Traditional scaling laws in natural language processing suggest that increasing model size and training data enhances performance. However, recent studies reveal deviations, particularly in large language models, where performance improvements decelerate—a phenomenon known as sub-scaling. This paper revisits these scaling laws by examining the impact of data quality and training strategies on model performance. Through extensive empirical analysis of over 400 models, we identify high data density and non-optimal resource allocation as key factors contributing to sub-scaling. High data density leads to diminishing returns due to redundant information, while optimal resource allocation is crucial for sustained performance improvements. We propose a sub-optimal scaling law that better predicts performance in sub-scaling regimes, highlighting the importance of data quality and diversity.

While large language models (LLMs) have demonstrated remarkable abilities across various fields, hallucination remains a significant challenge. Recent studies have explored hallucinations through the lens of internal representations, proposing mechanisms to decipher LLMs’ adherence to facts. However, these approaches often fail to generalize to out-of-distribution data, leading to concerns about whether internal representation patterns reflect fundamental factual awareness, or only overfit spurious correlations on the specific datasets. In this work, we investigate whether a universal truthfulness hyperplane that distinguishes the model’s factually correct and incorrect outputs exists within the model. To this end, we scale up the number of training datasets and conduct an extensive evaluation – we train the truthfulness hyperplane on a diverse collection of over 40 datasets and examine its cross-task, cross-domain, and in-domain generalization. Our results indicate that increasing the diversity of the training datasets significantly enhances the performance in all scenarios, while the volume of data samples plays a less critical role. This finding supports the optimistic hypothesis that a universal truthfulness hyperplane may indeed exist within the model, offering promising directions for future research.