# Beam Decoding Using the model's actual predictions of earlier time steps to predict the next output requires us to explore a search space - This is required when using any sequence-to-sequence model (image captioning, NMT, summarization, ...) - Greedy decoding suffers from sub-optimal decisions leading to even more sub-optimal decisions later on - Beam Decoding: explore multiple alternatives in parallel Example: ![[Beam Decoding process.png]] - When do we stop? Limit length to $\lfloor r \cdot m\rfloor$, where $m$ is the length of the source sentence and $r$ is some length ratio, e.g., $r=1.2$ - All translation candidates $C(Z)$ are compared and the most likely one is returned - $\hat{Y}_{\leq t}$ is $\in C(Z)$ if $\hat{y}_{t}=</ \mathrm{s}>$ or $t=\lfloor r \cdot m\rfloor$ - candidate score $s\left(\hat{Y}_{\leq t} \mid Z\right)=\frac{1}{t} \log p\left(\hat{Y}_{\leq t} \mid Z\right)$ normalize to compare candidates of different lengths - return $\hat{Y}=\underset{\hat{Y}_{\leq t} \in C(Z)}{\operatorname{argmax}} s\left(\hat{Y}_{\leq t} \mid Z\right)$ Fast training is important, but fast beam decoding is critical for actual applications - Computing $\log p\left(\hat{Y}_{\leq t+1} \mid Z\right)$ directly for each $t$ is inefficient - but does not require access to relevant network activations - Better: $\log p\left(\hat{Y}_{\leq t+1} \mid Z\right)=\log p\left(\hat{y}_{t+1} \mid \hat{Y}_{\leq t}, Z\right)+\log p\left(\hat{Y}_{\leq t} \mid Z\right)$ - requires access to the relevant layer activations from $n e t_{t}$ to compute $n e t_{t+1}$ - e.g., to compute $\mathrm{LSTM}_{t+1}$ the activations $\left(\mathbf{h}_{t}, \mathbf{c}_{t}\right)$ have to be exposed (not all packages directly expose LSTM cells) - Beam decoding is always slower than training due to frequent interactions with the CPU - Beam decoding performs better than greedy decoding - beam sizes beyond 25 often lead to decreases in quality - commonly used beam sizes vary between 5 and 12 - Beams can be represented as entries (rows) in a batch --- ## References