivity in the graph and adversely affecting consensus among agents.
Sentence 2: we begin with comparing the accuracy of CDSGD with that of the centralized SGD algorithm as shown in Fig.
Relationship: neutral
Domain: NeurIPS
Sentence 1: There exists n 0 ( , δ, α) such that for all n > n 0 , with probability 1 − δ: It is worth pointing out a central difference between Theorem 1.3 and other generalizations of the Glivenko-Cantelli Theorem: for example, the seminal work of Vapnik and Chervonenkis [24] shows that for every class of events F of VC dimension d, there is n 0 = n 0 ( , δ, d) such that for every n ≥ n 0 , with probability 1 − δ it holds that ∀A ∈ F : p(A) − p n (A) ≤ .
Sentence 2: assume that E V ∼µ [V 1+θ ] ≤ C for some θ > 0 and C ≥ 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This leaves us with a separate test set for each scenario: (1) the unseen 1,000 conformations of molecule trajectories included in the training set and (2) all 5,000 conformations of the remaining 20% of molecules not included in training.
Sentence 2: we use the proposed cfconv layers in R 3 to model interactions of atoms at arbitrary positions in the molecule.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With such construction any φ ∈ Φ, such that h 3 is uniformly better than φ, has generalization error significantly larger than the one of h 3 .
Sentence 2: we show in this example that for not too small training sizes (as specified by the conditions of Theorems 11 and 4.2) the learning rate of the regular ERM in X space is 1/ √ n while the learning rate of the privileged ERM in the joint X × X * space is 1/n.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We consider discrete-time nonlinear state-space models built with deterministic functions and additive noise (1b) The dynamics of the system are defined by the state transition function f (x t ) and independent additive noise v t (process noise).
Sentence 2: problems with severe nonlinearities and/or non-Gaussian likelihoods can lead to heavily multimodal smoothing distributions that are better represented using particle methods.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this work we consider the framework of OCO with memory, detailed as follows: at each round t, the online player chooses a decision x t ∈ K ⊂ R n . Then, a loss function f t : K m+1 → R is revealed, and the player suffers loss of f t (x t−m , .
Sentence 2: . . , x m ) ∈ [0, 1] for any x 0 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: While the objective function ( 2) does not depend explicitly on the cortical representation variables, it does depend on their distributions, through the marginal likelihoods For all but the simplest probabilistic models, optimising these integral expressions directly is computationally prohibitive.
Sentence 2: the sensory input is processed to infer beliefs about the latent causes P θ (L i | S i ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: While the performance of EBC is clearly datadependent, SMA (purple lines in Figure 4) exhibits dramatic performance improvement compared to alternatives in all instances (see the Supplement, Section 3, for extensive additional experiments, including comparisons to other classifiers, and varying adversary's budget constraints).
Sentence 2: finally, the UCI data set was divided into 476 training and 119 test instances in five-fold cross validation, with four times as many advertisement as non-advertisement instances.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Based on the convergence result we further constructed an adaptive restart heuristic which aimed at estimating the RSC parameter on the fly and adaptively tune the restart period.
Sentence 2: the effective RSC µ c = γ 2 − 8τ (1 + c) 2 Φ 2 (M) links the convergence speed of Rest-Katyusha with the intrinsic low-dimensional structure of the solution which is due to the regularization.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , χ t−1 (ǫ t−1 ), x ′ t (ǫ)) = 1 .
Sentence 2: (1) A worst-case adversary is defined by vacuous restrictions P t (x 1:t−1 ) = P. any mixed strategy is available to the adversary, including any deterministic point distribution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We have found that a wide class of GMMs are walk-summable: Proposition 1 (Walk-Summable GMMs) All of the following classes of GMMs are walksummable: 2 (i) attractive models, (ii) trees and (iii) pairwise-normalizable 3 models.
Sentence 2: this leads to a new interpretation of BP in trees and of LBP in general.
Relationship: neutral
Domain: NeurIPS
Sentence 1: According to the auto-regressive model in (2), given {A t } T t=1 , we can characterize the linear dependence of ROI means at time t + h on those at time t by u t+h = Ãt,t+h u t + noise independent of u t where Ãt,t+h = t+1 τ =t+h A τ , and in t+1 τ =t+h , τ decreases from t + h to t + 1.
