sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: The core consists of a three-layer, 2d convolutional neural network (CNN), applied separately to each frame, followed by a convolutional Gated Recurrent Unit (GRU) [14].
Sentence 2: we also demonstrate that the nonlinear feature representation learned on natural movies can transfer well to the noise domain by fine-tuning the last layer's weights, while the converse is not true (i. e. generalization from noise to movies).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In addition, H matrices enable a significant space advantage: since the fast Walsh-Hadamard transform can be computed without explicitly storing H, only O(n) space is required to store the diagonal elements of (D i ) k i=1 .
Sentence 2: we consider the variant S-Hybrid random matrix below, where D (U ) k is a diagonal matrix with iid Unif(S 1 ) random variables on the diagonal, independent of (D (R) i ) k−1 i=1 , and S 1 is the unit circle of C. We use the real part of the Hermitian product between projections as a dot-product estimator; recalling the definitions of §2, we use: Remarkably, this complex variant yields exactly half the MSE of the OJLT estimator.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We apply Theorem 1 noting that Ψ AM (u, v, p) = (u+v)/2 is continuous in all its arguments, and that the Bayes optimal classifier for P AM is of the requisite thresholded form.
Sentence 2: while there has been considerable amount of work on consistency of algorithms for univariate performance measures [16,[20][21][22], theoretical results on non-decomposable measures have been limited to characterizing the Bayes optimal classifier for F-measure [15,23,24], and some consistency results for F-measure for certain idealized versions of the empirical plug-in and decision theoretic methods that have access to the true class probability [15].
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Fig 2 , we report two values, W k 2 − (I − W k 1 A) 2 and θ k , obtained by the baseline LISTA model (4) trained under the noiseless setting.
Sentence 2: the training is modeled as: Many empirical results, e.g., [3][4][5][6][7], show that a trained K-layer LISTA (with K usually set to 10 ∼ 20) or its variants can generalize more than well to unseen samples (x , b ) from the same P(x, b) and recover x from b to the same accuracy within one or two order-of-magnitude fewer iterations than the original ISTA.
Relationship: neutral
Domain: NeurIPS
Sentence 1: • Optionally: If we have additional meta-information z, then the above mentioned networks could be conditioned to obtain the conditioning mapping φ(x m |z).
Sentence 2: their extensions to handle the case when the inputs or outputs are permutation invariant sets rather than fixed dimensional vectors is not trivial and researchers have only recently started to investigate them [5][6][7][8].
Relationship: neutral
Domain: NeurIPS
Sentence 1: For both languages, we extracted the following emission features: indicators for the words, their prefixes and suffixes of length 3, the previous and next words and the word shape according to the Stanford NLP pipeline 2,3 .
Sentence 2: in the English case, we found that the performance plateaued for any label matrix with rank greater than 20 and we see an improvement of 0.5% accuracy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, the work of [4] assumes the Bouquet Model where distributions are restricted to be isotropic Gaussians whereas the work of [5] assumes a more stringent model of sub-orthonormal matrices, something that even Gaussian designs do not satisfy.
Sentence 2: even after allowing the L 1 algorithm to run for 500 iterations, it was unable to reach the desired residual error of 10 −4 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: D = 0), or used spike history mapped to a set of 4 basis functions formed by othogonalising decaying exponentials with time constants 0.1, 10, 20, 40ms (similar to those used in [1]).
Sentence 2: it is important to note that the Gaussian model has free parameters for the singleneuron variability, whereas the conditional variance of the Poisson model is constrained to equal the mean.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The generator uses the loss E Z∼P Z D(G(Z)).
Sentence 2: for example, if we assume that d is not bounded from below and consider two points x, y ∈ M that are sufficiently close then a penalty term of the Lipschitz quotient as in (12) imposes a condition on the differential around x and y in the direction (x − y) only, i.e.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We propose a non-parametric Bayesian framework for modeling collections of such data.
