# TT-Sparse: Learning Sparse Rule Models with Differentiable Truth Tables

arXiv: https://arxiv.org/abs/2603.07606 · HTML: https://mlsanity.com/paper/2603.07606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Builds on (most cited first, 21 of 21)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [TabLLM: Few-shot Classification of Tabular Data with Large Language Models](https://mlsanity.com/paper/2210.10723/) (2022)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [TabM: Advancing Tabular Deep Learning with Parameter-Efficient Ensembling](https://mlsanity.com/paper/2410.24210/) (2024)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [Learning with Differentiable Perturbed Optimizers](https://mlsanity.com/paper/2002.08676/) (2020)
- [Differentiable Patch Selection for Image Recognition](https://mlsanity.com/paper/2104.03059/) (2021)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Convolutional Differentiable Logic Gate Networks](https://mlsanity.com/paper/2411.04732/) (2024)
- [Generalized Linear Rule Models](https://mlsanity.com/paper/1906.01761/) (2019)
- [Differentiable Weightless Neural Networks](https://mlsanity.com/paper/2410.11112/) (2024)
- [Differentiable Top-k Classification Learning](https://mlsanity.com/paper/2206.07290/) (2022)
- [Interpretable multiclass classification by MDL-based rule lists](https://mlsanity.com/paper/1905.00328/) (2019)
- [Neural Network-Based Rule Models With Truth Tables](https://mlsanity.com/paper/2309.09638/) (2023)

## Abstract (arXiv)

Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust. While rule-based models offer global and exact interpretability, learning rule sets that simultaneously achieve high predictive performance and low, human-understandable complexity remains challenging. To address this, we introduce TT-Sparse, a flexible neural building block that leverages differentiable truth tables as nodes to learn sparse, effective connections. A key contribution of our approach is a new soft TopK operator with straight-through estimation for learning discrete, cardinality-constrained feature selection in an end-to-end differentiable manner. Crucially, the forward pass remains sparse, enabling efficient computation and exact symbolic rule extraction. As a result, each node (and the entire model) can be transformed exactly into compact, globally interpretable DNF/CNF Boolean formulas via Quine-McCluskey minimization. Extensive empirical results across 28 datasets spanning binary, multiclass, and regression tasks show that the learned sparse rules exhibit superior predictive performance with lower complexity compared to existing state-of-the-art methods.