The scaling law assumptions utilized in this study, while informative, come with certain drawbacks and limitations that could impact the generalizability of the findings. One limitation is the assumption that smaller models can compensate for their lower learning efficiency by processing more tokens within the same budget. This assumption may not hold true in all cases, as the relationship between model size, data processing capacity, and performance can be influenced by various factors such as model architecture, task complexity, and dataset characteristics. Additionally, the scaling laws may not account for the non-linear complexities of language modeling tasks, where certain tasks may benefit more from larger models regardless of the computation budget. Moreover, the scaling laws may not consider the impact of hyperparameters, optimization techniques, or specific model configurations on the performance of language models. These limitations could affect the applicability of the scaling laws to different scenarios and models, potentially impacting the generalizability of the study's findings.