arXiv:2605.23901v1 Announce Type: new Abstract: Existing scaling laws for Large Language Models (LLMs), predominantly monotonic power laws, fail to explain emerging non-monotonic phenomena such as catastrophic overtraining and quantization-induced degradation, where performance deteriorates despite increased compute. We propose the Shannon Scaling Law, a unified theoretical framework that models LLM training as information transmission over a noisy channel, grounded in the Shannon-Hartley theorem. By mapping model parameters to channel bandwidth and training tokens to signal power, our formula
This paper offers a timely theoretical framework to understand and mitigate emerging challenges in LLM scaling, such as catastrophic overtraining, which are becoming more prevalent as models grow. It provides a new lens to interpret limitations observed in current LLM development.
A strategic reader should care because this research introduces a fundamental theoretical underpinning for LLM capacity, moving beyond empirical power laws to explain non-monotonic performance, which could reshape investment and development strategies in AI. Understanding these limits is crucial for efficient resource allocation and avoiding dead ends in LLM R&D.
The understanding of LLM scaling shifts from purely monotonic, empirical observations to a more theoretically grounded perspective that accounts for performance plateaus and degradation. This suggests that simply increasing compute or parameters may not always yield proportional returns, forcing a re-evaluation of current scaling paradigms.
- · AI researchers focused on theoretical foundations
- · Companies optimizing LLM training efficiency
- · Developers of foundational models seeking stability
- · Hardware developers providing optimized compute for specific LLM architectures
- · Researchers relying solely on empirical power laws for scaling
- · Projects indiscriminately increasing model size without theoretical guidance
- · Speculative investments based on infinite scaling assumptions
The re-evaluation of LLM scaling laws will lead to more nuanced strategies for model development and resource allocation.
This refined understanding could accelerate the development of more robust and efficient LLMs by guiding architectural choices and training methodologies.
The application of Shannon's principles might inspire new forms of AI architecture or learning paradigms that explicitly account for channel noise.
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Read at arXiv cs.LG