Dynamic link prediction method, system, device and medium based on selective state space and dual decoupling

Abstract

The application relates to the technical field of data processing, and discloses a dynamic link prediction method, system, device and medium based on a selective state space and a dual decoupling, the method comprising the following steps: obtaining a historical interaction sequence of a node pair to be predicted; performing recursive evolution on the sequence through a selective state space model with linear complexity to generate an excited feature at each historical moment; generating a feature modulation parameter according to calendar prior information of the interaction moment, modulating the excited feature, and obtaining an environment perception feature fused with calendar semantics; then decomposing the feature into a structure component and a semantic component through double-branch projection; and finally aggregating the two types of components of a source node and a target node and inputting the components into a prediction network to obtain an interaction probability. The application improves the precision and efficiency of link prediction.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a dynamic link prediction method, system, device and medium based on selective state space and dual decoupling. Background Technology

[0002] In complex real-world systems, various interactions typically occur continuously as asynchronous event streams. Continuous-Time Dynamic Graphs (CTDGs) can characterize this fine-grained evolutionary process over a continuous time scale, thus becoming an important tool for describing the dynamic changes of complex systems. Dynamic link prediction algorithms based on CTDGs are usually modeled based on the historical interaction information of nodes to infer future interaction relationships between nodes, and their prediction performance directly affects the efficiency of resource allocation and management in dynamic networks.

[0003] DyGFormer, a dynamic link prediction method based on the Transformer architecture, is a dynamic graph learning model whose core design idea is to learn the evolutionary rules of the dynamic graph solely from the historical one-hop interaction sequences of nodes. The specific implementation of this model includes the following key technical aspects: a) Neighbor co-occurrence encoding scheme. DyGFormer designs a neighbor co-occurrence encoding mechanism that explicitly mines the potential associations between nodes by statistically analyzing the frequency of occurrence of each neighbor in the historical sequences of the source and target nodes. This scheme transforms the historical interaction sequences of nodes into feature representations containing neighbor co-occurrence information to capture the correlations between nodes. b) Patching technique. To address the difficulty of modeling long historical sequences, DyGFormer employs a patching technique, dividing the complete interaction sequence into multiple sub-sequence fragments before inputting them into the Transformer to capture long-term temporal dependencies and reduce computational complexity. c) Self-attention mechanism modeling. DyGFormer utilizes the self-attention mechanism, a core component of the Transformer architecture, to globally model the node interaction sequences in the dynamic graph, capturing the dependencies between any two positions in the sequence, thereby achieving the representation of complex spatiotemporal dependencies. The advantage of this method is that it can capture long-term time dependencies well, and it achieved state-of-the-art performance on multiple public datasets at the time.

[0004] The dynamic link prediction method based on memory networks, namely TGN (Temporal Graph Networks), is a general and efficient deep learning framework for dynamic graphs, representing dynamic graphs as timestamped event sequences. The core implementation process of this model is as follows: a) Node memory module. TGN maintains an updatable memory vector for each node, used to compress and store the node's historical interaction information. Whenever a node participates in a new interaction event, its memory vector is updated asynchronously according to the event information, thus achieving continuous evolution of the node state. b) Message passing mechanism. When a new interaction edge occurs, TGN aggregates information such as the current memory of the source and target nodes, the timestamp of the interaction, and interaction features into a message through a message passing mechanism, used to update the memory state of the relevant nodes. c) Temporal encoding and embedding generation. TGN introduces a temporal encoding module to encode the interaction time information into a temporal feature vector, which is fused with the node's memory vector and the original node features. Finally, through a graph attention layer or MLP, an embedding representation of the node at any time is generated for downstream tasks such as link prediction. The advantage of this method lies in its ability to effectively compress and quickly update historical information through a memory mechanism, thus ensuring computational efficiency while possessing the ability to generalize to new nodes.

[0005] Despite the significant progress made by the aforementioned methods in dynamic link prediction tasks, the following shortcomings remain: First, computational efficiency bottleneck. The computational complexity of the self-attention mechanism in the Transformer architecture, represented by DyGFormer, increases quadratically with the sequence length L (O(L²)). This places a heavy computational burden on historical interaction data spanning long periods, limiting the model's ability to model long-term evolutionary information. Second, insufficient temporal semantic awareness. Existing algorithms often fuse temporal information through feature concatenation or simple weighting, making it difficult to effectively perceive multi-scale calendar prior information (such as the impact of weeks, months, and holidays on behavioral patterns). When faced with sudden changes in non-stationary environments, they often struggle to accurately characterize shifts in behavioral patterns. Third, juxtaposition of structural and behavioral features. Structural information and behavioral semantics are modeled together in existing models. When interaction mechanisms change rapidly, this coupling may weaken the model's ability to distinguish between different information sources, limiting its generalization performance in complex real-world scenarios.

[0006] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0007] The main objective of this invention is to provide a dynamic link prediction method, system, device, and medium based on selective state space and dual decoupling. This aims to solve the problem that the computational complexity of the self-attention mechanism based on the Transformer architecture in the prior art is too high, and the coupling and aliasing of structural and behavioral features makes it difficult to balance computational efficiency and prediction accuracy in long sequence processing.

[0008] The first aspect of this invention provides a dynamic link prediction method based on selective state space and dual decoupling, the dynamic link prediction method based on selective state space and dual decoupling includes the following steps: Obtain the historical interaction events of each node in the node pair to be predicted before the target time, construct the initial embedding of each historical interaction event, and arrange the initial embeddings in chronological order as the historical interaction sequence of each node in the node pair to be predicted. Each initial embedding in the historical interaction sequence of each node is sequentially input into the selective state space model. The hidden state of the corresponding node is recursively updated through the selective state space model. Based on the updated hidden state, the stimulated representation of the corresponding historical interaction moment is generated to obtain the stimulated representation sequence of each node. Extract the calendar prior information corresponding to each of the historical interaction events, generate feature modulation parameters based on the calendar prior information through a meta-learning supernetwork, and use the feature modulation parameters to perform feature modulation on the stimulated representation at the corresponding time in the stimulated representation sequence to obtain the environment-aware representation matrix of each node fused with calendar semantics. The environmental perception representation matrix of each node is projected into the structural subspace and the semantic subspace in a two-branch manner to obtain the structural components and semantic components of the corresponding node. The structural components and semantic components of the source node and the target node in the node pair to be predicted are aggregated, and the aggregation result is input into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time.

