arXiv:2512.22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly understood. This work formalizes the learning dynamics of transformer-based language models as an ordinary differential equation (ODE) system, then approximates this process to kernel behaviors. Departing from prior toy-model analyses, we rigorously analyze stochastic gradient descent (SGD) training for m
This research provides a more rigorous theoretical foundation for LLM scaling laws, an area previously dominated by empirical observations, emerging as the field matures.
Understanding the theoretical underpinnings of LLM scaling could unlock more efficient training, better model design, and more predictable performance improvements in advanced AI systems.
The shift from empirical observation to formalized mathematical models for LLM scaling provides a deeper understanding of how these powerful AI systems evolve and perform, potentially guiding future development away from purely trial-and-error approaches.
- · AI researchers
- · Large Language Model developers
- · Compute infrastructure providers
- · AI development relying solely on brute-force empirical scaling
Refined understanding of LLM training dynamics and scaling laws will inform more optimized model architectures.
More predictable and efficient LLM development could accelerate the deployment of advanced AI applications across various sectors.
Deeper theoretical insights might enable overcoming current limitations in AI performance earlier than anticipated, further accelerating AI's societal impact.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.CL