Title: NeuSymEA: Neuro-symbolic Entity Alignment via Variational Inference
Venue: NeurIPS 2025
Accepted: yes
Keywords: entity alignment

neuro-symbolic reasoning

knowledge graphs
Abstract: Entity alignment (EA) aims to merge two knowledge graphs (KGs) by identifying equivalent entity pairs. Existing methods can be categorized into symbolic and neural models. Symbolic models, while precise, struggle with substructure heterogeneity and sparsity, whereas neural models, although effective, generally lack interpretability and cannot handle uncertainty. We propose NeuSymEA, a unified neuro-symbolic reasoning framework that combines the strengths of both methods to fully exploit the cross-KG structural pattern for robust entity alignment. NeuSymEA models the joint probability of all possible pairs' truth scores in a Markov random field, regulated by a set of rules, and optimizes it with the variational EM algorithm. In the E-step, a neural model parameterizes the truth score distributions and infers missing alignments. In the M-step, the rule weights are updated based on the observed and inferred alignments, handling uncertainty. We introduce an efficient symbolic inference engine driven by logic deduction, enabling reasoning with extended rule lengths. NeuSymEA achieves a significant 7.6\% hit@1 improvement on $DBP15K_{ZH-EN}$ compared with strong baselines and demonstrates robustness in low-resource settings, achieving 73.7\% hit@1 accuracy on $DBP15K_{FR-EN}$ with only 1\% pairs as seed alignments. Codes are released at https://github.com/chensyCN/NeuSymEA-NeurIPS25.


Peer reviews:
comments: SUMMARY:
This paper proposes a principled neuro-symbolic reasoning framework via variational EM. It provides efficient optimization through logical decomposition, allowing effective reasoning over large knowledge graphs. The paper also proposes interpretable inference with Hard-anchor and Soft-anchor modes and provides empirical validation demonstrating NeuSymEA’s high alignment accuracy and informative rule-based interpretations on benchmark datasets.

STRENGTHS AND WEAKNESSES:
Quality: The proposed neuro-symbolic reasoning framework is derived in a principled way, although some assumptions and simplifications are applied. The experimental results seem to show the effectiveness of the proposed approach.

Clarity: Mostly clear but can benefit from additional information.

Significance: KG is no longer something critical in the LLM era. For this reason, the work is less important than before. In addition, If LLM is used, the performance of entity alignment may be further improved.

Originality: The proposed neuro-symbolic reasoning framework, although still falls into a standard framework, is sufficiently novel in the way the loss is selected and the optimization process is conducted.

QUESTIONS:
1. LLMs contain large amount of world knowledge and thus may be easily applied to the EA task. Why didn't you consider this as a baseline or additional source of information in the framework?
2. eq. 1 and 2: It's unclear how the confidence and probability is inferred in the symbolic setting.
3. line 194: What exactly does the split mean? is it a split over entities or relations? how would it work if you apply something learned from one dataset to another?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-06-13

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces NeuSymEA, a neuro-symbolic framework for entity alignment in knowledge graphs. The authors propose a unified model that leverages a variational EM algorithm to combine the strengths of neural and symbolic reasoning. The key ideas include modeling the joint probability of alignments in a Markov random field and using a novel logical deduction method to efficiently handle long-range rules. The experimental results on several benchmark datasets demonstrate the effectiveness and interpretability of the proposed approach.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1.  The unification of neural and symbolic methods via a variational EM algorithm is elegant and effective. By optimizing a single joint probability distribution, the framework allows the neural (E-step) and symbolic (M-step) components to mutually enhance one another. This principled approach creates a more coherent and powerful model compared to methods that treat the components separately.\n\n2.  The use of logical deduction to improve efficiency is a significant contribution. By decomposing long rules into unit-length sub-rules, the method avoids the exponential search space typically associated with symbolic reasoning. This makes the inference complexity linear with respect to rule length, allowing the model to leverage complex, multi-hop patterns in a scalable manner.\n\n3.  The framework demonstrates excellent performance, achieving state-of-the-art results on benchmark datasets and showing impressive robustness in low-resource scenarios. A key strength is its built-in explainer, which provides rule-based justifications and confidence scores for its predictions. This combination of high accuracy and strong interpretability is a major advantage.\n\n**Weaknesses:**\n\n1.  The comparison could be strengthened by including more recent baselines. The latest model in the comparison is from 2023.\n\n2.  The paper lacks a direct, head-to-head efficiency comparison with its baselines. While an analysis of NeuSymEA's own scalability and resource usage is provided, there is no data comparing its runtime, memory, or GPU consumption against key competitors. This information is essential for fully evaluating the practical performance trade-offs of the framework.\n\nQUESTIONS:\nSee the Weakness.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-29"}

comments: SUMMARY:
The paper proposes a variational EM method to align two sets of entities from two knowledge bases/graphs. The idea is to have two entity-matching score models: NN model parameterizing a score function, and symbolic model relying on rules. The two models are trained together using a variational EM method. The paper shows that the proposed approach outperforms several baselines (NN and symbolic) on several benchmarks.

STRENGTHS AND WEAKNESSES:
## Strengths
The paper shows strong results on several benchmarks. 

