# Explainable Neural Networks with Guarantees: A Sparse Estimation Approach

arXiv: https://arxiv.org/abs/2501.02010 · HTML: https://mlsanity.com/paper/2501.02010/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 2 Jan 2025.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Object Detectors Emerge in Deep Scene CNNs](https://mlsanity.com/paper/1412.6856/) (2014)
- [What Is One Grain of Sand in the Desert? Analyzing Individual Neurons in Deep NLP Models](https://mlsanity.com/paper/1812.09355/) (2018)
- [Interpreting Deep Visual Representations via Network Dissection](https://mlsanity.com/paper/1711.05611/) (2017)
- [Data-dependent Sample Complexity of Deep Neural Networks via Lipschitz Augmentation](https://mlsanity.com/paper/1905.03684/) (2019)
- [Deterministic PAC-Bayesian generalization bounds for deep networks via generalizing noise-resilience](https://mlsanity.com/paper/1905.13344/) (2019)
- [Why ResNet Works? Residuals Generalize](https://mlsanity.com/paper/1904.01367/) (2019)
- [Implicit Bias of Large Depth Networks: a Notion of Rank for Nonlinear Functions](https://mlsanity.com/paper/2209.15055/) (2022)
- [On Measuring Excess Capacity in Neural Networks](https://mlsanity.com/paper/2202.08070/) (2022)
- [Exploring and Adapting Chinese GPT to Pinyin Input Method](https://mlsanity.com/paper/2203.00249/) (2022)
- [Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation](https://mlsanity.com/paper/2204.00930/) (2022)
- [Fine-grained Generalization Analysis of Vector-valued Learning](https://mlsanity.com/paper/2104.14173/) (2021)
- [Fine-grained Generalization Analysis of Structured Output Prediction](https://mlsanity.com/paper/2106.00115/) (2021)
- [Learning Interpretable Concept Groups in CNNs](https://mlsanity.com/paper/2109.10078/) (2021)

## Abstract (arXiv)

Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel approach to constructing an explainable neural network that harmonizes predictiveness and explainability. Our model, termed SparXnet, is designed as a linear combination of a sparse set of jointly learned features, each derived from a different trainable function applied to a single 1-dimensional input feature. Leveraging the ability to learn arbitrarily complex relationships, our neural network architecture enables automatic selection of a sparse set of important features, with the final prediction being a linear combination of rescaled versions of these features. We demonstrate the ability to select significant features while maintaining comparable predictive performance and direct interpretability through extensive experiments on synthetic and real-world datasets. We also provide theoretical analysis on the generalization bounds of our framework, which is favorably linear in the number of selected features and only logarithmic in the number of input features. We further lift any dependence of sample complexity on the number of parameters or the architectural details under very mild conditions. Our research paves the way for further research on sparse and explainable neural networks with guarantee.