Go to ICLR 2026 Workshop GRaM homepageMutual Information and Task-Relevant Latent Dimensionality
Track: long paper (up to 8 pages)
Keywords: Latent Dimensionality, Dimensionality estimation, Intrinsic Dimension, Mutual Information, MI Estimation
TL;DR: We develop a mutual-information–based method for accurately inferring task-relevant dimensionality while preserving latent geometry, validated on synthetic noisy high-dimensional data and applied to critical and chaotic physics systems.
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, and we address this by introducing a hybrid critic that retains an explicit dimensional bottleneck while allowing flexible nonlinear cross-view interactions, thereby preserving the latent geometry. We further propose a one-shot protocol that reads off the effective dimension from a single over-parameterized hybrid model, without sweeping over bottleneck sizes. We validate the approach on synthetic problems with known task-relevant dimension. We extend the approach to intrinsic dimensionality by constructing paired views of a single dataset, enabling comparison with classical geometric dimension estimators. In noisy regimes where those estimators degrade, our approach remains reliable. Finally, we demonstrate the utility of the method on multiple physics datasets.
Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.
Submission Number: 79
Loading