sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: We pad and clip reviews to a length of 200 tokens, and learn 50-dimensional word vectors from scratch for a vocab size of 5,000.We train an LSTM with 64 hidden dimensions on this data.
Sentence 2: we did not observe the same behavior when turning off the corresponding component of the GLC, and believe it may be due to variance introduced during training by the difference in signal provided by the Forward method's C estimate and the clean labels.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , π T −1 ), where each π t : S → A is a (stationary) policy, we define the value V πt,...,πT −1 (s) ] as the expected (normalized) sum of rewards attained by starting at state s and the "clock" at time t, taking one action according to π t , taking the next action according to π t+1 , and so on.
Sentence 2: if θ * = arg min θ T (θ), then [1] presents a polynomial time algorithm that finds θ so that T (θ) ≤ (n + 1)T (θ * ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The DAE log-likelihood bound with and without walkback is respectively -116 and -142, confirming visual inspection suggesting that the walkback algorithm produces less spurious samples.
Sentence 2: algorithm 2: THE WALKBACK ALGORITHM is based on the walkback corruption process C( X|X), defined below in terms of a generic original corruption process C( X|X) and the current model's reconstruction conditional distribution P (X| X).
Relationship: neutral
Domain: NeurIPS
Sentence 1: However, they tend to struggle when data is scarce or when they need to adapt to new tasks within a few numbers of steps.
Sentence 2: the key idea behind MetaGAN is that imperfect generators in GAN models can provide fake data between the manifolds of different real data classes, thus providing additional training signals to the classifier as well as making the decision boundaries much sharper.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any v ∈ V , For any v ∈ V and l ∈ Lemma 1, which can be proved by FKG inequalities, suggests that given p l−1 (u → v), we may compute an upper bound on the influence.
Sentence 2: we take this approach of generating a subnetwork from the original network, yet we avoid the significant gap between the bound and the influence by considering the following directed acyclic subnetwork, in which there is no backtracking walk.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Recall that λ ě λ max yields βpλ,Ωq " 0, in which case ρ :" y ´X βpλ,Ωq " y is the optimal residual and y{λ max is the dual solution.
Sentence 2: the dual solution θpλ,Ωq is unique, while the primal solution βpλ,Ωq might not be.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is well-known that f * (z) = 1 2 z 2 .
Sentence 2: we show that for each X T g θ ∈ D α g , Fenchel's duality naturally leads to an explicit decomposition X T g θ = b 1 + b 2 , with one belonging to α √ n g B and the other one belonging to B ∞ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: To get even better initialization, we perform our initial optimization with a large degradation noise estimate (σ n = 2.5) and then perform the optimization with a lower estimate (σ n = 1).
Sentence 2: we explicitly use the Gaussiansmoothed natural image distribution as a prior, and we show that we can learn the gradient of its logarithm using a denoising autoencoder.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We denote their entries by a i , a i,j , a i,j,k , etc., depending on the number of dimensions.
Sentence 2: for any t such that λ t+1 < λ t , we have (σ t , {w  We evaluate the effectiveness and efficiency of our method SURF through numerical experiments on both synthetic and real data, and compare with various state-of-the-art regression methods, including LASSO, Elastic Net (ENet), Regularized multilinear regression and selection (Remurs) [Song and Lu, 2017], optimal CP-rank Tensor Ridge Regression (orTRR) [Guo et al., 2012], Generalized Linear Tensor Regression Model (GLTRM) [Zhou et al., 2013], and a variant of our method with Alternating Convex Search (ACS) estimation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If a 'state vector' is now defined to be the n-dimensional vector it is readily seen that x(t) is a basis for the stationary oblique predictor space X t := Y φ+ t / U φ+ t P φ t , which, on the basis of general geometric principles, can be shown to be a minimal state space for the process φ y (y), as in the linear case [3,5].
Sentence 2: ( 20)) and define the following matrices consisting of N − 1 columns: Xl+1 = Xl (:, 2 : N ), Xl = Xl (:, 1 : N − 1).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We make this comparison with continuous variables by discretely relaxing continuous priors using a discrete prior with a finite support set that contains much of the structure and information as its continuous analogue.
