sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Specifically we present a new chip with 32 × 32 cells, that can sequentially select the most active regions of the input stimuli, the Selective Attention Chip (SAC).
Sentence 2: several software [1,2,3] and hardware models [4,5,6,7] based on the concept of saliency map, winner-takes-all (WTA) competition, and inhibition of return (IOR) [8] have been proposed.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Considering these limitations of convex regularizations, we study non-convex regularizations [33]- [35] [39], which have the advantage of producing mildly or slightly shrunken parameter estimates so as to be able to preserve weak-effect disease-related brain regions and the advantage of avoiding selecting many disease-irrelevant regions.
Sentence 2: the linear transformation explored by LDA may not be effective.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With the (N × N ) kernel matrix K = 1 N Y T Y we define the Gaussian partition function x is an N dimensional integration variable.
Sentence 2: using , we can generate expressions that can be used in (2) to sum over the data which are not contained in the set D In the following λ k and u k will always denote eigenvalues and eigenvectors of the data dependent (i.e.
Relationship: neutral
Domain: NeurIPS
Sentence 1: An algorithm is called p,-margin successful if, for any input labeled sample, it outputs a hypothesis half-space that classifies correctly as many sample points as any half-space can classify correctly with margin p, (that is, discounting points that are too close to the separating hyper-plane).
Sentence 2: a hyper-plane h(w, t), where w E lR n and t E lR, correctly classifies (X, 17) if sign( < wx > -t) = 17 where < wx > denotes the dot product of the vectors w and x.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The problem of unmixing the dyes can be formulated as a matrix factorization problem: Here X is an n s × l column matrix, where l is the number of pixels and the entry X ij is the brightness of the i th pixel in the image in to the j th spectral band.
Sentence 2: we use a setup based on a set of fixed bandpass filters.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our framework is also similar to the Anytime Edge Evaluation (AEE*) framework [25] which deals with edge evaluation on a GBG.
Sentence 2: in order to specify BISECT, we need to define two options -a candidate test set selection function SelectCandTestSet(x A ) and a test selection function SelectTest(T cand , θ, x A ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: On one hand we want to minimize the upper bound of negative log likelihood of x 1 when feeding to the decoder inputs of the form (z 1 , f s (x 1 )) and (z 1 , f s (x 1 )), where z 1 are samples form the approximate posterior q(z|x 1 ).
Sentence 2: in Figure 6 we present results for interpolation and swapping.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Applying the same reasoning to the loss function in the regularized risk (1) we obtain the following loss l(x i , x i+1 , y i , y i+1 , x i , x i+1 , f ) as a stochastic estimate of the objective function defined in (5).
Sentence 2: see Figure 1 for illustrations of this idea.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this section, we consider the following linear system in which the goal is to minimize the expected return over 20 steps.
Sentence 2: figure 4 shows that when the Fisher information matrix is estimated using MC (BPG-MC), the BPG algorithm still performs better than MCPG, and outperforms the BPG algorithm in which the Fisher information matrix is estimated using ML (BPG-ML).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For instance, suppose P were uniform over all subtrees of T 0 , then log(1/(P (T )) = Ω(n), yielding a vacuous excess risk.
Sentence 2: for any classifier ĥ learned over a sample {X i , Y i } i , we are interested in the excess-risk E( ĥ) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: 3(a) for an example of a voxel v as shown in Fig. . For computing the diffusion predictions, we use a discrete grid in the sphere by uniformly sampling the spherical coordinates using L points in azimuth and elevation coordinates (Fig.
Sentence 2: we note that matrix M ∈ R N θ Nv×N f (Fig.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As [14] show for PCA, one can start with a random matrix that is only slightly larger than the true rank k of the correlation matrix, and with extremely high likelihood converge in a few iterations to within a small distance of the true principal components.
Sentence 2: because of the Zipfian distribution of words, many words are rare or even unique, and hence one is not in the asymptotic limit.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let u(x, t) be the synaptic input at time t to the neurons whose preferred stimulus is x.
