# Extracting Formulae in Many-Valued Logic from Deep Neural Networks

arXiv: https://arxiv.org/abs/2401.12113 · HTML: https://mlsanity.com/paper/2401.12113/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 14 of 14)

- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [Deep Neural Network Approximation Theory](https://mlsanity.com/paper/1901.02220/) (2019)
- [Representation Benefits of Deep Feedforward Networks](https://mlsanity.com/paper/1509.08101/) (2015)
- [The staircase property: How hierarchical structure can guide deep learning](https://mlsanity.com/paper/2108.10573/) (2021)
- [Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes](https://mlsanity.com/paper/2302.12553/) (2023)

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

- [Complete Identification of Deep ReLU Networks through Lukasiewicz Logic](https://mlsanity.com/paper/2602.00266/) (2026)

## Abstract (arXiv)

We propose a new perspective on deep ReLU networks, namely as circuit counterparts of Lukasiewicz infinite-valued logic -- a many-valued (MV) generalization of Boolean logic. An algorithm for extracting formulae in MV logic from deep ReLU networks is presented. As the algorithm applies to networks with general, in particular also real-valued, weights, it can be used to extract logical formulae from deep ReLU networks trained on data.