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TABLE OF CONTENTS
physics
Green functions for the initial-value problem
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machine learning
Cross-Stitch Network
Entire Space Multi-Task Model ESSM
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EQUATION LIST
physics
Green functions for the initial-value problem
#physics
#green functions
$$u(x,t)=\int\limits_{-\infty}^\infty f(x')Q(x,x',t)dx'+ \int\limits_{-\infty}^\infty g(x')P(x,x',t)dx'$$
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machine learning
Cross-Stitch Network
#machine learning
#multi task
$$\begin{bmatrix} \tilde{x}^{ij}_{A}\\\tilde{x}^{ij}_{B}\end{bmatrix}=\begin{bmatrix} a_{AA} & a_{AB}\\ a_{BA} & a_{BB} \end{bmatrix}\begin{bmatrix} x^{ij}_{A}\\ x^{ij}_{B} \end{bmatrix}$$
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Entire Space Multi-Task Model ESSM
#machine learning
#multi task
$$L(\theta_{cvr},\theta_{ctr})=\sum^{N}_{i=1}l(y_{i},f(x_{i};\theta_{ctr}))+\sum^{N}_{i=1}l(y_{i}\&z_{i},f(x_{i};\theta_{ctr}) \times f(x_{i};\theta_{cvr})) $$
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