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40
Semantic Compositionality through Recursive MatrixVector Spaces
"... Singleword vector space models have been very successful at learning lexical information. However, they cannot capture the compositional meaning of longer phrases, preventing them from a deeper understanding of language. We introduce a recursive neural network (RNN) model that learns compositional ..."
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Cited by 183 (11 self)
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. This matrixvector RNN can learn the meaning of operators in propositional logic and natural language. The model obtains state of the art performance on three different experiments: predicting finegrained sentiment distributions of adverbadjective pairs; classifying sentiment labels of movie reviews
Generating Text with Recurrent Neural Networks
"... Recurrent Neural Networks (RNNs) are very powerful sequence models that do not enjoy widespread use because it is extremely difficult to train them properly. Fortunately, recent advances in Hessianfree optimization have been able to overcome the difficulties associated with training RNNs, making it ..."
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Cited by 73 (3 self)
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for such tasks, so we introduce a new RNN variant that uses multiplicative (or “gated”) connections which allow the current input character to determine the transition matrix from one hidden state vector to the next. After training the multiplicative RNN with the HF optimizer for five days on 8 highend Graphics
A PARALLEL ALGORITHM FOR COMPUTING THE GROUP Inverse Via Perron Complementation
, 2005
"... A parallel algorithm is presented for computing the group inverse of a singular M–matrix of the form A = I − T, where T ∈ R^n×n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer’s Perron complementation approach to computing the Perron vector of an irreducible nonne ..."
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A parallel algorithm is presented for computing the group inverse of a singular M–matrix of the form A = I − T, where T ∈ R^n×n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer’s Perron complementation approach to computing the Perron vector of an irreducible
Inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation
"... In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors {xi} m i=1 in Cn and a set of complex numbers {λi} m i=1, find a centrosymmetric or centroskew matrix C in Rn×n such that {xi} m i=1 and {λi} m i=1 are the eigenvectors and eig ..."
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In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors {xi} m i=1 in Cn and a set of complex numbers {λi} m i=1, find a centrosymmetric or centroskew matrix C in Rn×n such that {xi} m i=1 and {λi} m i=1 are the eigenvectors
1. Statement of the Problem and Formulation of the Results
"... Abstract. Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations dx(t) = dA(t) · x(t) + df(t), where A: R+ → Rn×n and f: R+ → Rn (R+ = [0,+∞ [ ) are, respectively, matrix and vecto ..."
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Abstract. Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations dx(t) = dA(t) · x(t) + df(t), where A: R+ → Rn×n and f: R+ → Rn (R+ = [0,+∞ [ ) are, respectively, matrix
AN INVERSE ITERATION METHOD FOR EIGENVALUE PROBLEMS WITH EIGENVECTOR NONLINEARITIES
"... Abstract. Consider a symmetric matrix A(v) ∈ Rn×n depending on a vector v ∈ Rn and satisfying the property A(αv) = A(v) for any α ∈ R\{0}. We will here study the problem of finding (λ, v) ∈ R × Rn\{0} such that (λ, v) is an eigenpair of the matrix A(v) and we propose a generalization of inverse i ..."
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Abstract. Consider a symmetric matrix A(v) ∈ Rn×n depending on a vector v ∈ Rn and satisfying the property A(αv) = A(v) for any α ∈ R\{0}. We will here study the problem of finding (λ, v) ∈ R × Rn\{0} such that (λ, v) is an eigenpair of the matrix A(v) and we propose a generalization of inverse
Reducible spectral theory with applications to the robustness of matrices in maxalgebra
, 2009
"... Let a ⊕ b = max(a, b) and a ⊗ b = a + b for a, b ∈ R: = R ∪ {−∞}. By maxalgebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗), extended to matrices and vectors. The symbol Ak stands for the kth maxalgebraic power of a square matrix A. Let us denote by ε t ..."
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Cited by 11 (3 self)
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Let a ⊕ b = max(a, b) and a ⊗ b = a + b for a, b ∈ R: = R ∪ {−∞}. By maxalgebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗), extended to matrices and vectors. The symbol Ak stands for the kth maxalgebraic power of a square matrix A. Let us denote by ε
On sampling lattices with similarity scaling relationships
"... We provide a method for constructing regular sampling lattices in arbitrary dimensions together with an integer dilation matrix. Subsampling using this dilation matrix leads to a similaritytransformed version of the lattice with a chosen density reduction. These lattices are interesting candidates ..."
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Cited by 1 (1 self)
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candidates for multidimensional wavelet constructions with a limited number of subbands. 1. Primer on sampling lattices and related work A sampling lattice is a set of points {Rk: k ∈ Zn} ⊂ Rn that is closed under addition and inversion. The nonsingular generating matrixR ∈ Rn×n contains basis vectors
1. Statement of the Problem and Formulation of the Main Results
"... Abstract. Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem dx(t) = dA(t) · f(t, x(t)), xi(ti) = ϕi(x) (i = 1,..., n), where x = (xi) n i=1, A: [a, b] → Rn×n is a matrixfunction with bounded variation components, f: [a, b] ..."
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Abstract. Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem dx(t) = dA(t) · f(t, x(t)), xi(ti) = ϕi(x) (i = 1,..., n), where x = (xi) n i=1, A: [a, b] → Rn×n is a matrixfunction with bounded variation components, f: [a, b
CIRCULAR LAW FOR RANDOM MATRICES WITH UNCONDITIONAL LOGCONCAVE DISTRIBUTION
"... Abstract. We explore the validity of the circular law for random matrices with non i.i.d. entries. Let A be a random n×n real matrix having as a random vector in Rn×n a logconcave isotropic unconditional law. In particular, the entries are uncorellated and have a symmetric law of zero mean and unit ..."
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Abstract. We explore the validity of the circular law for random matrices with non i.i.d. entries. Let A be a random n×n real matrix having as a random vector in Rn×n a logconcave isotropic unconditional law. In particular, the entries are uncorellated and have a symmetric law of zero mean
Results 1  10
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40