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...comes from expanding the solution of the original problem in terms of the bottom eigenvectors of a graph laplacian. As the smaller SDPs coming from this fac <math>\,\min_{x_1,...,x_n}\Sigma_{i\sim j}{(\|x_i-x_j\|^2-d_{ij}^2)^2}</math> (1)<br /> ...

...the decoding strategies impact machine text. the author For example in the figure below, the GPT2 model tries to generate the continuation text given the con [[File: GPT2_example.png |caption=Example text|center |800px|caption position=bottom]] ...

[[File:figure_1_bengio.png |thumb|upright=1.75| Figure 1 Top: <ref>Bengio, Yoshua, Mesnil, Gregoire, Dauphin, Yann, and ´ Bottom: More generally, a GSN allows the use of arbitrary latent ...

...diagram of the difference in the architecture can be seen in the following figure. ...on (x-axis) and downsized to 32 x 32 (y-axis).|(Odena et al., 2016) Figure 2: (Left) Inception accuracy (y-axis) of two generators with resolution 128 x ...

...uction of the original input. This is analogous to learning a data-driven "bottom-up" representation of the input that is used to inform the higher-order "to [[File:Network.png |frame | center |Figure 1: The Helmholtz network structure. ]] ...

2) Visual relationship detection methods like message passing RNNs and predic 2) Vector embeddings to detect body joints of the various people in an image. ...

...prediction performance of methods is coefficient of determination (<math>R^2</math>). ...values of one or two parameters at a time, and then calculate the <math>R^2</math> for DNNs trained with the selected parameter settings. These results ...

...(p,q) \epsilon R_{ij}} (a_{kpq})</math> with everything defined as before. Figure 1 provides a numerical example that can be followed. ...he data is averaged with values of significantly lower intensities. Figure 2 displays an image of this. ...

...This is done by randomly nullifying features within images. Tramer et al [2], showed the state-of-the-art Ensemble Adversarial Training Method, which a [[File:non-targeted O.JPG| 600px|center]] ...

(2) What set of parameters, <math display="inline"> \vec{\lambda} </math>, bes ...iation is accomplished using a technique called automatic differentiation [2]. Importantly, the weights of the two neural networks will be shared, since ...

...esentations_for_Efficient_Architecture_Search#Primitive_operations section 2.3] are used to form small networks defined as ''motifs'' by the authors. To ...its bottom and only one complex motif at its top. Any motif in between the bottom and top levels can be defined as the composition of motifs in lower levels ...

...} J=\sum^K_{k=1}\sum_{\mathbf x \in C_k}\|\mathbf x - \boldsymbol{\mu}_k\|^2</math> ...math>\mathop{\min_{\mathbf Y}}K-tr(\mathbf{Y^{\rm T}(D^{\rm{1/2}}WD^{\rm{1/2}})Y})</math> ...

[[File:one-pixel-attack.jpg|500px|middle]] [[File:face2.jpg|200px|middle]] ...

2. Huang, Jingyue ...fication. It defines <math> region\left ( i,c\right ) </math> as the <math>2\times c+1</math> length region with middle word <math> \omega_i </math> whi ...

a_{t} =h_{t-1}^{cat} W^h + b^h \hspace{2cm} (2) [[File:StdRNN.png|650px|center||Figure 1: Recurrent Neural Network]] ...

2. The second idea is to train the system to not only produce a distribution .../en.wikipedia.org/wiki/Information_retrieval#Mean_average_precision mAP]). Figure 1 illustrates the higher difficulty of the detection process. ...

The following figure shows the network used to model the joint distribution The figure below shows a hybrid network where the top two layers have undirected conne ...

...be a random vector on <math>\,\Omega_{11}\times \Omega_{12} \times \Omega_{2}</math>, where <math>\,X = (U,V)</math>, and let <math>\,H_1 = H_{11} \otim ...decaying, as <math>\,W_{ij} = exp \left(\frac{- \|x_i - x_j \|^2}{\sigma^2}\right) </math>. Let D denote the diagonal matrix with elements <math>\, D_ ...

..._j ||^2/ 2\sigma_i ^2 )}{\sum_{k \neq i} \exp(-||x_i-x_k ||^2/ 2\sigma_i ^2 ) }</math> </center> ...q_{j|i} = \frac{\exp(-||y_i-y_j ||^2)}{\sum_{k \neq i} \exp(-||y_i-y_k ||^2) }</math> </center> ...

<math> \mathbf {E(F,G) = \|X-FG^T\|^2}</math> <math> J_{K-means} = \sum_{i=1}^n \sum_{k=1}^K g_{ik}||x_i-f_k||^2=||X-FG^T||^2 </math> ...