PRISM: Path-guided Reasoning and Interpretation for Semantic Models 🧠🔍

Overview

PRISM is a neuro-symbolic explanation framework for Link Prediction (LP) over Knowledge Graphs (KGs). It explains why a Knowledge Graph Completion (KGC) model predicts a missing fact by identifying the facts that are most relevant to the prediction.

PRISM combines symbolic reasoning with Knowledge Graph Embeddings (KGEs) to generate explanations that are:

• Faithful to the behaviour of the underlying LP model.
• Interpretable through explicit KG facts and symbolic reasoning patterns.
• Efficient by reducing the number of candidate facts that must be explored.

🎯 PRISM builds on top of the KELPIE [1] framework and extends it with neuro-symbolic explanation strategies that exploit both explicit semantic knowledge and latent embedding-based representations.

PRISM associates each predicted relationship with two complementary forms of explanation:

• Necessary explanations identify facts that are essential for the prediction. Removing these facts should weaken or invalidate the predicted relationship.
• Sufficient explanations identify additional facts that support the predicted relationship. Adding or emphasizing these facts should strengthen the prediction.

We empirically evaluate PRISM across 336 testbeds for necessary explanations and 336 testbeds for sufficient explanations, assessing explanation quality, faithfulness, interpretability, and computational efficiency.

Note: The complete reproducibility of all testbeds is estimated to require approximately five or six months.

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🔎 Exemplary Subgraph

Below is an example of how PRISM explains a missing link prediction in a KG:

The figure illustrates how PRISM uses symbolic rules, KG structure, and embedding-based relevance signals to generate necessary and sufficient explanations for a predicted missing relationship.

🧾 Repository Structure

Path	Description
data/	All experiment-related artifacts.
├── 0_rules/	Symbolic rules used during explanation generation.
├── 1_triple_store/	KG triples, including train, validation, and test splits.
├── 2_stored_models/	Pre-trained KGE models.
├── 3_filtered_ranks/	LP model predictions with ranking information.
├── 4_predictions/	Tab-separated triples used as input for explanation generation.
├── 5_explanations/	Explanations generated by PRISM and used for verification.
├── 6_statistics/	Evaluation metrics from explanation generation and verification.
├── 7_logging/	Logs for tracking experimental runs.
├── temp/	Temporary files generated during rule and triple processing.
scripts/	Benchmark-specific folders containing run.sh scripts and configuration files.
src/	Source code of the project.
├── embeddings/	Training, testing, explanation, and verification scripts for KGE models.
├── explanation_builders/	Logic for constructing necessary and sufficient explanations.
├── link_prediction/	Embedding model implementations and LP utilities.
├── model/	PRISM and KELPIE architecture logic.
├── prefilters/	Filtering strategies for selecting semantically relevant candidate facts.
├── relevance_engines/	Score computation for candidate explanatory triples.
├── rules/	Code and binaries for symbolic rule mining.
create_environment.sh	Shell script to install Python dependencies.
requirements.txt	Python dependency list.
config.py	Project-wide configuration values.

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🔁 Reproducibility of Experiments

Reproducing the results in our study is straightforward with the provided scripts and input configurations.

✅ Steps to Reproduce

1. Set up the environment

   bash create_environment.sh

2. Prepare symbolic rules

   Run AMIE [2] with the appropriate training triples:

   java -jar amie -const -minpca 0.7 -dpr -optimai path/to/train.txt > path/to/rules.txt

3. Navigate to a benchmark folder

   cd scripts/FrenchRoyalty  # or DB100K, FB15K-237, YAGO3-10

4. Edit the input configuration

   Update input.json or the benchmark-specific configuration file to specify:

   • the explanation mode: necessary or sufficient,
   • the embedding model: TransE, ComplEx, or ConvE,
   • the explanation builders to be used,
   • the rule files and prediction files.

5. Run explanation generation

   bash run.sh

6. Analyze the results

   Explanation and verification metrics are stored in the data/ folder, especially in:

   • 6_statistics/
   • 7_logging/

🧪 Our full experimental pipeline was executed using:

• OS: Ubuntu 20.04.5
• Python: 3.10
• GPU: NVIDIA A100 with 40 GiB VRAM
• CUDA: 12.2

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Running PRISM 🚀

Navigate to a benchmark-specific folder and execute run.sh to generate explanations:

cd scripts/FrenchRoyalty
bash run.sh

This executes the explanation extraction script, for example transe-fr-script.py, using the configuration specified in input_transe_fr.json. The script generates explanations across the selected explanation builders and stores the outputs in the corresponding data/ subfolders.