Sentence 2: we can go beyond this to additionally reduce computational and energy demands for the evaluation of Φ ¦ W. One approach is to constrain the elements of s w to be 0 or a power of 2 so that multiplication operations simply become efficient bit-shift operations [25][26][27].
Relationship: neutral
Domain: NeurIPS
Sentence 1: However, since x is arbitrary, ∂g(P f (x)) = ∂g(z) ⊇ ∂g(x) if g is not linear.
Sentence 2: since both P f and P g are increasing and nonexpansive, it follows easily that so is P f • P g , hence the existence of h ∈ Γ 0 so that P h = P f • P g . In a general Hilbert space H, we again easily conclude that the composition P f • P g is always a nonexpansion, which means that it is "close" to be a proximal map.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Refinement: Temporally Constrained Clustering Spectral clustering methods are designed for an unordered "bag" of feature vectors, but, in our case, the temporal ordering of image is an important source of information.
Sentence 2: let C 1 (t) denote the class label for image t, and g(c) = f (ID(c)); c = 1 . . . n denote cluster centers.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Two common factors make the global VB solution attainable in PCA and LRSC: first, a large portion of the degrees of freedom that the VB approximation learns are irrelevant, and the optimization problem can be decomposed into subproblems, each of which has only a small number of unknown variables; second, the stationary condition of each subproblem is written as a polynomial system (a set of polynomial equations).
Sentence 2: bayesian learning is often obstructed by computational difficulty: the rigorous Bayesian learning is intractable in many models, and its variational Bayesian (VB) approximation is prone to suffer from local minima.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let q be our ideal distribution for q given by q(x, y, z|`= 1) = f X,Y,Z (x, y, z), q(x, y, z|`= 0) = f CI X,Y,Z (x, y, z) and q(`= 1) = q(`= 0) = 0.5.
Sentence 2: if the classifier has accuracy close to random guessing, then f X,Y,Z (.)
Relationship: neutral
Domain: NeurIPS
Sentence 1: Comparison with Sample Complexity of Proposed Method: For Ising models, under uniform sampling of observed nodes, we established that the sample complexity of the proposed method scales as n = Ω(∆ 2 ρ −2 (log p) 3 ) for regular graphs with degree ∆.
Sentence 2: we employ latent graphical models for topic modeling.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Just as in the analyses of particle dynamics in dissipative quantum mechanics [4] we anticipate that the time-course of α(t) may exhibit qualitatively different types of behavior depending on the strength of the non-local terms.
Sentence 2: it is well known that, at least in some regimes, the problem with dissipation has a phase transition to a truly localized state.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that the first of the above terms involves the data while the second one only involves the prior.
Sentence 2: a temporal latent function x(t) ∈ R Q (with Q D), governs an intermediate hidden layer when generating the data, and the dth feature from the data vector y n is then produced from x n = x(t n ) according to where f d (x) is a latent mapping from the low dimensional space to dth dimension of the observation space and β is the inverse variance of the white Gaussian noise.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The strongest results of this kind establish Õ(S Ô AT ) regret for particular algorithms [4,5,6] which is close to the lower bound ( Ô SAT ) [4].
Sentence 2: the vast majority of e cient reinforcement learning has focused upon the tabula rasa setting, where little prior knowledge is available about the environment beyond its state and action spaces.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any choice of parameters (θ, g), there is a resulting vector of marginals µ The marginal polytope M is now the set of all such vectors µ that are realizable under some distribution P (x), and the partition function can equally be expressed in terms of the marginals [7]: where H(µ) is the entropy of the distribution, ∆(µ) is the vector of disagreement probabilities with entries ∆(µ) i,j = xi =xj µ ij,xixj , and stack(θ, g) adds the elements of θ and g into a single vector so that the sum can be written as an inner product.
Sentence 2: the result are inference schemes that optimize rigorous bounds on the partition function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: light-tailed distribution) is one whose tail decays at least as fast as a Gaussian distribution (i.e., exponential decay).
Sentence 2: since ReLU operation is pointwise, we have the identity y " AGpzq " AσpW 2 σpW 1 zqq " σpAW 2 σpW 1 zqq.
