I am studying a doctoral thesis on control-theory and have trouble understanding the notions and the notation introduced there. I am doing this out of interest on the subject, so I haven't had a related class to rely on.

It says that static neural networks can be described as $$ y=Z^T(x)\theta$$ where $y \in R^m ,x\in R^n ,\theta \in R^q,Z:R^n\rightarrow R^{q\times m}$ and Z is a continuous field that includes sigmoid functions.

I have actually taken Andrew Ng's ML course a few years ago. My problem is mainly the notation used here. Unfortunately the article I'm referring to is written in Greek, so you probably won't be able to understand it even if I post it.

For example, there is an unknown non-linearity $g(x)\in R^{m\times m }$ and it is stated that using neural networks we can approximate it as $$g(x)=g_a(x,\theta_g^*)+w_g(x)$$ where $w_g(x) \in R^{m \times m}$ is the modeling error and $$g_a(x,\theta_g^*)=\begin{bmatrix}Z_{g11}^T(x)\theta_g^* & \dots &Z_{g1m}^T(x)\theta_g^*\\\dots&\dots&\dots \\Z_{gm1}^T(x)\theta_g^* &\dots& Z_{mm}^T(x)\theta_g^*\end{bmatrix}$$ where $Z_{gij}:R^n\rightarrow R^{q_j}$ are continuous base functions (apparently sigmoid) but there is no other information on the form of $Z_{gij}$.Any idea what they might look like?


1 Answer 1


[Note: I don't have the "privilege" of adding this as a comment...]

If you're new to Neural Networks, I recommend these course notes and Andrew Ng's Machine Learning course over at Coursera (or, for that matter, the lecture notes from his class at Stanford).

Also, it may be helpful if you post the article to which you are referring...

  • $\begingroup$ Thanks for the reply...I updated my question!Could you take another look? $\endgroup$
    – Controller
    Jul 14, 2014 at 15:15

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