An Information Theory of Compute-Optimal Size Scaling, Emergence, and Plateaus in Language Models

Anuj K. Nayak; Lav R. Varshney

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arXiv · 2410.01243

An Information Theory of Compute-Optimal Size Scaling, Emergence, and Plateaus in Language Models

Anuj K. Nayak·Lav R. Varshney

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Abstract

Recent empirical studies show three phenomena with increasing size of language models: compute-optimal size scaling, emergent capabilities, and performance plateauing. We present a simple unified mathematical framework to explain all of these language model scaling phenomena, building on recent skill-text bipartite graph frameworks for semantic learning. Modeling the learning of concepts from texts as an iterative process yields an analogy to iterative decoding of low-density parity check (LDPC) codes in information theory. Thence, drawing on finite-size scaling characterizations of LDPC decoding, we derive the compute-optimal size scaling (Chinchilla rule) for language models. Further, using tools from random network theory, we provide a simple explanation for both emergence of complex skills and plateauing of performance as the size of language models scale. We see multiple plateaus.

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Anuj K. Nayak, Lav R. Varshney. 2024-10-02. An Information Theory of Compute-Optimal Size Scaling, Emergence, and Plateaus in Language Models. https://arxiv.org/abs/2410.01243

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