[0009] Optionally, in one embodiment of the present invention, constructing the initial embedding of each of the historical interaction events specifically includes: For any historical interaction event, obtain the first feature of the current node participating in the historical interaction event, the second feature of the interacting peer node, and the attribute feature of the interacting edge. Aggregate the first feature, the second feature, and the attribute feature to obtain the interaction context feature. Obtain the global index of the current node, and construct the node identifier representation of the current node by fusing the position encoding with the learnable node identifier vector; Obtain the relative time span between the historical interaction time of the historical interaction event and the target time, and encode the relative time span into a time embedding; The interaction context features, the node identifier representation, and the time embedding are fused and projected to generate the initial embedding of the historical interaction event.

[0010] Optionally, in one embodiment of the present invention, the step of sequentially inputting each of the initial embeddings in the historical interaction sequence of each node into a selective state space model, and recursively updating the hidden state of the corresponding node through the selective state space model, specifically includes: Each of the initial embeddings in the historical interaction sequence is sequentially input into the selective state space model, and for the currently input initial embedding, an input-dependent state transition matrix and an input matrix are generated; Based on the state transition matrix and the time-varying step size operator corresponding to the initial embedding of the current input, a discretized state transition matrix is ​​generated, and based on the input matrix and the time-varying step size operator, a discretized input matrix is ​​generated. Based on the discretized state transition matrix, the discretized input matrix, and the hidden state at the previous time step, the hidden state is recursively updated to obtain the hidden state at the current time step.

[0011] Optionally, in one embodiment of the present invention, the calendar prior information includes week phase information, month phase information and sudden event identifier, and the feature modulation parameters include scaling vector and translation vector; The process of extracting calendar prior information corresponding to each of the historical interaction events, generating feature modulation parameters based on the calendar prior information through a meta-learning supernetwork, and using the feature modulation parameters to modulate the stimulated representations at corresponding times in the stimulated representation sequence to obtain an environment-aware representation matrix fused with calendar semantics for each node, specifically includes: For any historical interaction event, obtain the weekly phase information, monthly phase information, and sudden event identifier corresponding to the historical interaction time of the historical interaction event, and encode the weekly phase information, monthly phase information, and sudden event identifier to obtain a calendar prior vector; The calendar prior vector is input into the meta-learning supernetwork, and the meta-learning supernetwork maps and generates the scaling vector and translation vector corresponding to the historical interaction event. Using the scaling vector and the translation vector, feature linear modulation is performed on the excited representations in the excited representation sequence that are at the same time as the historical interaction event to obtain the environmental perception representations corresponding to the historical interaction event. By combining the environmental perception representations corresponding to each historical interaction event in chronological order, an environmental perception representation matrix with fused calendar semantics for the corresponding node is obtained.

[0012] Optionally, in one embodiment of the present invention, the environmental perception representation matrix of each node is subjected to a bi-branch projection into the structural subspace and the semantic subspace to obtain the structural components and semantic components of the corresponding node, specifically including: The environmental perception representation matrix is ​​input into the structure projection layer and mapped to the structure subspace through the structure projection layer to obtain the structure representation matrix; The environmental perception representation matrix is ​​input into the semantic projection layer and mapped to the semantic subspace through the semantic projection layer to obtain the semantic representation matrix; Extract the state corresponding to the last moment from the structural representation matrix, and use it as the structural component of the corresponding node; Extract the state corresponding to the last moment from the semantic representation matrix, and use it as the semantic component of the corresponding node.

[0013] Optionally, in one embodiment of the present invention, the aggregation result is a joint characterization; The step of aggregating the structural and semantic components of the source node and the target node in the node pair to be predicted, and inputting the aggregation result into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time, specifically includes: Obtain the structural components and semantic components of the source node, and the structural components and semantic components of the target node; The structural components of the source node, the semantic components of the source node, the structural components of the target node, and the semantic components of the target node are concatenated to obtain a joint representation; The joint representation is input into the prediction network, and after being mapped by the prediction network, the predicted probability of the interaction relationship between the nodes to be predicted at the target time is output.

[0014] Optionally, in one embodiment of the present invention, the state transition matrix is ​​a structured diagonal matrix, and the selective state space model is configured with a predefined spectral decay matrix, wherein the spectral decay matrix is ​​a diagonal matrix and the diagonal elements of the spectral decay matrix are located in the interval (0,1), which is used to constrain the spectral radius of the hidden state during the recursive update process.

[0015] A second aspect of this invention provides a dynamic link prediction system based on selective state space and dual decoupling, wherein the dynamic link prediction system based on selective state space and dual decoupling is used to implement the dynamic link prediction method based on selective state space and dual decoupling as described in any of the above schemes; the dynamic link prediction system based on selective state space and dual decoupling includes: The historical interaction sequence construction module is used to obtain the historical interaction events of each node in the node pair to be predicted before the target time, construct the initial embedding of each historical interaction event, and arrange the initial embeddings in chronological order as the historical interaction sequence of each node in the node pair to be predicted. The state space evolution module is used to sequentially input the initial embeddings in the historical interaction sequence of each node into the selective state space model, recursively update the hidden state of the corresponding node through the selective state space model, and generate the stimulated representation of the corresponding historical interaction moment according to the updated hidden state, so as to obtain the stimulated representation sequence of each node. The calendar semantic modulation module is used to extract the calendar prior information corresponding to each of the historical interaction events, generate feature modulation parameters based on the calendar prior information through a meta-learning supernetwork, and use the feature modulation parameters to perform feature modulation on the stimulated representation at the corresponding time in the stimulated representation sequence to obtain the environment perception representation matrix of each node fused with calendar semantics. The structural-semantic decoupling prediction module is used to project the environment perception representation matrix of each node into the structural subspace and the semantic subspace in a two-branch manner to obtain the structural components and semantic components of the corresponding node. The structural components and semantic components of the source node in the node pair to be predicted are aggregated with the structural components and semantic components of the target node, and the aggregation result is input into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time.

