sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: It appears that quantizing convolutional layers too aggressively (e.g., 2-bit precision) can lead to accuracy loss if trained for the same period of time as the full precision variant.
Sentence 2: then there is a random stopping time R supported on {1, . . . , N } so that QSGD with quantization level s, constant stepsizes η = O(1/L) and access to stochastic gradients of f with Moreover, the communication cost is the same as in Theorem 3.4.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, in each round t, the base learner A receives not only the example x t , but also an o↵set y 0 t 2 R d for the prediction, and produces a prediction A(x t ) 2 R d , after which it receives the loss function `t and su↵ers loss `t(y 0 t + ↵A(x t )).
Sentence 2: as for competing with span(F), since linear loss functions are 0-smooth, we obtain the following easy corollary of Theorem 1: ] be a given parameter, and set B = ⌘N D. Algorithm 1 is an online learning algorithm for span(F) for losses in C with the following regret bound for any f 2 span(F): where 0 := P T t=1 `t(0) `t(f (x t )).
Relationship: neutral
Domain: NeurIPS
Sentence 1: LaSVM is an SMO-like solver for the dual version of problem (3-5) that optimizes one or two coordinates at a time, alternating process (on newly acquired examples, generated in our case by the FORCE-CONSTRAINT procedure) and reprocess (on previously seen support vectors or patterns) steps.
Sentence 2: [15] in the case of graph matching).
Relationship: neutral
Domain: NeurIPS
Sentence 1: These techniques express low-order moments of the observable distribution as a product of matrix parameters and use eigenvalue decomposition to recover these matrices.
Sentence 2: importantly, our unmixing technique does not require the training sentences be annotated with the tree topologies a priori, in contrast to recent extensions of [21] to learning PCFGs [24] and dependency trees [25,26], which work on a fixed topology.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A is here entirely determined by the covariance matrix of the vector ( X, Ỹ ) which also equals its correlation matrix (the normal scores have unit variance by definition), and thus the correlation matrix P parametrizing the Gaussian copula C P . In practice the problem is reduced to the estimation the Gaussian copula of (X, Y ).
Sentence 2: m. Rey is partially supported by the Swiss National Science Foundation, grant CR32I2 127017 / 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For standard PCA the asymptotic results are very accurate even for moderate data dimension, but for kernel PCA with a quadratic kernel we found that convergence to the asymptotic result was slow.
Sentence 2: since C in equation ( 1) only contains a finite number of symmetry-breaking directions then in the limit N → ∞ these will have zero measure as defined by H. in this limit the eigenvalue density would appear to be identical to the isotropic case.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , h p ) = 1 n n i=1 p j=1 τj (y i − h j (x i )), where τ denotes the p dimensional vector of quantile levels.
Sentence 2: for the sake of efficiency, we propose to use a Primal-Dual Coordinate Descent (PDCD) technique, recently introduced in [11].
Relationship: neutral
Domain: NeurIPS
Sentence 1: These wrappers are then used as features by a decision tree learner to find a categorization of the pages on the site that implies a simple hub structure, but which also largely agrees with the original bag-of-words classifier.
Sentence 2: on a real-world benchmark problem, this technique substantially improved the accuracy of a simple bag-of-words classifier, reducing error rate by about half.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In machine learning terms, we would like to achieve a flow that is "sparser" in the number of paths it uses.
Sentence 2: the boundary @M is regular in the sense that there exist positive constants ↵ > 0 and " 0 > 0 such that if " < " 0 , then for all points x 2 @M we have vol(B " (x) \ M ) ↵ vol(B " (x)) (where vol denotes the Lebesgue volume).
Relationship: neutral
Domain: NeurIPS
Sentence 1: And with s = jω, our synthesized BM design (passive) is where the two first-order systems are both low-pass filters (LPFs), with time constants τ 1 and τ 2 , respectively; b is a gain factor.
Sentence 2: both the cochlea's length (BM) and height (cochlear ducts) are discretized into a number of segments, with the original aspect ratio of the cochlea maintained.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The above simply says that the value of f (x) at a certain input x is the value of the standardised function s(z), for z = Wx ∈ R K , times a global scale σ f that changes the amplitude or power of the new function.
