Suppose we had a series of single-dimensional data points $X = \{x_1, x_2, \dots, x_n \}$, where $n$ is the number of data points and there corresponding output values $T = \{t_1, t_2, \dots, t_n \}$.

Now, I want to train a single neuron network given below to learn from the data (the model is bad, but I just wanted to try it out as an exercise).

Image for the Neural network model

The output function of this neuron would be a recursive function as:

$$ y = f(a_0 + a_1x + a_2 y) $$


$$ f(x) = \frac{1}{1 + e^{-x}} $$

for a given $x$.

The error function for such a model would be:

$$ e = \sum_{i=1}^N (y_i - t_i)^2 $$

How should I minimise this loss function? What are the derivatives that I need to use to update the parameters?

(Also, I am new to this problem, therefore it would be really helpful if you tell me sources/books to read about such problems.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.