The Stability of Singular Distribution: A Spectral Perspective on the Two-Phase Dynamics of Language Model Pre-training
arXiv:2605.26489v1 Announce Type: new Abstract: Large language model pre-training typically exhibits a two-phase trajectory: a fast initial loss drop followed by a prolonged slow improvement. We identify an underlying spectral phenomenon, Stability of Singular Distribution (SoSD), where the trace-normalized singular value spectrum stabilizes early, even as parameter matrices continue to evolve. We demonstrate that synchronization between SoSD and the slow-descent regime is widely observed across diverse architectures (GPT-2, LLaMA) and settings, including various schedules (Step-wise, WSD, Cos
This research provides a deeper, spectral understanding of the two-phase dynamics observed in large language model pre-training, offering insights at a time of intense focus on AI model efficiency and scaling.
A clearer understanding of LLM pre-training dynamics can lead to more efficient and predictable model development, impacting the economics and capabilities of AI systems across various applications.
The identification of 'Stability of Singular Distribution' as a core phenomenon provides a new theoretical lens for optimizing training processes, potentially accelerating progress in LLM development.
- · AI research institutions
- · Large language model developers
- · AI compute infrastructure providers
- · Inefficient LLM training methodologies
Improved understanding of LLM training dynamics leads to more robust and efficient model architectures.
Faster, more cost-effective development of advanced AI models could democratize access to powerful AI capabilities.
Enhanced LLM efficiency may accelerate the development and deployment of complex AI agents and applications, increasing their societal impact.
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Read at arXiv cs.LG