Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
Authors: Zhiqiang Wang
Jianghao Wen
Jianqing Liang
Venue: ICML 2025 poster (2025)
Keywords: Graph Neural Networks
Dynamic Graph
Spiking Neural Network
Graph Representation Learning
Primary area: deep_learning->graph_neural_networks
TL;DR: This work introduces Delay-DSGN, a dynamic spiking graph neural network with a learnable delay mechanism, to accurately capture temporal dependencies and mitigate information forgetting in dynamic graph representation learning.

Abstract: Dynamic graph representation learning using Spiking Neural Networks (SNNs) exploits the temporal spiking behavior of neurons, offering advantages in capturing the temporal evolution and sparsity of dynamic graphs. However, existing SNN-based methods often fail to effectively capture the impact of latency in information propagation on node representations. To address this, we propose Delay-DSGN, a dynamic spiking graph neural network incorporating a learnable delay mechanism. By leveraging synaptic plasticity, the model dynamically adjusts connection weights and propagation speeds, enhancing temporal correlations and enabling historical data to influence future representations. Specifically, we introduce a Gaussian delay kernel into the neighborhood aggregation process at each time step, adaptively delaying historical information to future time steps and mitigating information forgetting. Experiments on three large-scale dynamic graph datasets demonstrate that Delay-DSGN outperforms eight state-of-the-art methods, achieving the best results in node classification tasks. We also theoretically derive the constraint conditions between the Gaussian kernel's standard deviation and size, ensuring stable training and preventing gradient explosion and vanishing issues.

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
Zhiqiang Wang'
Jianghao Wen
Jianqing Liang'
Abstract
node classification and link prediction. Real-world graphs, however, are often dynamic, requiring dynamic graph rep- resentation learning methods to account for the temporal dependencies of nodes and edges in order to capture the graph ' evolving nature and generate more accurate repre- sentations. This ability is particularly important dynamic applications such as social network analysis and traffic flow prediction.
Dynamic graph representation learning using Spiking Neural Networks (SNNs) exploits the temporal spiking behavior of neurons, offering ad- vantages in capturing the temporal evolution and sparsity of dynamic graphs. However, existing SNN-based methods often fail to effectively cap- ture the impact of latency in information propaga- tion on node representations. To address this, we propose Delay-DSGN, a dynamic spiking graph neural network incorporating learnable delay mechanism. By leveraging synaptic plasticity, the model dynamically adjusts connection weights and propagation speeds, enhancing temporal cor- relations and enabling historical data to influence future representations. Specifically, we introduce Gaussian delay kernel into the neighborhood ag- gregation process at each time step, adaptively de- laying historical information to future time steps and mitigating information forgetting. Experi- ments on three large-scale dynamic graph datasets demonstrate that Delay-DSGN outperforms eight state-of -f--o---thttttt methods, achieving the best results in node classification tasks. We also theoretically derive the constraint conditions between the Gaus- sian kernel's standard deviation and size, ensuring stable training and preventing gradient explosion and vanishing issues.
In recent years, researchers have proposed various meth- ods to address the dynamic nature of graphs. Random wask- methods such as CAWs (Wang et al., 2021) and NeurTWs (Jin et al., 2022) capture contextual information from dynamic graphs by sampling random walk sequences of nodes, thereby enabling node encoding. Methods using graph neural networks (GNNs) aggregate information from neighhoring nodes based on the graph topology, often incor- porating different temporal modeling strategies to capture dynamic graph evolution. For instance, approaches like JODIE (Kumar et al., 2019), GAEN (Shi al., 2021) and CHNN (Yin al., 2024a) use recurrent neural networks (RNNs) (Cho et al., 2014) model temporal dependencies in graphs, while HTNE (Zuo al., 2018), D'DNE (Lu et al., 2019), and TREND (Wen & Fang, 2022) treat time as a continuous variable, modeling event timings through temporal point processes. However, these methods often require extensive sequence extraction or large-scale mem- ory units, leading to low modeling efficiency large-scala dynamic graphs
As class of low-power neural networks (Maass, 1997; Schliebs & Kasabov, 2013; Pfeiffer & Pfeil, 2018), Spiking Neural Networks (SNNs) utilize Poisson rate coding to con- vert continuous node features into sparse binary representa- tions, offering significant advantages modeling efficiency for large-scale graphs. Specifically, SNN neurons simplify internal computation through linear integration, avoiding complex nonlinear activations and matrix multiplications. Additionally, SNNs can capture temporal evolution patterns by accumulating and memorizing historical states, extend- ing beyond spatial neighborhood based information transfer. Recent works, such as SpikeGCN, STEN, SpikeNet, and Dy-SIGN (Zhu al., 2022; Xu et al., 2021: Li et al., 2023; Yin al., 2024b), combine SNNs with GNNs, employing
1. Introduction
Graph representation learning aims to map graph data, including nodes, edges, or entire graphs, into a low- dimensional vector spaces for downstream tasks such as
Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Com- puter and Information Technology, Shanxi University, Taiyuan 030006, Shanxi, China. Correspondence to: Jianqing Liang <liangiq @ww.xxxx..uucc..
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 20255 by the author(s).

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
graph convolution layers with SNN neurons to aggregate neighborhood information and alleviate the computational complexity associated with matrix multiplications and non- linear activations in GNNs.
heterogeneity. With this mechanism, changes in topology do not immediately affect node representations but take ef- fect after certain delay. Meanwhile, the presence of this delay allows historical information to influence node repre- sentations at the current time step, effectively alleviating the problem of information forgetting. Neurons can leverage this heterogeneous delay mechanism to recognize complex spatiotemporal spike patterns, thereby effectively capturing the influence of historical information current and future node representations.
New edge
Delay representation Information forget
To this end, we propose Delay-DSCG a dynamic spiking graph neural network with a learnable delay mechanism. Delay-DSGN integrates the synaptic delay mechanism into SNNs, so that the aggregated node features are not instan- taneously transmitted the neurons. Instead, the model adaptively learns appropriate delay times between neurons through Gaussian delay kemel, enabling delay representa- tion of features. This effectively mitigating the forgetting of historical information and generating more accurate node representation. Our main contributions are as follows:
Figure 1. Illustration of information dynamics in social network. At time fi, two nodes establish a connection without any inter- action, thus having no immediate impact on their representations (depicted by unchanged colors). At time ls, the two nodes begin exchanging information, leading to changes in their representations (depicted by color updates). Finally, at time f4, additional nodes participate in information exchange, where node representations are influenced by both current interactions and decayed historical information.
Despite progress in dynamic graph representation learning, significant challenges remain in accurately modeling the influence of historical information on current and future node representations, particularly with respect to delay rep- resentation and historical information forgetting. Existing methods typically update node representations by aggregat- ing current-time information, ignoring the possibility that such information may impact node representations at later time steps. This phenomenon, known as delay representa- tion, can be illustrated by the following example in social networks in Figure 1: at time point f1, a new edge added between nodes A and B, but the edge does not immediately affect the node representations of A and B; instead, the im- pact manifests at later time step. This delay effect reflects information propagation.
We propose Delay-DSGri a dynamic spiking graph neural network with a learnable delay mechanism, which dynamically adjusts connection weights and spike propagation speeds to achieve more accurate modeling of dynamic graph evolution.
We theoretically derive the constraint conditions be- tween the standard deviation and size of the Gaussian delay kernel, ensuring that the Delay-DSGN model avoids gradient explosion and vanishing problems dur- ing training.
Extensive experiments validate that Delay-DSGN out- performs current state-of-the-art methods in node clas- sification tasks across multiple dynamic graph datasets.
the inherent latency in Moreover, as dynamic graphs evolve, node representations are progressively updated, and earlier historical information tends to be overshadowed or forgotten due to the influence of new information. For example, over time, the represen- tation of node A may be influenced by several neighboring nodes, causing early neighbors' information to be diluted or lost, thereby erasing valuable historical context. Therefore, effectively modeling delay representation and mitigating his- torical information forgetting are key challenges in dynamic graph representation learning.
2. Related Work
2.1. Shallow Representation
Early dynamic graph representation learning focused on shallow encoding methods like matrix/tensor decomposi- tion and random walks, without leveraging the deep encod- ing capabilities of graph topology. Matrix decomposition methods, such as incremental SVD (Chen & Tong, 2015) and error-bound restart (Zhang et al., 2018), perform joint factorization of adjacency matrices over multiple time snap- shots obtain low-rank representations. Tensor decomposi- tion introduces time dimension into the adjacency matrix, forming a tensor to capture temporal evolution. Common approaches include CP and Tucker decomposition (Acar & Yener, 2009). In contrast, random walk methods generate se- quences of random walks from nodes (i.c., contextual infor- mation) to learn representations, capturing higher-order de-
Inspired by the synaptic plasticity of biological neurons (Izhikevich, 2006; Bowers, 2017; Hammouamri et al., 2024), we address the problems of delay representation and his- torical information forgetting in dynamic graph representa- tion learning by introducing a synaptic delay mechanism. Synaptic delay refers to the time it takes for information to propagate between neurons, which varies due to synaptic
2

