Yuxuan Li

Yijun Dong, Yicheng Li, Yunai Li et al.

Weak-to-strong (W2S) generalization is a type of finetuning (FT) where a strong (large) student model is trained on pseudo-labels generated by a weak teacher. Surprisingly, W2S FT often outperforms the weak teacher. We seek to understand this phenomenon through the observation that FT often occurs in intrinsically low-dimensional spaces. Leveraging the low intrinsic dimensionality of FT, we analyze W2S in the ridgeless regression setting from a variance reduction perspective. For a strong student-weak teacher pair with sufficiently expressive low-dimensional feature subspaces $\mathcal{V}_s, \mathcal{V}_w$, we provide an exact characterization of the variance that dominates the generalization error of W2S. This unveils a virtue of discrepancy between the strong and weak models in W2S: the variance of the weak teacher is inherited by the strong student in $\mathcal{V}_s \cap \mathcal{V}_w$, while reduced by a factor of $\mathrm{dim}(\mathcal{V}_s)/N$ in the subspace of discrepancy $\mathcal{V}_w \setminus \mathcal{V}_s$ with $N$ pseudo-labels for W2S. Our analysis further casts light on the sample complexities and the scaling of performance gap recovery in W2S. The analysis is supported by experiments on synthetic regression problems, as well as real vision and NLP tasks.

Brian S. Lin, Jiaxin Yuan, Zihan Zhou et al.

As large language models (LLMs) increasingly exhibit human-like capabilities, a fundamental question emerges: How can we enable LLMs to learn the underlying patterns from limited examples in entirely novel environments and apply them effectively? This question is central to the ability of LLMs in inductive reasoning. Existing research on LLM-based inductive reasoning can be broadly categorized based on whether the underlying rules are expressible via explicit mathematical equations. However, many recent studies in the beyond-equations category have emphasized rule design without grounding them in specific scenarios. Inspired by the parallels between inductive reasoning and human scientific discovery, we propose the task of LLM-Based Scientific Inductive Reasoning Beyond Equations and introduce a new benchmark, SIRBench-V1, to evaluate the inductive reasoning abilities of LLMs in scientific settings. Our experimental results show that current LLMs still struggle with this task, underscoring its difficulty and the need for further advancement in this area.