sequence models

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

A from-scratch test of recurrent forward passes and backprop through time. The signal is the shared-weight recurrence, accumulating gradients across timesteps, and explaining the vanishing-gradient problem. Here is the implementation.

A from-scratch test of gated recurrence. The signal is wiring the forget/input/output gates and candidate correctly, separating cell state from hidden state, and explaining why the additive cell path fixes vanishing gradients. Here is the implementation.

Sequence models are foundational and still asked, especially the gating that fixed RNNs and why attention won. The signal is connecting the vanishing-gradient story to the parallelism argument 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. The signal is the hidden-states plus transitions/emissions structure, and that Viterbi is dynamic programming for the single best state path, not a probability.