[0016] A third aspect of the present invention also provides an apparatus, wherein the apparatus includes: a memory, a processor, and a dynamic link prediction program based on selective state space and dual decoupling stored in the memory and executable on the processor, wherein when the dynamic link prediction program based on selective state space and dual decoupling is executed by the processor, it implements the steps of the dynamic link prediction method based on selective state space and dual decoupling as described above.

[0017] A fourth aspect of the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a dynamic link prediction program based on selective state space and dual decoupling, and the dynamic link prediction program based on selective state space and dual decoupling, when executed by a processor, implements the steps of the dynamic link prediction method based on selective state space and dual decoupling as described above.

[0018] Beneficial Effects: This invention provides a dynamic link prediction method, system, device, and medium based on selective state space and dual decoupling. By employing a linear complexity selective state space model instead of the Transformer as the core evolution engine, this invention reduces computational resource consumption in long sequence processing and overcomes the sequence length bottleneck caused by the quadratic complexity of traditional methods. This allows the model to efficiently process ultra-long interaction sequences without truncating the historical window. Simultaneously, through a meta-learning supernetwork, feature modulation parameters are adaptively generated based on calendar prior information at the interaction time, and the stimulated representation is dynamically modulated. This enables the model to perceive multi-scale calendar semantics such as weekly and monthly phases, enhancing its adaptability to sudden changes in interaction patterns under non-stationary environments. Furthermore, by using bi-branch projection to map environmental perception representations to mutually orthogonal structural and semantic subspaces, deep decoupling of long-term topological steady-state features and short-term behavioral intention features is achieved, eliminating discrimination interference caused by feature aliasing and improving the accuracy of link prediction. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of a preferred embodiment of the dynamic link prediction method based on selective state space and dual decoupling of the present invention; Figure 2 This is a schematic diagram of the framework of the dynamic link prediction method based on selective state space and dual decoupling of the present invention. Figure 3 This is a structural diagram of a preferred embodiment of the dynamic link prediction system based on selective state space and dual decoupling of the present invention. Figure 4 This is a structural diagram of a preferred embodiment of the device of the present invention.

[0021] Explanation of reference numerals in the attached figures: 100. Historical interaction sequence construction module; 200. State space evolution module; 300. Calendar semantic modulation module; 400. Structural semantic decoupling prediction module. Detailed Implementation

[0022] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are merely possible technical implementations of this invention and not all possible implementations. Based on the embodiments of this invention, those skilled in the art can obtain other embodiments without creative effort, and these embodiments are also within the protection scope of this invention.

[0023] First, the terms used in the embodiments of this invention will be introduced: CTDG, Continuous-Time Dynamic Graph; MLP, Multilayer Perceptron; AUC, Area Under the Curve; AP stands for Average Precision. FiLM, Feature-wise Linear Modulation; Adam, Adaptive Moment Estimation; TGN, Temporal Graph Networks; CAWN, Causal Anonymous Walks Network; RWTA, Random Walk with Temporal Attention; Transformer, Transformer architecture; Mamba, Mamba model (selective state-space model). DyGFormer, DyGFormer model; EdgeBank, the EdgeBank benchmark algorithm; FATDyG, FATDyG model; TFWaveFormer, TFWaveFormer model; CoDCL, CoDCL model; HyperEvent, HyperEvent model; Mamba-DD, Mamba-DD algorithm; S2D2, a structure-semantic dual decoupled representation space; NeurIPS, the conference on neural information processing systems; arXiv, the arXiv preprint platform; A dynamic graph is a network whose structure (nodes, edges) or properties (such as edge weights) change dynamically over time. Common dynamic graphs include social and communication networks, transportation and logistics networks, and biological and medical networks. The core value of dynamic graph data lies in its ability to more accurately model the real world. Complex real-world systems, such as social networks, financial markets, and transportation networks, have continuously evolving structures, and dynamic graphs are key to capturing this evolutionary nature.

[0024] This invention relates to dynamic link prediction technology, belonging to the interdisciplinary field of dynamic graph machine learning and knowledge engineering. Dynamic link prediction is a core task in mining the evolutionary patterns of dynamic networks, aiming to predict the possible interaction relationships between nodes in the future by capturing the co-evolutionary patterns of network topology and node attributes.

[0025] While the aforementioned existing technologies have made significant progress in dynamic link prediction tasks, they still have inherent limitations in handling ultra-long interaction sequences, modeling non-stationary evolutionary environments, and decoupling heterogeneous features. The following section objectively analyzes the shortcomings of each background technology by examining its specific technical solutions.

[0026] The Transformer architecture suffers from several inherent limitations. The Transformer architecture, exemplified by DyGFormer, relies on a self-attention mechanism to globally model the historical interaction sequences of nodes. However, this technical approach inherently introduces the following drawbacks: First, there is a contradiction between sequence length and the quadratic increase in computational complexity. The Transformer's self-attention mechanism requires calculating attention weights between any two positions in the sequence, and its computational complexity and memory consumption are directly proportional to the sequence length L (O(L²)). In continuous-time dynamic graphs, the historical interaction sequences of nodes can be extremely long (e.g., the Flight dataset has as many as 67 million interaction steps), which puts significant computational pressure on the Transformer when processing long-span data. Although DyGFormer employs a block-based processing technique to attempt to alleviate this problem, block-based processing is essentially a compromise that sacrifices the global coherence of the sequence, failing to fundamentally overcome the theoretical bottleneck of quadratic complexity, thus limiting the model's full utilization of complete long-term evolutionary information.

[0027] Second, positional encoding is insufficient for expressing temporal irregularities. Transformers rely on positional or temporal encoding to inject temporal information, but these encodings are usually predefined fixed functions or simple linear mappings. When the time intervals of interaction events are extremely unevenly distributed (e.g., dense in some periods and sparse in others), fixed positional encodings cannot flexibly characterize the actual semantic differences in time spans, resulting in limited ability of the model to perceive abrupt changes in interaction rhythm in non-stationary environments.