Sentence 2: in this section we consider the 32-input, moderate noise version of the Puma dataset.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For a p-dimensional MHP, we denote the intensity function of the i-th dimension by λ i (t).
Sentence 2: furthermore, let K and G denote the Gramian matrices where the i, j-th element correspond to K(s, s ), with s and s being the i-th and j-th element in S. Suppose that a ∈ R |S| is the coefficient vector such that f (k+ 1 2 ) i,j (•) = s∈S a s K(s, •), and that the projection step returns f Non-convex approach.
Relationship: neutral
Domain: NeurIPS
Sentence 1: First we find the analytical expressions relating the subthreshold voltage from the Adaptive Exponential Integrate-and-Fire model (AdEx) to the Spike-Response Model with escape noise (SRM as an example of a GLM).
Sentence 2: even if the exponential link-function overestimates the firing probability at these low voltages it rarely produces extra spikes.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Assuming that EP already yields a good approximation, the computation of a small number of these terms maybe sufficient to obtain the most dominant corrections.
Sentence 2: the small corrections arise as whenever terms y n m n are positive and large compared to the posterior variance, non-Gaussian terms f n (x) = t n (x n ) ≈ 1 for almost all values of x n which have significant probability under the Gaussian distribution that is proportional to q(x)/g n (x n ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: of features of Ii that rnatch the corresponding feature of the cue (njjm stands for the number of matching values in tl1e j-th image that have value i)} and the ntnnber of nlisulatcbing featq.res (njq stands tor the number of mismatching values in the fhimage).
Sentence 2: the decrease is large en.oug:h.~this factor tnust cause the LF and .HF old-item distributions to reverse position.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The more uncertainty (ie the larger ¡ ), the smaller the role of the top-down expectation q ¡ in determining Examples of just such effects can be found in Figure 1 (d).
Sentence 2: as long as the underlying parameters remain the same, ie `¡ does not change greatly, the inference process functions normally, as we can see in the first y steps in Figure 3(a).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In essence, such extensions work in a self-training way; the unlabeled data are assigned pseudo-class labels based on the constructed ensemble learner so far, and in turn the pseudo-class labels achieved will be used to find out a new proper learner to be added to the ensemble.
Sentence 2: finally it is worth stating that unlike most of existing regularization techniques used in semi-supervised learning, e.g., [5], [6], our regularization takes effect on both labeled and unlabeled data while theirs are based on unlabeled data only.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If we add a dual variable y and write µkrxk 1 = max kyk1µ y T rx, we obtain which is clearly of the form (1).
Sentence 2: pDHG typically does not converge when non-constant stepsizes are used, even in the case that k ⌧ k < 1/⇢(A T A) [13].
Relationship: neutral
Domain: NeurIPS
Sentence 1: The new log-likelihood function is where f j (x) is an exponential family member with its expectation parameter equal to the jth data vector and the constant denotes a term that does not depend on the unknown variables {q j } n j=1 .
Sentence 2: we can restrict the set of mixture components to the distributions centered at the data points, i.e., m j ∈ X .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, there is an absolute constant κ 0 > 0, such that for all large n, the following event holds with P X -probability at least 1 (ii) (variance inequality) There are absolute constants κ 1 , κ 2 > 0 such that for all large n, the following event holds with (iii) (mspe inequalities) Suppose that θ is chosen as θ = 2η/3 when η ∈ (0, 1 2 ), and that θ is chosen as θ = η 1+η when η > 1 2 .
Sentence 2: an important practical aspect of Theorem 1 is that for any given contrast c, the variance v ρ (X; c) can be easily estimated, since it only requires an estimate of σ 2 , which can be obtained from F . whenever theoretical bounds on d 2 2 (F 0 , F ) and b 2 ρ (X; c) are available, the right side of line ( 10) can be controlled.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To be more specific, we have encoder E take the image x c as input and derive its representation z, which is combined with its domain vector v c to reconstruct the image xc via Generator G. Thus, the objective function of VAE is defined as: where the first term aims at recovering the synthesized output in the same domain c, and the second term calculates Kullback-Leibler divergence which penalizes deviation of latent feature from the prior distribution p(z c ) (as z ∼ N (0, I)).