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Example input_transe_fr.json

{
  "dataset": "FR_Reduced_2K",
  "embedding_model": "TransE",
  "predictions": "FR_10.csv",
  "rules_file": "fr_reduced_2k_rules_optimai.csv",
  "editorial_rules": "FR_editorial_rules.csv",
  "dimension": 50,
  "batch_size": 1906,
  "negative_samples_ratio": 5,
  "e_regularizer_weight": 50.0,
  "v_regularizer_weight": 2.0,
  "margin": 2,
  "e_learning_rate": 0.003,
  "v_learning_rate": 0.00003,
  "e_epochs": 100,
  "v_epochs": 10,
  "thr": 0.7,
  "coverage": 3,
  "mode": "sufficient",
  "builders": ["kelpie", "pca", "frequency"]
}

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Parameter Description

Parameter	Description
dataset	Name of the dataset, for example FR_Reduced_2K.
embedding_model	KGE model used for LP, such as TransE, ComplEx, or ConvE.
predictions	CSV file containing the predictions to explain.
rules_file	Symbolic rules generated by AMIE.
editorial_rules	Optional user-defined rules.
dimension	Embedding vector dimension.
batch_size	Batch size for model training.
negative_samples_ratio	Number of negative samples per positive triple.
e_regularizer_weight	Regularization weight for embedding training.
v_regularizer_weight	Regularization weight during verification.
margin	Margin used in the loss function.
e_learning_rate	Learning rate for embedding training.
v_learning_rate	Learning rate for verification.
e_epochs	Number of epochs for embedding training.
v_epochs	Number of epochs used during verification.
thr	Threshold used for rule or candidate filtering, for example PCA confidence.
coverage	Number of explanations to return per prediction.
mode	Explanation type: necessary or sufficient.
builders	List of explanation builders to apply.

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⚙️ Hyperparameters for Training Knowledge Graph Embedding Models

The experimental evaluation encompasses three embedding representation spaces: TransE [6], ConvE [7], and ComplEx [8].

Model	Epochs	Batch Size	Learning Rate	Embedding Dim
TransE	100	2048	0.001	200
ConvE	500	128	0.003	200
ComplEx	50	128	0.1	100

💡 These hyperparameters were tuned for fair comparison and consistent results across benchmarks.

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📚 Benchmark Knowledge Graphs

📈 Statistics

Benchmark	Entities	Relations	Triples
French Royalty	2,601	12	10,526
YAGO3-10	123,086	37	1,080,264
FB15K-237	40,943	18	151,442
DB100K	99,604	470	695,572

📄 Benchmark Descriptions

• French Royalty 👑 [3]
  A curated KG derived from DBpedia about historical French royals, including facts such as gender, spouse, successor, and related relations.
  Entities: 2,601 | Triples: 10,526 | Relations: 12

• YAGO3-10 🌍 [9]
  A dense subset of the multilingual YAGO3 KG with rich information about persons, cities, sports, and organizations.
  Entities: 123,086 | Triples: 1,080,264 | Relations: 37

• FB15K-237 🎬 [10]
  A subset of Freebase with inverse relations removed to avoid data leakage, covering domains such as music, sports, film, and people.
  Entities: 40,943 | Triples: 151,442 | Relations: 18

• DB100K 📘 [11]
  A DBpedia-derived KG focused on hierarchical and structured relations. Only entities with rich neighborhoods are retained.
  Entities: 99,604 | Triples: 695,572 | Relations: 470

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License 📄

This project is licensed under the MIT License.

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References 📚

1. Andrea Rossi et al. (2022). Explaining Link Prediction Systems. SIGMOD.
2. J. Lajus et al. (2020). Fast and Exact Rule Mining with AMIE 3. ESWC.
3. Halliwell et al. (2021). User Scored Evaluation of Non-Unique Explanations. K-CAP.
4. Kristina Toutanova and Danqi Chen (2015). Observed versus Latent Features for Knowledge Base and Text Inference. ACL Workshop.
5. Jingxiong Wang et al. (2023). Attention-Based High-Low Level Features Interaction for Knowledge Graph Embedding. IPM.
6. Bordes et al. (2013). Translating Embeddings for Modeling Multi-Relational Data. NeurIPS.
7. Dettmers et al. (2018). Convolutional 2D Knowledge Graph Embeddings. AAAI.
8. Trouillon et al. (2016). Complex Embeddings for Simple Link Prediction. ICML.
9. Mahdisoltani et al. (2015). YAGO3: A Knowledge Base from Multilingual Wikipedias. CIDR.
10. Toutanova et al. (2015). Observed versus Latent Features for Knowledge Base and Text Inference. ACL.
11. Wang et al. (2023). Knowledge Graph Embedding Model with Attention-Based High-Low Level Features Interaction Convolutional Network. IPM.