[0028] The inherent limitations of memory-based network architectures. Memory-based network methods, exemplified by TGN, rely on maintaining a time-updated memory vector for each node and compressing historical information through message passing. However, this approach suffers from the following inherent drawbacks: First, the asynchronous nature of memory updates leads to the loss of long-range dependencies. TGN's memory updates are event-driven and asynchronous—each node's memory is only updated when it participates in an interaction. When two nodes do not interact for a considerable period, their memories cease evolving, making it impossible to effectively perceive macroscopic changes in the network topology within that time window. This "passive update" mechanism makes the model lack persistence in characterizing long-term topological steady-state features, making it difficult to capture the inherent, slowly evolving structural relationships between nodes.

[0029] Second, information loss occurs due to the capacity bottleneck of the memory vector. Memory networks compress all historical information using fixed-dimensional vectors. This lossy compression method inevitably faces an information bottleneck in long-sequence scenarios. When the number of historical interactions far exceeds the representational capacity of the memory vector, early interaction information is gradually covered up and forgotten, leading to a decline in the model's ability to identify long-term evolutionary patterns.

[0030] Third, there is the interference problem caused by the coupled modeling of structure and semantics. TGN and its derivative methods encode structural information (such as fixed topological relationships between nodes) and behavioral semantic information (such as short-term interaction intentions) in interaction events into the same memory vector without explicit separation at the feature level. When the network is in a non-stationary environment and the interaction mechanism changes rapidly, short-term semantic fluctuations will interfere with the characterization of long-term structural stability, while long-term structural features will smooth out the sensitive response that should be given to short-term mutations. The mutual interference between the two types of heterogeneous information reduces the model's discrimination accuracy in complex dynamic scenarios.

[0031] In addition to the specific problems of each of the aforementioned architectures, existing dynamic link prediction technologies also suffer from the following common issues: First, there is insufficient utilization of multi-scale calendar prior information. Both Transformer and memory network architectures primarily rely on the timestamps of interactive events themselves when processing temporal context, failing to fully exploit the macro-level temporal background information inherent in the moment of interaction (such as differences between weekdays and weekends, periodic rhythms, and the sudden impact of specific events). This high-level calendar semantics is crucial for understanding the periodic changes in node behavior patterns, but current technologies lack effective mechanisms to inject it into the model's evolutionary logic.

[0032] Second, the evolutionary logic in non-stationary environments lacks dynamic adjustment capabilities. The parameters of existing models remain fixed after learning, and their evolutionary logic cannot adaptively adjust to changes in the environmental context. When network behavior patterns undergo sudden changes (such as a surge in interactions caused by a sudden trending event on a social media platform), models with fixed parameters struggle to adjust their internal representation strategies in a timely manner, leading to a significant decline in predictive performance.

[0033] In summary, existing dynamic link prediction technologies have significant shortcomings in terms of computational efficiency, temporal semantic awareness, and collaborative modeling of structural and semantic features. The dynamic link prediction method based on selective state space and dual decoupling provided by this invention can achieve efficient long-range modeling, adaptive perception of non-stationary environmental semantics, and decoupling of heterogeneous feature information under linear computational complexity, thereby meeting the application needs of link prediction in large-scale, highly dynamic, and complex scenarios in the real world.

[0034] This invention overcomes the computational efficiency bottleneck in long-sequence scenarios. In practical applications such as traffic flow prediction, the historical interaction sequences of nodes are often extremely large (e.g., the flight records of a single airport node in a global aviation network can reach tens of thousands). Existing methods based on the Transformer architecture struggle to efficiently process such long-sequence data due to the quadratic computational complexity of the self-attention mechanism, forcing the system to truncate the historical window or reduce the sampling frequency. This inevitably leads to the loss of key evolutionary information and a decrease in prediction accuracy.

[0035] One of the objectives of this invention is to replace the Transformer as the core evolution engine with a selective state-space model that has linear computational complexity (O(L)), enabling the model to scan the entire historical interaction sequence in linear time, thereby significantly improving the processing efficiency of long sequences without losing historical information, and thus providing a feasible computational basis for real-time link prediction of large-scale dynamic networks.

[0036] This invention enhances the temporal semantic perception and adaptive capabilities in non-stationary environments. In scenarios such as e-commerce recommendations and social media analysis, user behavior patterns are non-stationary due to multi-scale calendar factors such as weekdays and weekends, promotional activities, and unexpected events. Existing temporal modeling methods either ignore these macro-temporal contexts or passively introduce them through simple feature concatenation, failing to dynamically adjust the model's behavioral logic according to the environmental context.

[0037] The second objective of this invention is to introduce a meta-learning-driven adaptive semantic prompting mechanism, enabling the model to autonomously generate feature modulation parameters based on heterogeneous calendar priors such as the weekly phase, monthly phase, and holidays at the interaction time, and dynamically adjust the evolution direction of the hidden state. This mechanism allows the model to adaptively adjust its internal representation strategy when facing sudden environmental changes or periodic patterns, significantly improving the prediction stability and accuracy in non-stationary dynamic scenarios.

[0038] This invention eliminates discriminative interference caused by the aliasing of structural and semantic features. In tasks such as friend recommendation in social networks and protein interaction prediction, the interaction behavior between nodes is simultaneously influenced by both long-term topological structure (such as users' inherent social circles) and short-term behavioral intentions (such as temporary interests or trending events). Existing methods encode these two types of heterogeneous information in a mixed manner, leading to mutual interference between the two types of signals when the interaction mechanism changes rapidly, thus weakening the model's discriminative ability.

[0039] The third objective of this invention is to construct a structural and semantic dual decoupled representation space. Through bi-branch projection and orthogonal constraint mechanisms, the evolutionary trajectory of nodes is decomposed into structural components reflecting long-term topological stability and semantic components reflecting short-term behavioral intentions. This design enables the model to clearly distinguish between two different predictive bases: "there is an inherent connection between nodes" and "nodes currently have an interaction impulse." This fundamentally eliminates the discrimination uncertainty caused by feature aliasing and enhances the interpretability of the model.