Sentence 2: as the discrete Poisson distribution is characterized by a rate parameter λ, the Poisson process 1 is characterized by a rate function λ(t); it has the property that over any given time interval T , the number of events occurring within that time is Poisson with rate given by λ = T λ(t).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Semidefinite optimization can be described as the problem of optimizing a linear function of a symmetric matrix subject to linear equality constraints and the condition that the matrix be positive semi-definite.
Sentence 2: as expected the maximal-alignment kernels' spectral transformation is zigzagged, diffusion and Gaussian field's are very smooth, while order constrained kernels' are in between.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This connection to generative models is very powerful, and can easily be extended to include missing data-one of the large advantages of generative models in machine learning.
Sentence 2: the expectation error ) over both the distribution of x and the distribution of nearest neighbor x N N for a given x: We then replace the posteriors p(C|x) and p(C|x N N ) as p c (x)/(p 1 (x) + p 2 (x)) and p c (x N N )/(p 1 (x N N ) + p 2 (x N N )) respectively, and approximate the expectation of the posterior x at a fixed distance d N from test point x using pc (x)/(p 1 (x) + p2 (x)).
Relationship: neutral
Domain: NeurIPS
Sentence 1: On one hand, from the table, we can see that our framework TLRisk greatly outperforms the baseline methods Image Only and Search+Image, no matter which dissimilarity function is applied.
Sentence 2: first of all, the loss function L(θ C , θ Xt , r = 1) can be formulated using distance functions between the two models θ C and θ Xt , so that Since the sizes of Θ C and Θ Xt are exponential in general, we cannot calculate Equation (3) straightforwardly.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 1 e ⌦(n 1/2 ) for all i 2 [m]: Now, let F 0 be the collection of all functions f j for which f j (S i ) = 1/2 + |S i |/(2n) on all sets {S i } m i=1 .
Sentence 2: the algorithm cannot learn any information about which function in F 0 generates the samples.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The solution is well known when λ = 0 since it corresponds exactly to the rescaled Chebyshev polynomial [Golub and Varga, 1961], but as far as we know there is no known result about its regularized version, thus making the "finite-step" version hard to analyze.
Sentence 2: if we wait at least O(N ) updates, then the extrapolation method is of the same order of complexity as the optimization algorithm.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In , the convergence rate for a time-varying topology was proved when the maximum of the subgradient is assumed to be bounded.
Sentence 2: eCD-PSGD is more robust to more aggressive quantization, as extremely low precision quantization can cause DCD-PSGD to diverge, since DCD-PSGD has strict constraint on quantization.
Relationship: neutral
Domain: NeurIPS
Sentence 1: I consider the usual Bayesian setup of supervised learning: A training set DN = {(Xi, y; ) Ii = 1 ... , N} (x E Rd and y E R) is known and the output for the new input x is predicted by the function f(x) which is sampled from the prior distribution of model outputs.
Sentence 2: for the simulations, I use analytical GP learning (scaling like CJ (N 3 )) [4] and a TAP mean field algorithm for Bayesian NN.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since the first betting round is a small portion of the entire game, storing a value for each state in a table required just 42 MB.
Sentence 2: while DeepStack defeated a set of non-elite human professionals in HUNL, it never defeated prior top AIs despite using over one million core hours to train the agent, suggesting its approach may not be sufficiently efficient in domains like poker.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since in the experimental section we do not exploit the solution to this problem for reasons that we will explain later, here we just sketch such procedure.
Sentence 2: we revise the theoretical approach presented in [13] by: i) giving a simpler and direct solution to the problem of devising an exact closed-form solution (full rank case) for the weights of a linear autoencoder network for sequences, highlighting the relationship between the proposed solution and PCA of the input data; ii) introducing a new formulation of the autoencoder learning problem able to return an optimal solution also in the case of a number of hidden units which is less than the rank of the full data matrix; iii) proposing a procedure for approximate learning of the autoencoder network weights under the scenario of very large sequence datasets.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Simple bounds to this quantity, like H , besides being hard to compute due to the presence of the supremum, are extremely conservative since the Rényi divergence is raised to the horizon H. We suggest the replacement of the Rényi divergence with an estimate )) defined only in terms of the policy Rényi divergence (see Appendix E.2 for details).
