Memorize, Adapt, Ignore: Diagnosing Robot Learning Mechanisms under Training Data Variation

Training data variation, whether through designing a domain randomization (DR) scheme in simulation or curating demonstrations for imitation learning, is a primary lever for improving the robustness of robotic manipulation policies. Yet its underlying mechanisms remain poorly understood, and practitioners typically select randomization parameters through expensive trial and error. We investigate these mechanisms through a series of case studies, randomizing object size, color, and type as well as scene lighting and linguistic prompts across settings including pick-and-place RL in ManiSkill and fine-tuning of vision-language-action (VLA) models on LIBERO and RoboTwin. We examine both model behavior and internal representations, using the empirical neural tangent kernel (NTK) as our primary diagnostic tool. We show that the NTK distinguishes a shift in the internal learning mechanism from \textit{memorizing} different situations with insufficient variation (e.g.\ learning what to do for a large cube, and what to do for a small cube) to \textit{adapting} to the situation at hand with sufficient variation. An NTK-based signal-to-noise ratio also helps distinguish when policies have learned to \emph{ignore} task-irrelevant factors (e.g.\ treating blue and red cubes identically, instead of learning a blue sub-policy and a red sub-policy). We use these diagnostics to develop practical guidance for designing DR schemes, selecting models, and detecting shortcut learning. We further compare different kinds of representations and validate our findings with real-world hardware experiments using ACT-based imitation learning.