[0040] In summary, this invention, through the organic combination of the three core technical means mentioned above, aims to provide an end-to-end dynamic link prediction solution that is computationally efficient, environmentally adaptive, and feature-decoupled. It can be widely deployed in dynamic relationship prediction modules in scenarios such as social networking services, financial risk control systems, intelligent traffic management, and bioinformatics analysis, and has clear application value and industrial promotion prospects.

[0041] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0042] The method of this invention can be deployed on servers, computer devices, or cloud computing platforms, and is executed by a processor calling program instructions stored in memory. Dynamic graphs include graph structure data that evolves over time, such as social networks, financial transaction networks, transportation networks, e-commerce interaction networks, and bioinformatics networks. This invention models the historical interaction sequences of the node to be predicted before the target time, and outputs the predicted probability that the node has an interaction relationship at the target time.

[0043] To address the computational bottlenecks of existing Transformer architectures in long sequence modeling, as well as challenges such as insufficient temporal semantic awareness and the aliasing of structural and behavioral features, this invention proposes the Mamba-DD algorithm. The core idea of ​​this algorithm is to utilize a selective state-space model with linear complexity as the underlying evolutionary engine, perceive changes in complex environmental context through a meta-learning-driven semantic cueing mechanism, and achieve deep decoupling of topological structure and interaction semantics using a dual decoupling framework. Mamba-DD mainly comprises three core modules: a causal dynamics operator, an adaptive meta-calendar semantic cueing system, and the structure-semantic dual decoupling representation space S2D2.

[0044] The dynamic link prediction method based on selective state space and dual decoupling described in the preferred embodiment of the present invention, such as... Figure 1 As shown, the dynamic link prediction method based on selective state space and dual decoupling includes the following steps: In step S10, the historical interaction events of each node in the node pair to be predicted before the target time are obtained, the initial embedding of each historical interaction event is constructed, and the initial embeddings are arranged in chronological order as the historical interaction sequence of each node in the node pair to be predicted.

[0045] In one possible implementation, the step of constructing the initial embedding of each of the historical interaction events specifically includes: for any historical interaction event, obtaining a first feature of the current node participating in the historical interaction event, a second feature of the interacting peer node, and attribute features of the interaction edge; aggregating the first feature, the second feature, and the attribute features to obtain an interaction context feature; obtaining the global index of the current node, fusing it with a learnable node identifier vector through position encoding to construct a node identifier representation of the current node; obtaining the relative time span between the historical interaction time of the historical interaction event and the target time, encoding the relative time span as a time embedding; and fusing and projecting the interaction context feature, the node identifier representation, and the time embedding to generate the initial embedding of the historical interaction event.

[0046] When constructing the initial embedding of historical interaction events, the system first obtains the first feature vector of the current node, the second feature vector of the interacting node, and the attribute feature vector of the interaction edge. These three are concatenated and mapped to interaction context features through a linear transformation, comprehensively expressing the static attributes and interaction relationship type of both parties at the time of the interaction. Simultaneously, the system generates a position vector based on the global index of the current node using sinusoidal position encoding, and adds it to a learnable node identifier vector to construct a node identifier representation. The system further calculates the relative time span between the historical interaction time and the target time, and encodes it into a temporal embedding through harmonic mapping. Finally, the system concatenates the interaction context features, node identifier representation, and temporal embedding, then inputs them into a nonlinear projection layer and maps them to a latent space of a unified dimension, generating the initial embedding of the historical interaction event. This implementation method fully integrates node attributes, interaction attributes, and temporal distance information into the initial embedding, providing a complete input representation for subsequent evolutionary modeling and effectively improving the model's ability to capture historical interaction semantics.

[0047] Specifically, firstly, the historical behavior of nodes is abstracted as a series of discrete instantaneous interaction embeddings in the latent space. For a given pair of nodes to be predicted... and its corresponding target time The model needs to retrieve the source nodes separately. With the target node The historical interaction sequence prior to this moment. For the sake of brevity, this invention uses nodes. The encoding process is illustrated using an example.

[0048] First, aggregate the interaction context features. For nodes... The first occurrence Secondary historical interaction events ,in This indicates the order of events sorted by absolute time. This invention retrieves and concatenates the features of the two participating nodes and their corresponding interaction edge attribute features: (1) in, Each is the current node Its historical interaction objects The basic feature vector, Represents the set of real numbers; Embed the attributes of this historical interaction edge; This represents a vector-level concatenation operation; The comprehensive characterization of the first The static semantic environment at the time of the next historical interaction.

[0049] This invention utilizes a fusion scheme of sinusoidal position coding and identifier embedding to construct initial node representations. : ; in, A learnable node identifier vector; Using a harmonic mapping function with the same structure as equation (3), by using the global index of the nodes Mapping to a high-dimensional space assigns a defined topological distinguishability to the initial features.

[0050] Subsequently, basic time span encoding is performed. To endow instantaneous embedding with time decay awareness, the historical interaction moment is calculated. Compared to the current prediction time relative span Through harmonic mapping function Convert it into a time embedding vector: (3) in, The initial time representation mapped to a higher-dimensional space reflects how close or distant historical events are relative to the current predicted moment.

[0051] Finally, latent space projection and sequence construction are performed. A nonlinear projection layer is used to map the aggregated features to a unified latent space dimension. Generate instantaneous embeddings that drive linear interaction kernels : (4) in, For the first The feature vector of the second interaction in the latent space; and These are the learnable parameters of the projection layer.

[0052] In summary, nodes The historical interactions were transformed into a length of Instantaneous embedding sequence This sequence provides a discrete input benchmark for the dynamic evolution based on the selective state-space model in subsequent chapters, thereby supporting the model to perform efficient state recursion for different nodes in the continuous latent space.

[0053] In step S20, the initial embeddings in the historical interaction sequence of each node are sequentially input into the selective state space model. The hidden state of the corresponding node is recursively updated through the selective state space model, and the stimulated representation of the corresponding historical interaction moment is generated according to the updated hidden state, so as to obtain the stimulated representation sequence of each node.

