# Minimal Sufficient Representations for Self-interpretable Deep Neural Networks

arXiv: https://arxiv.org/abs/2603.24041 · HTML: https://mlsanity.com/paper/2603.24041/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Deep Learning for Case-Based Reasoning through Prototypes: A Neural Network that Explains Its Predictions](https://mlsanity.com/paper/1710.04806/) (2017)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [DeepPINK: reproducible feature selection in deep neural networks](https://mlsanity.com/paper/1809.01185/) (2018)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Sparse-Input Neural Network using Group Concave Regularization](https://mlsanity.com/paper/2307.00344/) (2023)
- [Penalized Generative Variable Selection](https://mlsanity.com/paper/2402.16661/) (2024)

## Abstract (arXiv)

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 interpretability, reducing error by up to 30% on real-world datasets while automatically uncovering human-interpretable discriminative patterns. Our results suggest that interpretability and statistical rigor can be embedded directly into deep architectures without sacrificing performance.