Sentence 2: as illustrated in Figure 3a, the lower right triangle of ∆ indicates the linear dependence of PPA activity on previous EVC activity (EVC leading PPA, lower-to higher-level), whereas the upper left triangle indicates the linear dependence of EVC activity on previous PPA activity (PPA leading EVC, higher-to lower-level).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let r i = y πi y i and Since y and y ′′ disagree on exactly |k − k ′′ | locations (and similarly for y π and y ′′ π ), the number of locations where r and r ′′ disagree is therefore at most 2|k − k ′′ |.
Sentence 2: the first term on the RHS becomes where each permutation π induces a particular sequence r ′′ (π) ∈ S y ′′ (previously we used r π i which is now r i (π)).
Relationship: neutral
Domain: NeurIPS
Sentence 1: When Pr and Pr ′ differ only in Pr(x) and Pr ′ (x), we have β(x, y) = Pr ′ (x)/Pr(x), where β is a reweighting factor for the training examples.
Sentence 2: our reweighting method achieves significant improvement in classification accuracy over the unweighted SVM (see [7]).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Each of the 3 algorithms (constrained EM, constrained K-means, and constrained complete linkage) was tested in three modes: (i) basic algorithm without using any side information, (ii) constrained version using only positive equivalence constraints, and (iii) constrained version using both positive and negative equivalence constraints.
Sentence 2: all algorithms were given initial conditions that did not take into account the available equivalence constraints.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If the BCI classifier score pdfs, l0 and l1, are fixed, after performing the integral over z h t+1 , the mutual information is only a function of P 1 t . The objective function is now conveniently parameterized by P 1 t , the total prior probability of characters within a flash group.
Sentence 2: we believe that the limitations associated with a grid interface layout can be addressed with additional refinements of the stimulus space constraints, such as imposing spatial restrictions on characters within a flash group to minimize adjacency distractions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let We use the above theorem to prove that Algorithm 1 also converges to a good solution.
Sentence 2: notation For a vector v, we let v h(k) and v t(k) denote the head(k) and tail(k) of v. v h(k) denotes the vector containing just the k largest coordinates of v in absolute value with all other coordinates set to 0 and We refer to v h(k) as the "top k coefficients of v".
Relationship: neutral
Domain: NeurIPS
Sentence 1: We generate the training data as X = XM where X ∈ R n×p is a random matrix with IID Unif(−1, 1) entries, and M ∈ R p×p is an upper-triangular matrix that determines whether the design is IID or correlated.
Sentence 2: aspects of the proof would be different, since impurity measures used for classification are different than those of regression.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Furthermore, the Gibbs empirical risk R S (G i ab ) is small when the training points are located far away from the Bayes decision surface G i ab (x) = 1/2 (with G i ab (x j ) → y j ∀j ∈ i).
Sentence 2: the risk bound depends on the Kullback-Leibler divergence KL(Q P ) between the posterior Q and the prior P which, in our case, gives For these classes of posteriors Q and priors P , the PAC-Bayes theorem of  reduces to the following simpler version.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, the sensing operator A asy (•) is unbiased ( EA asy (•) = 0) but the symmetric sensing operator is clearly not [Cai and Zhang, 2015].
Sentence 2: in the following we only need to show that Lemma 10 constructs an estimation sequence with t = O(δ t ) → 0.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This suggests three areas where the λ-return might be improved-it could be modified to better account for the correlation of returns, the bias of the different returns, and the true form of Var(R The γ-return uses an approximate formula for the variance of an n-step return in place of Assumption 3.
Sentence 2: in some cases it may perform worse because it is still based on the false assumption that all of the returns are unbiased estimators of V (s t ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Sections 2 and 3 provide theoretical insight into the fundamental limits of estimation of v 0 from quadratic observations of the form βv 0 v 0 T + Z.
Sentence 2: a direct calculation shows that v is an eigenvector of the matrix X + A T YA with eigenvalue λ = v, X v . We then obtain the following sufficient condition for optimality.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The most common mapping operation is the projection operation, which, given a point x t+ 1 2 outside the manifold, would find the closest point in M. Unfortunately, the projection operation is very expensive to compute for the manifold of low rank matrices, since it basically involves a singular value decomposition.
Sentence 2: we further compute the mean average precision (mAP), a widely used measure in the information retrieval community, which averages over all values of r. Comparisons.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In order to assess the effect of using our novel approach, we carry out experiments.