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
pendencies between nodes. For example, (De Winter al., 2018) and (Sandra & Jochen, 2019) employed node2vec (Grover & Leskovee, 2016) and a variant of (Perozzi et al., 2014) for random walks over each network snapshot. Other related methods include DNE (Chen et al., 2019), (NodeEmbed (Singer et al., 2019), and DynSEM (Yu et al., 2017). CTDNE (Nguyen et al., 2018), incorporates temporal factors directly into the sampling process, learning embeddings with temporal walk sequences.
training issues in recurrent GNNs, further reducing memory consumption.
3. Problem Definition
Given a sequence of dynamic graph snapshots (G',G²,... ,....., G where represents the total number of time steps in the dynamic graph, each snapshot is defined as G = =(V, E", X*), where V and E are the sets of nodes and edges in snapshot G", respectively, containing all nodes and edges that have appeared in {G* ..... G*). The topology of the graph G is represented by the adjacency matrix A' E R N where N is the number of nodes. Additionally, X E RR- represents the node features at time step 1, where d is the feature dimension of each node.
2.2. GNN-Based Representation
GNNs leverage graph topology to encode node represen- tations, enhancing the learning of structural information. By integrating RNNs, static GNNs are extended for dy- namic process modeling. GC-LSTM (Chen et al., 2022) and Dyngraph2Seq (Gao et al., 2019) combine GCN (Kipf & Welling, 2017) with LSTM (Hochreiter & Schmidhu- ber, 1997). TGN (Rossi et al., 2020) and JODIE (Kumar et al., 2019) update node hidden states using RNNs units for representation learning. EvolveGCN (Pareja al., 2020) adjusts GNNs weights over time using RNNs to capture dynamic information in evolving networks. Additionally, TGAT (Xu et al., 2020) introduces temporal encoding and self-attention mechanisms to aggregate neighbor node fea- tures across time, enhancing the understanding of topologi- cal changes in dynamic graphs. DyRep (Trivedi et al., 2019), based on temporal point processes, captures both graph-level and node/edge-level temporal variations. TREND (Wen & Fang, 2022) uses Hawkes processes to model the impact of historical events on current ones, analyzing neighborhood formation effects on nodes through Hawkes conditional in- tensities.
Our goal is to learn a parameterized model (=;(0) that maps node features 2² at each time step to a fieedddieensionll embedding R2 (d < input feature dimension), capturing dynamic node evolution for tasks like temporal node classi- fication.
4. Delay-DGSN
This section introduces the proposed Delay-DGSN in detail, as shown in Figure 2. We will introduce the method from the following three aspects: dynamic graph sampling and feature encoding, delay convolution and temporal modeling, and temporal feature aggregation and model optimization.
4.1. Dynamic Graph Sampling and Feature Encoding
In dynamic graph modeling based on SNNs, graph sampling and node spike feature encoding are fundamental compo- nents, also integral to mechanism in Delay-DSGN, this section briefly introduces these components. For details, see (Li et al., 2023).
To clarify the delay
2.3. SNN-based Representation
To address the high computational cost of dynamic graph representation learning, researchers have explored applying low-power SNNs to graph data. STEN (Xu et al., 2021) and SpikingGCN (Zhu et al., 2022) combine GCN with SNNs, where GCN aggregates neighborhood information, and SNNs encode node features as spike signals, simulating time steps. SpikeGCL. (Li et al., 2024) links graph con- trastive learning with spike. These methods achieve promis- ing results on static graphs. Additionally, SpikeE (Dold & Garrido, 2021), R-GCN (Chian et al., 2021), and GRSNN (Xiao et al., 2024) use spike for knowledge graphs, repre- senting relationships spike time differences. Recent work has extended SNNs to dynamic graphs, such SpikeNet (Li et al., 2023) and Dy-SIGN (Yin et al., 2024b). These approaches leverage the dynamic characteristics of SNNs, where each graph snapshot corresponds to a time step in the SNN, capturing the temporal evolution of graphs. Dy-SIGN extends the concept of implicit fixed-point equilibrium to graph learning (Gu et al., 2020), addressing evaluation and
For the graph sampling, the dynamic graph is divided into snapshots over fixed time intervals, with each snap- shot corresponding to a time step t. At each time step i, the graph sampler performs neighbor sampling Go and AG = G - G For each target node v, T sets of neigh- bor nodes {Nv, .,, N*) are sampled on each graph snapshot. This division method helps capture both global structural information and fine-grained temporal node infor- mation. After neighbor sampling, the feature aggregation for the sampled neighbor set N is performed through graph convolution layer, generating the hidden representation A; of node v at time step t:
h = h W. @ AGG u E NO),
(I)
where, when t = 0, the initial hidden representation is the node feature xe; W. and W., are learnable weight matrices; the aggregation function AGG is average aggregation; @
3

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
Graph Snapshot Sequence
Ti
Delay
neuron!
time step
Delayeo
neuron2
neuron neuron2
LIF neuron
Aggregation
Bord 5. S
T2
12
-M--
-
FC (Temporal pooling)
LIF neuron
Aggregation
Neighborhood Sample
Integrate Leaky
Loss(y,
Delay kernel
Aggregation
2/
Prediction
GNN_I
SNN
GNN_2
Delay SNN
Classification
Figure 2. An overview of the Delay-DSGN. The dynamic graph is divided into fixed-interval snapshots. For each snapshot, sccond-order neighbors are sampled, and GNN aggregates neighbor information, while SNN encodes the information into spike representations. In the Delay-SNN SNN layer, the model adaptively adjusts the center of the Gaussian delay kernel to capture varying temporal delay characteristics, generating node-level delay representations. A multi-timescale fusion mechanism further integrates representations across different time steps, ultimately producing the final embedkiings for downstream tasks.
denotes vector addition.
kaj. defined
For the node spike feature encoding, after generating the hidden representations of nodes through neighbor aggrega- tion, the LIF (Leaky Integrate-and-Fire neuron mechanism is utilized to convert the float-valued representation into sparse spike representation s This process generates a set of spike representations for the node over time steps: {st, .e....,.?), This spike encoding not only retains the essential information of the node features but also reduces computational complexity through sparsification.
kig[n] Waj exp (-(n - (K, -di - 1))2)
(3)
2a²
where diy E [0, K. 1] and Waj are the synaptic delay and weight between neurons i and j; E IR is the standard deviation; and n E [O...., K, delay index of the kernel. The introduction of the Gaussian kernel aims to smoothly model the delay effect different time steps. By learning dij. the model can dynamically adjust the center of the Gaussian kernel, accurately captur- ing information under different time delays. The learned delays have a certain degree of interpretability. as detailed in Appendix B. The synaptic weight wy further enhances the model's ability to adaptively adjust the importance each synapse, improving the model's expressiveness and flexi- bility. The delay convolution kernel ki is then convolved
denotes the temporal
4.2. Delay Convolution and Temporal Modeling
Delay convolution and temporal modeling are to Delay- DGSN, capturing temporal dependencies and historical in- fluences on node representations through delay convolution and the LIF neuron mechanism.
4.2.1. DELAY CONVOLUTION KERNEL
with the padded spike sequence 8e ( feature input:
to produce the delay
Inspired by temporal convolution in CNNs, Delay-DGSN uses delay convolution kernel of size K,, with K, as the maximum delay step. To maintain the sequence length after convolution, the node feature spike sequence s (.4 (where j is a node feature) zero-padded on the left by K, steps:
T(i.0) = kis se (.0)
(4)
This delay representation preserves current spike informa- tion while integrating historical spikes, with the delay convo- lution kernel weighting contributions across time, enriching the node representation with temporal dynamics.
5.0 [0, 0, 0, (699,
4.2.2. TEMPORAL MODELING
To implement temporal shifts, Delay- DGSN uses a Gaussian kernel function to construct the delay convolution kernel
The delay features obtained from Equation (4) are fed into LIF neurons for dynamic membrane potential updates and

