[2603.24041] Minimal Sufficient Representations for Self-interpretable Deep Neural Networks

Statistics > Methodology arXiv:2603.24041 (stat) [Submitted on 25 Mar 2026] Title:Minimal Sufficient Representations for Self-interpretable Deep Neural Networks Authors:Zhiyao Tan, Liu Li, Huazhen Lin View a PDF of the paper titled Minimal Sufficient Representations for Self-interpretable Deep Neural Networks, by Zhiyao Tan and 2 other authors View PDF HTML (experimental) Abstract:Deep neural networks (DNNs) achieve remarkable predictive performance but remain difficult to interpret, largely due to overparameterization that obscures the minimal structure required for interpretation. Here we introduce DeepIn, a self-interpretable neural network framework that adaptively identifies and learns the minimal representation necessary for preserving the full expressive capacity of standard DNNs. We show that DeepIn can correctly identify the minimal representation dimension, select relevant variables, and recover the minimal sufficient network architecture for prediction. The resulting estimator achieves optimal non-asymptotic error rates that adapt to the learned minimal dimension, demonstrating that recovering minimal sufficient structure fundamentally improves generalization error. Building on these guarantees, we further develop hypothesis testing procedures for both selected variables and learned representations, bridging deep representation learning with formal statistical inference. Across biomedical and vision benchmarks, DeepIn improves both predictive accuracy and interp...