Dynamic Growth Learning

• Dynamic Growth Learning is a set of algorithmic strategies that capture evolving graph structures by integrating temporal dynamics and multi-scale structural features.
• It encompasses diverse model classes including high-order dynamic GNNs, deep network growth predictors, scalable time-encoded models, and neuromorphic spiking neural networks.
• Empirical studies demonstrate that DGL frameworks improve predictive accuracy, scalability, and robustness through effective temporal encoding and biologically inspired network adaptations.

Dynamic Growth Learning (DGL) encompasses algorithmic and architectural strategies aimed at modeling, predicting, or enabling dynamic evolution in graph-structured or neural data, typically by capturing the temporal and structural variability intrinsic to real-world networks and neuro-inspired systems. DGL methods span multiple paradigms, including dynamic graph neural networks, end-to-end structure-based network growth predictors, scalable tensor frameworks, and biologically-inspired network expansion mechanisms. The term is used both descriptively (referring to the learning of dynamic, evolving phenomena) and algorithmically (as a specific mechanism for adaptively growing structure or function in a model).

1. Objectives and Technical Foundations

In dynamic graph learning, the canonical objective is, given a sequence of time-indexed graph snapshots $\mathcal{G} = \{G_1, \ldots, G_T\}$, with $G_t = (V, E_t, X_t)$ and node features $X_t \in \mathbb{R}^{N \times F}$, to learn a node embedding tensor $H \in \mathbb{R}^{N \times F' \times T}$ that jointly models the temporal evolution of features and adaptation to changing structural dependencies in $E_t$. Such embeddings support a variety of downstream tasks—including link prediction, node classification, and anomaly detection—necessitating the explicit capture of both high-dimensional temporal signals and complex structural motifs (Wang, 7 Jun 2025).

A central problem is effective information propagation across both time and graph topology, with requirements for scalability to large $N$ and $T$. Methodologies differ in their architectural specifics (e.g., message-passing GNNs, deep convolutional graph descriptors, temporal encodings, pathway-growing SNNs), but all share the need to represent and act upon evolving topologies or connectivity distributions.

2. Model Classes and Algorithmic Variants

2.1 High-Order Dynamic GNNs with Structural Innovation

Standard dynamic GNNs aggregate node features via message passing over evolving $E_t$, but often disregard higher-order patterns such as multi-hop overlaps or community structure. NO-HGNN (Wang, 7 Jun 2025) addresses this by explicitly quantifying neighborhood overlap using the Jaccard coefficient:

$$\hat p_{i,j,t} = \frac{|N(i,t) \cap N(j,t)|}{|N(i,t) \cup N(j,t)|}$$

Raw overlap tensors are normalized via softmax to obtain attention weights for message passing. The model substitutes or augments adjacency-based propagation tensors with these overlap tensors in a high-order GNN backbone, allowing message weights to reflect both adjacency and multi-hop neighborhood correlation. This approach enables direct modeling of richer structural motifs, leading to improved predictive accuracy in dynamic link prediction and node embedding.

2.2 Deep Learning for Network Growth Prediction

Dynamic Growth Learning in the context of end-to-end network growth regression is exemplified by DeepGraph (Li et al., 2016). Here, a static graph snapshot is first mapped to a heat kernel signature (HKS) descriptor that compresses multi-scale topological information, which is then processed by a dual-axis, multi-resolution convolutional neural network. The network regresses future growth metrics (such as $\Delta |V|$ or $\Delta |E|$) in a temporally shifted window using mean-squared error objectives with log-scaled targets:

$$y = g(\mathcal{G}^{(t)}, \Delta t) = \log_2(y^{o} + 1)$$

This framework enables the unsupervised discovery of growth-driving structure, outperforming traditional hand-crafted graph descriptors and graph kernels.

2.3 Scalable Time-Encoded Dynamic GNNs

ScaDyG (Wu et al., 27 Jan 2025) focuses on scalability for large-scale dynamic graphs, introducing a time-aware topology reformulation (TTR) that preprocesses temporal message passing in a weight-free, sparse-matrix scheme. Dynamic temporal encoding employs sets of exponential kernels to capture multi-scale decay in edge and node features:

$$T_e(\Delta t) = [\exp(\gamma_1 \Delta t), \ldots, \exp(\gamma_{d_e} \Delta t)]$$

A hypernetwork-driven message aggregation mechanism tailors node-level transformation matrices, enhancing adaptive temporal fusion. The overall effect is a pipeline in which temporal evolution can be fully decoupled between preprocessing and inference, allowing parameter and time complexity to scale in the number of nodes and time steps rather than the number of interactions.

