Updates and Boundaries

The Boundary Evolving

The same states can be drawn as boundary lines. This lesson overlays the exact zero-score line after each update and names the final line.

highlighted = computed this step

The boundary after each update

Every update gives a new line w*x+b=0. The legend lists the exact state after each update, ending at w=(2,-1), b=0.

wx+b=0w x+b=0
Boundary evolutionEach line is w*x+b equals zero after one update.Boundary after each updatePerceptron boundary evolutionTraining points with exact boundary lines after each update.0:+11:+12:-13:-1updatesu1: w=(1,0), b=1u2: w=(1,-1), b=0u3: w=(2,0), b=1u4: w=(2,-1), b=0final boundary: w=(2,-1), b=0

Why the final line works here

The final state makes the boundary 2x-y=0. Its sign matches all 4 displayed labels.

2x−y=02x-y=0
Boundary evolutionEach line is w*x+b equals zero after one update.Boundary after each updatePerceptron boundary evolutionTraining points with exact boundary lines after each update.0:+11:+12:-13:-1updatesu1: w=(1,0), b=1u2: w=(1,-1), b=0u3: w=(2,0), b=1u4: w=(2,-1), b=0final boundary: w=(2,-1), b=0

Summary

The plot is an overlay of exact boundary states, not an animation. The final state separates only the shown data in this run.

final shown boundary separates the shown rows\text{final shown boundary separates the shown rows}
Boundary evolutionEach line is w*x+b equals zero after one update.Boundary after each updatePerceptron boundary evolutionTraining points with exact boundary lines after each update.0:+11:+12:-13:-1updatesu1: w=(1,0), b=1u2: w=(1,-1), b=0u3: w=(2,0), b=1u4: w=(2,-1), b=0final boundary: w=(2,-1), b=0