Title: Interpretable and Parameter Efficient Graph Neural Additive Models with Random Fourier Features
Venue: NeurIPS 2025
Accepted: yes
Keywords: Interpretability

Graph Neural networks

Finite Impulse Response Filters

Random Fourier Features
Abstract: Graph Neural Networks (GNNs) excel at jointly modeling node features and topology, yet their black-box nature limits their adoption in real-world applications where interpretability is desired. Inspired by the success of interpretable Neural Additive Models (NAM) for tabular data, Graph Neural Additive Network (GNAN) extends the additive modeling approach to graph data to overcome limitations of GNNs. While being interpretable, GNAN representation learning overlooks the importance of local aggregation and more importantly suffers from parameter complexity. To mitigate the above challenges, we introduce Graph Neural Additive Model with Random Fourier Features (G-NAMRFF), a lightweight, self‐interpretable graph additive architecture. G-NAMRFF represents each node embedding as the sum of feature‐wise contributions where contributions are modeled via a Gaussian process (GP) with a graph- and feature-aware kernel. Specifically, we construct a kernel using Radial Basis Function (RBF) with graph structure induced by Laplacian and learnable Finite Impulse Response (FIR) filter. We approximate the kernel using Random Fourier Features (RFFs) which transforms the GP prior to a  Bayesian formulation, which are subsequently learnt using a single layer neural network with size equal to number of  RFF features. G-NAMRFF is light weight with $168\times$ fewer parameters compared to GNAN. Despite its compact size,  G-NAMRFF matches or outperforms state-of-the-art GNNs and GNAN on node and graph classification tasks, delivering real-time interpretability without sacrificing accuracy.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new model for graph data named Graph-aware neural additive model with random features (G-NAMRFF). It assumes that the outputs are additive functions. The component-functions are drawn from a Gaussian prior (GP) with covariance generated from a graph-reweighed square exponential kernel. Two theoretical results are derived in Section 4. The method is compared to standard procedures in Section 6 for node and graph classification datasets.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- I did enjoy reading the article. Everything is well-explained and clean. \n- The approach seem to be motivated by proposing small models. It is highlighted that the approach requires 168  times less parameters than GNAN without destroying the performance. \n\n\nWeaknesses:  \n- My overall impression is that everything is quite straightforward: The method is just regression with a specific GP, Theorem 4.1 seems (at least intuitively) to be clear. While there is nothing wrong with the paper, I did miss some deeper insights. \n- The expressivity of an additive model is very limited and in learning tasks often just inappropriate, e.g. if the inputs are highly correlated. The authors should have invested much more in motivating how the inclusion of the covariance could overcome that such that one can learn large function classes with G-NAMRFF. Without some more theoretical insights on that, I find the approach hard to believe.\n\nQUESTIONS:\n- Could you make this deep, by staking G-NAMRFF layers on top of each other?\n- I did not understand Theorem 2.1 (for instance what do you mean with approximated?) and the statement could be wrongly formulated. Could you provide a reference or a proof? \n- Can you address the issue of the expressivity?\n\nLIMITATIONS:\nI did not find anything in the text discussing the potential limitations of this work.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-26"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces G-NAMRFF, a lightweight, interpretable model for graph learning. It improves upon GNAN (the only existing glass-box GNN architecture) by using Random Fourier Features (RFFs) to approximate Gaussian process kernels, reducing parameter complexity while maintaining interpretability. G-NAMRFF represents node embeddings as feature-wise contributions, with a graph-aware kernel based on Radial Basis Function (RBF) and Laplacian. It outperforms SOTA black-box GNNs and GNAN on node and graph classification tasks, providing real-time interpretability without sacrificing accuracy.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n1. The proposed G-NAMRFF is a novel method that effectively reduces the parameters of existing graph neural additive networks while maintaining strong interpretability and performance.\n\n2. Extending the Random Fourier Features-based kernel approximation to the Graph Neural Additive Model is an intriguing approach and offers valuable potential for future research.\n\n3. This paper provides sufficient theoretical and empirical analysis, particularly through real-world node and graph classification experiments, runtime analysis, and ablation studies, all of which demonstrate the effectiveness of the proposed methods.\n\n4. The paper is well-written, with a clear logical structure that makes it easy to read.\n\n### Weaknesses\nAlthough I believe this paper presents a novel contribution, it still has some issues.\n1. The paper contains several minor errors; I have provided a few examples and kindly ask the authors to review them:  \n    a) The description of Figure 1 does not specify what the x-axis represents.  \n    b) Theorem 2.1 lacks the necessary references.  \n    c) Some figures and tables are missing punctuation after the captions, such as Figures 1 and 2, and Table 2.  \n    d) The notation is inconsistent, for example, the Laplacian matrix in Theorem 4.2 is not written in boldface capital letters.  \n2. The paper focuses solely on parameter complexity and does not address time complexity.\n3. No code is provided for reproducibility.\n\nQUESTIONS:\n1. Please analyze the time complexity of the method proposed in this paper, specifically the time complexity of Algorithm 1. How does it compare to that of GCN?\n2. In line 61, the authors mention that GNAN requires O(N+E) distance computations per node. Why is this considered 'quadratic scaling'?\n\nLIMITATIONS:\nNo. Please see the Weaknesses and Questions Section.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

comments: SUMMARY:
This paper introduces the Graph Neural Additive Model with Random Fourier Features (G-NAMRFF), a novel, lightweight, and self-interpretable model for graph-structured data. The interpretability is achieved by additive modelling, i.e., the output of a node is a sum of each individual channels of transformed features without channel mixing. A core design to avoid the quadratic complexity of global feature aggregation, is to leverage random Fourier features to approximate a graph kernel that captures node-pairwise interaction.

STRENGTHS AND WEAKNESSES:
**Strengths**
- The paper tackles the critical problem of computational complexity and parameter efficiency in interpretable GNNs.
- A theoretical quantification of robustness is provided, which is crucial for model generalization.
- Extensive experiments demonstrate interpretability with descent predictive performance.
- The paper is well-written and easy to follow


**Weaknesses**
- There could be concerns about model capacity, since the overall model is pretty much linear. The expressivity problem could be worse since there is no feature mixing for interpretability.  
- In the main experiments, it is not clear how the number of parameters of the proposed method is compared to other baselines. This is of particular interest as being lightweight is one of the main motivations.
- Minor: equation (1), I believe it should be $f_{k}(x_{j,k})$.

QUESTIONS:
Please see **Weaknesses**.

LIMITATIONS:
The authors did not discuss any potential limitations. Please see **Weeknesses** for possible improvements.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-06-30

comments: SUMMARY:
This paper studies a graph neural additive model that leverages random Fourier features to yield a relatively less complex and self-interpretable graph additive architecture, referred to as G-NAMRFF.

STRENGTHS AND WEAKNESSES:
**Strengths**

1. G-NAMRFF offers interpretability, which makes it suitable for real applications that require transparent decisions. 
2. G-NAMRFF requires a substantially less complex computing architecture relative to existing approaches. 
3. G-NAMRFF is shown to be robust to small perturbations in the graph structure, lending stability to its decisions. 
4. G-NAMRFF achieves competitive performance in node and graph classification tasks. 

**Weaknesses**
1. The effectiveness of the model seems to depend on careful fine-tuning of a large set of hyperparameters.
2. The interpretability aspect is limited to static data.
3. The effectiveness of G-NAMRFF beyond graph or node classification tasks is not clear.

QUESTIONS:
See strengths and weaknesses section.

LIMITATIONS:
The authors claim that their work has no limitations. I disagree with this assessment (see weaknesses section above).
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-07