Sentence 2: we find that with STD, the network can have slowdecaying plateau states, that is, the network being stimulated to an active state by a transient input will decay to silence very slowly in the time order of STD rather than that of neural signaling.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As long as we can show that the values we obtain for α are upper bounds, then we can show that the objective function will decrease after the forward-backward routine, as the existing sequence of states is also a valid path (with no new incurred penalties).
Sentence 2: (Note: there are no burn-in iterations and all samplers are initialized with a randomly initialized 20-state labeling.)
Relationship: neutral
Domain: NeurIPS
Sentence 1: For prediction, both iMedLDA and gMedLDA are slightly slower than fMedLDA.
Sentence 2: for those data with non-zero Lagrange multipliers (i.e., the data are around the decision boundary or misclassified), the second term will bias the model towards a new posterior distribution that favors more discriminative representations on these "hard" data points.
Relationship: neutral
Domain: NeurIPS
Sentence 1: GD with 1-norm regularization behaves like GD for small k and like EG for large k. The GD algorithm keeps all the small weight around and the weight of the first component only grows linearly.
Sentence 2: one way to closely approximate the above version space algorithm is to run the Exponentiated Gradient (EG) algorithm [KW97b] with a large learning rate.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is obtained in much the same way as we obtain an adaptive regret bound for the fixed-share forecaster in the next result.
Sentence 2: for instance, for a given horizon T , the discounts β t,T may be larger as t is closer to T . in a game-theoretic setting, the earlier losses may matter more then the more recent ones (because of interest rates), in which case β t,T would be smaller as t gets closer to T . We mostly consider below monotonic sequences of discounts (both non-decreasing and non-increasing).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The corresponding constrained relaxation to the maximum-likelihood problem has the form Using this model instead of ones we saw previously, we sacrifice less on the front of the approximation to the true likelihood, at the expense of increased computational effort.
Sentence 2: based on this expression , we have, for every k: where we have used the fact that , for every symmetric matrix R, we have Using again the Lipschitz continuity properties of the weighted log-sum-exp function, we obtain that for every Q, the absolute error between Z(Q) and Z card (Q) is bounded as follows: a measure of quality is D st (Q), the distance, in l 1 -norm, between the model and the class of standard Ising models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: [29] assume that an appropriate choice of weights on visual feature vectors for a given question vector sufficiently captures the joint representation for answering.
Sentence 2: the effects of other various options, Skip-Thought Vectors [12] for parameter initialization, Bayesian Dropout [5] for regularization, image captioning model [10] for postprocessing, and the usage of shortcut connections, are explored in Appendix A.1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 2 Reusing the flow from the previous step gives an additional speedup.
Sentence 2: . . ≥ γ M . equations ( 12) constitute the parametric submodular minimization problem as defined above, which reduces to the monotonic parametric max-flow problem for pairwise E. Let • denote the largest integer not exceeding an argument of the operation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We observe significant speed-ups brought by our algorithm, which is almost 50 times faster than the convex ones.
Sentence 2: due to the nuclear norm penalty, these convex optimization algorithms need to do full singular value decomposition (SVD) to solve the proximal mapping of nuclear norm at each iteration, which results in an extremely high time complexity of O(d 3 ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: ( 8) Now, we use dynamic programming approach that has been used to solve 0-1 Knapsack problems including MCKP given in (7) [28].
Sentence 2: we define the maximum payoff one can collect with budget b among goods {1, ..., n} when the bid value x k is restricted to the set D t for each good k as Then, the following recursion can be used to solve for V K (B) which gives the optimal solution to (8): (9) This is the Bellman equation where V n (b) is the maximum total payoff one can collect using remaining budget b and remaining n goods.
Relationship: neutral
Domain: NeurIPS
Sentence 1: ¡ ¦ , which holds because ¡ ¦ is a transfer function, we get: Furthermore we assume orthogonality (see also below) given by: and get accordingly: We now apply PLANCHEREL'S theorem [5] in order to transfer the integral into the timedomain and prove that it is negative.