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
spike generation. The LIF neuron simulates the basic be- havior of biological neurons, and its computation can be expressed as:
trainable weight matrix W, E RdxT is applied to perform weighted pooling along the temporal dimension, enabling weighted fusion of features from different time steps:
Integrate: V((L)) -V((,111) + (1 3) Σ 16.00
(5)
T Σ
Zo W
Zu & W..t
Fire: S/:,0) @(V th
(6) where i E [1, df denotes the i-th feature, and represents the importance of feature at different time steps. The final result Z, W, E Rd is obtained by performing element- wise multiplication between Zu and W,, followed by row- wise summation. The aggregation process fuses temporal information into a unified representation, which is fed into a fully connected layer to generate node classification results.
Rest: Vi(itt) = Vi(it) s((t)) s(i.t)((1111 (1.1-11)
(7)
th
Update: v((,,) = ((it) + Tthe vih (1it-11
(8)
where (y(8.)) represents the membrane potential of neuron for node u at time step I, and / is the leakage constant con- trolling the decay between the current input and historical information. O denotes the step function, and (i,tt-) ) th is the threshold of neuron at the previous time step. When vi(h.) th ((( > O, the membrane potential exceeds the threshold, triggering a spike, s((tt) 1; otherwise, s(t+.) 0. We adopt soft reset mechanism, which, com- pared to hard reset, retains part of the voltage exceeding the threshold, thereby preserving more information. The neuron's 's threshold is updated adaptively, as proposed in SpikeNet, by adjusting the decay factors y and Teh-
During optimization, Delay-DGSN uses a temporal regu- larization term to penalize discrepancies between feature representations at different time steps, reducing noise from insignificant temporal fluctuations. The regularization term R is defined as:
R Σ
=
2
2
(10)
where z and 2f are the node representations at time steps and t respectively. This regularization enhances robustness by smoothing consecutive node representations, focusing on meaningful long-term trends over short-term noise. Finally. Delay Delay-DGSNT is optimized with cross-entropy loss as the objective function. The overall loss function is:
By combining delay convolution with the LIF neuron mech- anism, Delay-DGSs generates node representations rich in temporal information. Delay convolution integrates spike information across time steps using a Gaussian kernel, while LIF neurons refine it through dynamic membrane updates. The resulting node representation =t incorporates both cur- rent and historical information from the past K2- - steps, effectively modeling temporal dynamics. Learnable delay parameters di further allow adaptive adjustments, enabling Delay-DGSN to handle complex temporal dependencies in dynamic graphs with greater flexibility and expressiveness.
L == LCE + XR.
(11)
where LCE is the cross-entropy loss and X is the regulariza- tion coefficient.
5. Theoretical Analysis
In the Delay-DGSN model, the Gaussian delay kernel is used to capture the temporal dependencies between nodes, To ensure that the model effectively controls the gradient flow during training and avoids issues such as gradient ex- plosion and vanishing gradients, the following theorem pro- vides the necessary conditions for the standard deviation o and kernel size K₃ of the Gaussian delay kernel.
4.3. Temporal Feature Aggregation and Model Optimization
The delay convolution primarily addresses the problem of weighted aggregation of historical information within sin- gle time step. In dynamic graphs, topological changes (such as the evolution of communities in social networks) often span multiple time steps. Therefore, aggregating informa- tion from only a single time step is insufficient to fully capture these complex topological variations. By integrat- ing node representations across different time steps into unified feature, it becomes possible better model these long-ten dependencies and intricate topological evolutions. In addition, this approach compensates for the information loss caused by the spiking activation characteristics in SNNs. Specifically, the model stacks the node representations 2! across all time steps to form a feature matrix Z, E RdxT that incorporates temporal dimension information. Then, a
Theorem 5.1 (Gradient Stability and Gaussian Delay Kernel Condition). In the Delay-DGSN model, assume the loss function L is differentiable with respect to the output HG, of feature i at time step t, and the model uses Gaussian delay kernel lig (n) with standard deviation a and kernel size K₃- The Gaussian delay kernel has the form:
Mey)) (n-))))
(n
kig = =exp
(12)
20²
where Pig = Ke - dig - 1, and day is the learnable de- lay parameter. Let W Wmar = maxi,j |wsy| and K Kiaa
5

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
max; Ei= [wigh where F is the lotal feature dimension. If the Gaussian delay kernel's s standard deviation a and kernel size Ks satisfy the following condition:
based on Tmall sales records, is a bipartite user-product graph with edges representing purchases, and the top five product categories as labels. The Patent, from the U.S. patent database, has nodes for patents, edges for citations, and six main categories. For Tmall and Patent, time win- dows of 10 and 2 generate 19 and 13 graph snapshots, re- spectively. Table summarizes the dataset statistics.
(Kg
1)2
(13)
81n
Amax
moux
then, during the backpropagation process, the gradient of the spike sequence 5 (t=n) with respect to the loss function B1. satisfies the following bound for any pair of features
6.2. Evaluation Metries
To comprehensively evaluate the classification performance of the model, we use two commonly used metrics: Fl- macro and F1-micro. F1-maero calculates the average of precision and recall across all classes, making it suitable for imbalanced datasets, Its formula is:
8a my
i and j:
ÖL
aL th
C.
(14)
0s!t-m
0s!
[t)
j=1
where the constant C' is given by:
1 2P, P
F1 mamroo
(16)
F
bayl - exp (-(Ks (-(Ks-1~n)
n' 111s)) ) (15)
C= Σ 1=1
20²
where P. and R2 represent the precision and recall of class i, and n is the total number of classes.
Proof. The proof of this theorem involves deriving the gra- dient bounds under the assumption of Gaussian delay kernel behavior and utilizing the properties of temporal spike se- quences in the Delay-DGSN model. Full details can be found in the Appendix A.
F1-micro, on the other hand, computes the overall precision and recall across all classes, making it suitable for balanced datasets. Its formula is:
2P Reniero
Fluiero Pinimo + Rmiieo
(17)
Under the given conditions, this theorem ensures Delay- DGSN effectively controls gradient propagation, preventing explosion vanishing. It also guides parameter selection for the Gaussian delay kernel, enabling accurate temporal modeling and stable training.
where Pmiero and Rmicro are the aggregated precision and recall across all classes.
6.3. Experimental Setup
demonstrate the superiority of the Delay-DSGN, we compare it with existing methods. These include static graph-based methods DeepWalk (Perozzi al., 2014) and Node2Vec (Grover & Leskovee, 2016), dynamic graph meth- ods based on point processes M2DNE (Lu et al., 2019) and HTNE (Zuo et al., 2018), RNN-based methods EvolveGCN (Pareja et al., 2020), iatention-basee methods TGAT (Xu et al., 2020), and two spiking methods SpikeNet (Li et al., 2023), Dy-SIGN (Yin et al., 2024b).
6. Experiments
6.1. Datasets
To evaluate the effectiveness of Delay-DSGN, we selected three large-scale datasets, which are commonly used for validating dynamic graph representation learning models. These datasets are DBLP (Lu et al., 2019), Tmall (Lu et al., 2019), and Patent (Hall et al., 2001), as listed in Table 1.
The experimenta follows the same settings with (Li et al., 2023). For each training ratio (i.c., 40%.60% and 80%), we compute the F1 F1-macro and F1-micro scores. The hidden dimension for all methods is set to 128, the batch size is 1024, and the total number of training epochs is 100.
Table 1. The statistics of datasets.
DBLP
Tmall
Patent
Nodes
28,085 236,894
577,314 4,807,545 186
2,738,012 13,960,811 25
Edges
6.4. Experimental Results
Time steps
27
Classes 10
6
6.4.1. PERFORMANCE COMPARISON
Table 2 summarizes the classification results on the DBLP, Tmall, and Patent across various training ratios. Delay- DSGN achieves state-of-the-an performance in dynamic graph representation learning, consistently outperforming
The DBLP, from a computer science research database, rep- resents authors as nodes, with edges indicating collabora- tions, and papers classified into 10 categories. The Tmall,
6

