Mutual information and task-relevant latent dimensionality
arXiv:2602.08105v1 Announce Type: cross Abstract: Estimating the dimensionality of the latent representation needed for prediction — the task-relevant dimension — is a difficult, largely unsolved problem with broad scientific applications. We cast it as an Information Bottleneck question: what embedding bottleneck dimension is sufficient to compress predictor and predicted views while preserving their mutual information (MI). This repurposes neural MI estimators for dimensionality estimation. We show that standard neural estimators with separable/bilinear critics systematically inflate the inferred dimension, […]