4.2.2 INDEPENDENCE CRITERION

$$\mathbb{Z}$$

  

![0_image_0.png](0_image_0.png)

$$\frac{\partial\quad Z}{\partial\theta_{i}}\equiv0$$ $$\quad Z$$
$$\frac{\partial}{\partial\theta_{i}}\left(\begin{array}{c c c}{{}}&{{}}&{{}}\\ {{}}&{{Z}}\ +\sum_{n}^{l}\frac{}{n!}k_{n}\ \Delta H}\end{array}\right)\equiv0$$
$$\mathbf{U}$$

## 5. Boltzmann Machines

$$\mathbf{j}$$
$$\begin{array}{r l}{\mathrm{D}}&{{}\mathrm{ff}}\\ {s_{i}\;\in\;\{0,\;\;\}}\end{array}$$
$$\begin{array}{c c c}{{H}}&{{s\ \ w}}&{{\quad\sum_{i}w_{i}\,s_{i}\,+\,-\sum_{i,j}w_{i j}\,s_{i}\,s_{j}}}\\ {{}}&{{}}&{{}}\\ {{w_{i j}\,\equiv\,w_{j i}\quad}}&{{\quad w_{i i}\,\equiv0\quad\mathrm{U}}}\end{array}$$
$$\mathrm{{H}}$$

U

$$\mathbf{T}^{\prime}$$

f