Sentence 2: a prime example of this alternating procedure is Proximal Policy Optimization (PPO) [44], that has displayed remarkable performance on continuous control tasks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In two typical cases using 500 and 5000 training points full GP runs in 0.24 seconds (for 500 training points) and in 34 seconds (for 5000 training points), VDMGP runs in 0.35 and 3.1 seconds while SPGP-DR runs in 0.01 and 0.10 seconds.
Sentence 2: 2 Available at http://theoval.cmp.uea.ac.uk/ ˜gcc/competition/ Temp: 106 dimensions 7117/3558 training/testing data, SO2: 27 dimensions 15304/7652 training/testing data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For an input image I and a given pair of kernels, we can measure the data log-likelihood by associating each window with the maximum likelihood kernel: We search for a blurring model p k0 such that, when combined with the model p 1 (derivatives of the unblurred image), will maximize the log-likelihood of the observed derivatives: One problem we need to address in defining the likelihoods is the fact that uniform areas, or areas with pure horizontal edges (the aperture problem) don't contain any information about the blur.
Sentence 2: yet, the histogram structure of different images is not identical, and we found that trying to deblur one image using the statistics of a different image doesn't work that well.
Relationship: neutral
Domain: NeurIPS
Sentence 1: There is a clear divide with improved performance from the Schatten-∞ based methods.
Sentence 2: letting Ũdiag(s) ṼT X represent the rank-k+ 1 approximate SVD, then the approximate #-operator corresponds to the low-rank approximation and the reweighted remainder, We note that the #-operator is also defined for the ∞ norm, however, for notational clarity, we will denote this as x and leave the # notation for the Schatten-∞ case.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given a domain X and covariance function K(•, •) ∈ X × X → R, a Gaussian process (GP) over the space of real-valued functions of X specifies the joint distribution at any finite set X ⊂ X : where the f = {f n } N n=1 are (latent) values associated with each x n ∈ X, and K ff is the Gram matrix, the evaluation of the covariance function at all pairs (x i , x j ).
Sentence 2: this is in contrast to the IVM, in which sites excluded from the active set have parameters clamped to zero, and where those included are not iterated to convergence, such that the necessary fixed point conditions do not hold.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that the original algorithm in [11] is designed for batch mode active learning.
Sentence 2: the evaluation function L(D l , D u , x s ) essentially consists of two components: L s,s − det(L a,a )/L s,s and Minimizing the first component is equivalent to minimizing L s,s because L a,a is independent from the selected instance x s . Since L = (K +λI) −1 , we have to choose an instance with small L s,s , we select the instance with large self-similarity K s,s .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Acknowledgements -Thanks to Paul Hoyer, Jarmo Hurri, Bruno Olshausen, Liam Paninski, Phil Sallee, Eero Simoncelli, and Harri Valpola for discussions and comments.
Sentence 2: although it is clear that the variability degrades performance on many perceptual tasks of the laboratory, it might well be that it plays an important function in everyday sensory tasks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The model is constructed according to the principle of separation of time scales: processes that operate in the 100-1000 ms range are modeled as accurately as possible, those that vary on a much shorter time scale are assumed to instantaneously achieve their steady-state values, and those that occur over longer time scales, such as slow inactivation, are assumed constant.
Sentence 2: dopamine release results in the amplification of key ion currents, leading to the emergence of bistability, which not only modulates the peak firing rate but also introduces a temporal and state dependence of the model's response, thus improving the detectability of temporally correlated inputs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We randomize the procedure in the following manner: (i) C ∼ W(p, I p×p ), (ii) x i ∼ N (0, C), (iii) q ∼ B(1, 1) for the first and q ∼ B(1, 4) for the second cases, (iv) I(j ∈ A) ∼ Bernoulli(q) for j = 1, . . . , p where I(.)
Sentence 2: [12] choose to further mix over a and a global λ while fixing the values of b and φ.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While we cannot prove that the algorithms converge to the minimum, in all the applications we have tried, they perform very well.
