# Learning Interpretable Differentiable Logic Networks for Tabular Regression

arXiv: https://arxiv.org/abs/2505.23615 · HTML: https://mlsanity.com/paper/2505.23615/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 56 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 30 of 35)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Atom: Low-bit Quantization for Efficient and Accurate LLM Serving](https://mlsanity.com/paper/2310.19102/) (2023)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [Neural Oblivious Decision Ensembles for Deep Learning on Tabular Data](https://mlsanity.com/paper/1909.06312/) (2019)
- [FINN: A Framework for Fast, Scalable Binarized Neural Network Inference](https://mlsanity.com/paper/1612.07119/) (2016)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [Supersparse Linear Integer Models for Optimized Medical Scoring Systems](https://mlsanity.com/paper/1502.04269/) (2015)
- [Deep Neural Decision Trees](https://mlsanity.com/paper/1806.06988/) (2018)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Adaptive Neural Trees](https://mlsanity.com/paper/1807.06699/) (2018)

## Built on by (most cited first, 2 of 2)

- [LILogic Net: Compact Logic Gate Networks with Learnable Connectivity for Efficient Hardware Deployment](https://mlsanity.com/paper/2511.12340/) (2025)
- [Learning Interpretable Differentiable Logic Networks for Time-Series Classification](https://mlsanity.com/paper/2508.17512/) (2025)

## Abstract (arXiv)

Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed Differentiable Logic Networks (DLNs) to address these issues for tabular classification based on relaxing discrete logic into a differentiable form, thereby enabling gradient-based learning of networks built from binary logic operations. DLNs offer interpretable reasoning and substantially lower inference cost. We extend the DLN framework to supervised tabular regression. We first redesign the final output layer (the SumLayer) to support continuous targets. More critically, we find the original two-phase training procedure used for classification is suboptimal for regression, and thus develop a unified, single-stage optimization procedure. We also demonstrate that temperature annealing of the network's differentiable relaxations is decisive for achieving stable convergence and high accuracy. We evaluate the resulting model on 15 public regression benchmarks, comparing it with modern neural networks and classical regression baselines. Regression DLNs match or exceed baseline accuracy while preserving interpretability and fast inference. Our results show that DLNs are a viable, cost-effective alternative for regression tasks, especially where model transparency and computational efficiency are important.