3D Logistic Regression Trainer

Training data

Samples 220

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,w₃

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bias b

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How it works

Every point lives in a real 3-feature space (x₁, x₂, x₃), drawn from one of two Gaussian blobs. The classifier computes z = w₁x₁ + w₂x₂ + w₃x₃ + b and squashes it through the sigmoid to get a probability. The teal plane is the literal decision surface z = 0 — every point sitting on it is a 50/50 call — reconstructed from the model's current weights and redrawn every epoch as gradient descent moves them.

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 gradient-descent step size; too high and the plane overshoots and wobbles, too low and it drifts slowly toward the optimum.
L2 regularization λ — shrinks the weight vector, keeping the plane from tilting to an extreme angle chasing a few noisy points.
Class separation / noise — pull the blobs apart or tighten their spread and the plane snaps to a clean split almost immediately; overlap them and it settles at the best achievable compromise.
Orbit — drag to rotate the camera around the point cloud; the plane is real 3-D geometry, not a billboard, so its tilt reads correctly from any angle.

Real-world relevance: the same linear-plus-sigmoid unit, trained with this identical gradient rule, sits at the output of nearly every deep classifier — this is what a hyperplane genuinely separating classes in feature space actually looks like.

Class 0 Class 1 Decision plane (z=0)

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