CarbonScaling: Extending Neural Scaling Laws for Carbon Footprint in Large Language Models

Large language models (LLMs) increasingly follow neural scaling laws that tie performance gains to rapidly expanding computational budgets, raising concerns about the sustainability of frontier-scale training. Existing carbon-estimation methods largely depend on regression over historical runs and fail to capture critical system-level factors, including hardware heterogeneity, distributed parallelism, communication overhead, and architectural sparsity. We present \textit{CarbonScaling}, a hardware-aware analytical framework for modeling the carbon scaling behavior of frontier LLM training. The framework integrates neural scaling laws, distributed training strategies, accelerator and interconnect modeling, and operational and embodied carbon accounting to estimate feasible hardware configurations and associated emissions. CarbonScaling jointly models tensor, pipeline, data, and expert parallelism while incorporating memory, bandwidth, utilization, and runtime constraints. Experimental validation demonstrates substantially higher fidelity than regression-based baselines and highlights the growing importance of embodied carbon at trillion-parameter scales. Source code: \url{https://github.com/UnchartedRLab/CarbonScaling}.