I've been studying Boltzmann machines lately and was wondering if anyone could give me a "high-level" explanation or motivation for the energy function used:
$$E = -\sum_{i<j} w_{ij} \, s_i \, s_j - \sum_i \theta_i \, s_i$$
where:
- $w_{ij}$ is the connection strength between unit $j$ and unit $i$,
- $s_i$ is the state, $s_i \in \{0,1\}$, of unit $i$.
- $\theta_i$ is the threshold of unit $i$
Why do we use this particular function? What is the motivation? Is it modelled after some real world phenomena? Could we use a different one?