Sentence 2: the interesting thing about this experiment is the fact that no filter ever is allowed to see global information, except through S. even though W is blind to anything larger than a 16 × 16 patch, through the inhibition of S, the model is able to learn the placement of facial structures and long edges.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To circumvent these issues we explicitly incorporate the prior knowledge that a neuron only reads out from one particular location in space and model each neuron with a spatial transformer layer [19] with a single grid point reading from v ijk .
Sentence 2: we optimized the objective using ADAM [43] and a two stage training schedule with step size 0.005 and 0.001, respectively.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The condition ŷj , ĝj > 0 holds as long as the negative gradient ĝj is pointing towards the minimum of the loss (w.r.t.
Sentence 2: in fact, there are now a number of works that provide alternatives to BatchNorm [1,3,13,31], but none of them seem to bring us any closer to understanding this issue.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We set the "width" parameter in the Gaussian kernel to be the mean of all pair-wise training data distances, a standard heuristic.
Sentence 2: a similarity function K : X × X → R is said to be an ( , B)-good similarity for a learning problem with respect to a loss function L : R → R + where > 0 if for some transfer function f : R → R and some weighing function w : One can see that taking the loss functions as L(x) = 1 x<C f γ gives us Equation 3 which defines a good similarity under the 0−1 loss function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A good indication that this is not the case is that (2) is NP-hard, even in the noiseless case when ) for rank(X ⇤ )  k [20] (if we don't require RIP, we can have each A i be non-zero on a single entry in which case (2) becomes a matrix completion problem, for which hardness has been shown even under fairly favorable conditions [13]) 3 .
Sentence 2: for any stationary point U this implies Now using the isometry property of A i gives us the following result.
Relationship: neutral
Domain: NeurIPS
Sentence 1: There have been some examples of deployed active learning with human feedback; for human perception [11,17], interactive search and citation screening [18,19], and in particular by research groups from industry, for web content personalization and contextual advertising [20,21].
Sentence 2: for example, serving many (near) simultaneous 'getQuery' requests is straightforward; one can simply enlarge the pool of workers by launching additional slave machines and point them towards the web request queue, just like typical web-apps are scaled.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Theorem 1 For any τ, α ∈ (0, 1), every policy tree π ∈ Π b0,D,K satisfies with probability at least 1−τ , where Vπ (b 0 ) is the estimated value of π under any set of K randomly sampled scenarios for belief b 0 .
Sentence 2: regularization does not appear beneficial to this problem, possibly because it is mostly deterministic, except for the sensing action.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Recent research has combined (iii) and (iv) within a single model [6], and methods have been developed recently to address (v) while performing (iv) [5].
Sentence 2: in [6] model selection was performed (for the number of features and number of neurons) and a maximum likelihood (ML) "point" estimate was constituted for the model parameters; since a fixed number of clusters are inferred in [6], the model does not directly allow for the "appearance"/"disappearance" of neurons, or for any temporal dependence to the spike statistics.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We propose "Adept," an adaptive stimulus selection method that can optimize population objective functions.
Sentence 2: to examine how Adept performs in the presence of noise, we first recorded a "ground-truth", spike-sorted dataset in which 2,000 natural images were presented (100 ms flashes, 5 to 30 repeats per image randomly presented throughout the session).
Relationship: neutral
Domain: NeurIPS
Sentence 1: As is typical in supervised learning, in multiset prediction a model , then evaluated on a separate test set {(x i , Y i )} n i=1 using evaluation metrics m(•, •) that compare the predicted and target multisets, i.e.
Sentence 2: this is analogous to the experiments on MNIST Multi, where the performance gap increased when moving from four to ten digits.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The chosen action influences the observable state of the environment in a stochastic fashion and imposes some loss on the learner.
Sentence 2: aim to solve the optimization problem q t+1 = arg min q∈∆(M ) q, ˆ t subject to the constraint D (q q t ) ≤ ε for some ε > 0.
