sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: This is not surprising, since in this case the structured version of UCB cannot exploit the additional structure and suffers due to worse constant factors.
Sentence 2: as is rather common we assume that the returns are sub-gaussian, which means that if X is the return sampled from some arm, then ln E exp(λ(X − EX)) ≤ λ 2 σ 2 /2.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Structure learning faces several challenges: the number of possible structures is super-exponential in the number of variables while the required sample size might be even exponential.
Sentence 2: state-of-the-art structure learning techniques: covariance selection [5] and graphical lasso [6], since it has been shown theoretically and experimentally that they both converge to the maximum likelihood estimator.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It would be interesting to see whether a large step size can be used for any p > 0.
Sentence 2: staying with these goals, we propose the z update augmentation term of BADMM to be: B φ (Bz, c − Ax t+1 ), instead of the quadratic penalty term 1 2 Ax t+1 + Bz − c 2 2 in (3).
Relationship: neutral
Domain: NeurIPS
Sentence 1: If one needs to solve problem (1) for high dimensional data, the use of standard second-order methods such as interior-point methods is precluded (see for instance [6]), since they need to solve large systems of linear equations to compute the Newton steps.
Sentence 2: in fact, we can think of trivial examples where the replicates formulation has not a unique solution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We use θ to denote the vector of parameters θ ij , and denote the partition function by Z(θ) to highlight its dependence on these parameters.
Sentence 2: as in TRW, it can be shown that the solution is not dependent on the decomposition (as long as each edge appears in some structure), and the problem is equivalent to maximizing a linear function over the marginal polytope (which can be done in polynomial time for planar graphs).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We propose two computationally efficient algorithms that match the query complexity lower bound within log n factor and are completely parameter free.
Sentence 2: we estimate If there is no cluster of size at least M E x formed so far, we select a new element yet to be clustered and query it exactly once with the existing clusters (that is by selecting one arbitrary point from every cluster and querying the oracle with it and the new element), and include it in an existing cluster or create a new cluster with it based on the query answer.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Specifically, while the method based on the log derivative trick is currently the most general one, it has been observed to severely suffer from high variance problems [12,14,10] and thus it is only applicable together with sophisticated variance reduction techniques based on control variates.
Sentence 2: given that we can reparametrize x i as described above (and all differentiability conditions mentioned above hold), the gradient from ( 11) can be equivalently written as Clearly, the above expression is an expectation of the reparametrization gradient from eq.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Namely, we propose an algorithm that • provably produces an accurate estimate of the lifted target X from only n = O k log d k measurements, and • can be computed in polynomial time through efficient convex optimization methods.
Sentence 2: then for any pair of k × k-sparse matrices X and X with disjoint supports we have Ψ XΨ T , Ψ X Ψ T ≤ 2δ 2k X F X F . Proof.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Now, notice that the problem of minimizing T t=m h t (X) is a PSD relaxation to the minimization problem T t=m ft (x), and for the optimal solution it holds that: where x * = arg min x∈K T t=m ft (x).
Sentence 2: the hidden convexity of the problem allows us to bypass this issue by a simple and tight Positive Semi-Definite (PSD) relaxation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We also believe that ideas of searching through comparisons form a bridge between many well known search techniques in metric spaces to perceptually important (non-metric spaces) situations, and could lead to innovative practical applications.
Sentence 2: by inequality 2, we have: By property 5, there are at most O(D 3 log n) such samples at level i + 1, i.e.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Once new state vector W ′ is proposed we accept it with probability min 1, We compute P (W |λ, γ) and P (W ′ → W ) in a closed form, while we approximate the posterior P (Y |W ) by sampling L Gibbs samples while keeping W fixed.
Sentence 2: when adding a new group k ′ we select the birth and death time of the group at random such that 1 ≤ T B k ′ ≤ T D k ′ ≤ T . For removing groups we randomly pick one of existing groups k ′′ and remove it by setting W (t) k ′′ = 0 for all t. Finally, to update the birth and death time of an existing group, we select an existing group and propose new birth and death time of the group at random.
Relationship: neutral
Domain: NeurIPS
Sentence 1: However, a quadratic surrogate model also has quadratically many parameters which we have to estimate from a (ideally) very small data set.
Sentence 2: the intuition of the natural gradient is that we want to obtain an update direction of the parameters of the search distribution that is most similar to the standard gradient while the KL-divergence between new and old search distributions is bounded.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Alternative functions could be found by solving the optimization problem, subject to some constraints, for example that f be monotone increasing, have zero Gaussian mean, and saturate for large |x|.
