# Provable FDR Control for Deep Feature Selection: Deep MLPs and Beyond

arXiv: https://arxiv.org/abs/2512.04696 · HTML: https://mlsanity.com/paper/2512.04696/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 20 of 20)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression](https://mlsanity.com/paper/1804.09753/) (2018)
- [DeepPINK: reproducible feature selection in deep neural networks](https://mlsanity.com/paper/1809.01185/) (2018)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [The Asymptotic Distribution of the MLE in High-dimensional Logistic Models: Arbitrary Covariance](https://mlsanity.com/paper/2001.09351/) (2020)
- [False Discovery Rate Control via Data Splitting](https://mlsanity.com/paper/2002.08542/) (2020)
- [Metropolized Knockoff Sampling](https://mlsanity.com/paper/1903.00434/) (2019)
- [Controlling False Discovery Rate Using Gaussian Mirrors](https://mlsanity.com/paper/1911.09761/) (2019)
- [A Scale-free Approach for False Discovery Rate Control in Generalized Linear Models](https://mlsanity.com/paper/2007.01237/) (2020)
- [Spectrum-Aware Debiasing: A Modern Inference Framework with Applications to Principal Components Regression](https://mlsanity.com/paper/2309.07810/) (2023)
- [Neural Gaussian Mirror for Controlled Feature Selection in Neural Networks](https://mlsanity.com/paper/2010.06175/) (2020)
- [False Discovery Rate Control Under General Dependence By Symmetrized Data Aggregation](https://mlsanity.com/paper/2002.11992/) (2020)
- [On the testing of multiple hypothesis in sliced inverse regression](https://mlsanity.com/paper/2210.05873/) (2022)
- [High-Dimensional Single-Index Models: Link Estimation and Marginal Inference](https://mlsanity.com/paper/2404.17812/) (2024)

## Built on by (most cited first, 1 of 1)

- [Model-Agnostic FDR Control via Group Gaussian Mirror and Permutation SHAP](https://mlsanity.com/paper/2608.00989/) (2026)

## Abstract (arXiv)

We develop a flexible feature selection framework based on deep neural networks that approximately controls the false discovery rate (FDR), a measure of Type-I error. The method applies to architectures whose first layer is fully connected. From the second layer onward, it accommodates multilayer perceptrons (MLPs) of arbitrary width and depth, convolutional and recurrent networks, attention mechanisms, residual connections, and dropout. The procedure also accommodates stochastic gradient descent with data-independent initializations and learning rates. To the best of our knowledge, this is the first work to provide a theoretical guarantee of FDR control for feature selection within such a general deep learning setting. Our analysis is built upon a multi-index data-generating model and an asymptotic regime in which the feature dimension n diverges faster than the latent dimension q*, while the sample size, the number of training iterations, the network depth, and hidden layer widths are left unrestricted. Under this setting, we show that each coordinate of the gradient-based feature-importance vector admits a marginal normal approximation, thereby supporting the validity of asymptotic FDR control. As a theoretical limitation, we assume B-right orthogonal invariance of the design matrix, and we discuss broader generalizations. We also present numerical experiments that underscore the theoretical findings.