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
Table Results of node classification tasks. The results averages from five runs with different random seeds, with the hest results
highlighted in bold. (Trratio: training ratio. denotes consuions
Metric
Thratio
Delp Walk
Node2Vec
HTNE
M'DNE
EvolveGCN
TGAT
SpikeNet
Dy-SIGN
Delay-SGN
40%
67.08
66.07
67.68
69.02
67.22
71.18
70.88
70.94:0.1
72.32+0.4
Ma-FI
60%
67.17
66.81
68.24
69.48
69.78
71.74
71.98
72.07=0.1
74.1620.3
80%
67.12
66.93
68.36
69.75
71.20
72.15
74.65
74.67+0.5
76.5420.4
DBLP
40%
66.53
66.80
68.53
69.23
69.12
71.10
71.98
71.9==0.1
72.56=0.2
Mi-F1
60%
66,89
67.37
68.57
69.47
70.43
71.85
72.35
72.
74.44=0.3
80%
66.38
67.31
68.79
69.71
71.32
73.12
74.86
74.9640.2
76.87=0.5
40%
67.08
54.37
54.81
57.75
53,02
56,90
58.84
57 17,4880.1
60.25+0.1
Ma-FI
60%
67.17
54.55
$4.89
57.99
$4.99
57.61
61.13
60.9440.2
62.56+0.3
80%
67.12
54.58
54.93
58.47
55.78
58.01
62.40
61.89+0.1
64.02+0.2
Tmall
40%
66.53
60.41
62,53
64.21
59.96
62.05
63.52
62.93+403
64.32a0.1
Mi-F1
60%
66.89
60.56
62.59
64.38
61.19
62,92
64.84
64.10= 10=0.3
66.20=0.2
80%
66.38
60.66
62.64
64.65
61.77
63.32
66.10
65.82+0.2
67.88=0.4
40%
67.08
69.01
79.67
81.51
83.53
83.57=0.3
83.72=0.1
Ma-F1
60%
67.17
69.08
79.76
81,56
83.85
83. 83.77+0.2
84.01=0.1
80%
67.12
68.99
80.13
81.57
83,90
83.2
84.20=0.1
Patent
40%
66.53
68. 18.14
79.39
80.79
83.48
83 83,50=0.2
83.6620.1
Mi-FI
60%
66.89
68.20
79.75
80.81
83.80
83.4740.1
83.9720.1
80%
66.38
68. 10
80.01
80.93
83.88
83.90+0.2
84.15a0.1
all baseline methods. For instance, the DBLP, it achieves an Mi-FI score of 76.87% 80% training ratio, out- performing the second-best method, Dy-SIGN, by 2.21 %. On the Tmall, Delay-DSGN achieves an Mi-FI score of 67.88% 4.56% higher than TGAT. On the large-scale Patent, delivers the best Ma-Fl score 84.20%, showcasing its scalability and robustness.
start training from the same weight initialization. Each con- dition run five times, and the average result is reported.
The results in Figure 3 show that the Delay-DSGN model with the delay module performs better across all datasets, validating the importance of the delay mechanism in model- ing long-term dependencies in dynamic graphs.
While dynamic methods like HTNE and M.DNE improve upon static approaches by incorporating temporal informa- tion, their high computational complexity limits their scala- bility. As shown in Table 2, these methods fail to produce results on the large Patent due to excessive training costs. In contrast, Delay-DSGN leverages sparse binary representa- tions and an efficient synaptic delay mechanism, enabling it model temporal dependencies accurately while main- taining computational efficiency, making it well-suited for large-scale, real-world dynamic graphs.
Delay-SCN
TGAT
EvilveoCN
DBLP
Tmail
Patent
6.4.2. ABLATION STUDY
Figure 4. Comparison of training times for different methods on the DBLP, Tmall, and Patent. The training durations are presented in units of (sgoossscond//ppoch)).
To further investigate the impact of the delay mechanism in Delay-DSGN and evaluate the effectiveness of spike-delay learning for dynamic graph representation, we designed the following ablation experiments. We compared Delay- DSGN with two bascline models: the fixed random delay model and the no-delay model. The fixed random delay model initializes the delay values randomly at the begin- ning of training and keeps them constant throughout. The no-delay model removes the delay module and adjusts the hidden layer structure by increasing the number of neurons ensure that all models have the same parameter count and
6.4.3. TIME EFFICIENCY
To validate the computational efficiency of SNN-based methods, compared the training time of Delay-DSGN with other dynamic graph methods (Dy-SIGN, SpikeNet, EvolveGCN, and TGAT). All experiments were run on a Titan RTX GPU, and we compared the time cost per train- ing epoch. As shown in Figure 4, the SNN-based methods significantly reduce training time. By using sparse binary

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
DBLP
0.7
dGV Delce
0.442
Sib Dato
376
Macro-FF
Macro--
Macro
173
0.33
172
0.422
45%
60%
00%
50%
30%
40%
60%
00%
DBLP
Fatent
1.14
0.7
No
Delk Deloy
No
Delly
667
0.343
Micro.F1
Micro-F
644
072
372
662
80%
0.332
40%
Figure 3. Results of the delay mechanism ablation study. The six figures respectively show the classification performance of Delay-DSGN compared other delay mechanisms (fixed random delay, no delay) on the DBLP, Tmall, and Patent under different training set proportions.
activation functions instead of continuous real-valued acti- vations in traditional GNNs, SNNs effectively reduce putational complexity. As result, SNN-based methods have a clear advantage in terms of computational efficiency. Although Delay-DSGN introduces the delay module, which increases the number of parameters, this has a negligible impact on the overall training time. Compared other SNN methods such SpikeNet and Dy-SIGN, Delay-DDSGN maintains comparable training times while achieving supe- rior classification performance. These results demonstrate that Delay-DSGN maintains the computational efficiency of SNNs while providing significant performance improve- ments.
73.0
24-
60.
72.5
50
72.0
60:
71.0
62.6
(a) DBLP
(b) Tmall
Figure 5, Parameter experiment results on the DBLP and Tmall under different settings of dm a. In heatmap, the color bar represents the performance score, with darker colors indicating higher performance.
6.4.4. PARAMETER SENSITIVITY ANALYSIS
This section explores the effect of the maximum delay time dm and standard deviation
memory ability. Therefore, moderate value of a retain important time step information while considering contri- butions from neighboring time steps. Larger dm values increase the receptive field of the delay kernel, allowing the model to better capture multi-step temporal dependen- cies in dynamic graphs. Experimental results on the DBLP and Tmall confirm that larger dm, and moderate settings significantly improve model performance.
the performance of the Delay-DSGN model. In the experiments, we set dm to {1, 3, 5, 9} and a to (0.25, 0.5, 0.75, 1, 2), while keeping other parameters fixed.
The results in Figure 6 show that when dm, = 1, the model performs similarly to the no-delay model, as the Gaussian kernel has minimal influence. As d,, increases, if is set too small, the model overly focuses on the spike information at delayed time steps, causing information loss. Conversely, if a is too large, the weights of the delay kernel become too smooth, leading the model to assign almost equal impor- tance to information across all time steps, losing its selective
7. Conclusion and Future Work
This paper proposes the Delay-DSGN, which introduces a learnable delay mechanism inspired by biological synaptic
8

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
plasticity. This approach successfully enhances the temporal correlation of information propagation between nodes and preserves historical information, effectively overcoming the challenges faced by existing dynamic graph representation methods that fail to model information propagation delays. The experimental results demonstrate that Delay-DSGN outperforms eight state-of-the-ar methods across multiple large-scale dynamic graph datasets in node classification tasks. More importantly, we provide theoretical conditions for selecting the standard deviation and kernel size of the Gaussian delay kernel, ensuring that the model avoids gra- dient explosion and vanishing issues during training. Future work will focus on further exploring the delay mechanism to improve the model's s adaptability and performance on more complex and diverse dynamic graph datasets.
Cho, K., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F,, Schwenk, H., and Bengio, Y. Learning phrase representations using RNN encoder-decoder for statistical machine translation. In Proceedings the 2014 Conference on Empirical Methods in Natural Language Processing, pp. 1724-1734, 2014.
De Winter, S., Decuypere, T., Mitrović, S., Baesens, B., and De Weerdt, J. Combining temporal aspects of dynamic networks with node2vec for more efficient dynamic link prediction. In /EEE/ACM International Conference on Advances in Social Networks Analysis and Mining, pp. 1234-1241, 2018
Dold, D. and Garrido, J. S. Spike: spike-based embeddings for multi-relational graph data. In International Joint Conference on Neural Nenworks, pp. 1-8, 2021.
Acknowledgement
Gao, Y., Wu, L., Homayoun, H., and Zhao, L. Dyn- graph2seq: Dynamic- Synamic-graph-to-iie graph-to-sequenee interpretable learning for health stage prediction in online health fo- rums. IEEE International Conference on Data Mining, pp. 1042-1047, 2019.
This work is supported by the National Natural Sci- ence Foundation of China (Nos. 62272285, 62376142, U21A20473).
Impact Statement
Grover, A. and Leskovec, J. Node2vec: Scalable feature learning for networks. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Dis- covery and Data Mining, pp. 855-864, 2016.
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
Gu, F., Chang, H., Zhu, W., Sojoudi, S., and El Ghaoui, L. Implicit graph neural networks. In Advances in Neural Information Processing Systems, volume 33, pp. 11984- 11995, 2020.
References
Acar, F. and Yener, B. Unsupervised multiway data analysis: A literature survey. IEEE Transactions on Knowledge and Data Engineering. 21(1):6-22 2009.
Hall, B. H., Jaffe, A. B., and Trajtenberg, M. The nber patent citation data file: lessons, insights and methodological tools. Technical report, National Bureau of Economic Research, 2001.
Bowers, J. Parallel distributed processing theory in the age of deep networks. Trends in Cognitive Sciences, 21 (12):950-961, 2017.
Hammouamri, I., Khalfaoui-Hassan L., and Masquelier, T. Learning delays in spiking neural networks using dilated convolutions with learnable spacings. In International Conference on Learning Representations, 2024.
Chen, C. and Tong, H. Fast eigen-functions tracking dynamic graphs. In Proceedings of the 2015 SIAM In- ternational Conference on Data Mining, pp. 559-567, 2015.
Hochreiter, S. and Schmidhuber, J. Long short-term memory. Neural Comput, 98)) 1997.
Chen, C., Tao, Y., and Lin, H. Dynamic network embed- dings for network evolution analysis. arXiv preprint arXiv: Ntt::/906.08800 2019.
Izhikevich, E. M. Polychronizaatio:: Computation with spikes. Neural Comput, 18(2):245-82, 2006.
Chen, J., Wang, X., and Xu, X. Ge-lstm: Graph convolu- tion embedded Istm for dynamic network link prediction. Applied Intelligence, 52(7):7513-75) 2022.
Jin, M., Li, Y.-F,, and Pan, S. Neural temporal walks: Motif-aware representation learning on continuous-time dynamic graphs. Advances in Neural Information Pro- cessing Systems, volume 35, pp. 19874-19886, 2022.
Chian, V. C., Hildebrandt, M., Runkler, T., and Dold, D. Learning through structure: towards deep neuromorphic knowledge graph embeddings. In International Confer- ence on Neuromorphic Computing, pp. 61-70, 2021.
Kipf, T. N. and Welling, M. Semi-supervised classifica- tion with graph convolutional networks. International Conference on Learning Representations, 2017.