Sentence 2: the following six values of z are locations of the poles at the integration endpoints and determine the salient features of the spectral density: In the Supplementary Material, we establish the relative ordering of constants 0 ≤ ζ ≤ η ≤ η , which implies that the minimum and maximum eigenvalues of H (0) are given by, The Supplementary Material also shows that the equality η = ζ only holds for linear networks, which implies that the minimum eigenvalue is nonzero for every nonlinear activation function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A Banach space B is said to be uniformly Fréchet differentiable if for all f, g ∈ B, lim t∈R,t→0 exists and the limit is approached uniformly for f, g in the unit sphere of B.
Sentence 2: it can be seen that many RKBSs (B pd p (R d ) for any 1 < p < ∞) have the same r.k (ignoring the scaling factor which can be made one for any p by choosing µ to be a probability measure).
Relationship: neutral
Domain: NeurIPS
Sentence 1: To move from a location s towards a goal position s , we can consider a constrained gradient ascent procedure on the value landscape: 2 where π(s ) has been absorbed into the parameter α.
Sentence 2: the presence of a reward-induced neuromodulator could allow for potentiation between the assembly and the attractor network neurons active when the animal receives a reward at a particular location.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Moreover, for gamma-like distributions, the convolution integral tends to increase the shape parameter, which means that gamma parameter estimates produced by fitting transition durations will overestimate the amount of 'memory' in the process 7 .
Sentence 2: for n > 4 and µ m (ξ) relatively small, the distribution has a gamma-like behavior, where new memory update transitions are suppressed near recent transitions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We visualize some of the qualitative results of our approach in Fig.
Sentence 2: we assess the occurring performance changes of two configurations: (i) by only adding the bounding box regression loss into the objective function ('Train'), i.e., both the segmentation net and the object localization net are trained but only the segmentation net is deployed; (ii) by training and applying the object localization net ('Apply').
Relationship: neutral
Domain: NeurIPS
Sentence 1: The key idea is to treat stragglers as "erasures" and use ECC to retrieve the result after a subset of fast workers have finished.
Sentence 2: (J 1 ) k×k is GΛG , (J 2 ) k×(n−k) is GΛH , and Consider an alternative way of doing linear inverse using n > k workers.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To further display the advantage of reciprocal connection, we also calculate the situation when a single network receives both input cues.
Sentence 2: to get clear understanding of the effect of reciprocal connections, we decouple the dynamics of z 1 and z 2 by studying the dynamics of their their difference, z d = z 1 − z 2 , and their summation, z s = z 1 + z 2 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Random Features has been proposed as a kernel approximation method [2,3,10,5], where a Monte-Carlo approximation is used to approximate (3), so that the solution to (1) can be obtained by The corresponding approximation error as proved in [2,Appendix B], can be bounded by ϵ given D = Ω(1/ϵ 2 ) number of random features, which is a direct consequence of the uniform convergence of the sampling approximation (4).
Sentence 2: a line of research has thus been devoted to kernel approximation methods that aim to preserve predictive performance, while maintaining computational tractability.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our method achieves comparable sparsity with irregular fine-grained pruning and maintains the model accuracy to a great extent.
Sentence 2: at each iteration during the inner loop, the only update is to swap the i-th and j-th slices in the D-th dimension of W . for S, we only need to swap the i-th and j-th rows without recomputing the tensor contraction.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 4 (right) shows that using longer rollouts, while not increasing the number of parameters, increases performance: 3 unrolling steps improves speed of learning and top performance significantly over 1 unrolling step, 5 outperforms 3, and as a test for significantly longer rollouts, 15 outperforms 5, reaching above 90% of levels solved.
Sentence 2: we investigated several types of rollout policies (random, pretrained) and found that a particularly efficient strategy was to distill the imagination-augmented policy into a model-free policy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We thank Bruno Olshausen, Pieter Abbeel, Sara Bolouki, Roger Grosse, Benjamin Packer, Austin Shoemaker and Joelle Skaf for helpful discussions.
Sentence 2: then, for each combination, we defined the convergence point as the point at which the objective value reaches within 1% relative error of the observed "optimal" objective value.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In greater detail, for any function f evaluated at a regular grid, for x ∈ (i/K, (i + 1)/K] and f (x) = f (1/K) for x ≤ 1/K; and the interpolation matrix is Our proposal, waveMesh, solves the following convex optimization problem where , and W ∈ R K×K is the usual DWT matrix.
Sentence 2: the novelty of our approach is a reversal of the direction of interpolation, i.e., interpolation from fitted values on the regular grid i/K (i = 1, . . . , K), to approximated fits on the raw data x i (i = 1, . . . , n).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Pairs of monocular responses are generated by integrating image intensities weighted by pairs of phase quadrature RF profiles, which are the real and imaginary parts of a complex-valued Gabor function ( ): ( where and are the spatial frequency and the phase of the left and right monocular RFs, and is a zero mean Gaussian with standard deviation , which is inversely proportional to the spatial frequency bandwidth.
