# On the verification of Embeddings using Hybrid Markov Logic

arXiv: https://arxiv.org/abs/2312.08287 · HTML: https://mlsanity.com/paper/2312.08287/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 13 Dec 2023.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [Measuring Neural Net Robustness with Constraints](https://mlsanity.com/paper/1605.07262/) (2016)
- [Introduction to Neural Network Verification](https://mlsanity.com/paper/2109.10317/) (2021)
- [Embedding Comparator: Visualizing Differences in Global Structure and Local Neighborhoods via Small Multiples](https://mlsanity.com/paper/1912.04853/) (2019)
- [Abstraction based Output Range Analysis for Neural Networks](https://mlsanity.com/paper/2007.09527/) (2020)
- [Neuro-Symbolic Verification of Deep Neural Networks](https://mlsanity.com/paper/2203.00938/) (2022)
- [Scalable and Equitable Math Problem Solving Strategy Prediction in Big Educational Data](https://mlsanity.com/paper/2308.03892/) (2023)

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

- [Verifying Relational Explanations: A Probabilistic Approach](https://mlsanity.com/paper/2401.02703/) (2024)
- [Disentangling Fine-Tuning from Pre-Training in Visual Captioning with Hybrid Markov Logic](https://mlsanity.com/paper/2503.13847/) (2025)

## Abstract (arXiv)

The standard approach to verify representations learned by Deep Neural Networks is to use them in specific tasks such as classification or regression, and measure their performance based on accuracy in such tasks. However, in many cases, we would want to verify more complex properties of a learned representation. To do this, we propose a framework based on a probabilistic first-order language, namely, Hybrid Markov Logic Networks (HMLNs) where we specify properties over embeddings mixed with symbolic domain knowledge. We present an approach to learn parameters for the properties within this framework. Further, we develop a verification method to test embeddings in this framework by encoding this task as a Mixed Integer Linear Program for which we can leverage existing state-of-the-art solvers. We illustrate verification in Graph Neural Networks, Deep Knowledge Tracing and Intelligent Tutoring Systems to demonstrate the generality of our approach.