# LassoFlexNet: Flexible Neural Architecture for Tabular Data

arXiv: https://arxiv.org/abs/2603.20631 · HTML: https://mlsanity.com/paper/2603.20631/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 29 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [On Embeddings for Numerical Features in Tabular Deep Learning](https://mlsanity.com/paper/2203.05556/) (2022)
- [TabM: Advancing Tabular Deep Learning with Parameter-Efficient Ensembling](https://mlsanity.com/paper/2410.24210/) (2024)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [TabR: Tabular Deep Learning Meets Nearest Neighbors in 2023](https://mlsanity.com/paper/2307.14338/) (2023)
- [TabReD: Analyzing Pitfalls and Filling the Gaps in Tabular Deep Learning Benchmarks](https://mlsanity.com/paper/2406.19380/) (2024)
- [A Performance-Driven Benchmark for Feature Selection in Tabular Deep Learning](https://mlsanity.com/paper/2311.05877/) (2023)
- [LassoLayer: Nonlinear Feature Selection by Switching One-to-one Links](https://mlsanity.com/paper/2108.12165/) (2021)

## Abstract (arXiv)

Despite their dominance in vision and language, deep neural networks often underperform relative to tree-based models on tabular data. To bridge this gap, we incorporate five key inductive biases into deep learning: robustness to irrelevant features, axis alignment, localized irregularities, feature heterogeneity, and training stability. We propose LassoFlexNet, an architecture that evaluates the linear and nonlinear marginal contribution of each input via Per-Feature Embeddings, and sparsely selects relevant variables using a Tied Group Lasso mechanism. Because these components introduce optimization challenges that destabilize standard proximal methods, we develop a Sequential Hierarchical Proximal Adaptive Gradient optimizer with exponential moving averages (EMA) to ensure stable convergence. Across 52 datasets from three benchmarks, LassoFlexNet matches or outperforms leading tree-based models, achieving up to a 10% relative gain, while maintaining Lasso-like interpretability. We substantiate these empirical results with ablation studies and theoretical proofs confirming the architecture's enhanced expressivity and structural breaking of undesired rotational invariance.