Sentence 2: the contributions of this paper are highlighted as follows: • We propose a Unified Feature Disentanglement Network (UFDN), which learns deep disentangled feature representation for multi-domain image translation and manipulation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Based on the new bound, we develop a distributed, key-value-free inference algorithm in the MAPREDUCE framework, which can fully exploit the memory cache mechanism in fast MAPREDUCE systems such as SPARK.
Sentence 2: in comparison, InfTucker utilizes the Kronecker-product properties to calculate the gradients and has to perform eigenvalue decomposition of the covariance matrices in each tensor mode.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Notice that although we do not explicitly write the dependence on M , all of the above quantities implicitly depend on the choice of M . The analysis of the optimization in (3) shows that, with high probability, L RB (θ) is strictly concave with λ 2 (H(θ)) ≤ −C b γ 1 γ 2 γ 3 λ 2 (L) < 0 for all θ ∈ Ω b (Lemma C.3), and the gradient is also bounded with ∇L RB (θ * ) ≤ C b γ −1/2 2 ( j p j log d) 1/2 (Lemma C.2).
Sentence 2: as the ground truth θ * , we use the ML estimate of PL weights over the entire data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The trends in speedup are opposite: our method requires extra optimizations that dominate training time at extremely small D; at very large D we use estimator ( 6), so our method requires less overall time.
Sentence 2: we have a cost c : R × Y → R, where c(•, y) is convex for y ∈ Y, and a reproducing kernel Hilbert space (RKHS) of functions F with kernel K. Given a sample {(x i , y i )} n i=1 , the usual 2 -regularized learning problem is to solve the following (shown in primal and dual forms respectively): where • 2 denotes the Hilbert space norm, c * (α, y) = sup z {αz − c(z, y)} is the convex conjugate of c (for fixed y) and G = [K(x i , x j )] n i,j=1 denotes the Gram matrix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In order to relate it to other values of , we need a little more flexibility: for given ✏ 0 and (`, F, P ⇤ ), we define which excludes a band of predictors that approximate the best predictor in the model to within excess risk ✏.
Sentence 2: the setting of sequential prediction (also called online learning) [2] makes no probabilistic assumptions about the source of the data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The proof of Theorem 3 is given in Appendix B.
Sentence 2: we estimate the transition probabilities from the sample path using simple frequency estimates: as a consequence of the Markov property, for each state, the frequency estimates converge at a rate that depends only on the number of visits to the state, and in particular the rate (given the visit count of the state) is independent of the mixing time of the chain.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We extend now this restart scheme to solve non-smooth or Hölder smooth convex optimization problem under the sharpness assumption.
Sentence 2: in general, an error bound is an inequality of the form where ω is an increasing function at 0, called the residual function, and x may evolve either in the whole space or in a bounded set, see Bolte et al.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To deal with this problem, we treat the process X t for times t between consecutive observations kτ < t < (k + 1)τ as a latent unobserved random variable with a posterior path measure given by where y is the collection of observations y k and δ(•) denotes the Dirac-distribution encoding the fact that the process is known perfectly at times τ k . Our goal is to use an EM algorithm to compute the maximum posterior (MAP) prediction for the drift function f (x).
Sentence 2: we have also defined the corresponding approximate posterior drift as well as the functions There are two main problems for a practical realization of this EM algorithm: 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We try three different solvers: regret-matching, Hedge, and projected replicator dynamics.
Sentence 2: responses to equilibrium strategies computed by Double Oracle will (i) overfit to a specific equilibrium in the n-player or general-sum case, and (ii) be unable to generalize to parts of the space not reached by any equilibrium strategy in the zero-sum case.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We show in the supplement that SSVM parameters that assign nonnegative scores to all labelings achieve exactly the same hinge loss (and thus the same generalization error) as without the nonnegativity constraint.
