# Comparing Differentiable Logics for Learning Systems: A Research Preview

arXiv: https://arxiv.org/abs/2311.09809 · HTML: https://mlsanity.com/paper/2311.09809/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 15 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Results](https://mlsanity.com/paper/2212.10376/) (2022)
- [On Robustness Metrics for Learning STL Tasks](https://mlsanity.com/paper/2003.06041/) (2020)
- [Logic of Differentiable Logics: Towards a Uniform Semantics of DL](https://mlsanity.com/paper/2303.10650/) (2023)
- [Continuous Safety Verification of Neural Networks](https://mlsanity.com/paper/2010.05689/) (2020)

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

- [Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs](https://mlsanity.com/paper/2401.06379/) (2024)

## Abstract (arXiv)

Extensive research on formal verification of machine learning (ML) systems indicates that learning from data alone often fails to capture underlying background knowledge. A variety of verifiers have been developed to ensure that a machine-learnt model satisfies correctness and safety properties, however, these verifiers typically assume a trained network with fixed weights. ML-enabled autonomous systems are required to not only detect incorrect predictions, but should also possess the ability to self-correct, continuously improving and adapting. A promising approach for creating ML models that inherently satisfy constraints is to encode background knowledge as logical constraints that guide the learning process via so-called differentiable logics. In this research preview, we compare and evaluate various logics from the literature in weakly-supervised contexts, presenting our findings and highlighting open problems for future work. Our experimental results are broadly consistent with results reported previously in literature; however, learning with differentiable logics introduces a new hyperparameter that is difficult to tune and has significant influence on the effectiveness of the logics.