Questions in Lecture 2 - Neural networks of machine learning

In the weight space view, the weights represent points while the inputs represent planes. Another term for what the inputs represent is:

Vectors

Constraints

正确 

We can think of the inputs as partitioning the space into two halves. Weights lying in one half will get the answer correct while on the other half they will give the incorrect answer (which half is determined by the output class). That is, the inputs will constrain the set of weights that give the correct classification results.

Weights

Space

True or false: assuming the input and weights are finite, just because a set of inputs has a feasible space does not mean that they also have a generously feasible space.generously means margin, it might be more flexible than a real one

True

False

正确 

Assuming that no three points are collinear, what is the minimum number of 2D inputs do we need before we can construct a dataset that the perceptron cannot solve? Note that with the bias these inputs will be 3D, but the extra dimension is trivially set to 1.

2

3

4

正确 

One way to see this is to write out a general linear system:

\left(

acebdf111

\right) ⎝⎛​ace​bdf​111​⎠⎞​

We can see that since no three points are collinear, this system must be invertible, meaning it is possible to satisfy any set of constraints defined by the variables. An impossible to solve case was shown in the lecture for 4 points.

5