[0054] In one possible implementation, the step of recursively updating the hidden state of the corresponding node through the selective state space model specifically includes: sequentially inputting each of the initial embeddings in the historical interaction sequence into the selective state space model; generating an input-dependent state transition matrix and an input matrix for the currently input initial embedding; generating a discretized state transition matrix based on the state transition matrix and the time-varying step-size operator corresponding to the currently input initial embedding, and generating a discretized input matrix based on the input matrix and the time-varying step-size operator; and recursively updating the hidden state based on the discretized state transition matrix, the discretized input matrix, and the hidden state at the previous time step to obtain the hidden state at the current time step.

[0055] When performing recursive updates of the selective state-space model, the system generates input-dependent state transition matrices and input matrices in real time at each time step based on the initial embedding of the current input using low-rank projection. Then, using the time-varying step-size operator corresponding to the current input, the continuous state transition matrix is ​​discretized into a discretized state transition matrix using the zero-order preservation method, and the continuous input matrix is ​​discretized into a discretized input matrix. Finally, according to the recursive update equation, the updated hidden state at the current time step is obtained by multiplying the hidden state from the previous time step with the discretized state transition matrix and adding the product of the discretized input matrix and the current input. This implementation allows the model to complete a full scan of historical sequences of arbitrary length with linear computational complexity, significantly improving the efficiency of long sequence processing without losing historical information, while also ensuring the stability of numerical computation.

[0056] In one possible implementation, the state transition matrix is ​​a structured diagonal matrix, and the selective state space model is configured with a predefined spectral decay matrix, which is a diagonal matrix and the diagonal elements of the spectral decay matrix are located in the interval (0,1), used to constrain the spectral radius of the hidden state during the recursive update process.

[0057] The system fixes the state transition matrix in the selective state-space model as a structured diagonal matrix, with all off-diagonal elements set to zero, retaining only the diagonal elements as adjustable parameters. This allows each dimension of the hidden state in the state update equation to evolve independently, significantly reducing the computational overhead of matrix multiplication. Simultaneously, the system configures a predefined spectral decay matrix for the model, also a diagonal matrix, with diagonal elements taking positive values ​​between 0 and 1 and remaining unchanged during training. In each time step of the recursive update, the system multiplies the discretized state transition matrix element-wise with the spectral decay matrix before using it to update the hidden state. This ensures that each dimension of the hidden state decays gradually at a fixed rate during the recursive process, constraining the spectral radius of the hidden state to always be less than 1. This implementation ensures that historical information decays progressively without abrupt changes when the model traverses tens or even hundreds of recursive steps, avoiding both gradient explosion and gradient vanishing, and guaranteeing the numerical stability and convergence of modeling ultra-long sequences.

[0058] Specifically, secondly, in obtaining nodes Historical interaction sequence Subsequently, this invention introduces a causal dynamics operator. It is used to model sequences.

[0059] This operator maps discrete instantaneous interaction signals into potential state representations that evolve over time, thereby characterizing the dynamic changes in node behavior.

[0060] Furthermore, by combining the parameter selection mechanism defined in equation (5), the operator adaptively adjusts the features at different time steps, enabling it to better adapt to non-stationary interactive environments.

[0061] (5) in, For the first t The initial embedding vector of each historical interaction event. d The length of the embedding vector. Let be the size of the hidden state in the selective state-space model. t For time step index, For the input matrix, The learnable weight matrix is ​​the input matrix. For the bias term of the input matrix, To output the projection matrix, The learnable weight matrix is ​​the output matrix. This is the bias term of the output matrix. for Time-varying step size operator, This is the step size offset parameter. The learnable weight matrix is ​​the step-size projection. This is the learnable bias vector for the step-size projection. It is a vector of all 1s. and Used to map inputs to the state space. Parameters This plays a regulatory role: when its value is small, the model tends to retain historical information; when its value is large, the model updates the state more quickly to respond to new input changes.

[0062] To characterize the operator In the The mechanism of action at each interaction moment is modeled as a type of nonlinear mapping in this invention, and its calculation process can be represented as a recursive update form under a discretized state-space model.

[0063] To further describe the dynamic transmission of information during the interaction, a set of parameters that adjusts with changes in the input signal is introduced. ,in This determines the degree of historical memory. Used to characterize the effect of the current input on the hidden state update. Used to map hidden states to the output space, generating a dynamic representation of the current time step.

[0064] The above parameters are generated by the projection process under low-rank constraints, and their specific form is shown below: (6) Among them, the time-varying step size operator This determines the operator's inheritance gain from historical states.

[0065] Then, the state transition matrix of the causal dynamic operator With input matrix The zero-order hold map is generated in real time using equation (7).

[0066] (7) Unlike traditional linear time-invariant systems, this operator captures nodes through the following difference evolution equation. Latent dynamic characteristics : (8) Among them, the predefined spectral attenuation matrix It is designed in a structured diagonal form to ensure the numerical stability and computational convergence of the operator in long-range recursion.

[0067] Ultimately, the causal dynamic operator maps the high-dimensional state manifold through a selective projection matrix. Return to the observation space to generate stimulated characterization : (9) Through the continuous action of this operator, the original interaction sequence is transformed into an evolutionary representation matrix that deeply integrates temporal causal relationships. This mapping process essentially utilizes the "selective" scanning capability of the operator, while maintaining... Under the premise of time complexity, the identification of nonlinear systems with complex topological evolution laws was completed.

[0068] In step S30, calendar prior information corresponding to each of the historical interaction events is extracted, and feature modulation parameters are generated based on the calendar prior information through a meta-learning supernetwork. The feature modulation parameters are then used to modulate the stimulated representations at corresponding times in the stimulated representation sequence to obtain an environment-aware representation matrix that fuses calendar semantics for each node.