Relationship: neutral
Domain: NeurIPS
Sentence 1: K subspaces (each of dimension at most r): U k denotes the basis spanned by k-th estimated subspace and O d⇥r ⇢ R d⇥r denotes the set of orthonormal matrices, i.e., U T U = I if U 2 O d⇥r .
Sentence 2: when initialized within a small constant distance to the true subspaces, our method converges to the global optima (and recovers true subspaces) in time linear in the number of points.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The time axis is discrete, with index n = 1, 2, .... At stage n, the following events occur: (i) the input instance is presented to the classifiers (but not to the agent); (ii) each classifier a ∈ A outputs f n (a) ∈ [0, 1], which is the probability of the input to belong to class 1, and simultaneously the agent chooses a classifier a n ; and (iii) the correct label of the instance, b n ∈ {1, −1}, is revealed.
Sentence 2: we have two classifiers, and we assume that the outputs of these classifiers lie in the set ≥ λ such that γ 1 > γ, γ 2 < γ, and λ ≥ 0.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the generative process, the hidden variable of feature f m for an object y t , F m t ∼ Bernoulli(a To compute the probability of the feature matrix F 6 , in which the parameters a and b are integrated out analytically, we use the counting variables c 00 m , c 01 m , c 10 m , and c 11 m to record the 0 → 0, 0 → 1, 1 → 0, and 1 → 1 transitions f m has made in the binary chain m. The stochastic process that derives the probability distribution in terms of these variables is defined as follows.
Sentence 2: to employ the H&K's model for tasks that require clustering objects with rich linguistic features (such as event coreference resolution), or to extend this model in order to enclose additional observable properties is a challenging task [22,25].
Relationship: neutral
Domain: NeurIPS
Sentence 1: r t (π) = E[ρ t ] where ρ t is drawn from the distribution r(s t ).
Sentence 2: restricting D to probability measures on (0, 1) and applying Lemma 1, we get To finish the proof, we note that γ < 1 and, by definition, We use the MDP of the previous section with a different policy class which we now describe.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If the primate visual system uses recurrence in lieu of greater network depth to perform object recognition, then a shallower recurrent model with a suitable form of recurrence should achieve recognition accuracy equal to a deeper feedforward model [Liao and Poggio, 2016].
Sentence 2: cNNs trained to recognize objects in the ImageNet dataset predict the time-averaged neural responses of cortical neurons better than any other model class.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then the exposure process is given by E(t) = B N (t).
Sentence 2: suppose Ψ : [0, T ] → R n×n is a non-increasing matrix function, then for every fixed constant intensity if and only if Ψ(t) satisfies if where The next theorem shows that if Ψ(t) satisfies ( 7), then one can calculate η(t) for piecewise constant intensity µ : [0, T ] of form (9).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The complexity of ECOC with a code of length l and code-distance δ is at most Õ(dl) and at least dδ/2.
Sentence 2: in many practical applications, we will prefer not to employ kernels (either because of shortage of examples, which might lead to a large estimation error, or due to computational constraint), and in such cases we expect to see a large difference between the methods.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Finally, given the forces acting on the bodies at time t, f t , and the collision coefficient c, the constrained dynamics can be formulated as the following mixed LCP  where [a, , ⇣] T are slack variables for the inequality constraints, and [v t+dt , e , c , f , ] T are the unknowns.
Sentence 2: the model is able to learn the paddle parameters quickly from random trajectories, improving the control precision, and leading to high reward, as shown in Figure 6 Figure 5: Even though the baseline is able to achieve lower MSE over one-step predictions of the dynamics of the Cartpole environment (left), the physics engine-based controller is able to achieve a higher reward very quickly (right).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Mixture models and nonparametric family [Jaakkola and Jordon, 1999, Gershman et al., 2012, Dai et al., 2016a are the natural generalization.
Sentence 2: the most important difference is that CVB couples the adversarial component with original models through optimization embedding, which is flexible enough to approximate the true posterior and promote the learning sample efficiency.
