Globalization made the world flat, AI drills holes into the infinitesimally small

The function of deep learning

When approximation is the best we have

The function of deep learning

When approximation is the best we have

The function of deep learning

When approximation is the best we have

The function of deep learning

When approximation is the best we have

\[ f_4 : [0..255]^{3*n*n} \to \{0, 1\} \] \[ f_4(M)= \begin{cases} 0 & \sum_{i=1}^{n^2} f_3(V_i) \le \frac{n^2} 2 \\ 1 & \text{otherwise} \end{cases} = \] \[ = \begin{cases} 0 & \quad f_3(r_1,g_1,b_1) + f_3(r_2,g_2,b_2) + ... f_3(r_{n^2},g_{n^2},b_{n^2}) \le \frac{n^2} 2 \\ 1 & \quad otherwise \end{cases} \]

The function of deep learning

When approximation is the best we have

The function of deep learning

When approximation is the best we have

Source: Facial expression recognition and histograms of oriented gradients: a comprehensive study (2015)

The function of deep learning

When approximation is the best we have

\[ g : [0..255]^{3*n*n} \to \{0, 1\} \] Next

So let's take a step back and reconsider what we are trying to do. We a function defined like so:

We know that there is a mapping between the domain and the codomain.

We know, or we presume, that the mapping is deterministic and that there is a logic to it, that there is a reason a particular input leads to a particular output.

We just can't express it fully because of the relational and contingent way the image is interpreted.

There is no linear relation between any one feature and the mood of the piece. It could be an accumulation of elements; a feature could change in intensity without affecting the mood until, suddenly, it reverses it. But we can easily validate if the mapping has been done correctly.

So, what if we could, somehow, store the probability an input has to be mapped onto the desired output set, in a way that takes account of those nonlinear relations and interactions between the input parameters.

That is precisely what artificial neural networks do.