The paper presents a mathematical theory for learning semantic languages using abstract learners. Key highlights:
Semantic languages are defined using a skill-text bipartite graph, where skills represent the latent capabilities required to understand texts.
Two types of abstract learners are introduced - 1-skill learners and Poisson learners. These learners can learn skills by repeatedly being presented with training texts.
Density evolution analysis is used to show the emergence of learned skills when the ratio of the number of training texts to the number of skills exceeds a certain threshold. This threshold corresponds to a sharp drop in the testing error, defined as the probability that a randomly selected text can be understood by the learner.
The analysis also provides a scaling law for the testing error with respect to the ratio of training texts to skills.
The trained learners can be used for semantic compression, where texts are encoded using the indices of the learned skills required to understand them. This enables more efficient compression compared to traditional lossless compression.
The paper discusses the application of the trained learners in a semantic communication system, where the semantic encoder/decoder is separate from the physical channel encoder/decoder.
The key contribution is the development of a mathematical framework to explain the emergence of learned skills in large language models, which is an active area of research.
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arxiv.org
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by Kuo-Yu Liao,... ที่ arxiv.org 04-11-2024
https://arxiv.org/pdf/2404.07009.pdfสอบถามเพิ่มเติม