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On the verification of Embeddings using Hybrid Markov Logic

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Anup Shakya, Abisha Thapa Magar, Somdeb Sarkhel, Deepak Venugopal

Machine Learning · Submitted 13 Dec 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We illustrate verification in Graph Neural Networks, Deep Knowledge Tracing and Intelligent Tutoring Systems to demonstrate the generality of our approach.

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arXiv ID2312.08287 (version 1)
Pith IDGEISMVBJ, Pith's permanent record of this paper and its review
CitationAbisha Thapa Magar, Anup Shakya, Deepak Venugopal, Somdeb Sarkhel. "On the verification of Embeddings using Hybrid Markov Logic." arXiv:2312.08287 (2023). https://pith.science/paper/GEISMVBJ
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,893 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.08 · human participants 0.09 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.05 0.03 asserted 1.00
s1 However, in many cases, we would want to verify more complex properties of a learned representation. gap 0.89 0.08 0.03 asserted 0.62
s2 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. contribution 0.66 0.84 0.19 asserted 0.99
s3 We present an approach to learn parameters for the properties within this framework. contribution 0.54 0.93 0.07 asserted 1.00
s4 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. method 0.83 0.95 0.15 asserted 1.00
s5 We illustrate verification in Graph Neural Networks, Deep Knowledge Tracing and Intelligent Tutoring Systems to demonstrate the generality of our approach. contribution 0.77 0.91 0.26 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.49.

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  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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.

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