Sentence 2: can be used as a confidence measure for distinguishing DIN and DOUT.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Step 2: keep p(w) fixed, based on the factorization assumption p({z}) = i p(z i ) and p 0 ({z}) = i p 0 (z i ), the distribution p(z) for each sample i can be obtained by solving the following problem: where Similarly, by introducing a set of Lagrangian multipliers β(y), we can get: and the dual variables β(y) can be obtained by solving the following dual problem: where P i (C) = { y β(y) = C, β(y) ≥ 0, ∀y}.
Sentence 2: we can introduce a set of marginal dual variables and transfer the dual problem (12) to an equivalent form with a polynomial number of constraints.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We show that glm is approximately proportional to ols in random design GLMs, regardless of the predictor distribution.
Sentence 2: if S ✓ [n], let U S denote the |S| ⇥ p matrix obtained from U by extracting the rows that are indexed by S. For a symmetric matrix M 2 R p⇥p , max (M) and min (M) denote the maximum and minimum eigenvalues, respectively.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, in the realizable case, i.e., when the data arise from an actual quantum state, the average L 1 loss per iteration is O( p n/T ).
Sentence 2: an n-qubit state ⇢ induces a function f on the set of two-outcome measurements E defined as f (E) := Tr(E⇢).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Here we have overloaded the notation for a doubly convolutional layer to denote a DCNN which contains correspondingly shaped doubly convolutional layers (the DCNN in Table 1 thus corresponds to DCNN-128-4-3-2).
Sentence 2: we have also confirmed that replacing a convolutional layer with a doubly convolutional layer consistently improves the performance, regardless of the depth of the layer.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In consequence, the assumption of uniform prior taken by SIBA is closer to the real one.
Sentence 2: this extraction process can be characterized by vector t = t 1 , t 2 . . . t l where t k is the number of marbles of color y k extracted, with t = l k=1 t k . The probability of extracting a color distribution of marbles t, given the initial color distribution of the urn T is described by the multivariate hypergeometric distribution Consider the case in which the total number of marbles in the urn, T , is known but that the color distribution, T, is unknown.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The problem of such greedy approach is target leakage: feature xi k is computed using y k , the target of x k . This leads to a conditional shift [30]: the distribution of xi |y differs for training and test examples.
Sentence 2: for all test examples, the value of the greedy TS is p, and the obtained model predicts 0 for all of them if p < t and predicts 1 otherwise, thus having accuracy 0.5 in both cases.
Relationship: neutral
Domain: NeurIPS
Sentence 1: These two opposing mechanisms ensure that the cell will remain at a constant activity under steady-state conditions.
Sentence 2: with a transient change in the presynaptic frequency, h, the initial postsynaptic frequency is given by: (3) As derived from Equation 3, we see that the transient change in the neuron's spiking rate is dependent on the contrast of the input spiking rate, dfd Ii- Hence, the transient gain of the neuron is equal to the ratio of the postsynaptic spiking rate to the presynaptic input rate and it decreases with the input rate.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We consider modeling the data set D using models indexed by a complexity index k, 1 :::; k :::; kmax • For example, the models could be finite mixture probability density functions (PDFs) for vector Xi'S where model complexity is indexed by the number of components k in the mixture.
Sentence 2: we define y = y(x) as a scalar function of x, namely a prediction at x.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Among the shallow multi-task methods, MTRL gives the best accuracies, showing that exploiting task relationship may be more effective than extracting shared feature subspace for multi-task learning.
Sentence 2: in the tensor normal prior, the row covariance matrix Σ 1 models the relationships between features (feature covariance), the column covariance matrix Σ 2 models the relationships between classes (class covariance), and the mode-3 covariance matrix Σ 3 models the relationships between tasks in the -th layer network parameters {W 1, , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The non-zero entries of κ are displayed in Figure 2 as functions of the parameter t. An edge contributes strongly to the kernel value, if two genotypes agree on it, but the common event (occurrence or non-occurrence of the mutation) was unlikely (Figure 2, solid and dashed line).
Sentence 2: the application of the Fisher kernel idea to mutagenetic trees leads to a kernel that measures similarity of evolutionary escape in a way that corresponds well to virological intuition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Clearly we see that each function contributes differently to represent the input and more information is gained from f 2 compared to the former case.
Sentence 2: while some of these methods have produced good results on datasets such as CIFAR-10 and SVHN, none has produced low precision networks competitive with full-precision models on large-scale classification tasks, such as ImageNet.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Hence, substituting the discriminant function ( 6) into (4), we have the prediction rule Then following the principle of MED learning, we define probabilistic max-margin matrix factorization (PM 3 F) as solving the following optimization problem Note that our probabilistic formulation is strictly more general than the original M 3 F model, which is in fact a special case of PM 3 F under a standard Gaussian prior and a mean-field assumption on p(U, V ).
