Learn where one class becomes another.
Label your data, watch probabilities change, and explore the boundary between two classes.
PROBABILITY LANDSCAPE
Two features · one straight boundaryP(class 1) = sigmoid(z)
P(class 1) = 00.5 · uncertain1
Squares = class 0; circles = class 1. Dashed outlines mark incorrect predictions. Editing data resets training. Up to 100 points.
Ready
EPOCH / POINTS0 / 0
BINARY CROSS-ENTROPY—
TRAINING ACCURACY—
CLASS 0 / CLASS 10 / 0
Loss and classification tell different stories.
| Predicted 0 | Predicted 1 | |
|---|---|---|
| Actual 0 | 0 | 0 |
| Actual 1 | 0 | 0 |
These metrics describe the training data, not unseen-data performance. Loss measures probability quality; accuracy counts thresholded decisions.
Probability first. Class second.
Predict class 1 when its probability is at least this threshold. This changes the boundary and confusion matrix, not the learned weights or loss.
How learning works
- Score: z = w₁X₁ + w₂X₂ + b.
- Probability: sigmoid(z) maps the score to 0–1.
- Learn: gradient descent adjusts the weights to reduce binary cross-entropy.
With these two raw features, the decision boundary is straight. It cannot separate XOR perfectly. Probabilities near 0.5 indicate uncertainty; confidence does not guarantee correctness.