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arxiv: 2501.15461 · v4 · submitted 2025-01-26 · 💻 cs.LG

Mamba-Based Graph Convolutional Networks: Tackling Over-smoothing with Selective State Space

Xin He , Yili Wang , Wenqi Fan , Xu Shen , Xin Juan , Rui Miao , Xin Wang This is my paper

Pith reviewed 2026-05-23 04:39 UTC · model grok-4.3

classification 💻 cs.LG
keywords graph neural networksover-smoothingmambaselective state spacegraph convolutional networksdeep GNNsmessage aggregationnode representation
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The pith

MbaGCN borrows selective state space modeling from sequences to let graph networks distinguish neighborhood messages and avoid over-smoothing in deep layers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to show that the over-smoothing problem in graph neural networks arises because standard layers cannot tell apart the value of messages coming from different neighborhoods. It proposes MbaGCN, whose three layers—Message Aggregation, Selective State Space Transition, and Node State Prediction—together let the model weigh and retain neighborhood information selectively. A reader who accepts the premise would expect this to keep node features distinct even when many layers are stacked, opening the door to deeper models on graphs that need long-range structure. The authors present the work as a basic framework for moving Mamba-style selection into graph learning rather than as a universal performance winner.

Core claim

MbaGCN introduces a new GNN backbone built from the Message Aggregation Layer, the Selective State Space Transition Layer, and the Node State Prediction Layer. These components together adaptively aggregate neighborhood information by importing the selective state space mechanism originally developed for sequence modeling. The resulting architecture supplies greater flexibility and scalability to deep graph models and thereby addresses the root cause of over-smoothing.

What carries the argument

The Selective State Space Transition Layer, which applies input-dependent selection to neighborhood messages so that more relevant information is retained while less relevant information is filtered.

If this is right

  • Deep GNNs become able to maintain distinguishable node representations instead of collapsing to a single vector.
  • Message aggregation gains input-dependent flexibility that fixed-sum or mean operations lack.
  • The same three-layer pattern supplies a reusable starting point for other sequence-to-graph transfers.
  • Scalability improves because the selective mechanism does not require extra normalization or residual tricks to reach greater depths.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the transfer succeeds, the same selective-state idea could be tested on other non-Euclidean domains such as meshes or point clouds.
  • One could measure whether the added selection step changes the effective receptive field size compared with ordinary message passing.
  • The framework invites direct replacement of the state-space transition with other linear-time sequence operators to test which property of Mamba matters most for graphs.

Load-bearing premise

The selective state space selection rule developed for linear sequences can be moved directly onto graph neighborhoods and will correctly rank the importance of messages arriving from different nodes.

What would settle it

Training MbaGCN at increasing depths on a standard citation or social graph and measuring whether the average pairwise distance between node embeddings continues to shrink toward zero.

Figures

Figures reproduced from arXiv: 2501.15461 by Rui Miao, Wenqi Fan, Xin He, Xin Juan, Xin Wang, Xu Shen, Yili Wang.

Figure 1
Figure 1. Figure 1: Comparison of GCN, MAMBA, and MbaGCN. (a) Tra [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The Framework of MbaGCN. h ′ (t) = Ph(t) + Qx(t), y(t) = Rh(t). (1) Due to the challenges in solving the above equation within the deep learning paradigm, the discrete space state model [Gu et al., 2021] introduces additional parameter ∆ to discretize the aforementioned system, which can be formu￾lated as follows: h(t) = P¯h(t) + Q¯ x(t) y(t) = Rh(t) (2) where P¯ = exp(∆P) Q¯ = (∆P) −1 (exp(∆P) − I) · ∆Q (… view at source ↗
Figure 3
Figure 3. Figure 3: Performance of baselines and the proposed MbaGCN with 2/4/6/8/10 layers. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Graph Neural Networks (GNNs) have shown great success in various graph-based learning tasks. However, it often faces the issue of over-smoothing as the model depth increases, which causes all node representations to converge to a single value and become indistinguishable. This issue stems from the inherent limitations of GNNs, which struggle to distinguish the importance of information from different neighborhoods. In this paper, we introduce MbaGCN, a novel graph convolutional architecture that draws inspiration from the Mamba paradigm-originally designed for sequence modeling. MbaGCN presents a new backbone for GNNs, consisting of three key components: the Message Aggregation Layer, the Selective State Space Transition Layer, and the Node State Prediction Layer. These components work in tandem to adaptively aggregate neighborhood information, providing greater flexibility and scalability for deep GNN models. While MbaGCN may not consistently outperform all existing methods on each dataset, it provides a foundational framework that demonstrates the effective integration of the Mamba paradigm into graph representation learning. Through extensive experiments on benchmark datasets, we demonstrate that MbaGCN paves the way for future advancements in graph neural network research.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces MbaGCN, a novel GNN backbone inspired by the Mamba selective state space model. It consists of three components—the Message Aggregation Layer, the Selective State Space Transition Layer, and the Node State Prediction Layer—that are claimed to work together to adaptively aggregate neighborhood information, thereby mitigating over-smoothing and enabling deeper, more scalable GNNs. Experiments on benchmark datasets are presented to support the framework, with the authors noting that it may not consistently outperform all existing methods.

