The Task: 2-Pixel Symmetry
A 1×2 "image" is symmetric if both pixels match. It is asymmetric if they differ. Click a case to analyze it.
Why Linear Classification Fails
In the raw input space, no single straight line can separate the green circles (symmetric) from the red squares (asymmetric).
The MLP Solution
The network learns two hidden features to transform the space.
Hidden Layer Feature Equations
h₁: Both Pixels Dark
h₁ = ReLU(1·x₁ + 1·x₂ - 1.5)
Fires only near (1,1)
h₂: Both Pixels Light
h₂ = ReLU(-1·x₁ - 1·x₂ + 0.5)
Fires only near (0,0)
Select a case above to see activations
Hidden Layer Space (h₁, h₂)
The transformation maps inputs to 3 points. They are now linearly separable.