# Improving Neural-based Classification with Logical Background Knowledge

arXiv: https://arxiv.org/abs/2402.13019 · HTML: https://mlsanity.com/paper/2402.13019/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 16 of 16)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [Coherent Hierarchical Multi-Label Classification Networks](https://mlsanity.com/paper/2010.10151/) (2020)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)
- [Neuro-Symbolic Entropy Regularization](https://mlsanity.com/paper/2201.11250/) (2022)
- [Integrating Learning and Reasoning with Deep Logic Models](https://mlsanity.com/paper/1901.04195/) (2019)
- [Semantic Strengthening of Neuro-Symbolic Learning](https://mlsanity.com/paper/2302.14207/) (2023)
- [T-Norms Driven Loss Functions for Machine Learning](https://mlsanity.com/paper/1907.11468/) (2019)

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

- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [Attack logics, not outputs: Towards efficient robustification of deep neural networks by falsifying concept-based properties](https://mlsanity.com/paper/2510.03320/) (2025)

## Abstract (arXiv)

Neurosymbolic AI is a growing field of research aiming to combine neural networks learning capabilities with the reasoning abilities of symbolic systems. This hybridization can take many shapes. In this paper, we propose a new formalism for supervised multi-label classification with propositional background knowledge. We introduce a new neurosymbolic technique called semantic conditioning at inference, which only constrains the system during inference while leaving the training unaffected. We discuss its theoritical and practical advantages over two other popular neurosymbolic techniques: semantic conditioning and semantic regularization. We develop a new multi-scale methodology to evaluate how the benefits of a neurosymbolic technique evolve with the scale of the network. We then evaluate experimentally and compare the benefits of all three techniques across model scales on several datasets. Our results demonstrate that semantic conditioning at inference can be used to build more accurate neural-based systems with fewer resources while guaranteeing the semantic consistency of outputs.