Why is linear or problem inseparable


Why is the xor problem linearly indivisible?

When you read the textbook, it’s often said that perceptrons (single layer neural networks) can’t solve the xor problemWhy???


Perceptrons deal with linear problems

An xor problem is a nonlinear problem

What is linearly separable?

Whether an n-dimensional binary dataset is linearly separable depends on whether there is an n-1-dimensional linear space to split the dataset into two parts.


  • For a one-dimensional line (or curve), “linear divisibility” is the ability to have a point that bisected the line (or curve) according to some rule.
  • For a two-dimensional plane, “linearly separable” means that you can have a line that splits the plane in two by some rule.
  • For a three-dimensional space, “linearly separable” is the ability to have a plane that splits the space in two according to some rule.

The appeal can be visually seen through drawing and extended to higher dimensional space

  • For an n-dimensional space, “linearly separable” means that you can have an n-1 dimensional space that splits an n-dimensional space in two according to some rule.

Why is linear or problem inseparable

Why does the perceptron deal with linear problems?

To be continued (added next time)

Why is an xor problem a nonlinear problem?

Give an explanation on zhihu, I think it is ok
Jump link — go zhihu

The four points on the plane, (0,0) (1,1) are of one kind, (0,1) (1,0) are of another kind. The idea of linear separability is that you can divide two classes on both sides of a line by a line on the plane ax+by+c=0. If there is such a line, then

Substitute (0,0) (1,1) into the equation of the line (it can be assumed that this class is on the positive side of the line, and the other class is on the negative side of the line) :

c>0 (1)

a+b+c>0 (2)

So let’s substitute 0,1, 1,0 into the equation of the line

b+c<0 (3)

a+c<0 (4)

And PI (3) + PI (4) – PI (1) contradicts PI (2), so there is no such line

In other words, we can’t make one cut and cut a flat surface into four parts

It takes two straight lines to divide this hetero or plane, but the idea of linear division is one size fits all

Additional reading

Why is logic independent or linear?

When we say “the xor problem is linearly indivisible,” the default premise isThe xor problem of a two-dimensional plane is linearly indivisible

It’s linearly separable if it’s projected onto a three dimensional plane

Why is linear or problem inseparable

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