Relationship: neutral
Domain: NeurIPS
Sentence 1: An intuitive way of achieving this is by studying the odds of r t+1 ∈ {0, r + 1} conditional on r t = r: p(r t+1 = r + 1|y 1:t+1 , r t = r, m t ) p(r t+1 = 0|y .
Sentence 2: conversely, as β → 0, one recovers the KLD which cannot treat any observation as an outlier.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Hence H satisfies this weak-learning condition.
Sentence 2: let C ⊆ R m×k and matrix B ∈ R m×k , which we call the baseline; we say a weak classifier space H satisfies the condition (C, B) if In ( 2), the variable matrix C specifies how costly each misclassification is, while the baseline B specifies a weight for each misclassification.
Relationship: neutral
Domain: NeurIPS
Sentence 1: An alternative strategy followed by some other methods relies on selecting a subset of the MRF nodes at each scale (based on some criterion) and then fixing their labels according to the optimal solution estimated at the current scale (essentially, such methods contract the entire label set of a node to a single label).
Sentence 2: here we will also make use of a pruned solution space S(M, A), which is defined based on a binary function A : V × L → {0, 1} (referred to as the pruning matrix hereafter) that specifies the status (active or pruned) of a label for a given vertex, i.e., During optimization, active labels are retained while pruned labels are discarded.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This extends learning kernel ideas and helps explore kernel combinations leading to better performance.
Sentence 2: for any such stationary point µ ⋆ , F (µ ⋆ ) = y ⊤ (K µ ⋆ + λI) −1 y = y ⊤ y λ , which is clearly a maximum.
Relationship: neutral
Domain: NeurIPS
Sentence 1: So, with high probability this overcomes the at most γ 8 m x incorrect bias of neighbors that have already updated, and so the points will indeed update correctly as desired.
Sentence 2: because of the high noise rate, learning this function directly would require a very large number of queries to be made (for noise rate η, one would necessarily require Ω( paper is to what extent this difficulty can be alleviated by providing the agents the ability to engage in a small amount of local communication among themselves.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Definition 4 (Factored Dec-POMDP).
Sentence 2: . . , t k }, and a collection of binary and vertical compatibility relations between tiles H, V ⊆ L × L. A tiling is a mapping of board locations to tile-types, t : {0, . . . , n − 1} × {0, . . . , n − 1} → L; such a tiling is consistent just in case (i) the origin location of the board receives tile-type 0 (t(0, 0) = tile 0 ); and (ii) all adjoint tile assignments are compatible: (∀x, y) t(x, y), t(x + 1, y) ∈ H & t(x, y), t(x, y + 1) ∈ V. The TILING problem is thus to decide, for a given instance, whether such a consistent tiling exists.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Following [5], we can model the linear term directly in the quadratic term if we augment all data points with an extra feature of value 1, i.e., x T ← [1, x T ].
Sentence 2: when Ω(•) = • 1 , we need to solve It is well known that the optimal solution of max h∈H |h T Γ c h| is the dominant eigenvector of Γ c . we simply need to find the dominant eigenvector h c of each Γ c and select ĥ as the h c with largest singular value |h T c Γ c h c |.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We thus evaluate our method in two different settings using existing datasets: (1) we validate our 3D pose predictions using Human3.6M [13] which provides accurate 3D and 2D poses for 15 different actions captured in a controlled indoor environment; (2) we evaluate on Leeds Sport dataset (LSP) [16] that presents in-the-wild images together with full-body 2D pose annotations.
Sentence 2: we train an end-to-end CNN classifier for 3D pose estimation and show that, with our synthetic training images, our method outperforms state-of-the-art results in terms of 3D pose estimation in controlled environments and shows promising results for in-the-wild images (LSP).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Inhibitive interaction, Θ = π/2 Excitatory interaction, Θ =0 Physiological experiments [2][3] have demonstrated that the neuronal activities in the classical receptive field are suppressed by responses outside the CRF to stimuli with similar motions including both directions and speeds on the center and surrounding regions.
Sentence 2: the phase tuning can give a good classification of velocity differences.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To provide for an expressive dynamics model, we can represent the parameters of this distribution (e.g., the mean and covariance of a Gaussian) as nonlinear, parametric functions of the current state and action, which can be arbitrarily complex but deterministic.
