Log Loss, Per Sample

Accuracy only asks whether the model picked the right side. Log loss asks how confidently it did so — and punishes confident mistakes far harder than hesitant ones.

For one example with true label y (either 0 or 1) and predicted probability p that the label is 1:

Only one half of that ever survives: when y = 1 the second term vanishes and the loss is -log(p); when y = 0 the first vanishes and it's -log(1 - p). Either way it reduces to the negative log of the probability you assigned to the correct answer.

Task: write log_loss_per_sample(y_true, probs) returning a list — one loss per example, each rounded to 4 decimal places. Don't average them.

• log is the natural logarithm (math.log).
• Every probability is strictly between 0 and 1, so you never take the log of zero and never need to clip anything.
• The loss is always positive. A perfect, confident answer approaches 0; p = 0.5 costs about 0.693 whichever way the label falls.

The per-sample list is more useful than the average while debugging: sort it and the worst few entries are the examples your model is confidently wrong about, which is usually where the mislabelled data lives.