ŷ = w·x + b
L = (1/N)Σ(ŷ−y)²
w ← w − η·∂L/∂w
b ← b − η·∂L/∂b
Same "physics lens" as the 3D version, flattened to one feature: the loss is a bowl-shaped bowl in (w, b) space, and gradient descent is a ball rolling downhill under a force equal to −∇L, with learning rate η as the step size.
- Data Points — number of samples (x, y) generated from a hidden linear function plus noise.
- Noise — standard deviation of random scatter added to the target, making the fit harder.
- Learning Rate — step size η in the weight update; too high overshoots and oscillates, too low converges slowly.
- Training / Pause — runs or freezes the gradient-descent updates so you can inspect the current line and loss curve.
The bottom strip plots MSE loss against iteration — a smoothly falling curve means convergence, a bouncing one means the learning rate is too high.