Sentence 2: we want to express © ¥¤ by the environmental transferfunctions ¨¢ 7 3¨¦ and ¨¢ `¦ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: This implies that the neuronal gain functions -the firing rate of the post-synaptic neurons as a function of the average • http) / culture.neurobio.ucla.edu/ "'pel firing rate of the pre-synaptic neurons -must be sigmoidal: small at low firing rate to provide stability, high at intermediate firing rate to provide a threshold (at an unstable equilibrium), and low again at high firing rate to provide saturation and a stable attractor.
Sentence 2: in such networks, activity among excitatory cells results in inhibitory feedback.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Learning and anticipation are central features of cerebellar computation and function (Bastian, 2006): the cerebellum learns from experience and is able to anticipate events, thereby complementing a reactive feedback control by an anticipatory feed-forward one (Hofstoetter et al., 2002;Herreros and Verschure, 2013).
Sentence 2: after having established the gradient descent algorithm, we can implement the same rule in an on-line manner, dropping the repetitiveness assumption inherent to trial-by-trial learning and performing all computations locally in time.
Relationship: neutral
Domain: NeurIPS
Sentence 1: These MUDs have good convergence properties and do not need a training sequence to decode the received bits, but they need large training sequences before their probability of error is low.
Sentence 2: most of last generation digital communication systems such as Global Positioning System (GPS), wireless 802.11b, Universal Mobile Telecommunication System (UMTS), etc, may take advantage of any improvement on this topic.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Placing a weight d i on each sample, we could optimize the sum F (d) = m i=1 d i Fi and obtain a tractable optimization problem.
Sentence 2: although left for future work, we suspect that the same techniques we present here can also be extending to these other cases, potentially providing a wide range of analogous results that still apply under off-policy sampling.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Like the region term, the object term is defined by a logistic function that maps object features φ o : P o , v hz , I → R n to probability of each object class.
Sentence 2: in this phase, the algorithm behaves exactly as in [7] by iteratively proposing re-assignments of pixels to regions (variables R) and recomputes the optimal assignment to the remaining variables (S and v hz ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The simulations were performed on graphs with p = 100 nodes, expected neighborhood size of s = 10, sample size n = 300, and (1) , (2) ∼ N (0, 1 p ).
Sentence 2: in the finite sample regime we conjecture Assumptions 4.1 and 4.2 to be weaker than the faithfulness assumption: violations of faithfulness as well as of Assumptions 4.1 and 4.2 correspond to points that are close to conditional independence hypersurfaces [39].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Another way to view this is to think of a pair of opposite -polarity "basis vectors" sharing the same coefficient α t . The most closely related potential function technique to ours is that of SVMs [9], where the classification margin (and thus the bound on generalization) is maximized by a simultaneous optimization with respect to all of the training points.
Sentence 2: in contrast to SVMs, however, we offer an on-line and incremental learning machine for building kernel discriminants whose complexity (number of kernel evaluations) can be directly controlled (traded off for accuracy).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We first consider the basic proximal-gradient method in the convex case: Proposition 1 (Basic proximal-gradient method -Convexity) Assume (H) and that we iterate recursion (3) with y k = x k . Then, for all k 1, we have with The proof may be found in [29].
Sentence 2: for example, we can establish that inexact proximalgradient methods converge under some closedness assumptions on the mapping induced by the approximate proximity operator, and the assumption that the algorithm used to compute the inexact proximity operator achieves sufficient descent on problem (2) compared to the previous iteration x k−1 [16].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Recently, a growing number of researchers have argued for a probabilistic approach to vision, in which the functioning of the visual system is interpreted as performing Bayesian inference in latent variable models, see e.g.