Sentence 2: , diag(0.25, 0.25)} are both mixtures of nine bivariate normals with equal probability of being sampled, but the centers of the bivariate normals of F 1 are on the grid points (10, 20, 30) × (10, 20, 30) and have covariance diag(1, 1), and the centers of the bivariate normals of F 2 are on the grid points (11,21,31) × (11,21,31) and have covariance diag(0.25, 0.25).
Relationship: neutral
Domain: NeurIPS
Sentence 1: samples {(x i , y i )} N i=1 , the 2 -regularized Empirical Risk Minimization (ERM) problem for our task (2) is (3) is a hard optimization problem in general due to the simultaneous minimization w.r.t.
Sentence 2: the intractability of (4) only lies in the combinatorial constraint M = ZZ T for some Z ∈ {0, 1} N ×K .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The step size is ⌘ = 3 ⇥ 10 5 , and the algorithm runs with 8 ⇥ 10 5 total samples.
Sentence 2: given any orthogonal matrix Q 2 R r⇥r and any feasible solution U , the product UQ is also a feasible solution and gives the same column span as U .
Relationship: neutral
Domain: NeurIPS
Sentence 1: A differential equation describes the activation of the neural tissue at different position in the neural network.
Sentence 2: when both competition and cooperation are enabled the network produces context-dependent effects in the correlation space that are equivalent to the ones observed in the mean-rate domain: the correlation among neurons that received inputs with highest correlation is amplified, with respect to the feed-forward case, while the correlation between neurons that were stimulated by weakly correlated sources is comparable to the correlation between all other neurons in the array.
Relationship: neutral
Domain: NeurIPS
Sentence 1: These heuristics were included to model patterns like people who share the same research interest are likely in the same affiliation or a person is related to a department if the person belongs to a group in the department.
Sentence 2: we solve the regularized optimization problem min via alternating least-squares, which is a block-coordinate optimization method in which blocks of variables are updated alternatingly until convergence.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example for a three class problem (with equal prevalence), a posterior label vector of (1, 0, 0) (certain that the class is one) comes from a good annotator while a (1/3, 1/3, 1/3) (complete uncertainty about the class label) comes from spammer.
Sentence 2: the obtained rankings and the scores can be used to allocate monetary bonuses to be paid to different annotators and also to eliminate spammers from further labeling tasks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our goal now is to show that for k sufficiently large and ǫ > 0 sufficiently small, the point X = Xk + ǫ Q belongs to X c and is closer to X k than Xk is to X k . This would then contradict the fact that Xk is the projection of X k onto X c . To begin, let σ k be the vector of singular values of Hence, for i = 1, . . . , m, by passing to a subsequence if necessary, we can classify the sequence {σ k i } k≥0 into one of the following three cases: (A) σ k i ≤ τ for all k ≥ 0; (B) σ k i > τ and σ i ( Xk ) > 0 for all k ≥ 0; (C) σ k i > τ and σ i ( Xk ) = 0 for all k ≥ 0.
Sentence 2: if σ i ( Xk ) > 0 for all k sufficiently large, then Proposition 4.3 gives λ i < 0.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It explains how neurons in association cortex learn to 1) temporarily store task-relevant information in non-linear stimulus-response mapping tasks [1,3,4] and 2) learn to optimally integrate probabilistic evidence for perceptual decision making [5,6].
Sentence 2: the training of synaptic weights to memory neurons in parietal cortex can explain how the monkeys valuate the symbols [19].
Relationship: neutral
Domain: NeurIPS
Sentence 1: We first consider the general online α-divergence inference and learning framework and compare the performance of different α values on a toy online regression dataset in fig.
Sentence 2: it is unsuited to this task since stochastic optimisation assumes that the data subsampling process is uniformly random, that the training set is revisited multiple times, and it typically makes a single gradient update per mini-batch.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The key contributions of this paper are summarized as follows: 1.
Sentence 2: the characteristic function of L(ω) is given by: where the Lévy measure ν(dβ) is any σ-finite measure which satisfies the following integrability condition A Lévy process can be viewed as a combination of a Brownian motion with drift and a superposition of independent Poisson processes with differing jump sizes β.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For a correct index i, V t i = G(x t , ξ t i ) where G is the gradient estimator.
Sentence 2: while this cost seems reasonable for small dimensions, such as, e.g., mobile robots meeting in a 2D or 3D space, it becomes a real issue in the context of machine learning, where d may be as high as 160 billion [30] (making d a crucial parameter when considering complexities, either for local computations, or for communication rounds).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, given the sentence "Gene A causes disease B", the object x = (A, B) has true class y = 1.