## Weaknesses

* The paper is quite difficult to read, and especially to check the correctness of the EM. For instance, why optimizing (4) & (5) will have the same effect of minimizing the KL? Could the authors explain the intuition behind (9, 10, 11)? why do they make sense?

* Following the "heuristic" of selecting "positive" examples, and the trick for equation (4), in the E and M steps, I'm not pretty sure whether this is EM (could the authors prove that the log-likelihood of the observed data increases?). Instead, I think this is more like a co-training approach because:
   * in step E: the symbolic model annotate data for the NN model
   * in step M: the NN model annotate data for the symbolic 

* In section 4.1, it's unclear to me how a new rule is created. Do we have to consider all possible combinations of unit rules? 

* Line 217 "NeuSymEA unifies them under a joint probability objective." -- which "joint probability" is that? 

* One baseline is PRASE. However, this baseline, from the original paper, is unsupervised learning. Then is it fair for comparison? Also, from the PRASE paper, different benchmarks are used. How well does the proposed approach perform on those benchmarks?

QUESTIONS:
Please see above.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-01

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis research introduces NeuSymEA, a system for entity alignment between two knowledge graphs. The system combines symbolic reasoning (which is accurate and interpretable) with neural models (which handle large-scale noisy data well).\nPrevious work focused on single knowledge graphs, but NeuSymEA specifically handles alignment across different knowledge graphs (currently no more than two at a time).\nThe system treats alignment as a joint probability problem using a Markov random field with logical rule guidance. It uses a variational EM algorithm for training: the neural model predicts alignment probabilities (E-step), then the symbolic model updates rule weights (M-step). To speed up inference, long logic rules are broken into smaller steps.\nThe system also includes an explainer module that shows which logic paths support each predicted alignment. NeuSymEA achieves strong performance on benchmark datasets, especially with limited labeled data, demonstrating both effectiveness and interpretability.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\nQuality\n\nThe proposed method is technically sound and well-motivated. The use of a variational EM algorithm to jointly optimize symbolic rule weights and neural parameters is principled and well-grounded in probabilistic modeling.\nThe paper provides a clever decomposition strategy for long logic rules, which significantly improves inference scalability without compromising symbolic reasoning depth.\nEmpirical evaluation is comprehensive and includes standard EA benchmarks (e.g., DBP15K) with both high-resource and low-resource settings, showcasing consistent gains over prior baselines.\n\nClarity\nThe overall structure is logical, with motivation, methodology, and experiments clearly stated.\nKey components such as the symbolic explainer, logical decomposition, and variational EM training are explained with sufficient technical detail.\nDespite the technical complexity, the authors make a commendable effort to keep the exposition readable, especially around the symbolic-neural interaction.\n\nSignificance\nThis paper tackles a key challenge: matching information across different knowledge sources, not just fill in missing facts within one.\nThe proposed method improves both accuracy and explainability—two things that usually don’t go well together in ML systems.\nIt also includes a feature (explainer component) that explains why the system made a match, which is especially useful in fields like medicine or language translation, where understanding the reasoning behind results is very important.\n\nOriginality\n\nThis work introduces a new way to combine logic rules with a probabilistic learning method to match entities across different knowledge graphs.\nIt also includes a smart trick: breaking down long and complex logic rules into smaller, simple steps to keep the system fast and manageable.\nFinally, it adds an explanation tool that works in two modes—one using only known matches, and another using both known and predicted matches—making the system’s decisions easier to understand and trust.\n\n\nWeaknesses\nQuality\n\nThe paper should better explain how inference quality is affected by pseudo-label noise in the early stages.\nThe one-to-one matching heuristic used to reduce false positives is not rigorously analyzed or justified — a more formal treatment or ablation would strengthen the argument.\n\nClarity\n\nCertain parts of the paper, especially those introducing dense notation (e.g., η, p_sub, rule decomposition), could be more clearly explained or accompanied by examples. In particular, equations sometimes appear without adequate narrative grounding.\nThe treatment of evaluation metrics across symbolic and neural models is briefly reconciled, but the equivalence assumption between recall and hit@1 could be more carefully justified.\n\nSignificance\n\nRight now, the method can only match two knowledge graphs at a time, and the authors don’t yet explain how it could be expanded to handle many at once.\nIt’s also not clear how well the system works when the graphs are very different in structure or topic, which would be useful to test.\nWhile the paper presents the idea of combining logic and learning as something new, some parts seem borrowed from earlier work. It would help if the authors made it clearer what parts are truly original.\n\nQUESTIONS:\n1) In M-step description the paper states that the model uses a greedy one-to-one matching strategy to reduce false positives during pseudo-label generation. However, this step appears to be a heuristic and is not rigorously analyzed. Could you elaborate on how NeuSymEA's performance is affected by this heuristic and which alternative approaches have you considered?\n\n2) I understand that the authors mentioned this following as limitation of their current work. Still, how do you envision NeuSymEA extending to multi-KG scenario? Could you briefly describe how such an extension could be designed and what would be the pain points?\n\nLIMITATIONS:\nThe main limitation of this work (as mentioned by the authors) the fact that NeuSymEA is designed for pairwise alignment only and multi-KG cases are currently not supported.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-01"}