[0069] In one possible implementation, the calendar prior information includes week phase information, month phase information, and sudden event identifier, and the feature modulation parameters include scaling vector and translation vector; step S30 specifically includes: for any historical interaction event, obtaining the week phase information, month phase information, and sudden event identifier corresponding to the historical interaction time of the historical interaction event, and encoding the week phase information, month phase information, and sudden event identifier to obtain a calendar prior vector; inputting the calendar prior vector into the meta-learning supernetwork, and generating the scaling vector and translation vector corresponding to the historical interaction event through the meta-learning supernetwork; using the scaling vector and the translation vector, performing feature linear modulation on the stimulated representations in the stimulated representation sequence that are at the same time as the historical interaction event to obtain the environmental perception representation corresponding to the historical interaction event; combining the environmental perception representations corresponding to each historical interaction event in chronological order to obtain the environmental perception representation matrix of the corresponding node fused with calendar semantics.

[0070] When generating calendar prior vectors, the system first extracts the interaction time of the current historical interaction event, retrieves the corresponding weekly phase, monthly phase, and domain-specific event identifier for that time, maps the weekly and monthly phases to dense embedding vectors using a learnable lookup table, encodes the event identifiers to embedding vectors using a lookup table, and encodes the transient time intervals between adjacent interaction events to continuous-time embeddings using harmonic mapping. These embeddings are then concatenated to obtain a multi-granularity calendar prior vector. The system inputs this vector into a meta-learning supernetwork, outputting a scaling vector and translation vector corresponding to the current time. A sigmoid function is used at the output to limit the gain of the scaling vector. The system recalibrates by element-wise multiplying the scaling vector with the stimulated representation of the current time, and then adds it element-wise to the translation vector to introduce an environment-driven semantic shift, obtaining the environment-aware representation of the current time. After performing the above operations sequentially on all historical times, the environment-aware representations of each time are combined chronologically to form the environment-aware representation matrix for that node. This implementation allows the model to adaptively adjust its representation strategy based on the macro-calendar background of the interaction time, effectively responding to sudden changes in behavior patterns in non-stationary environments and improving the stability and accuracy of predictions.

[0071] Specifically, furthermore, in response to the problem of periodic mutations and distribution shifts in the non-stationary evolution of dynamic graphs, this invention introduces a semantic prompting mechanism based on meta-learning.

[0072] This mechanism constructs a macroscopic calendar prior to characterize the impact of temporal context on network evolution. Based on this, it utilizes the hypernetwork to generate data-related feature modulation operators to dynamically adjust node representations.

[0073] The above design enables the model to supplement missing contextual information during evolution, thereby better adapting to structural changes in non-stationary scenarios.

[0074] The first step is to construct a multi-scale calendar prior representation.

[0075] To capture the micro-temporal rhythms and macro-cyclical patterns behind interactive behaviors, this invention first extracts the... Transient time interval of each interaction : (10) in The reference time for the start of the sequence is defined as the time of interaction. Subsequently, the corresponding periodic phase is retrieved by... Lunar phase and emergency symbols in specific fields Constructing heterogeneous granularity collaborative calendar prior vectors : (11) Here, the position encoding operator Harmonic mapping consistent with equation (3) is employed to enhance sensitivity to continuous time spans; periodic embedding operator Then, a learnable lookup table is used to map discrete temporal semantics to the latent space. It comprehensively depicts the macro-spatial and temporal context in which the current interaction occurs.

[0076] The second step is to generate meta-hints for the hypernetwork and parameters.

[0077] Considering that environmental interventions often lead to heterogeneity in node behavior patterns, this invention introduces parameters... Meta-hint hypernetwork As a parameter generator, Predict the hidden layer modulation vector pair at the current time based on calendar priors. : (12) in, These represent the generated feature scaling vector and translation vector, respectively. To ensure the stability of the numerical evolution, the output is constrained using the Sigmoid function. The gain magnitude. This set of "meta-hint" parameters essentially encapsulates the logic of how environmental semantics intervenes in the dynamic state trajectory.

[0078] The third step is to modulate and fuse environmental perception features. Finally, meta-cues are injected into the original excited representation generated by the causal dynamics operator through the characteristic linear modulation mechanism FiLM. (See equation (9)) to realize the feature reconstruction of environmental perception: (13) in, For layer normalization operation; This represents element-wise multiplication. Under this mechanism... Responsible for recalibrating the importance of interactive features based on calendar context, and Responsible for introducing environment-driven semantic offsets.

[0079] In summary, through Through step-by-step recursion and meta-hint injection, the system ultimately generates nodes. Evolutionary characterization matrix This matrix deeply integrates individual dynamic inertia with macroscopic environmental semantics, providing a high-fidelity original representation for the dual decoupling of structure and semantics in subsequent chapters.

[0080] In step S40, the environment perception representation matrix of each node is projected into the structural subspace and the semantic subspace in a two-branch manner to obtain the structural components and semantic components of the corresponding node. The structural components and semantic components of the source node in the node pair to be predicted are aggregated with the structural components and semantic components of the target node, and the aggregation result is input into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time.

[0081] In one possible implementation, the steps of obtaining the structural and semantic components of the corresponding node specifically include: inputting the environment-aware representation matrix into the structural projection layer, mapping it to the structural subspace through the structural projection layer to obtain the structural representation matrix; inputting the environment-aware representation matrix into the semantic projection layer, mapping it to the semantic subspace through the semantic projection layer to obtain the semantic representation matrix; extracting the state corresponding to the last time step from the structural representation matrix as the structural component of the corresponding node; and extracting the state corresponding to the last time step from the semantic representation matrix as the semantic component of the corresponding node.

[0082] The system performs a two-branch decoupling process on the environment-aware representation matrix that has been integrated with calendar semantics. A first structural projection matrix maps this matrix to a structural subspace to obtain a structural representation matrix, where each row corresponds to the structural state of the node at a given historical moment, reflecting the node's inherent, slowly evolving long-term topological associations. A second semantic projection matrix maps the same matrix to a semantic subspace to obtain a semantic representation matrix, where each row corresponds to the semantic state of the node at a given moment, reflecting the node's instantaneous interaction tendency driven by the current context. The structural and semantic subspaces are geometrically orthogonal, ensuring that the two types of heterogeneous information are perpendicular to each other in the vector space, eliminating feature aliasing. The system extracts the state at the last moment from the last row of the structural representation matrix as the structural component of the node, and extracts the state at the last moment from the last row of the semantic representation matrix as the semantic component. This implementation decomposes the aliased evolutionary trajectory into two types of features reflecting long-term inherent topology and short-term instantaneous utility, fundamentally eliminating the mutual interference between structural information and behavioral semantics, and significantly enhancing the model's discriminative ability and interpretability in complex scenarios.

