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<math>P(w|h)=\frac{e^{\sum_{k=1}^N \lambda_i f_i(s,w)}} {\sum_{w=1} e^{ \sum_{k=1}^N\l ...e\sum_{k=1}^N \lambda_i f_i(h,w)} {\sum_{w=1} e \sum_{k=1}^N\lambda_i f_i(h,w)}</math> ...

...egrate. Additionally, we would like to be able to compute the posterior $p(h\mid x)$ over hidden variables and, by Bayes' rule, this requires computatio ...his lower bound. Observe that, for any parametrized distribution $q_{\phi}(h\mid x)$, we have ...

...can be absorbed in the connections weights to the next layer. <math>\tilde{h}_j(\mathbf{x}) = h_1(\mathbf{x}) - h_2(\mathbf{x}) ...th>n_0</math> dimensional function <math>\tilde{h} = {[\tilde{h}_1, \tilde{h}_2, \ldots, ...

'''Proof''': Firstly, we need to establish <math>H</math> and <math>\pi</math> matrices commute. Since <math>H</math> is a centering matrix, we can write it as <math>H=I_{n}-11^{T}</math>. ...

...in both F and G simultaneously <ref name='S. S Lee'> Lee S. S and Seung S. H; “Algorithms for Non-negative Matrix Factorization”. </ref> Also, the facto ...rent value by some factor. In <ref name='S. S Lee'> Lee S. S and Seung S. H; “Algorithms for Non-negative Matrix Factorization”. </ref>, they prove tha ...

...nt to the eigenvalues of the Hessian matrix <math display="inline">\textbf{H}(f)</math> being bounded between <math display="inline">\alpha</math> and < ...y <math display="inline">H</math> iterations (where <math display="inline">H</math> is determined by <math display="inline">Q</math>). ...

...izing cursive handwriting <ref> A. Graves, S. Fernandez, M. Liwicki, H. Bunke, and J. Schmidhuber, [http://papers.nips.cc/paper/3213-unconstrai ...sis of the more complicated LSTM network that has composite <math>\mathcal{H}</math> functions instead of sigmoids and additional parameter vectors asso ...

...<math>g\,</math> reconstructs <math>x\,</math>. When <math>L\left(x,g\left(h\left(x\right)\right)\right)</math> denotes the average reconstruction error ...mathcal{J}_{AE}\left(\theta\right) = \sum_{x\in\mathcal{D}}L\left(x,g\left(h\left(x\right)\right)\right) </math> ...

...layer output matrix <math>\mathbf{H}</math> of ELM is given as: <math>{\bf H}=\left[\begin{matrix} {\bf h}({\bf x}_1)\\ ...

.../filter size to be 4*H and the number of attention heads to be H/64 (where H is the size of the hidden layer). Next, we explain the changes that have be ...which usually is harder. However, if we increase <math display="inline">\\H</math> and <math display="inline">\\E</math> together, it will result in a ...

variables H in addition to X, with the Markov chain state (and mixing) involving both X and H. Here H is the angle about ...

...is the <math>0^{\text{th}}</math> layer and the output layer is the <math>H^{\text{th}}</math> layer). The input <math>X</math> is a vector with <math> ...dom network output <math>Y</math> is <math>Y = q\sigma(W_H^{\top}\sigma(W_{H-1}^{\top}\dots\sigma(W_1^{\top}X)))\dots),</math> where <math>q</math> is a ...

...selects whether the hidden state is to be updated with a new hidden state h˜. The reset gate r decides whether the previous hidden state is ignored. ]] ::<math> r_j=\sigma([\mathbf{W}_r\mathbf{x}]_j+[\mathbf{U}_r\mathbf{h}_{t-1}]_j )</math> <br/> ...

The vocabulary is represented by a matrix <math> \mathbf{E}\in \mathbb{R}^{h \times v} </math> with a look up layer, denoted by the embedding <math> e_\ ...define the local context unit <math> \mathbf{K}_{\omega_i}\in \mathbb{R}^{h\times\left (2c+1\right )}</math>. Let <math> \mathbf{K}_{\omega_i,t} </math ...

...ight matrix from the projection layer to the hidden layer and the state of H would be: <math>\,h=tanh(Ha + b)</math> where A is the concatenation of all <math>\,a_i</math> ...

...ode G which passes the ball to nodes I & D. Node F passes the ball to node H which passes the ball to the already visited node, I. Therefore all nodes a H ...

...dentically distributed), <math>X</math> and associated hidden labels <math>H</math> are generated by the following model: $$P(X, H) = \prod_{i = 1}^N P(X_{i,1}, \dots , X_{i,N_i}| H_i)P(H_i) \quad \quad \ ...

...ngle af+bg,h\rangle=a\langle f,h\rangle+b\langle g,h\rangle,\,\forall\,f,g,h\in\mathcal{F}</math> and all real <math>\,\!a</math> and <math>\,\!b</math> ...f\otimes g)h:=f\langle g,h\rangle_{\mathcal{G}} \quad</math> for all <math>h\in\mathcal{G}</math> ...

<math>(f\otimes g)h:=f<g,h>_\mathcal{G}</math> for all <math>h\in \mathcal{G}</math> where <math>H,K,L\in \mathbb{R}^{m\times m},K_{ij}:=k(x_i,x_j),L_{i,j}:=l(y_i,y_j) and H_ ...

[3] H. B. McMahan. Follow-the-regularized-leader and mirror descent: Equivalence [4] T. Mikolov, A. Deoras, D. Povey, L. Burget, and J. H. Cernocky. Strategies for training large scale neural network language mode ...