modelone sigmoid neuron (= logistic regression): ŷ = σ(w₁x₁ + w₂x₂ + b), ŷ read as P(y = 1). only three numbers ever learn — w₁, w₂, b — so the drawn boundary is always the straight line where ŷ = 0.5.
data100 fixed points, 50 per class, in the unit square, embedded in this file. the clouds overlap: no straight line gets all 100 right, and this run tops out around 94%.
startalways the same one-off random draw: w₁ −0.5308 · w₂ 0.9308 · b 0. ↺ reset returns to it, so every run is exactly reproducible.
objectiveper-point log-loss E = −y·ln(ŷ) − (1−y)·ln(1−ŷ). the chart tracks its mean over all 100 points, measured after each completed epoch.
update rulestochastic gradient descent, one point at a time in fixed order 1…100 (one pass = one epoch): w ← w + α(y−ŷ)x, b ← b + α(y−ŷ). every point nudges the line, even correctly classified ones (unlike the perceptron trick), and each step descends only that one point's error — which is why the boundary wobbles instead of gliding.
deliberately absentno shuffling, no mini-batches, no momentum, no regularisation, no train/test split — loss and accuracy are measured on the same 100 points it trains on.
learning rate & stoppingα is constant (default 0.01); moving the slider mid-run applies from the next step. there is no convergence test — training simply stops after the set number of epochs (default 100). the default run lands at mean loss 0.3249, accuracy 94%.
accuracya point counts as correct when its predicted side agrees with its class: ŷ > 0.5 for y = 1, ŷ ≤ 0.5 for y = 0. accuracy can plateau while the loss still falls — the line keeps improving its confidence without flipping any point.