What Do Latent Action Models Actually Learn?

Latent action models (LAMs) aim to learn action-relevant changes from unlabeled videos by compressing changes between frames as latents. However, differences between video frames can be caused by controllable changes as well as exogenous noise, leading to an important concern -do latents capture the changes caused by actions or irrelevant noise? This paper studies this issue analytically, presenting a linear model that encapsulates the essence of LAM learning, while being tractable. This provides several insights, including connections between LAM and principal component analysis (PCA), desiderata of the data-generating policy, and justification of strategies to encourage learning controllable changes using data augmentation, data cleaning, and auxiliary action-prediction. These findings are validated through numerical simulations, as well as experiments in more realistic settings. This investigation is the first to rigorously investigate how the structure of observations, actions, and noise influence LAM learning.