The content discusses the problem of language generation in the limit, where an algorithm is given an unknown target language K from a countable list of candidate languages C, and must generate new strings from K that have not been seen before. This is in contrast to the well-studied problem of language identification in the limit, where the goal is to identify the true language K.
The key insights are:
While language identification in the limit is impossible in general, language generation in the limit is always possible, even against an adversary that enumerates strings from K in a worst-case fashion.
The algorithm maintains a sequence of "provisional languages" that are consistent with the finite sample seen so far, and continually refines this sequence as new strings are revealed. It generates new strings from the highest-indexed provisional language that is a subset of all other consistent provisional languages.
This approach highlights a fundamental difference between identification and generation - where identification requires naming the true language K, generation only requires producing new unseen strings from K.
The algorithm avoids the need for explicit probabilistic assumptions, showing that language generation is possible even in an adversarial setting with minimal structure. This suggests that the core reasons for the tractability of language generation may be more fundamental than just exploiting empirical distributional properties.
To Another Language
from source content
arxiv.org
Key Insights Distilled From
by Jon Kleinber... at arxiv.org 04-11-2024
https://arxiv.org/pdf/2404.06757.pdfDeeper Inquiries