Sentence 2: olshausen and Field suggested [12] that the firing rates of the neurons correspond to the maximum a posteriori (MAP) estimate of the latent variables, given the image input: An important problem with this kind of a MAP representation is that it attempts to represent a complex posterior distribution using only a single point (at the maximum).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let T n denote the family of all multi-class decision trees with n internal nodes in dimension d. In Appendix J, we derive the following upper bound on the Rademacher complexity of T n : All of the experiments in this section use T n as the family of base hypothesis sets (parametrized by n).
Sentence 2: assume that Φ is twice differentiable and that Φ (u) > 0 for all u ∈ R. Then, the projected coordinate descent algorithm applied to F converges to the solution α * of the optimization max α≥0 F (α) for F = F sum , F = F maxsum , or F = F compsum .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the same reason, there might be no (conditional) dependence between W and a possible unmeasured common parent of X and Y .
Sentence 2: [16] derives analytical bounds under (3) given a fixed, numerical value of w . We know of no previous analytical bounds as an algebraic function of w . In the Supplementary Material, we provide a series of algebraic bounds as a function of our free parameters.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We call these critical state-action pairs, Crit(P ) := {(i, a) : a / ∈ O(i; P, A) ∧ (∀ > 0, MakeOpt(i, a; P, ) = ∅)} .
Sentence 2: if we keep exploring and never exploit the knowledge accumulated, we will not behave optimally.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In fact, if f ✓ is a bijection between samples in high probability regions, then f 1 ✓ is automatically also such a bijection.
Sentence 2: intuitively, if (x, v) lies in a high probability region, then both f ✓ and f 1 ✓ should propose a state in another high probability region.
Relationship: neutral
Domain: NeurIPS
Sentence 1: By exploiting convex duality of the sub-problems and eigenvector properties, a solvable convex formulation of the problem can be derived that preserves solution equivalence to the original.
Sentence 2: for the bundle method we developed, whenever the size of B is larger than a given constant b, we will keep the active points of B that correspond to the first b largest α values, and drop the remaining ones.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To the best of our knowledge, this is the first algorithm in machine learning that directly constructs a convex relaxation for a bi-level optimization based on the inner optimality conditions.
Sentence 2: we next detail the solution to the former, relegating the latter to Appendix D. Given M , we optimize over (π, θ, γ, v) by projected LBFGS [33].
Relationship: neutral
Domain: NeurIPS
Sentence 1: This bound is very similar to bound obtained in Theorem 1, and says that the function f is robust, as long as the eigengap between the second and third eigenvalues is sufficiently large for G(X) and G − (x), and the second eigenvalue does not change significantly if we slightly perturb the distance threshold used to determine whether an edge exists in the graph in question.
Sentence 2: is there a way to construct a graph such that the neighborhood structure of the graph captures the neighborhood of datapoints with respect to the metric in question?
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let ∂ K L(α, •) denote the gradient w.r.t.
Sentence 2: suppose now we are only given an indefinite kernel matrix K 0 ∈ S n . Luss and d'Aspremont [15] proposed the following max-min approach to simultaneously learn a proxy PSD kernel matrix K for the indefinite matrix K 0 and the SVM classification: Let For simplicity, we refer to the following function defined by f (α) = min as the objective function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In addition, p 2 = 1 − p and µ 2 = β 4 w 2 = ( 1−pα 2 1−p ) 2 p 2 α 4 η 2 ≤ p 2 α 2 σ 2 4(1−p) 2 .
Sentence 2: let φ : R d → R * + be a strictly positive weight function such that E[φ(X)] = 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the wake of the success of TS in these online learning problems, a natural question is whether and how TS can be applied to dueling bandits to further improve the performance.
Sentence 2: in addition, for a Copeland winner i * ∈ C, let L C = K j=1 1(p ji * > 1/2) be the number of arms that beat arm i * .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Each S ∈ S in objective ( 13) must be S = {j} for some j ∈ V. The objective then becomes f (u) = ∑ j∈V w {j} u j + const, a form of standard VC.