Relationship: neutral
Domain: NeurIPS
Sentence 1: From the definition of H − , we can choose f : For Part 3, first note that, for any φ, ψ is continuous on [0, 1] and ψ(0) = 0 by Lemma 4, part 6, and hence θ i → 0 implies ψ(θ i ) → 0.
Sentence 2: (1996), Mendelson (2002), but simpler.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is worth mentioning that models based on multinomial or Poisson likelihoods such as LDA [3], HDP [27], FTM [29] and PFA [32], also enjoy this property.
Sentence 2: in [32], h kn is provided with a beta-Bernoulli process prior by letting π kn = π k ∼ Beta(cǫ, c(1 − ǫ)), meaning that every document has on average the same probability of seeing a particular topic as active, based on corpus-wide popularity.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We experimentally validated that SING was able to embed music notes into a small dimension vector space where the pitch, instrument and velocity were disentangled when trained with this spectral loss, as well as synthesizing pairs of instruments and pitches that were not present in the training set.
Sentence 2: next are two 1x1 convolutions with 4096 channels and ReLU as an activation function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In order to address this shortcoming, in recent years several authors have proposed to learn object classifiers from weakly-labeled Internet images, such as photos retrieved by keyword-based image search engines.
Sentence 2: for each class k, we train a binary SVM on the data obtained by merging D t k with D s k , where the data in the latter set is assumed to contain only positive examples, i.e., no outliers.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, a human labelling of a short segment of the song could be automatically extrapolated to the remainder of the song, using energy spikes in the audio signal to fine-tune the placement of beats.
Sentence 2: the particle filter version produces 16 correct answers, two double-speed, two half-speed, two syncopated, and the same three 'switching' tracks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This lower bound follows from the minimax lower bound proofs for regression in the next section.
Sentence 2: let ∂D denote the boundary of D and define the set of boundary points as , where C o = 6 √ dκ 0 , then for all p ∈ P X , all pairs of points x 1 , x 2 ∈ supp(p) \ B and all D ∈ D, with probability > 1 − 1/m, for large enough m ≥ m 0 , where m 0 depends only on the fixed parameters of the class P XY (γ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: A Markov chain is defined using these affinities by setting the transition probability 3 4 (' ) from vertex 5) to vertex to be proportional to the edge affinity, 0 6 (' ) .
Sentence 2: as ¡ ¨ § © , the Markov chain approaches the stationary distribution x , ¢ ¥ x e . Assuming the graph is connected with edges having non-zero weights, it is convenient to interpret the Markovian relaxation process as perturbations to the stationary distribution, ) , where B ¥ § is associated with the stationary distribution x and x ) ¥ 2c B w x ) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our contribution is in proving that kernel quadratures can be consistent even when the integrand does not belong to the assumed RKHS, i.e., when the integrand is less smooth than assumed.
Sentence 2: then the points are defined as X i = {iz/n} ∈ [0, 1] d for i = 1, . . . , n. Here z is selected so that the resulting worst case error (2) becomes as small as possible.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Stepsizes for LAG-WK, LAG-PS, and GD are chosen as α = 1/L; to optimize performance and guarantee stability, α = 1/(M L) is used in Cyc-IAG and Num-IAG.
Sentence 2: the original idea of LAG comes from a simple rewriting of the GD iteration (2) as Let us view ∇L m (θ k )−∇L m (θ k−1 ) as a refinement to ∇L m (θ k−1 ), and recall that obtaining this refinement requires a round of communication between the server and the worker m. to save communication, we can skip the server's communication with the worker m if this refinement is small compared to the old gradient; that is, m ≥ 0, if communicating with some workers will bring only small gradient refinements, we skip those communications (contained in set M k c ) and end up with where M k and M k c are the sets of workers that do and do not communicate with the server, respectively.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Essentially, if this number is less than some Φ-dependent constant κ, the BP/OMP solution is proven to be equivalent to the minimum ℓ 0 -norm solution.
Sentence 2: we will henceforth refer to w SBL as the solution of this algorithm when initialized at Γ = I M and ŵ = Φ † t. 1 In [9] (which extends work in [10]), we have argued why w SBL should be considered a viable candidate for solving (1).
Relationship: neutral