Sentence 2: a set function F : 2 V → R is submodular if its marginal gains, F (a|S) ≡ F (S ∪a)−F (S) are decreasing, i.e.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Hence, its advantage over the untruncated one narrows as the number of measurements increases, thus straightening out the heavy tails.
Sentence 2: observe that almost all {a i } vectors have a squared normalized inner-product smaller than 10 −2 , while half of the inner-products are less than 10 −3 , which implies that x is nearly orthogonal to many a i 's.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We consider a general continuous game model for the rewards in multi-agent online learning: ), where N is the set of N agents, X i is a convex and compact subset of R di representing the action space of agent i, and r i : For the rest of the paper, we set d = N i=1 d i , which denotes the dimension of the joint action space: A ⊂ R d . Variables associated with agent i are denoted by subscripts.
Sentence 2: as a quick outline here (the details are in appendix), pick an arbitrary Nash equilibrium a * ∈ A * .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We also considered B = n/10, the performance among these algorithms are similar to the case B = n/5.
Sentence 2: regarding the comparison among these algorithms, we use the number of SFO calls (see Definition 2) to evaluate them since the number of PO calls of them are the same except ProxSVRG (which is already clearly demonstrated by Figure 2).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The idea is that if our dataset X consists of linearly uncorrelated features (as can be obtained by applying a whitening procedure), then a measure of the higher-order dependence between two features can be obtained by looking at the correlation of their energies (squared responses).
Sentence 2: for instance, the completely-connected layers are connected to all the maps within a 2-by-2 spatial window.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Figure 4(b) shows the recall results on METAFILTER.
Sentence 2: the specific contributions of this paper are: (1) We formulate a continuous-time regression model for longitudinal network data with time-dependent statistics (and time-varying coefficients for the additive form); (2) we develop an accurate and efficient inference scheme for estimating the regression coefficients; and (3) we perform an experimental analysis on real-world longitudinal networks and demonstrate that the proposed framework is useful in terms of prediction and interpretability.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The Fourier transform of (4) results in the stationary, positive definite autocovariance function where stationarity implies dependence on input domain differences k(τ The SG kernel may also be derived by considering a latent signal f (x) = √ 2 cos(ω(x + φ)) with frequency uncertainty ω ∼ N (µ, ν) and phase offset ωφ.
Sentence 2: 6 Experiments Section 6.1 demonstrates the performance of the CSM kernel and the accuracy of the DFT approximation In Section 6.2, the DFT approximation for the CSM kernel is used in a Bayesian HMM framework to cluster time-varying multi-channel LFP data based on the full cross-spectrum; the HMM states here correspond to states of the brain during LFP recording.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We took w ∼ U (−3, 3), x = w 2 + n x with n x ∼ U (−1, 1), y = 4 |w|+n y with n y ∼ U (−1, 1), z = 2 sin x+2 sin y+n z with n z ∼ U (−1, 1).
Sentence 2: we accept the model where the time interval between the current and the next eruption is a function of the duration of the current eruption, but reject the reverse model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The urn view allows us to compare this model to other priors on infinite trees.
Sentence 2: if it has reached node but will not stay there, it descends to existing child i with probability (N i +N i≺• )/(N ≺• +γ) and instantiates a new child with probability γ/(N ≺• +γ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the template model of Perrone and Stone [3], a template invariant to translation velocity or depth structure is obtained by summing the responses of the most active sensor at each image location.
Sentence 2: each flow template can become approximately rotation-invariant by subtracting a gain field activity that is a multiplication of the eye velocity t with a derivative template activity 80/ 8R that is specific for each flow template.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given the walk-sum interpretation from Proposition 1, one can check that x (n) → J −1 h element-wise as n → ∞.
Sentence 2: using this analysis, we show that the non-stationary ET iteration ( 6) converges in walk-summable models for an arbitrary choice of subgraphs {S n } ∞ n=1 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then we are not at a local minimum to L(γ) if there exists a second convex cone C formed from a subset of columns of Φ such that t ∈ C ⊂ C Φ , i.e., C is a tighter cone containing t. In Figure 1(right), we obtain a tighter cone by swapping x for φ 2 .