2.4 Temporal Pathway Growth in Spiking Neural Networks

Dynamic Growth Learning also denotes a specific temporal pathway expansion mechanism in CogniSNN (Huang et al., 12 Dec 2025). The random-graph SNN backbone is endowed with dynamic-configurability through a time-indexed gating of neural pathways. At each timestep $t$, an increasing set of pathways (ordered by betweenness centrality) becomes active:

$$\mathcal{P}^{(t)} = \{p_1, \ldots, p_{q(t)}\}, \qquad q(t) = \begin{cases} t \left\lfloor \frac{|P|}{T} \right\rfloor\,, \quad 1\leq t<T\ |P|, \quad t=T \end{cases}$$

The cumulative output is averaged for final inference, while learning proceeds through surrogate gradient backpropagation. This mechanism enables improved robustness and timestep flexibility, mimicking experience-dependent structural plasticity observed in biological neural circuits.

3. Key Methodologies

Model/Class	Main Technical Innovation	Usage/Prediction Type
NO-HGNN (Wang, 7 Jun 2025)	Neighborhood-overlap attention in HGNN	Dynamic link prediction
DeepGraph (Li et al., 2016)	HKS and multi-res CNN graph descriptors	Network growth regression
ScaDyG (Wu et al., 27 Jan 2025)	Preprocessing-only temporal propagation	Scalable graph tasks
CogniSNN+DGL (Huang et al., 12 Dec 2025)	Temporal pathway growth by BC ranking	SNN robustness, flexibility

NO-HGNN and ScaDyG exploit explicit high-order or temporal signal encoding, while DeepGraph leverages spectral-topological descriptors for prediction on static snapshots. The DGL methodology in CogniSNN brings nonparametric plasticity to neuromorphic SNNs.

4. Empirical Performance and Experimental Evidence

Empirical results across these lines consistently show the value of dynamic growth modeling. In NO-HGNN (Wang, 7 Jun 2025), ablations confirm that neighborhood-overlap-aware message passing yields 1–3% F1-score and 1–2% accuracy gains over prior dynamic and static GNNs on canonical benchmarks such as ask-ubuntu and bitcoin-alpha.

DeepGraph (Li et al., 2016) reduces MSE in growth prediction by 3–12% versus strong hand-crafted and kernel-based baselines, and captures structural correlates (community count, triadic closure, density) without explicit feature engineering.

ScaDyG (Wu et al., 27 Jan 2025) achieves up to 30% higher MRR (ranking) and 42% higher NDCG (multi-label affinity) on link and node-affinity prediction across 12 datasets. It consistently yields lower runtime and parameter counts, addressing critical efficiency bottlenecks.

In CogniSNN (Huang et al., 12 Dec 2025), DGL increases robustness to noise and frame loss by 8–16% and significantly enhances performance under reduced-timestep inference, with minimal energy overhead relative to static SNNs.

5. Biological Inspiration and Neural Plasticity

The DGL methodology in CogniSNN directly draws from cortical mechanisms of experience-dependent plasticity. By growing new pathways along internal timesteps, CogniSNN simulates ongoing rewiring that is observed in synaptic remodeling in vivo. This contrasts with standard pruning paradigms and enables better performance under input perturbation and flexible deployment contexts—an effect essential for neuromorphic hardware (Huang et al., 12 Dec 2025).

A plausible implication is that temporally staged or structure-adaptive models may bridge some of the classical gaps between artificial and biological learning, particularly for tasks requiring resilience to nonstationary environments.

6. Scalability, Limitations, and Future Directions

Dynamic Growth Learning approaches introduce various trade-offs in scalability, model complexity, and generalizability. Tensor-based and preprocessing-intensive models (NO-HGNN, ScaDyG) scale more efficiently compared to fully recurrent or attention-based frameworks, especially in large graphs or long histories. ScaDyG demonstrates parameter reductions up to $50\times$ and up to $60\times$ faster training per epoch compared to baselines (Wu et al., 27 Jan 2025).

Limitations include:

• NO-HGNN is presently limited to discrete-time snapshots and pairwise overlap; extensions to continuous-time and higher-order motifs are open research directions (Wang, 7 Jun 2025).
• CogniSNN+DGL does not implement adaptive synaptogenesis or online re-ranking of pathway importance, and pruning is only implicit through weight decay (Huang et al., 12 Dec 2025).
• DeepGraph’s supervised targets require temporally annotated growth signals, restricting utility in unsupervised or online settings (Li et al., 2016).

Future work extends toward:

• Integration with graph transformer architectures for more flexible temporal aggregation
• Modeling higher-order structural motifs (e.g., triangles, cliques) beyond pairwise overlap
• Efficient deployment in neuromorphic systems with strict hardware constraints
• Unified frameworks for multitask prediction on dynamic, attribute-rich, or multimodal graphs

By systematically embedding structural and temporal signals at multiple architectural levels, Dynamic Growth Learning frameworks offer robust, scalable, and biologically motivated solutions for learning in temporally evolving and structurally complex networks.