The cross-entropy scaling law has long served as a key tool for guiding the development of large language models. It shows that cross-entropy loss decreases in a predictable power-law rate as the model size increases. However, recent evidence indicates that this law breaks down at very large scales: the loss decreases more slowly than expected, which causes significant trouble for developing large language models. In this paper, we hypothesize that the root cause lies in the fact that cross-entropy itself does not truly scale; instead, only one of its hidden components does. To investigate this, we introduce a novel decomposition of cross-entropy into three parts: Error-Entropy, Self-Alignment, and Confidence. We show both theoretically and empirically that this decomposition precisely captures the training dynamics and optimization objectives. Through extensive experiments on multiple datasets and 32 models spanning five orders of magnitude in size, we find that only error-entropy follows a robust power-law scaling, while the other two terms remain largely invariant. Moreover, error-entropy constitutes the dominant share of cross-entropy in small models but diminishes in proportion as models grow larger. This explains why the cross-entropy scaling law appears accurate at small scales but fails at very large ones. Our findings establish the error-entropy scaling law as a more accurate description of model behavior. We believe it will have wide applications in the training, understanding, and future development of large language models.

Instruction tuning is a supervised fine-tuning approach that significantly improves the ability of large language models (LLMs) to follow human instructions. For programming tasks, most models are finetuned with costly human-annotated instruction-response pairs or those generated by large, proprietary LLMs, which may not be permitted. We propose SelfCodeAlign, the first fully transparent and permissive pipeline for self-aligning code LLMs without extensive human annotations or distillation. SelfCodeAlign employs the same base model for inference throughout the data generation process. It first extracts diverse coding concepts from high-quality seed snippets to generate new tasks.

Learning reward functions remains the bottleneck to equip a robot with a broad repertoire of skills. Large Language Models (LLM) contain valuable task-related knowledge that can potentially aid in the learning of reward functions. However, the proposed reward function can be imprecise, thus ineffective which requires to be further grounded with environment information. We proposed a method to learn rewards more efficiently in the absence of humans. Our approach consists of two components: We first use the LLM to propose features and parameterization of the reward, then update the parameters through an iterative self-alignment process. In particular, the process minimizes the ranking inconsistency between the LLM and the learnt reward functions based on the execution feedback. The method was validated on 9 tasks across 2 simulation environments. It demonstrates a consistent improvement over training efficacy and efficiency, meanwhile consuming significantly fewer GPT tokens compared to the alternative mutation-based method.

Despite showing increasingly human-like abilities, large language models (LLMs) often struggle with factual inaccuracies, i.e. "hallucinations", even when they hold relevant knowledge. To address these hallucinations, current approaches typically necessitate high-quality human factuality annotations. In this work, we explore Self-Alignment for Factuality, where we leverage the self-evaluation capability of an LLM to provide training signals that steer the model towards factuality. Specifically, we incorporate Self-Eval, a self-evaluation component, to prompt an LLM to validate the factuality of its own generated responses solely based on its internal knowledge. Additionally, we design Self-Knowledge Tuning (SK-Tuning) to augment the LLM's self-evaluation ability by improving the model's confidence estimation and calibration. We then utilize these self-annotated responses to fine-tune the model via Direct Preference Optimization algorithm. We show that the proposed self-alignment approach substantially enhances factual accuracy over Llama family models across three key knowledge-intensive tasks on TruthfulQA and BioGEN.