In other words can a linear classifier learn to correctly assign a class (label 0 to 3) for an input of 3 bits? Intuitively this cannot work, since the half-adder circuit contains an XOR block, which cannot be solved by a linearly classifier(with applying a kernel trick-transformation to the data).

In a lecture I just got told that intuitively the sum function should be a linear function. But a linear classifier doesn't perform well on the task, getting about 75% accuracy, which is to be expected when trying to linearly classify XOR. Since the sum function seems the be a linear function, where does the non-linearity come from exactly? Some kind of change in representation of the data(bits to integers?)

So, can a linear regressor or classifier learn to sum 3 bits into an integer between 0-3? Why or why not?

EDIT: Assume you have a dataset like this:

x0   x1   x2   y
0     0    0   0
1     0    0   1
1     1    0   2
1     0    1   2
1     1    1   3
...

In other words can a linear classifier learn to correctly assign a class (label 0 to 3) for an input of 3 bits? Intuitively this cannot work, since the half-adder circuit contains an XOR block, which cannot be solved by a linearly classifier(with applying a kernel trick-transformation to the data).

In a lecture I just got told that intuitively the sum function should be a linear function ($\mathbb{1}^Tx=y$). But a linear classifier doesn't perform well on the task, getting about 75% accuracy, which is to be expected when trying to linearly classify XOR. Since the sum function seems the be a linear function, where does the non-linearity come from exactly? Some kind of change in representation of the data(bits to integers?)

So, can a linear regressor or classifier learn to sum 3 bits into an integer between 0-3? Why or why not?

EDIT: Assume you have a dataset like this:

x0   x1   x2   y
0     0    0   0
1     0    0   1
1     1    0   2
1     0    1   2
1     1    1   3
...

In other words can a linear classifier learn to correctly assign a class (label 0 to 7) for an input of 3 bits? Intuitively this cannot work, since the half-adder circuit contains an XOR block, which cannot be solved by a linearly classifier(with applying a kernel trick-transformation to the data).

In a lecture I just got told that intuitively the sum function should be a linear function. But a linear classifier doesn't perform well on the task, getting about 75% accuracy, which is to be expected when trying to linearly classify XOR. Since the sum function seems the be a linear function, where does the non-linearity come from exactly? Some kind of change in representation of the data(bits to integers?)

So, can a linear regressor or classifier learn to sum 3 bits into an integer between 0-7? Why or why not?

In other words can a linear classifier learn to correctly assign a class (label 0 to 3) for an input of 3 bits? Intuitively this cannot work, since the half-adder circuit contains an XOR block, which cannot be solved by a linearly classifier(with applying a kernel trick-transformation to the data).

In a lecture I just got told that intuitively the sum function should be a linear function. But a linear classifier doesn't perform well on the task, getting about 75% accuracy, which is to be expected when trying to linearly classify XOR. Since the sum function seems the be a linear function, where does the non-linearity come from exactly? Some kind of change in representation of the data(bits to integers?)

So, can a linear regressor or classifier learn to sum 3 bits into an integer between 0-3? Why or why not?

EDIT: Assume you have a dataset like this:

x0   x1   x2   y
0     0    0   0
1     0    0   1
1     1    0   2
1     0    1   2
1     1    1   3
...