From Generalist to Specialist Representation
Provides foundational theoretical guarantees for unsupervised learning of task-relevant representations, addressing a key problem in representation learning for downstream tasks.
The paper proves that, in a fully unsupervised nonparametric setting, the structure between time steps and tasks is identifiable, and task-relevant latent representations can be disentangled from irrelevant parts via sparsity regularization, establishing the first general nonparametric identifiability guarantees for moving from generalist to specialist models.
Given a generalist model, learning a task-relevant specialist representation is fundamental for downstream applications. Identifiability, the asymptotic guarantee of recovering the ground-truth representation, is critical because it sets the ultimate limit of any model, even with infinite data and computation. We study this problem in a completely nonparametric setting, without relying on interventions, parametric forms, or structural constraints. We first prove that the structure between time steps and tasks is identifiable in a fully unsupervised manner, even when sequences lack strict temporal dependence and may exhibit disconnections, and task assignments can follow arbitrarily complex and interleaving structures. We then prove that, within each time step, the task-relevant latent representation can be disentangled from the irrelevant part under a simple sparsity regularization, without any additional information or parametric constraints. Together, these results establish a hierarchical foundation: task structure is identifiable across time steps, and task-relevant latent representations are identifiable within each step. To our knowledge, each result provides a first general nonparametric identifiability guarantee, and together they mark a step toward provably moving from generalist to specialist models.