Sentence 2: we use U i to denote the ith row of U , and V j likewise.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let h t denote a history up to stage t and s(h t ) denote the last state of history h t . We use π ht (a) to represent the probability of choosing an action a at state s(h t ), following a policy π and under a history h t . A t + 1 stage history, with h t followed by action a and state s ′ is written as (h t , a, s ′ ).
Sentence 2: denote the uncertainty set by P = s Ps .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Further, this result requires only the expected loss = E[ t ] to have a quadratic lower bound -the individual losses t themselves need not do so.
Sentence 2: the following Proposition shows that existence of a quadratic lower bound is actually a local condition; so long as the expected loss has a quadratic lower bound in a neighborhood of w , it must do so over the entire space W : Finally, we provide a simple motivating example of an interesting problem we can solve with an α-acutely convex loss that is not strongly convex: computing the median.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We generated synthetic networks consist of 1024 nodes and about 2500 edges using Kronecker graph model [35]: core-periphery network (CP) (parameters [0.9,0.5;0.5,0.3]), hierarchical community network (HC) (parameters [0.9,0.1;0.1,0.9]), and the Forest Fire model [36]: with forward and backward burning probability 0.2 and 0.17.
Sentence 2: such models yield dense graphs [7] and are less appropriate for predicting unseen interactions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We are given a training set of image and label pairs {(I t , l t )} N t=1 and the task is to predict the value of l t (e.g.
Sentence 2: at first glance, a very simple way of using the classification RBM of the previous section in the multi-fixation setting would be to set x = x 1:K = [x 1 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: With some assumptions on S and f t , this algorithm achieves a regret of O( Although the algorithm is simple, it needs to solve a constrained optimization problem at every time step, which might be too time-consuming for online implementation when the constraints are complex.
Sentence 2: note that the algorithm in [19] cannot be applied since the clipped constraints do not satisfy the required Slater condition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The performance of this process is measured by how accurately it retrieves the phrase structure of the input string.
Sentence 2: our two main methods, projection-based Markov Models (PMM) and constraint satisfaction with classifiers (CSCL) are shown to perform very well on the task of predicting NP and SV phrases, with CSCL at least as good as any other method tried on these tasks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While the proposed framework is flexible in simultaneously tackling data in various feature representations, the formulation itself is general in that it is established upon graph embedding.
Sentence 2: an ensemble kernel function k (or an ensemble kernel matrix K) is then defined by the learned model from binary-class data {(x i , y i ∈ ±1)} will be of the form: Optimizing both the coefficients {α i } N i=1 and {β m } M m=1 is one particular form of the MKL problems.
Relationship: neutral
Domain: NeurIPS
Sentence 1: During the training of Gaifman models, neighborhoods are generated for tuples of objects d ∈ D n based on the parameters r and k. We first describe the procedure for arbitrary tuples d of objects and will later explain where these tuples come from.
Sentence 2: the feature vector v = (v 1 , ..., v |Φ| ) for tuple d, and neighborhood N ∈ N r,k (d), written as v N , is constructed as follows Deciding D |= ϕ for a structure D and a first-order formula ϕ is referred to as model checking and computing ϕ(D) is called ϕ-counting.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Generally, network structures designed specifically for image classification are directly used as default backbone structure for other tasks including detection and segmentation, but there is seldom backbone structure designed under the consideration of unifying the advantages of networks designed for pixellevel or region-level predicting tasks, which may require very deep features with high resolution.
Sentence 2: 4 Experiments and Results For image classification, we evaluate our network on the ImageNet 2012 classification dataset [25] that consists of 1000 classes.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that Wz in RFF can be written as Rg, where R is a scaled orthogonal matrix such that each row has norm ||z|| 2 and g is distributed according to N (0, I d ).
Sentence 2: let z = x y , and z = ||z||, then Based on the definition of ORF, w 1 , w 2 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . < γ T , start by sampling from the prior π ξ (θ), then applies successive importance sampling steps, from π ξ,γt−1 (θ|D) to π ξ,γt (θ|D), leading to importance weights proportional to: When the importance weights become too skewed, one rejuvenates the particles through a resampling step (draw particles randomly with replacement, with probability proportional to the weights) and a move step (move particles according to a certain MCMC kernel).
Sentence 2: as any other Monte Carlo method, it may be too slow for large datasets.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Furthermore, it seems unlikely that a comparative framework could be built by independently choosing "ideal" penalty parameters λ, λ: Meinshausen and Bühlmann [8], for example, demonstrate that a seemingly reasonable oracle estimator of λ will not lead to consistent support recovery in the Lasso.
Sentence 2: in high-dimensional settings where n p, ordinary least squares is generally inappropriate.
Relationship: neutral