Motivation

We need to understand how language models develop complex skills. Previous works on probing and evaluating language models gives evidence that LMs can learn abstractions and composition abilities grows with scale. We aim to understand further in two axis:

• Sample complexity as a measure of compositional abilities. LMs do not generalize perfectly, but rather jaggedly. Sample complexity at the difficulty frontier may be a fine-grained way to characterize how well they generalize.
• Abstract “skills” that can (ideally mechanistically) explain OOD generalization.
• Why does scaling compute continue to work? Can we observe that the marginal difficulty of skill learning is independent of the complexity of the skill?
• Mechanistic side: localization of the learned skill, and that could lead to explanation of model scale vs learning speed
• Scale up the compositional skill synthetic data generation, and see if the pattern holds.

RQ1: How “skewed” can the training length distribution be?

RQ2: How does skill abstraction help with OOD generalization?

RQ3: Composition scaling law with compute

RQ4: Tracking skill learning on a data-point level