Google

The notation `Ψ(Yi)` represents the subset of sequences within the candidate set `Yi` at step `i` that are considered complete.

Notation for the Set of Complete Sequences

The entire search space, denoted by $$\mathcal{Y}$$, is constructed by aggregating all complete sequences generated throughout the step-wise expansion process. It is formally defined as the union of the sets of complete sequences, $$\Psi(Y_i)$$, from each step $$i=1$$ up to a maximum sequence length, $$n_{\text{max}}$$. The formula is: $$\mathcal{Y} = \Psi(Y_1) \cup \Psi(Y_2) \cup \dots \cup \Psi(Y_{n_{\text{max}}})$$ This expression provides a constructive definition of the search space as the collection of all valid, terminated hypotheses.

Formula for the Search Space as a Union of Complete Sequences

In a step-wise sequence generation process, `Yi` represents the set of all candidate sequences at step `i`. Explain what the notation `Ψ(Yi)` signifies and describe the defining characteristic of any sequence included in this specific subset.

Defining the Set of Complete Sequences

In a step-wise sequence generation process, the set denoted by `Ψ(Yi)` contains all candidate sequences from step `i` that will be expanded to create new, longer sequences in the subsequent step.

In a sequence generation process, a sequence is considered 'complete' if it ends with a special `⟨EOS⟩` token. At a given step `i`, the set of all candidate sequences is `Yi = {('The', 'cat', 'sat'), ('The', 'cat', 'slept', '⟨EOS⟩'), ('The', 'dog'), ('The', 'dog', 'barked', '⟨EOS⟩')}`. If `Ψ(Yi)` represents the subset of sequences in `Yi` that are complete, which of the following correctly identifies `Ψ(Yi)`?

Learn Before

Related