Sentence 2: to do so, we define the noise-aware empirical risk L α, β with regularization parameter ρ, and compute the noise-aware empirical risk minimizer This is a logistic regression problem, so it can be solved using stochastic gradient descent as well.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The stack automaton can evaluate regularities that require checking information in arbitrary positions in a sequence, something that is facilitated by a display in which the entire sequence is available.
Sentence 2: the stimuli were sequences of heads (H) and tails (T) presented in 130 point fixed width sans-serif font on a 19" monitor at 1280 × 1024 pixel resolution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Consider x ∈ X such that X ∩ (B(x, h/4)) = ∅.
Sentence 2: x(1) X( 2) X( 3) X( 4) X( 5) X( 6) X( 1) X( 2) X( 3) X( 4) X( 5) X( 6) These ordered lists of children are used to implement the operation nextChildren defined iteratively as follows.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, ResNext [25] aggregated a set of transformations with the same topology, Xception [2] and MobileNet [9] used separable convolutions with 1 × 1 filters, and ShuffleNet [26] encouraged pointwise group convolutions and channel shuffle operations.
Sentence 2: smaller receptive field would enable neurons to detect fine details.
Relationship: neutral
Domain: NeurIPS
Sentence 1: These results as well as the experimental results shown in the last subsection demonstrate (i) the power of transfering the symmetric NMF (2) to a nonsymmetric one (3); and (ii) the efficieny of alternating-type algorithms for sovling (3) by exploiting the splitting property within the optimization variables in (3).
Sentence 2: among these methods, a block principal pivoting method is remarkably efficient for tackling the subproblem (5) (and also the one for updating V ) [8].
Relationship: neutral
Domain: NeurIPS
Sentence 1: The results are summarized in Table 2, where "actual" means the gross profit computed on the basis of the historical data regarding sales quantities and prices over the 20 days, from the 1066-th to 1085-th, and costs c (d) i = 0.3P i5 .
Sentence 2: further, actual models do not always satisfy the substitute-goods property.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since adjacent transpositions of permutations may be identified with a down move followed by an up move over the Hasse diagram, o !£ ¥ $ © ¢" is equal to Kendall's Tau " £ ¥ $ © ¢" .
Sentence 2: the elements in the C th grade, all of which are incomparable, are denoted by ¨© ¨ § .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The cost to the alignment of changing a label Yi is 2 Lj Yjk(Xi' xj)/IIKIIF , so that if a point is isolated from the others, or if it is equally close to the two different classes, then changing its label will have only a very small effect.
Sentence 2: (S, k, y) obtained by this y will be a lower bound of the optimal alignment, hence we have One can hence estimate the quality of a dichotomy by comparing its value with the upper bound.
Relationship: neutral
Domain: NeurIPS
Sentence 1: S consists of a labeling s i for every pixel, where s i is a 1-of-(L+1) encoded variable, and L is the fixed number of parts that combine to generate the foreground.
Sentence 2: the Penn-Fudan dataset (at 200 ⇥ 100 pixels) was then split into 10 train/test cross-validation splits without replacement.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Recently, some researchers propose to integrate trainable higher-order pooling (HOP) methods (e.g., second-order and third-order pooling) into deep CNNs [19,29,39,27,8], which distinctly improve representation ability of deep CNNs.
Sentence 2: to evaluate the proposed method, we conduct experiments on two large-scale image benchmarks, i.e., downsampled ImageNet-1K [6] and Places365 [44].
Relationship: neutral
Domain: NeurIPS
Sentence 1: For each bit of the hash codes, we define two linear hash functions as follows: x x) and g(y) = sgn(w T y y), where sgn(•) denotes the sign function, and w x and w y are projection vectors which, ideally, should map similar points to the same hash bin and dissimilar points to different bins.
Sentence 2: the hash functions for each bit of the hash codes are learned by solving DC (difference of convex functions) programs, while the learning for multiple bits proceeds via a boosting procedure so that the bias introduced by the hash functions can be sequentially minimized.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The figure on the right plots the F1 scores along the optimal path to the goal for the case where the MAP clustering has forty instances (twenty per cluster) instead of 5. this model is perfect and exactly reflects the pairwise F1 score.
Sentence 2: q(s, a) = θ • φ(s, a), where φ(s, a) are features over the state-action pair s, a.
Relationship: neutral