Logistic Regression Trainer

Training data

Samples 240

Class separation 1.60

Noise (spread) 1.00

Gradient descent

Learning rate η 0.30

L2 regularization λ 0.00

Epoch

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Accuracy

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Loss (BCE)

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|∇w|

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w₁, w₂

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bias b

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How it works

Each point is drawn from one of two Gaussian blobs in a 2-D feature space. The classifier is a single linear unit: it computes z = w₁x₁ + w₂x₂ + b, squashes it through the sigmoid σ(z) = 1/(1+e⁻ᶻ) to get a probability, and predicts the positive class when that probability exceeds 0.5 — exactly where z = 0, the straight decision boundary drawn on the field.

p = σ(w·x + b)
L = −(1/N) Σ [y·log(p) + (1−y)·log(1−p)] + (λ/2)‖w‖²
∇w = (1/N) Σ (p−y)·x + λw,  ∇b = (1/N) Σ (p−y)
w ← w − η∇w,  b ← b − η∇b

Learning rate η — the step size along the negative gradient each epoch; too high overshoots and oscillates, too low crawls toward the minimum.
L2 regularization λ — penalizes large weights, shrinking them toward zero and softening an overly sharp boundary on noisy or separable data.
Class separation / noise — widen the gap between the blobs or shrink their spread and the loss drops toward zero almost immediately; overlap them and the boundary settles wherever it best trades off the two classes' errors.
Background shading — every pixel is colored by the model's actual current probability output, so the soft red↔blue gradient you see is the literal decision surface, not an illustration of one.

Real-world relevance: this is the same batch gradient descent loop that trains logistic regression, and the linear layer at the end of nearly every deep classifier, on real tabular and text features — spam filters, churn prediction, medical risk scoring.

Class 0 Class 1 Decision boundary (z=0)