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
Kumar, S., Zhang, X., and Leskovec, J. Predicting dynamic embedding trajectory in temporal interaction networks. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1269-1278, 2019.
Sandra, M. and Jochen, D. W. Dyn2vee: Exploiting dy- namic behaviour using difference networks based node embeddings for classification. In Proceedings of the In- ternational Conference on Data Science, pp. 149-200, 2019.
Li, J., Yu, Z... Zhu, Z... Chen, L., Yu, Q., Zheng. Z., Tian, S., Wu, R., and Meng, C. Scaling up dynamic graph representation learning via spiking neural networks. In Proceedings of the AAAI Conference on Artificial Intelli- gence, volume 37, pp. 1588-8596, 2023.
Schliebs, S. and Kasabov, N. Evolving spiking neural net- work-a a survey. Evolving Systems, 4:87-98, 2013.
Shi, M.. Huang, Y., Zhu, X., Tang, Y., Zhuang, Y., and Liu, J. Gaen: Graph attention evolving networks. In Proceedings of the 30th International Joint Conference on Artificial Intelligence, pp. 1541-1547 2021.
Li, J.. Zhang, H., Wu, R.. Zhu, Z., Wang, B., Meng, C., Zheng, Z., and Chen, L. A graph is worth 1 1-bit spikes: When graph contrastive learning meets spiking neural networks. In International Conference on Learning Rep- resentations, 2024.
Singer, U., Guy, I., and Radinsky, K. Node embedding over temporal graphs. In Proceedings of the 28th Inter- national Joint Conference on Artificial Intelligence, pp. 4605-4610 2019.
Lu, Y., Wang, X., Shi. C., Yu, P. S., and Ye, Y. Temporal network embedding with micro- and macro-dynamies. In Proceedings of the 28th ACM International Confer- ence on Information and Knowledge Management, pp- 469-478, 2019.
Trivedi, R., Farajtabar, M., Biswal, P., and Zha, H. Dyrep: Learning representations over dynamic graphs. In Inter- national Conference on Learning Representations, 2019.
Wang. Y., Chang, Y.-Y., Liu, Y., Leskovec, J., and Li, P. Inductive representation learning in temporal networks via causal anonymous walks. In International Conference on Learning Representations, 2021.
Maass, W. Networks of spiking neurons: the third genera- tion of neural network models. Neural networks, 10(9): 1997.
Wen, Z. and Fang. Y. Trend:
Temporal event and node dy- namics for graph representation learning. In Proceedings of the ACM Weh Conference, pp. 1159-1169, 2022.
Nguyen, G. H., Lee, B., Rossi, R. A., Ahmed, N. K., Koh, E., and Kim, S. Continuous-time dynamic network embeddings. In Proceedings of the ACM Web Conference, pp. 969-976, 2018.
Xiao, M., Zhu, Y., He, D., and Lin, Z. Temporal spiking neural networks with synaptic delay for graph reasoning, In International Conference on Machine Learning, pp. 54341-54362 2024.
Pareja, A., Domeniconi, G., Chen, J., Ma. T., Suzumura, T., Kanezashi, H., Kaler, T., Schardl, T., and Leiserson, C. Evolvegen: Evolving graph convolutional networks for dynamic graphs. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pp. 5363-5370, 2020.
Xu, D., Ruan, C., Korpeoglu, E.,, Kumar, S., and Achan, K. Inductive representation learning on temporal graphs. In International Conference on Learning Representations, 2020.
Perozzi, B., AI-Rfou, R., and Skiena, S. Deepwalk: On- line learning of social representations. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 701-710, 2014.
Xu, M., Wu, Y., Deng, L., Liu, F., Li, G., and Pei, J. Ex- ploiting spiking dynamics with spatial-temporal feature normalization in graph learning. In Proceedings of the 30th International Joint Conference on Artificial Intelli- gence, pp. 3207-3213, 2021.
Pfeiffer, M. and Pfeil, T. Deep learning with spiking neu- rons: Opportunities and challenges. Frontiers in Neuro- science, 12:774, 2018
Yin, N., Feng, F., Luo, Z.,, Zhang, X., Wang, W., Luo, X., Chen, C., and Hua, X.-S. Dynamic hypergraph convolu- tional network. In Proceedings of the IEEE 38th Interna- tional Conference Data Engineering, pp. 1621-1634, 2022.
Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F, and Bronstein, M. Temporal graph networks for deep learning on dynamic graphs. arXiv preprint arX1v:2006.10637, 2020.
Yin, N., Shen, I.,, Xiong, H., Gu, B., Chen, C., Hua, X.-S., Liu, S., and Luo, X. Messages are never propagated alone: Collaborative hypergraph neural network for time-series forecasting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(4):2333-2)) 2347, 2024a.
Sajjad, H. P., Docherty, A., and Tyshetskiy, Y. Efficient representation learning using random walks for dynamic graphs. arXiv preprint arxiv: 1001.900.000 00466, 2019.
10

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
Yin, N., Wang, M., Chen, Z., De Masi, G., Xiong, H., and Gu, B. Dynamic spiking graph neural networks. In Proceedings of the AAAI Conference Artificial Intelli- gence, volume 38, pp.
2024b.
Yu, W., Cheng, W., Aggarwal, C. C., Chen, H., and Wang. W. Link prediction with spatial and temporal consistency in dynamic networks. In Proceedings of the 26th Inter- national Joint Conference on Artificial Intelligence, pp. 3343-3349, 2017.
Zhang, Z., Cui, P., Pei, Wang, X., and Zhu, W. Timers: Error-boundee svd restart dynamic networks. In Pro- ceedings of the AAAI Conference on Artificial Intelli- gence, volume 32, pp. 224-231, 2018.
Zhou, L., Yang, Y., Ren, X., Wu, F., and Zhuang. Dy- namic network embedding by modeling triadic closure process. In Proceedings of the AAAI Conference on Arti- ficial Intelligence, volume 32, pp. 571-578, 2018.
Zhu, Z., Peng, J., Li, J., Chen, L., Yu, Q., and Luo, S. Spiking graph convolutional networks. In Proceedings of the 31th International Joint Conference on Artificial Intelligence, pp. 2434-2440, 2022.
Zuo, Y., Liu, G., Lin, H., Guo, J., Hu, X., and Wu, Em- bedding temporal network via neighborhood formation. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 2857-2866, 2018

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
A. Proof of Theorem 5.1
A.I. Notation
Loss function.
h Output of feature j at time step t.
x (t-)), Spike firing sequence of feature at time step t
ka |n]: Gaussian delay kernel value from feature j. with delay steps K, 1 n.
Wijz Synaptic weight from feature to feature j.
Standard deviation of the Gaussian delay kernel, controlling the diffusion of delayed signals.
g Size of the Gaussian delay kernel, with K, indicating the maximum delay steps.
dy: Delay steps between features and j. a learnable parameter in the model.
maxx Maximum value of the sum of absolute synaptic weights for any feature i, i... Kmax = max; E /wig].
W m Maximum absolute synaptic weight, i.c., Wmax = max((.)) Jaayl-
F: Total number of features.
C: Upper bound constant for gradient propagation, defined as the sum of the product synaptic weights and Gaussian delay kernel values.
A.2. Proof Process
Step 1: Apply the Chain Rule to Expand the Gradient
By the chain rule, the gradient of the loss function L with respect the spike firing sequence s! (t-n) is expressed as:
0L
0L
dh
(18)
05 n-
ah
0s d.((-n) (t-n)
JEF
where:
0L is the gradient of the loss function with respect to the output of feature time step t.
ang
0n
represents the impact of spike fired by feature i at time step on the output of feature j at time step
0.
an
Step 2: Calculate
0e (e-w
In the Delay-DSGN model, the output h of feature j at time step defined as:
K
h1
Wis
key [ - m) s()
(t-n)
(19)
iEF
n=0
Thus, for a specific n n', the impact of the spike fired by feature time step n' on the output of feature j at time step / is:
aht
Σ
Way hig K2
n/),
(20)
as (t-n')
JEF
12

