Logistic Regression Trainer

Supervised classification starts here: a logistic regression model learns a straight decision boundary by real batch gradient descent on the binary cross-entropy loss. This simulator generates two overlapping Gaussian blobs in a 2-D feature space, then repeatedly computes the model's actual predicted probability for every point, measures how wrong those predictions are, and nudges the weights and bias down the true gradient of the loss — the same three-line update rule (compute probability, compute gradient, step) used to train the linear layer at the end of nearly every classifier. Watch the boundary line rotate and slide and the shaded probability field sharpen as loss falls and accuracy climbs, and tune learning rate, L2 regularization, class separation and noise to see exactly how each one changes convergence.