Significance. If the claimed transfer of Mamba's input-dependent selectivity to graph neighborhoods can be rigorously shown to preserve stability and permutation invariance while distinguishing neighborhood importance, the work would provide a new architectural primitive for deep GNNs. This could open avenues for scalable models that avoid the uniform convergence typical of repeated message passing. The honest admission that performance gains are not guaranteed across all datasets is a positive aspect of the presentation.

major comments (2)
  1. The Selective State Space Transition Layer is presented as the key mechanism for distinguishing importance across neighborhoods via Mamba-style input-dependent selection. However, the manuscript provides no equations or derivation showing how the discretization parameters (B, C, Δ) or the state transition are redefined to operate on unordered graph neighborhoods rather than ordered 1D sequences (see abstract and model description). This mapping is load-bearing for the central claim that the architecture solves over-smoothing through adaptive aggregation.
  2. No stability analysis or multi-hop propagation properties are given for the hidden-state update under the proposed graph-adapted SSM. Without this, it is unclear whether repeated application of the Selective State Space Transition Layer remains well-defined or avoids the very convergence the paper seeks to prevent.
minor comments (1)
  1. The abstract repeats the high-level description of the three layers without adding concrete technical distinctions; a single crisp sentence on the novelty of the state-transition adaptation would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the potential of transferring Mamba-style selectivity to graph neighborhoods. We address each major comment below and will revise the manuscript accordingly to provide the requested mathematical details and analysis.

read point-by-point responses

  1. Referee: The Selective State Space Transition Layer is presented as the key mechanism for distinguishing importance across neighborhoods via Mamba-style input-dependent selection. However, the manuscript provides no equations or derivation showing how the discretization parameters (B, C, Δ) or the state transition are redefined to operate on unordered graph neighborhoods rather than ordered 1D sequences (see abstract and model description). This mapping is load-bearing for the central claim that the architecture solves over-smoothing through adaptive aggregation.

    Authors: We agree that an explicit derivation of the graph adaptation is necessary to substantiate the central claim. In the revised manuscript we will insert a new subsection (immediately following the description of the Selective State Space Transition Layer) that supplies the missing equations. The subsection will (i) define how the discretization parameters B, C, and Δ are computed from the aggregated neighborhood features rather than from a linear sequence, (ii) show that the resulting state transition remains permutation-invariant by construction (via symmetric aggregation before the selective SSM step), and (iii) demonstrate that input-dependent selectivity is preserved because the selection is driven by the aggregated node features rather than by arbitrary node ordering. revision: yes

  2. Referee: No stability analysis or multi-hop propagation properties are given for the hidden-state update under the proposed graph-adapted SSM. Without this, it is unclear whether repeated application of the Selective State Space Transition Layer remains well-defined or avoids the very convergence the paper seeks to prevent.

    Authors: We acknowledge the absence of a formal stability argument. The revised manuscript will contain an additional analysis section that examines the multi-hop behavior of the graph-adapted SSM. The section will (i) provide a recurrence relation for the hidden-state update across layers, (ii) argue that the selective mechanism (via input-dependent Δ) introduces an adaptive forgetting factor that prevents uniform convergence to a single representation, and (iii) support the argument with both a sketch of bounded-norm propagation and new empirical results on deeper (8- and 16-layer) variants of MbaGCN. revision: yes

Circularity Check

0 steps flagged

No circularity detected; architecture proposal is self-contained

full rationale

The paper proposes MbaGCN as a new GNN backbone inspired by the external Mamba paradigm, describing three components at a conceptual level to adaptively aggregate neighborhood information. No equations, parameter fits, self-citations, or uniqueness theorems appear in the provided text that would reduce any claim to a self-referential definition or input. The transfer of selective state space ideas is presented as an analogy for design, not a derived result that loops back by construction. This is a standard model-introduction paper with independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no information on free parameters, axioms or invented entities used in the model.

pith-pipeline@v0.9.0 · 5746 in / 1115 out tokens · 57182 ms · 2026-05-23T04:39:48.901942+00:00 · methodology

discussion (0)

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