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
where the Gaussian delay kernel kig defined
ksy [n] = exp
Pij = K2 dis
(21)
2r²
Step Bound the Gradient
Substituting the above results into the gradient expression, we get:
aL
aL
F Riy(Ks - n']
Σ
Wij
(22)
0s; 10( nt-n)
Dh
j=1
Using the triangle inequality and the properties of absolute values, we obtain:
OL
F
aL
F Kij Kij[Ka - =n1],
Wayl
(23)
0s
[t-n)
Oh!
j=1
j=1
Define the constant C as:
F
F
((Ks - 1 - pis)
C=
Σ
Wiyl
kig [K,
1 - n'1 =
Σ
Wiyl
cxp
(24)
20
jml
Thus, the gradient is bounded by:
0L
F
0L
CC.
(25)
0s
(t-
Th
j=1
Step 4: Ensure C is Bounded to Prevent Gradient Explosion and Vanishing
To prevent C from becoming too large or too small, and avoid gradient explosion or vanishing, we impose appropriate constraints on the Gaussian delay kernel's standard deviation o and kernel size K,,
Preventing Gradient Explosion:
Since W max max((.j) |woy] and Kmax max; Ej-1 |Wggl, and also Ejnn |way| Kmax, have:
(K, - 1 n²' pij)² 12
F Wuil I Kiaxx
Wiyl
exp
(26)
202
This guarantees that C will not exceed Kmaxx preventing gradient explosion.
Preventing Gradient Vanishing:
To prevent from being too small, we ensure that the value of the Gaussian delay kernel at the boundaries of the delay range (i.e., n 0 and n. K, 1) is above a threshold e, i.e.,
(n 1i5))
exp
2 e,
(27)
202
Assuming the delay center (sg is the center of the kernel, i.e., May
K,-1 2
the maximum distance between and Piy is:
13

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
K -
n
Múj S
(28)
Thus, to ensure that the Gaussian delay kernel's 's value does not fall below at the boundaries n = 0 and n K, - 1, we require:
K,-1
exp
2 E,
(29)
2r²
Taking the natural logarithm of both sides:
(K, - -1)²
2 In(();
(30)
80²
Solving for o::
(K, - 1)2
0² 2 8( 8(-In(E))
(31)
Thus,
(K. - 1)2 8( In(c)))
V
(32)
To ensure that e accounts for the influence of all feature dimensions, we set:
Kmax
(33)
W max
Therefore:
[K. 1)2 8( In(())
(K, - 1)2
(34)
81n
Kax
This ensures that the standard deviation a of the Gaussian delay kernel is sufficiently large to prevent the kernel values from becoming too sharp, thus avoiding the gradient vanishing issue.
B. Interpretability of Delay
In our model, the delay parameters are initialized randomly following a normal distribution within a predefined range. This initialization strategy ensures that the model begins with a diverse set of potential delay values, allowing it to explore various temporal dependencies during training. For instance, when the maximum delay constrained to time units, the initial delay values are sampled from a normal distribution defined over the interval [0, 5].
After training on the DBLP, observe that the learned delay distribution slightly shifts to the right compared the initial distribution. This shift indicates that in academic settings, interactions and influences often take longer to materialize, reflecting the typically slower pace at which scholarly collaborations develop and propagate through the network. In contrast, when evaluating the model on the Tmall, the learned delay distribution exhibits slight leftward skew. This behavior aligns well with the nature of online consumer behavior, where users tend to respond quickly to items or promotions, resulting in shorter interaction delays. The Patent exhibits larger delays, with a more uniform distribution toward the right, suggesting that the impact of patents generally takes longer time diffuse and manifest. Despite sharing the same initialization
14

---

Delay-DSGN: A Dynamic Spiking Graph Neural Network with Delay Mechanisms for Evolving Graph
distribution, the model consistently learns dataset-specific delay values across multiple training runs, demonstrating its ability to adapt to inherent temporal characteristics.
DBLP Max-Delay
Tmall Max Delay
Patent Max Max-Delay
Hdii aalen Doles
0.3-
0.8
0.7
0.6
9.5-
0.5
0.3-
0.3
0.2
0.
0.1
(a) DBLP
(b) Tmall
(c)
Patent
Figure 6. The probability density histograms the initial and trained models across three datasets.
15


