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For example, faster-whisper's transcribe function takes an argument

beam_size: Beam size to use for decoding.

What does "beam" mean?

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Beam search

The beam search is a algorithm to find probable output sequences for an input sequence, so it has been used for decoding in the context of sequence-to-sequence tasks, like machine translation. It's an alternative to a greedy search, which just samples the most likely token at every step (which is not guaranteed to find the most likely sequence, though), that can keep a set of solutions.

I think I first encountered this algorithm a few years ago while reading this important paper, which refers to this Alex Graves' paper, which actually contains a description and the pseudocode of a beam search, but I had forgotten about it, so I decided to review it :)

A good description can be found here (section 7.2.3) or here.

If you're familiar with search algorithms like breadth-first search (BFS), think of beam search as a similar search algorithm, where nodes are the tokens from some vocabulary and the edges are the probabilities of selecting a certain token given the previously selected tokens (important!). In fact, it can be viewed as a generalization of BFS (exhaustive search) - if you set the beam size equal to the vocabulary size, you get BFS.

The following image (taken from here, which provides a nice explanation) should give you the intuition

enter image description here

What is a beam? Just a guess

Now, I don't know the origin of the term beam in this context or why it's called beam search. In some papers I've come across (example), the beam acts like an object that has properties like the size (beam size).

However, it could refer to the paths or the polygon formed by the external nodes at each layer from the first to the last, which is kind of similar to or could remind us of a light beam (image taken from here).

enter image description here

The terminology is not very important, unless you're only interested in the history of the algorithm, which I assume not

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    $\begingroup$ So the "beam" is the path through this search tree? $\endgroup$
    – Geremia
    Aug 8, 2023 at 3:49
  • $\begingroup$ @Geremia That's one possibility, but I am not 100% sure. Like I wrote, I found the term "beam" alone only in a couple of papers and both of them seem to use it as an abstraction that contains the parameters of the beam search. If we consider the meaning of "beam size/width" (which is the number of nodes we consider at each layer), then the "beam" could also refer to all paths down the search graph/tree, which, together, form kind of a beam - the term may originate from the term light beam. This is just a guess but it kind of makes sense. $\endgroup$
    – nbro
    Aug 8, 2023 at 8:54
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Here is Guillaume Klein's answer at the issue section of the Git repository:

"Beam Search" in Wikipedia:
  Additionally, the beam size/beam width is controlling the number of paths that are explored at each step when generating an output.

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