# LassoNet: A Neural Network with Feature Sparsity

arXiv: https://arxiv.org/abs/1907.12207 · HTML: https://mlsanity.com/paper/1907.12207/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2019.

## Built on by (most cited first, 30 of 82)

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- [Sparsity in Continuous-Depth Neural Networks](https://mlsanity.com/paper/2210.14672/) (2022)
- [LLM-Lasso: A Robust Framework for Domain-Informed Feature Selection and Regularization](https://mlsanity.com/paper/2502.10648/) (2025)
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- [Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networks](https://mlsanity.com/paper/2204.01682/) (2022)
- [The Contextual Lasso: Sparse Linear Models via Deep Neural Networks](https://mlsanity.com/paper/2302.00878/) (2023)
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- [Unveiling the Power of Sparse Neural Networks for Feature Selection](https://mlsanity.com/paper/2408.04583/) (2024)
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## Abstract (arXiv)

Much work has been done recently to make neural networks more interpretable, and one obvious approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or ℓ1-regularized) regression assigns zero weights to the most irrelevant or redundant features, and is widely used in data science. However the Lasso only applies to linear models. Here we introduce LassoNet, a neural network framework with global feature selection. Our approach enforces a hierarchy: specifically a feature can participate in a hidden unit only if its linear representative is active. Unlike other approaches to feature selection for neural nets, our method uses a modified objective function with constraints, and so integrates feature selection with the parameter learning directly. As a result, it delivers an entire regularization path of solutions with a range of feature sparsity. On systematic experiments, LassoNet significantly outperforms state-of-the-art methods for feature selection and regression. The LassoNet method uses projected proximal gradient descent, and generalizes directly to deep networks. It can be implemented by adding just a few lines of code to a standard neural network.