Reviews:
[{"review_id": "GIlv5LttpP", "reviewer": "Reviewer_zQNf", "summary": "This paper proposes Delay-DSGN, a dynamic spiking graph neural network that incorporates a delay convolution kernel, which dynamically adjusts the weight of information at different time steps. Through the delay convolution kernel, Delay-DSGN captures temporal dependencies and historical influences on node representations, then fed into LIF neurons for spike generation. After temporal modeling, Delay-DSGN combines node representations across time steps into a unified representation and finally uses regularization and cross-entropy loss to prevent gradient explosion and vanishing issues.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your meticulous review of our work and the valuable feedback provided.\n\n**Response to Weaknesses 1 and Question 1:**\n\n When a new edge is added to a graph, it may indeed represent an immediate interaction demand. However, in reality, there is usually a time lag between \"establishing a connection\" and \"producing an effect.\" For instance, in social networks, after user A posts content, user B may take several days to respond; in traffic networks, congestion propagation requires time. These phenomena indicate that delays in information propagation are an inherent property of dynamic graph evolution. Therefore, our motivation is to explicitly model these delays to more accurately capture the dynamics and temporal dependencies. Delay-DSGN adaptively learns the delay parameters $\\mu_{ij}$ within the delay kernel, dynamically determining appropriate delay value. This ensures that the speed of information propagation adapts to different application scenarios while preventing excessive delays.\n\n**Response to Weaknesses 2:** \n\nNeither our model nor the fixed random delay model includes a decay value for random initialization. The key difference lies in whether the delay parameters are learnable or remain fixed after initialization.\n\n**Response to Question 2:** \n\nWhen the number of synaptic connections in a neural network layer far exceeds the number of possible discrete delay positions, randomly initialized delays can cover the entire effective time range. For example, with 10 possible delay positions and 1000 synaptic connections, all delay positions will be covered. Thus, the necessity of moving delay positions away from their initial state diminishes. In this way, a fixed random delay model can achieve good performance by optimizing connection weights to capture temporal characteristics.\n\n**Response to Weaknesses 3:** \n\n* The core innovation of Delay-DSGN lies in its first-ever deep integration of biologically inspired delay mechanisms with dynamic graph modeling, along with rigorous theoretical guarantees for model stability. Specifically, Delay-DSGN explicitly models multi-step dependencies using learnable Gaussian delay kernels, capturing the relationship between topological connection strengths and signal propagation delays in dynamic graphs. Additionally, it provides strict upper bounds for gradient propagation in the spatiotemporal domain driven by delay kernels, offering theoretical guidance for model parameter selection. Compared to traditional SNNs and GNNs, Delay-DSGN not only enhances biological fidelity and temporal processing for SNNs but also introduces a groundbreaking delay perspective to dynamic graph modeling methods. \n* Although current research mainly focuses on SNNs, the delay mechanism can be regarded as a type of temporal convolution method. This approach shows potential for extension to other types of dynamic models when dealing with time-series data. Future work will further explore the application scope of this mechanism.\n\n**Response to Question 3:**\n\nThe delay convolution kernel primarily addresses the weighted aggregation of historical information within a single time step. However, topological changes in dynamic graphs often span multiple time steps. By integrating node representations from different time steps into a unified feature, it becomes possible to better capture long-term dependencies and complex topological evolutions. Secondly, this approach compensates for the sparsity of spike signals, mitigating information loss caused by the sparse nature of spike signals.\n\n**Response to Question 4:** \n\nSince Delay-DSGN introduces additional delay time parameters, to balance the total number of parameters, we increased the number of hidden neurons in the no-delay model. Additionally, we conducted experiments on a standard SNN model without adding extra neurons. The comparative experimental results are as follows:\n|  | Metric   | No-Delay SNN | Standard SNN |\n|---------|----------|:--------------:|:--------------:|\n| DBLP    | Ma-F1    | 71.00  | 70.88|\n|         | Mi-F1    | 71.65| 71.98 |\n| Tmall   | Ma-F1    | 59.34| 58.84|\n|         | Mi-F1    | 63.55| 63.52 |\n| Patent  | Ma-F1    | 83.57| 83.53 |\n|         | Mi-F1    | 83.55| 83.48 |\n\n**Response to Other Comments or Suggestions:**\n\n- Equation (4) describes the node features processed with delay, which are subsequently used as input in Equation (5).\n- We understand your questions about Equations (9) and (15) mainly concern the notation $w$，and we apologize for not providing sufficient explanations in the original manuscript. Here are the specific modifications:\n\n    - For Equation (9), $w_t$ represents the weight of the features at time step $t$, which is obtained through an element-wise multiplication of $Z_v^t$ and $w_t$, followed by a row-wise summation. \n    \n    - For Equation (15), $w_{ij}$ represents the weight between neuron $i$ and neuron $j$.", "claims_and_evidence": "yes", "methods_and_evaluation_criteria": "yes", "theoretical_claims": "yes", "experimental_designs_or_analyses": "The experimental design is well-structured, but I have concerns regarding the analysis.", "relation_to_broader_scientific_literature": "A new exploration in spike neural networks for dynamin  graph learning.", "essential_references_not_discussed": "no", "other_strengths_and_weaknesses": "**Strengths**\n\n1. This paper considers the historical information in neighborhood aggregation, mitigating historical information forgetting.\n2. The delay convolution kernel uses the learnable synaptic delay and weight to make the information of different time steps participate in convolution with different weights.\n\n**Weaknesses**\n\n1. The motivation for delaying the information propagation is not clearly and convincing explained.\n2. The fixed random delay model with randomly initialized decay values is unreasonable, since earlier information is more likely to be weighted lower than more recent information.\n3. The novelty of this paper is rather limited. Apart from the design of delay convolution kernel, Delay-DSGN is similar to standard SNNs. Moreover, the extensibility of delay convolution kernel is restricted to SNNs.", "other_comments_or_suggestions": "For the formulation, there are three different symbols, please check the Eqs. 4, 9, and 15.", "questions_for_authors": "1. When adding a new edge, why doesn't it immediately affect the representations of the two nodes that the edge connects? How can the delay representation ensure that it does not cause information latency, leading to inaccurate node representation?\n2. Why the fixed random delay model with randomly initialized decay values outperforms the no-delay model, and sometimes is competitive with Delay-DSGN?\n3. Since the delay convolution kernel has already captured the temporal dependencies and historical influences on node representations, why do Delay-DSGN still need to combine node representations from different time steps into a unified feature?\n4. Why is the number of neurons set to a higher value in the no-delay model? It will lead to an unfair performance comparison between Delay-DSGN and no-decay model.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "kBHZV3xhoS", "reviewer": "Reviewer_nXzL", "summary": "This paper introduces Delay-DSGN, a dynamic spiking graph neural network that incorporates a learnable delay mechanism to enhance the representation of evolving graphs. By modeling synaptic delays with a Gaussian kernel, the model effectively captures temporal dependencies and mitigates information forgetting. The paper provides theoretical guarantees to address gradient issues and demonstrate the model's effectiveness through experiments on three large-scale dynamic graph datasets.   \n\nOverall, the paper offers a timely and promising contribution to dynamic graph learning and spiking neural networks.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your meticulous review of our work and the valuable feedback provided.\n\n**Response to Experimental Designs or Analyses 1:**\n\nIn our experiments, we compared eight methods across three datasets using two metrics. To assess the statistical significance of improvements by our proposed method over the baselines, we conducted Friedman tests. The results are:\n|Metric |F-Value |P-Value|\n|-|-|-|\n|Ma-F1|18.1170|0.0204|\n|Mi-F1|18.6072|0.0171|\n\nWith all P-values are less than the significance level $ \\alpha = 0.05 $, indicating that our method's average ranking is significantly different from the baselines for both metrics.\n\n**Response to Essential References Not Discussed:**\n\nWe have made additions to the \"Related Work\" section: \"GC-LSTM integrates LSTM into GCN to model the temporal evolution of node features. It captures temporal dependencies through hidden state transitions. In contrast, Delay-DSGN introduces a delay convolution kernel to explicitly parameterize propagation delays. DyRep utilizes temporal point processes to model the triggering intensity and time intervals of events. Its core lies in describing the probabilistic patterns of event occurrences rather than capturing the dynamic delay effects of information propagation.\" \n\n**Response to Weaknesses:**\n\nPlease refer to the first response to Reviewer WWHS.\n\n**Response to Concerns:**\n* **Regarding zero-padding, convolution processes:** For example, at the current timestep, two neurons from the previous layer aggregate information to one neuron in the current layer. The inputs are spike trains from these two neurons, each containing activity information across four timesteps (the current timestep and three historical timesteps). Neurons exhibit different delays. Before convolution, the input sequences undergo left-side zero-padding (with padding length equal to $K_s−1$) to accommodate the convolution kernel size. Convolution kernel construction: The hyperparameter $K_s$ represents the size of the delay convolution kernel, and $K_s−1$ is the maximum delay time. The values in the delay convolution kernel follow a Gaussian distribution, with the center position located at $K_s−d−1$. Subsequently, the padded sequences are convolved with the delay-specific kernels constructed between each pair of neurons. This operation fuses weighted information across timesteps, generating a new output spike sequence that aggregates information from two neurons to one.\n* **Regarding the computational cost of larger delay windows:** This does not increase the computational cost. A larger delay window means a larger delay convolution kernel, which results in more left zero-padding, but the number of convolution computations remains unchanged.\n* **Rationale for Choosing the Gaussian Kernel:** \n  - Learnable Temporal Shift: The parameter $μ$ controls the central position of the delay, enabling the model to explicitly learn the delay magnitude. The smoothness of the Gaussian kernel ensures gradient stability during training.\n  - Adjustable Receptive Field: The variance parameter $σ$ modulates the receptive field of the delay kernel, allowing it to capture multi-step historical information.\n* **Network Architecture:** The dynamic graph is divided into fixed-interval snapshots. For each snapshot, second-order neighborhood sampling captures multi-hop dependencies, and first-order aggregation integrates local features. Features are encoded into spike representations using SNNs, converting continuous data into spike trains. Second-order aggregation incorporates broader context. In the Delay-SNN layer, the model dynamically adjusts the Gaussian delay kernel's center to capture varying temporal delays, generating node delay representations. Multi-timescale fusion integrates representations across timesteps, producing final embeddings used for downstream tasks.\n* **SNN-GNN Interaction and Benefits of SNNs for Dynamic Graphs:**\nAfter traditional GNN-based neighborhood aggregation, the threshold-triggering mechanism of SNNs replaces conventional nonlinear activation functions. Advantages of SNNs for Dynamic Graphs: SNNs inherently accumulate membrane potentials across timesteps, aligning naturally with the discrete timestep nature of dynamic graphs. At each timestep, node information is stored in the membrane potential of SNN neurons. This potential is inherited to the next timestep, preserving historical states and enabling the modeling of graph evolution.\n\n**Response to Weaknesses Theoretical Claims:**\n\nThank you for your valuable feedback. Your insights have provided us with an important perspective. To further explore this issue, we plan to conduct more detailed experiments focusing on: Evaluating our method's performance on dynamic graphs with diverse temporal patterns and topological structures. Testing our theoretical findings with additional real-world datasets to ensure their validity and applicability in practical scenarios.", "claims_and_evidence": "This claim is supported by comprehensive experimental results showing improvements in both macro and micro $F1$ scores, as well as a theoretical gradient stability proof provided in the appendix. \n\nThe evidence is generally convincing, although some parameter choices could benefit from clearer justification.", "methods_and_evaluation_criteria": "The use of F1-macro and F1-micro as evaluation metrics is appropriate for the node classification tasks presented. \n\nThe method details are mostly clear; however, some parts of the zero-padding and convolution process could be described in greater detail for complete reproducibility.", "theoretical_claims": "The proof assumes that the Gaussian kernel’s influence is stable across different graph structures, but real-world dynamic graphs may have highly irregular temporal patterns. $Relevant$ $discussion$ on the $robustness$ of the theoretical bounds in these settings is necessary.", "experimental_designs_or_analyses": ">The experiments are well-structured and reproducible, but a few aspects could be improved:\n\n•\tThe paper reports standard deviations, but statistical significance tests (e.g., t-tests) are not provided to confirm that the improvements are meaningful rather than random variation.