At Gmail's scale (300B+ emails/year), you can't run a BERT model on every email — it's too expensive. The real-world approach is cascaded classification: (1) Simple rules catch obvious spam (known bad senders, blocked domains), (2) TF-IDF + lightweight ML handles most categorization (cheap, fast), (3) Neural models handle ambiguous cases that simpler models aren't confident about. This cascade reduces expensive GPU inference by 90%+ while maintaining accuracy.

Since an email goes into exactly ONE category (mutually exclusive), softmax is the right choice. Softmax forces all 4 probabilities to sum to 1: P(Primary) + P(Social) + P(Promotions) + P(Updates) = 1. The email goes to the category with the highest probability. Sigmoid would allow multiple categories simultaneously (multi-label), which isn't what Gmail's inbox tabs do.

With only 500 labeled examples, training a neural network from scratch would badly overfit. TF-IDF + Naive Bayes is a solid baseline (~85% on many tasks). But fine-tuned BERT consistently outperforms both, even with very few examples, because it brings knowledge from pretraining on billions of words. BERT already 'understands' language — you just need to teach it your specific label scheme. Studies show BERT matches 100K-example traditional ML accuracy with as few as 500 examples.

Overall accuracy hides per-class performance in multi-class settings. The cost matrix is asymmetric: missing an important email (false negative for Primary) has far higher real-world cost than showing a promotional email in Primary (false positive). Gmail uses a confidence threshold: only classify as non-Primary if the model is >95% confident. Borderline cases default to Primary as a safety measure. This is a design decision, not a model limitation — asymmetric costs demand asymmetric thresholds.