Sentence 2: locally minimizing our new problem ( 14) is clearly superior to locally minimizing (1).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Understanding the differences between approximated kernel methods and neural networks is crucial to use them optimally in practice.
Sentence 2: we use validation sets of size 1, 000 for Gisette, 10, 000 for MNIST, 50, 000 for CoverType, 5, 000 for CIFAR10, 3, 560 for Adult, 4, 500 for Letter, and 1, 290 for USPS.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The initial state distribution is π 0 ∈ R K . The Markov structure dictates that z t ∼ Mult(π zt−1 ), and the observations follow x t ∼ Φ(θ zt ).
Sentence 2: if we introduce a new parameter β, and generalize the transition probabilities to be Pr(z where φ = βφ, then the mean of the distribution is the same in the scaled distribution (namely, m j ) while the variance is scaled.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this case, the sequence { i } as defined will decrease until it reaches the largest value such that max ts g ts (log ) = log .
Sentence 2: similarly to (18) and ( 19), we have The steady-state solution of (20) yields an estimate of the variances of the log-belief log p t by σ 2 t = u∈Γt σ 2 ut ; this estimate is typically much smaller than the bound (18) due to the strict sub-additive relationship between the standard deviations.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , w ⇤ T } over the m functions, by randomly perturbing the uniform distribution.
Sentence 2: w t [i] is the probability of picking function L i 2 L. The adversary picks a distribution w t based on some arbitrary no-regret learning algorithm on the m actions in L. For concreteness consider the case where the adversary picks a distribution based on the multiplicative weight updates algorithm, i.e., Subsequently the learner picks a solution x t that is the output of the ↵-approximate stochastic oracle on the distribution selected by the adversary at time-step t. Write ✏(T ) = q 2 log(m) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The differences in performance between DFacTo (ALS) and CPALS and between DFacTo (GD) and CPOPT can partially be explained by the fact that DFacTo (ALS, GD) is implemented in C++ while CPALS and CPOPT use MATLAB.
Sentence 2: we downloaded Version 2.5 of the Tensor Toolbox, which is implemented in MATLAB 4 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The resulting state of applying a sequence of complete actions π = a 1 , ..., a n in s with respects to D i is defined as: A planning problem with incomplete domain D is P = D, I, G where I ⊆ F is the set of propositions that are true in the initial state (and all the remaining are false), and G is the set of goal propositions.
Sentence 2: since possible preconditions and effects can be represented as random variables, they can in principle be modeled using graphical models such as Makov Logic Networks and Bayesian Networks [14].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Finally, in Section 6.4 we empirically demonstrate the differences between our approach and the previously discussed fast-adaptation algorithms.
Sentence 2: as we might have expected, the only difference between the bounds for the two versions of Algorithm 1 is in the term ϕ(W s ), i.e., the distance between the optimal weights w * and the source weights W s . for the mixture version we have the (smoothened) minimum distance to the source tasks' weights (Equation ( 5)), while for the Gaussian one we have the distance to the mean of such weights.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (2) W-RankNet and W-ListMLE also outperform other baselines on LETOR such as Regression, Ranking SVM, Rank-Boost, FRank [15], ListNet and SVMMAP [18].
Sentence 2: the pointwise approach, such as subset regression [5] and McRank [10], views each single object as the learning instance.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Θ ∈ {0, 1} h×t , Θ 1 = k1), then M can have negative elements, but the spectral constraint M 1 = 1 still holds (see proof in Appendix C).
Sentence 2: the totally corrective update is expensive because given α and β, each evaluation of the objective f itself requires an optimization over S 1 , S 2 , and Z 3 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Under the competition (mediated by recurrent connections and divisive normalization) from the neighboring neurons which are less affected by SFA, the bump tends to shift to the neighborhood; and at the new location, SFA starts to destabilize neuronal responses again.
Sentence 2: interestingly, we find that when the intrinsic speed of the network is greater than that of the external drive, anticipative tracking occurs for sufficiently weak stimuli; and different SFA amplitude results in different anticipative times.
Relationship: neutral