\n\n•\tWhile the impact of $\\sigma$ and $d_m$ is explored (Figure 5), the authors do not discuss the computational cost of larger delay windows.", "relation_to_broader_scientific_literature": "The paper is well-positioned within dynamic graph learning and spiking neural network literature. \n\nHowever, while the discussion on the biological plausibility of delay mechanisms is interesting, it could benefit from more references to neuromorphic computing models (e.g., event-driven SNNs). \n\nAdditionally, there is limited comparison between delay-based mechanisms and other temporal modeling approaches, such as continuous-time point processes used in DyRep and TGN.", "essential_references_not_discussed": "The paper lacks a discussion of some relevant temporal graph learning works, such as GC-LSTM, a model with an LSTM embedded in a GCN, and DyRep, which uses a temporal point process to model event-driven graph evolution. \n\nA brief discussion of these methods, particularly how they differ from Delay-DSGN, would enhance the paper’s contextual positioning.", "other_strengths_and_weaknesses": ">Strengths:\n\n•\tThe incorporation of a learnable delay mechanism in the spiking graph neural network framework is a novel idea, blending insights from neuroscience and graph learning.\n\n•\tThe paper presents theoretical guarantees for the stability of the training process, ensuring the model avoids gradient explosion or vanishing, which is an important contribution.\n\n>Weaknesses:\n\n•\tThe authors did not present the learning process or distribution characteristics of the delay mechanism in the graph data. Relevant evidence would provide a clearer explanation.", "other_comments_or_suggestions": "The network architecture is shown in Figure 2, but it lacks a more detailed explanation. \n\nThe integration of Spiking Neural Networks with the graph neural network approach should be explained more clearly. \n\nHow does the SNN layer interact with the graph convolution layer, and what benefits does this bring to dynamic graph representation learning?", "questions_for_authors": "1. Does the delay mechanism perform differently on irregular graphs, such as those with sparse or heterogeneous structures?\n\n2. Additionally, the paper adopts a Gaussian delay kernel—what was the rationale behind this choice?'\n\n\n\n## update after rebuttal\n\nThank you for the detailed response, which effectively addressed my main concerns. I appreciate the clarity provided and am happy to update my score accordingly. I recommend Accept.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LdkGmdXls1", "reviewer": "Reviewer_WWHS", "summary": "This paper introduces Delay-DSGN, a novel dynamic spiking graph neural network that incorporates a learnable synaptic delay mechanism to enhance dynamic graph representation learning. The authors argue that existing SNN-based methods struggle with temporal information propagation and historical forgetting, and they propose a Gaussian delay kernel to address this issue. The model is evaluated on three large-scale dynamic graph datasets for node classification, demonstrating superior performance over eight state-of-the-art baselines. The authors also provide a theoretical analysis of the stability conditions for the delay kernel, ensuring the model avoids gradient explosion and vanishing issues.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your meticulous review of our work and the valuable feedback provided.\n\n**Response to Weaknesses and Question 1:**\n\nIn our model, delay parameters are randomly initialized following a normal distribution within a specified range. For example, when the maximum delay is set to 5, the initial delays are sampled from a normal distribution over the interval $[0, 5]$. Training results on the DBLP show that the learned delay distribution is slightly shifted to the right, indicating that academic collaborations and influences often require a longer time to become evident. For the Tmall, the learned delay distribution is slightly skewed to the left, reflecting the typically rapid user responses and interactions in e-commerce environments. The Patent exhibits larger delays, with a more uniform distribution toward the right, suggesting that the impact of patents generally takes a longer time to diffuse and manifest. Despite sharing the same initialization distribution, the model consistently learns dataset-specific delay values across multiple training runs, demonstrating its ability to adapt to inherent temporal characteristics. \n| Delay Interval | Initialization Density | DBLP Post-Training Density | Tmall Post-Training Density | Patent Post-Training Density |\n|----------------|------------------------|----------------------------|-----------------------------|------------------------------|\n| 0-1           | 0.0  | 0.0| 0.08  | 0.0|\n| 1-2           | 0.2       | 0.17| 0.29         | 0.13                         |\n| 2-3           | 0.6     | 0.5                        | 0.46                        | 0.35                         |\n| 3-4           | 0.2                    | 0.28                       | 0.17                        | 0.33                         |\n| 4-5           | 0.0                    | 0.05                       | 0.0                           | 0.19                         |\n\n**Response to Theoretical Claims:**\n\nThank you for your valuable feedback. We have added an extra analysis in the experimental section and visualized the training loss curves. Unfortunately, we are unable to display the figures here, so we provide the following explanation. When $σ$ is outside the derived range, the model's loss during training on the DBLP remains largely unchanged. In contrast, when $σ$ is within the derived range, the training loss consistently decreases, indicating that the model is able to learn and optimize effectively.\n\n**Response to Essential References Not Discussed and Question 2:**\n\nWe have added a new paragraph in the related work section as follows:\n\"Unlike the memory module in TGN, our delay mechanism explicitly models multi-step dependencies through differentiable temporal kernels, thereby mitigating the gradient decay issues inherent in RNN architectures. Compared to the Hawkes process used in TREND, the biologically inspired spike-delay mechanism in Delay-DSGN is better suited for handling discretized timestep-based graph updates. \" We have compared our approach with attention-based methods such as TGAT. We will endeavor to include experimental comparisons with TGN to further demonstrate the effectiveness and advantages of our proposed method.\n\n**Response to Other Comments Or Suggestions:**\n\nThank you for your valuable feedback and careful corrections on our paper. Based on your suggestions, we have carefully revised and improved the issues mentioned in the text as follows:\n* In line 15 on page 2, “effectively mitigating historical information forgetting” has been revised to “effectively mitigating the forgetting of historical information” for improved clarity and grammatical accuracy.\n* At the location of Equation (5) on page 4, we have added a reference to Equation (4) to better clarify the relationships between the different parts of the formulas.\n* Regarding the comparison with eight methods but only seven results being presented in the experiments, we confirmed that this was due to the omission of one method in the table. We have now updated the table to include all the mentioned methods. Due to character limitations, the results of the omitted comparison methods on the three datasets are as follows:\n\n| Dataset | Metrics | Training | DeepWalk |\n|---------|---------|----------|----------|\n| DBLP    | Ma-F1 | 40%| 67.08  |\n|         |         | 60%| 67.17|\n|         |         | 80%      | 67.12    |\n|         | Mi-F1   | 40%| 66.53    |\n|         |         | 60%| 66.89    |\n|         |         | 80%| 66.38    |\n| Tmall   | Ma-F1   | 40%| 49.09    |\n|         |         | 60%| 49.29    |\n|         |         | 80%  | 49.53    |\n|         | Mi-F1   | 40%| 57.11    |\n|         |         | 60%| 57.34    |\n|         |         | 80%| 57.88    |\n| Patent  | Ma-F1   | 40%| 72.32    |\n|         |         | 60%| 72.25    |\n|         |         | 80%  | 72.05    |\n|         | Mi-F1   | 40% | 71.57    |\n|         |         | 60% | 71.53    |\n|         |         | 80%| 71.38    |", "claims_and_evidence": "The paper makes several key claims:\n1. Delay mechanisms improve long-term temporal modeling in dynamic graphs.\n2. Delay-DSGN outperforms existing dynamic graph models (e.g., Dy-SIGN, SpikeNet) in node classification.\n3. Theoretical analysis ensures stable training of the Gaussian delay kernel.\n\nThe evidence provided supports these claims reasonably well:\n1. The experimental results on three large-scale datasets demonstrate consistent improvements over state-of-the-art methods.\n2. The ablation study comparing learnable delays vs. fixed delays vs. no delay strengthens the argument that delayed information propagation is beneficial.\n3. The theoretical section derives conditions for stable training, although additional empirical validation (e.g., loss landscape analysis) would further reinforce this claim.\n\nHowever, the paper does not provide enough analysis on the interpretability of learned delays—are the learned delays consistent across different datasets?", "methods_and_evaluation_criteria": "The choice of node classification as the primary evaluation task and the focus on classification accuracy (Ma-F1, Mi-F1) is appropriate, as it aligns with common benchmarks in dynamic graph learning. However, the dataset-specific hyperparameter tuning is not fully discussed.", "theoretical_claims": "The paper provides a sound theoretical analysis of the conditions required for stable training of the Gaussian delay kernel, ensuring that the model avoids gradient explosion and vanishing issues. The proof (Appendix A) correctly applies the chain rule and leverages the properties of Gaussian functions to derive a well-structured bound on the standard deviation ($\\sigma$) and kernel size ($K_s$).\n\nThe derivation is mathematically reasonable, and the constraints appear well-motivated. One potential improvement would be an empirical validation of how training behaves when $\\sigma$ is set outside the derived bounds. A brief numerical analysis confirming the theoretical stability conditions would further strengthen this claim.", "experimental_designs_or_analyses": "The authors claim that the delay mechanism effectively preserves historical information and mitigates the information forgetting issue in dynamic graphs. This claim is supported by comprehensive experimental results showing improvements in both macro and micro F1 scores, as well as a theoretical gradient stability proof provided in the appendix. The evidence is generally convincing, although some parameter choices could benefit from clearer justification.", "relation_to_broader_scientific_literature": "This work aligns well with research in dynamic graph learning and spiking neural networks, building on prior studies in GNNs for dynamic graphs (TGAT, EvolveGCN, Dy-SIGN) and spiking neural networks for graphs (SpikeNet).", "essential_references_not_discussed": "The paper should consider discussing:\n1. “Temporal Graph Networks” (Rossi et al., 2020, ICLR), which also models long-term dependencies in dynamic graphs using memory-based approaches.\n2. “A Hawkes process-based graph neural network: TREND” (Wen et al., 2022, WWW), which provides an alternative view on modeling temporal dependencies.", "other_strengths_and_weaknesses": "Strengths:\n1. A novel delay-based temporal mechanism, inspired by biological synaptic plasticity, which offers a fresh perspective in GNN research.\n2. Impressive empirical results on large-scale dynamic graphs, with meaningful comparisons to both non-spiking and spiking methods.\n3. A solid mathematical foundation, providing a theoretical basis for stable training.\n\nWeaknesses:\nThe interpretability of learned delays is somewhat limited—it’s not entirely clear what the model is learning and whether the delays correspond to real-world temporal phenomena.", "other_comments_or_suggestions": "1. Typos:\nI. Page 2, Line 15: \"effectively mitigating historical information forgetting\" → \"effectively mitigating the forgetting of historical information\".\nII. Page 4, Equation (5): Should reference Equation (4) for clarity.\n2. The paper mentions a comparison with 8 methods, but the experimental results only present 7. Is this due to an omission of one method or a typographical error?", "questions_for_authors": "1. Are the learned delays consistent across training runs, or do they vary significantly with different initializations?\n2. How does Delay-DSGN compare to attention-based methods like TGN in terms of handling long-term dependencies?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a dynamic spiking graph neural network to capture the impact of latency in information propagation with a learnable mechanism. It dynamically adjusts connection weights and propagation speeds with a Gaussian delay kernel to adaptively delay historical information. Theoretical and experimental justifications demonstrate its superiority in high-performance and stable training processes. The claims are supported by clear and convincing evidence.  This paper possesses a novel delay-based temporal mechanism and solid theoretical justification.  In the rebuttal, the authors try to clarify the motivation for the delay.
Decision: Accept (poster)