Seq2seq, encoder–decoder and beam search

Two networks, one vector

Machine translation maps a source sequence $\mathbf{x}=(x_1,\dots,x_S)$ to a target sequence $\mathbf{y}=(y_1,\dots,y_T)$ of a different length with a different word order — a many-to-many task with no alignment (6.4 Recurrent neural networks and BPTT). Sutskever, Vinyals & Le (2014) and Cho et al. (2014) solved it with two RNNs. The encoder reads the source and compresses it into its final hidden state, the context vector $\mathbf{c}=\mathbf{h}^{\text{enc}}_S$. The decoder is a conditional language model (6.2 Classical NLP and n-gram language models) initialized with $\mathbf{c}$ that emits the target one token at a time:

Training maximizes the log-likelihood of reference translations, $\sum_t\log P(y_t\mid y_{<t},\mathbf{x})$ — the same next-token cross-entropy as every language model, now conditioned on an input. The 2014 system used 4-layer LSTMs with 1,000-dimensional states and found that reversing the source sentence helped a lot, because it shortened the distance between the first source words and the first target words — a hint that the fixed vector was already straining.

Teacher forcing and exposure bias

During training the decoder receives the true previous token $y_{t-1}$ as input (teacher forcing), so all $T$ steps can be computed with the reference prefix and the loss is well-defined. At inference there is no reference: the decoder feeds back its own prediction $\hat y_{t-1}$. This mismatch is exposure bias — the model has never seen its own mistakes during training, so one wrong token can push it into states it never learned to recover from. Mitigations include scheduled sampling (occasionally feed the model's own sample during training), sequence-level training with the evaluation metric as reward, and, in the LLM era, reinforcement learning on sampled outputs (8.3 Alignment: RLHF, PPO, DPO, GRPO and Constitutional AI).

Decoding: greedy vs beam search

The decoder defines a distribution over all target sequences; we want a high-probability one. Greedy decoding takes $\arg\max$ at each step — fast, but an early safe choice can rule out a better sentence. Beam search keeps the $B$ best partial hypotheses: at each step expand every hypothesis by all $V$ tokens, score them by cumulative log-probability and keep the top $B$; a hypothesis is finished when it emits ⟨/s⟩. Because log-probabilities are negative, longer sequences are penalized, so scores are usually length-normalized, $\text{score}(\mathbf{y})=\frac{1}{T^\alpha}\sum_t\log P(y_t\mid y_{<t},\mathbf{x})$ with $\alpha\approx0.6$–$0.7$.

Worked example ($B=2$). Step 1 probabilities: $a$ 0.5, $b$ 0.3, $c$ 0.2 → log-probs $-0.693$, $-1.204$, $-1.609$; keep $a$ and $b$. Step 2: after $a$ the model spreads out ($x$ 0.35, $y$ 0.33, $z$ 0.32); after $b$ it is confident ($x$ 0.9). Cumulative scores: $ax=-0.693-1.050=-1.743$, $bx=-1.204-0.105=-1.309$. The beam keeps $bx$ (probability $0.27$) ahead of $ax$ ($0.175$) — but greedy would have committed to $a$ at step 1 and returned $ax$. Beam sizes of 4–10 are typical for translation; much larger beams often hurt (the "beam search curse": the model's highest-probability outputs are often short or generic). For open-ended generation with LLMs, sampling methods replace beam search entirely (8.5 Decoding and sampling).

BLEU and why it is not enough

BLEU compares a candidate translation with one or more references using modified n-gram precision: the count of each candidate n-gram is clipped at its maximum count in any reference. The classic example — candidate "the the the the the the the" against the reference "the cat is on the mat" — gets $p_1=2/7$, because the occurs at most twice in the reference. BLEU combines $p_1,\dots,p_4$ geometrically and multiplies by a brevity penalty so that short outputs cannot game precision:

with $c$ the candidate length and $r$ the reference length (computed at corpus level). BLEU correlates with human judgement at the corpus level but not sentence by sentence: it is blind to synonyms and paraphrase, depends on tokenization, and rewards matching the reference's surface form. Character-level chrF, learned metrics such as COMET and BERTScore, and LLM-as-judge evaluation (8.7 Evaluating LLMs) are used alongside it today.

The bottleneck

Everything the decoder knows about the source must squeeze through one vector of a few hundred numbers. Cho et al. showed translation quality dropping sharply as sentence length grew beyond the training lengths; Sutskever's source reversal was a workaround, not a fix. The 2015 remedy was to let the decoder look back at all encoder states at every step, weighting them by relevance — attention, the subject of 6.7 Attention is born and the seed of the transformer.

The vocabulary you will reuse

Where this shows up later

• Attention removes the bottleneck — 6.7 Attention is born; the transformer's encoder, decoder and cross-attention — 7.1 Attention Is All You Need: the big picture, 7.7 Encoder–decoder: T5, BART and choosing an architecture.
• Autoregressive generation, teacher forcing and exposure bias in LLM training — 7.6 Decoder-only: GPT and autoregressive generation, 8.3 Alignment: RLHF, PPO, DPO, GRPO and Constitutional AI; sampling instead of beam search — 8.5 Decoding and sampling.
• Encoder–decoder speech and multimodal models — 8.10 Multimodal models; BLEU's limits foreshadow LLM evaluation problems — 8.7 Evaluating LLMs.