sequence models

Beam search is the decoding algorithm everyone cites and few can code correctly. The signal is keeping k hypotheses by cumulative log-prob, adding logs (not multiplying probs), and handling completed sequences and length. Here is a correct implementation and the tradeoffs.

A build-it-yourself check on recurrent forward passes and backprop through time. What matters is the shared-weight recurrence, summing gradients over timesteps, and articulating the vanishing-gradient problem. The code follows.

A build-it-yourself check on gated recurrence. What matters is wiring the forget/input/output gates and candidate correctly, keeping cell state distinct from hidden state, and explaining why the additive cell path cures vanishing gradients. The code follows.

Sequence models remain interview staples, particularly the gating that repaired RNNs and the reason attention took over. What matters is linking the vanishing-gradient narrative to the parallelism case that let transformers ride the scaling wave.

HMMs are the classic probabilistic sequence model behind speech and tagging, and Viterbi is how you decode them. What matters is the hidden-states plus transitions/emissions structure, and that Viterbi is dynamic programming for the single best state path, not a probability.