Changhao Jiang, Ming Zhang Fudan University, Yifei Cao Fudan University, Junjie Ye, Xiaoran Fan, Shihan Dou, Zhiheng Xi, Jiajun Sun Fudan University 等 15 位作者
The GPT-4 technical report suggests that downstream performance can be predicted from pre-training signals, but offers little methodological detail on how to quantify this. This work address this gap by modeling knowledge retention, the capacity of a pre-trained language model to memorize factual information from its corpus, and introduce a principled method to estimate it prior to training. We propose Size-dependent Mutual Information (SMI), an information-theoretic predictor that integrates knowledge frequency, knowledge specificity, and model size to forecast closed-book question answering (QA) accuracy. SMI is validated through large-scale document retrieval over the disclosed pre-training corpora of 21 public and 3 custom models, combined with a robust multi-template QA evaluation. Experiments show that SMI significantly outperforms repetition-based baselines and achieves R² > 0.7 in predicting QA accuracy for models above 1B parameters, without additional training. The analysis further reveals diminishing returns from scaling data and model size and provides evidence for an intrinsic upper bound on knowledge retention achievable by pre-training alone, motivating retrieval and other augmentation strategies.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表
Yuming Yang Fudan University, Mingyoung Lai University of Toronto, Wanxu Zhao, Xiaoran Fan, Zhiheng Xi, Mingqi Wu, Chiyue Huang, Jun Zhao 等 16 位作者
Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that align closely with the student model’s current behavior but overlooking more informative ones. Addressing this, we propose Rank–Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically balance learning signal strength and behavioral alignment by combining low absolute probability with relatively high-ranked tokens under the student model.Concretely, RSR is defined as the ratio of a trajectory’s average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training reasoning performance (average Spearman 0.86), consistently outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表