Sentence 2: we seek a labeling l where l i ∈ L ∪ ⊘ identifies the line (and vanishing point) that edge i belongs to, or assigns outlier label ⊘.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We now wish to generalize the results to the population of the United States (U.S.), but we find the distribution P (x, y, z) in LA to be different from the one in the U.S. (call the latter P * (x, y, z)).
Sentence 2: we also consider issues relative to the variance of the estimand aiming for improving sample efficiency and increasing statistical power.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This model assumes that only pairwise (or second-order) correlations exist between the representations of different items.
Sentence 2: the minimal color change condition taps the conditional probability of the memory for the target given the memories for the distracters, p(ŝ t |ŝ −t = s −t ) where −t represents the indices of the distracter items, because the actual dis- tracters s −t are shown during test.
Relationship: neutral
Domain: NeurIPS
Sentence 1: So a generative mechanism would keep sampling the functions and deliver them when the conditions hold true.
Sentence 2: it has a 1/poly(γ (1) ) dependence which could be bad if γ (1) is too small: intuitively, if γ (1) is too small then you will wait for a long time in step 2 of Algorithm 1 for β t−1 to decrease without proceeding to f (2) , incurring large regret (f + B) in the process.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To show the linear time and space complexity, recall that the differentiation w.r.t.w k,j can be efficiently computed by back-propagation in a top-down pass of S once we have computed τ S t=1 c t u t in a bottom-up pass of S. Remark.
Sentence 2: this is not the case for SPNs, where the effective number of mixture components is τ S = Ω(2 H(S) ), which also depends on the input network S. To simplify the notation, for each t ∈ [τ S ], we define c t n i=1 p t (x i ) 1 and u t w p 0 (w) (k,j)∈T tE w k,j dw.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that the standard graph-Laplacian formulation sets d = m. (e) Y : μi = |Y T v i | if i ≤ d; 0 otherwise.
Sentence 2: we consider a feature transformation of the form ψ(x) = S 1/2 ψ(x), where S is an appropriate positive semi-definite operator on H. The following result establishes an equivalent feature space formulation of the semi-supervised learning method in Figure 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Furthermore single-linkage algorithms are known to provably recover a ground truth clustering if the similarity function has some stability properties [6].
Sentence 2: let G i,j be a subgraph of G with vertex set V i ∪ U j containing any edge (v, u) ∈ E(G) where v ∈ V i and u ∈ U j .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For I i ∈ I i we denote by A(I i ) the set A(h) and by P (I i ) the player P (h) for any h ∈ I i . I i is the information partition of player i; a set I i ∈ I i is an information set of player i.
Sentence 2: at each information set, we sample an action uniformly randomly with probability and according to the player's current strategy σ t . Through experimentation we found that = 0.6 worked well across all games; this is interesting because the regret bound suggests δ should be as large as possible.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Another paradigm that appears to share many features of the 2AFC task is the Go/NoGo (GNG) task [6], (see Luce [5] for a review), where one stimulus category is associated with an overt Go response that has to be executed before a response dead-line, and the other stimulus (NoGo) requires withholding response until the response deadline has elapsed.
Sentence 2: various versions of augmented DDM have been used to fit GNG behavioral data, with one variant in particular suggesting that the decision threshold in GNG ought to be higher than 2AFC [2], in an apparent contradiction to our model's predictions (Figure 4).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The lower panels demonstrate the robustness of the methods on highly noisy (large σ) data, in which case the estimated errorbars become significant, but the performance degrades only slightly.
Sentence 2: biophysically accurate models of single cells are typically formulated compartmentally -a set of first-order coupled differential equations that form a spatially discrete approximation to the cable equations.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the case of Figure 3 (c), the convolution is still a skewed one, but the scale of this skewness is less than the original ones.
Sentence 2: figure 5 (b) shows the theoretical and empirical probability of underestimation Pr( V π + (s 1 ) < E V π + (s 1 )).
Relationship: neutral