Binary Cross Entropy Loss

Interactive Binary Cross Entropy Loss Demo

See how BCE loss "punishes" wrong predictions through both visual intuition and mathematical precision. The red "glow" shows punishment intensity!

Model Confidence: 70%

Show Optimal Show Worst Case Reset

Mathematical Foundation: Binary Cross Entropy Loss

1. Binary Cross Entropy Formula:

BCE(y, p) = -[y × log(p) + (1-y) × log(1-p)]

Where y = true label (0 or 1), p = predicted probability (0 to 1)

Show Sample Calculation

2. Why This Works:

• Perfect prediction: BCE = 0 when p=1 and y=1, or p=0 and y=0

• Wrong confident prediction: BCE → ∞ as p→0 when y=1 (or p→1 when y=0)

• Uncertainty: BCE = log(2) ≈ 0.693 when p=0.5 regardless of y

The logarithmic penalty severely punishes confident wrong predictions, creating a strong learning signal

Step-by-Step: How Data Transforms into Loss

Raw Data

Sites with known liquefaction outcomes

→

Model Predictions

Probability of liquefaction (0-1)

→

BCE Loss

Punishment for wrong predictions

→

Learning Signal

Gradient updates to improve model

1. Training Data (Ground Truth)

2. Model Predictions + Decision Boundary

3. Loss "Punishment" (Visual)

4. Loss Curves (Mathematical View)