Sentence 2: these approaches can be categorized by how they represent the state distribution: deterministic, particle, and parametric methods.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Steps 2-3, UCRL2 computes estimates pk (s |s, a) and rk (s, a) for the transition probabilities and mean rewards from the observations made before episode k. In Step 4, a set M k of plausible MDPs is defined in terms of confidence regions around the estimated mean rewards rk (s, a) and transition probabilities pk (s |s, a).
Sentence 2: when a learner explores suboptimal actions, this may take him into a "bad part" of the MDP from which it may take about D steps to reach again a "good part" of the MDP.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 4 Cutting-Plane Algorithm using Belief Propagation In the previous section we established that BP on a carefully designed GM using non-intersecting odd-sized cycles solves the MWM problem when the corresponding MWM-LP relaxation is tight.
Sentence 2: initially, set m 1→0 , m 0→1 by n 1→0 , n 0→1 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Now, using the Hammersley Clifford theorem [1] and assuming only up to pairwise clique potentials to be nonzero, the joint distribution over the labels x given the observations y can be written as, where Z is a normalizing constant known as the partition function, and -A i and -I ij are the unary and pairwise potentials respectively.
Sentence 2: the MAP estimates of the labels were obtained using graph-cuts for both the models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Ideally, we want the LML error to be of order 1 of less, since much larger errors could severely affect the results of a comparison (e.g., differences of LML of 10 points or more are often presented as decisive evidence in favor of one model [26]).
Sentence 2: we have shown on both synthetic and real model-fitting problems that, given a contained budget of likelihood evaluations, VBMC is able to reliably compute valid, usable approximations in realistic scenarios, unlike previous methods whose applicability seems to be limited to very low dimension or simple likelihoods.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 3 It is worth pointing out that in the tabular case, IMLinUCB reduces to CUCB [7], in the sense that the confidence radii in IMLinUCB are the same as those in CUCB, up to logarithmic factors.
Sentence 2: for ray graphs with ω = 0.8 and ω = 0.7, our estimated growth are respectively O(L 2.488 ) and O(L 2.467 ), which are again close to the expected O(L 4 ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: 9) using these samples: which is also log-concave and thus efficiently maximized for φ.
Sentence 2: the conditional intensities for the two cells are then given by where k y and k z are linear filters representing each cell's receptive field, h yy and h zz are filters operating on each cell's own spike-train history (capturing effects like refractoriness and bursting), and h zy and h yz are a filters coupling the spike train history of each neuron to the other (allowing the model to capture statistical correlations and functional interactions between neurons).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Unfortunately, only one of the paired comparisons was statistically reliable by a two-tailed Bonferroni corrected t-test: (0, 1) versus x * (p = .027).
Sentence 2: figure 3b uses the PPF mean to estimate the optimum duration, and this duration is plotted against n requires a strategy for selecting the next experiment.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The off-policy evaluation problem satisfies the absolute continuity assumption if µ(s | x) > 0 whenever π(s | x) > 0 with probability one over x ∼ D. Using Assumption 1, we can now apply the techniques from the combinatorial bandit literature to our problem.
Sentence 2: 1 from the introduction shows that PI provides a consistent multiplicative improvement in RMSE over IPS, which suffers due to high variance.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, many tasks in computer vision can be naturally formulated in terms of energy minimization where the energy function has the form: , where θ p and θ p,q are univariate and pairwise potentials.
Sentence 2: proposition 1 provides the lower bound As stated in Section 4.5, T k can be deleted from further consideration when β k = ∞ or µ.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Besides, for the different random walk, we compute the corresponding transition matrix P t based on features from the different layer of similarity branch which represent different semantic levels, thus the information will be propagated gradually according to different levels' semantic similarities.
Sentence 2: this work was supported by the grants of National Natural Science Foundation of China (61702301), China Postdoctoral Science Foundation funded project (2017M612272), Fundamental Research Funds of Shandong University, National Natural Science Foundation of China (61332015) and National Basic Research grant (973) (2015CB352501).
Relationship: neutral