[0083] Specifically, to extract key features from the aliased evolutionary trajectories, this invention designs a structural and semantic dual decoupling spatial framework. This module targets nodes. Evolutionary characterization matrix The process decomposes the representation into long-term topological steady-state components and short-term behavioral intention components. The core logic of this design lies in the fact that individual evolution is typically driven by two forces: firstly, long-term stability determined by historical topological relationships, manifested as slowly evolving structural genes; and secondly, short-term fluctuations driven by the instantaneous environment, manifested as high-frequency shifts in interactive intentions. By projecting different subspaces, these two types of heterogeneous signals with significantly different frequencies can be effectively separated.

[0084] First, perform dual subspace projection. Define the projection matrix. The evolutionary representation matrix that incorporates environmental semantics will be used. Mapping to the structure subspace and the intention subspace. This process is achieved through the following nonlinear affine transformation: (14) in, Capture nodes separately The long-term steady state of the topology and the transient features of the semantics. Furthermore, to achieve a deep separation of structural and semantic features, this invention introduces an orthogonality constraint loss into the optimization objective, forcing the two subspaces to remain geometrically orthogonal.

[0085] Finally, temporal pooling and feature aggregation are performed. To construct the final representation for the prediction task, this invention takes the last time step of the sequence. The corresponding decoupled outputs are cascaded to obtain nodes. The final evolutionary representation vector : (15) in The system fully encapsulates the entire information chain, from historical interaction embedding to dynamic evolution, and then to environmental perception modulation and subspace decoupling. Through this process, the system obtains the global representation of the source nodes in the pairs to be predicted. Global representation of the target node .

[0086] In one possible implementation, the aggregation result is a joint representation; the step of obtaining the prediction probability that the node to be predicted has an interaction relationship at the target time specifically includes: obtaining the structural component and semantic component of the source node, and the structural component and semantic component of the target node; concatenating the structural component, semantic component, structural component, and semantic component of the source node to obtain a joint representation; inputting the joint representation into the prediction network, and outputting the prediction probability that the node to be predicted has an interaction relationship at the target time after mapping by the prediction network.

[0087] In the aggregation and prediction phase, the system retrieves structural and semantic components from the calculated source node data structure and target node data structure, concatenating them sequentially to form a joint representation vector. This joint representation fully encompasses the long-term topological genes and short-term behavioral intentions of both the source and target nodes, achieving alignment and fusion of the two types of nodes in two feature spaces. The system inputs this joint representation into a prediction network composed of multiple fully connected layers, outputting probability values ​​between 0 and 1 after nonlinear mapping, representing the likelihood of an interaction between the predicted node pair at the target time. This implementation method, through explicit component concatenation, ensures that the prediction network can simultaneously perceive the structural and semantic information of both source and target nodes, improving the accuracy and reliability of the final prediction.

[0088] Specifically, the objective function and optimization strategy are finally determined. First, the loss for the link prediction task is defined. For a given observed interaction edge... Based on the negative sample edges obtained through random sampling, this invention uses a multilayer perceptron to predict the joint representation of the source node and the target node, thereby obtaining the probability of interaction. : (16) in, This is a vector concatenation operation. The negative log-likelihood loss is used as the main objective. (17) in, For real labels, This represents the total number of edges in the current training batch.

[0089] Subsequently, the orthogonality constraint loss for dual decoupling is defined. To explicitly induce subspace independence and prevent semantic aliasing between structural genes and interaction intent features, this invention introduces an orthogonality penalty term based on the Frobenius norm for the representation matrices of all nodes participating in the computation within a batch: (18) in, For the first k The structural representation matrix of each node, For the first k The semantic representation matrix of each node, This represents the total number of nodes involved in the current training batch. This serves as the node index. This item achieves deep decorrelation of the representation space by suppressing covariance crossover between different functional subspaces.

[0090] Finally, the overall optimization objective function is constructed. This combines the aforementioned losses and... Regularization term, the final loss function Represented as: (19) in, To balance the hyperparameters of decoupling strength, This is the weight decay coefficient. These are the full set of learnable parameters for the model.

[0091] See Figure 2 The following describes the algorithm for dynamic link prediction based on selective state space and dual decoupling: Input: Dynamic Graph Interactive Batch Node historical interaction index, sequence length Decoupling balance factor Weight decay coefficient Learning rate Maximum number of iterations ; Output: Mamba-DD parameters Interaction has probability ; K1: Initialization ; K2: while the maximum number of iterations has not been reached And the model did not converge; K3:foreach do; K4: foreach node do; K5: Search The historical sequence is aggregated according to equations (1)-(3) and the time span is encoded; K6: Generated according to equation (4) ; K7:for i =1to L do; K8: Generated according to equation (6) ; K9: Update the hidden state using (8) ; K10: Generate the excited characterization according to equation (9) ; K11:endfor; K12: Constructed according to equations (10)-(11) ; K13: Generator prompt parameters See equation (12); K14: According to equation (13) Perform FiLM modulation to obtain the environment perception matrix. ; K15: According to equation (14) and ; K16: Constructed according to formula (15) ; K17:endfor; K18:endfor; K19: For each pair within a batch Equation (16) calculates the prediction probability. ; K20: Calculated using equation (17) ; K21: Equation (18) is used for calculation. ; K22: Calculate the overall objective function ; K23: Perform backpropagation of execution error, based on gradient. Update parameters using the Adam optimizer ; K24:end.

[0092] It should be noted that, based on the above technical solutions, the key inventive points of this invention can be summarized into the following three levels.

[0093] Key Point 1: Linear Complexity Causal Dynamics Modeling Based on Selective State Space Core Invention Idea: To replace the Transformer with the Mamba selective state-space model as the basic evolutionary architecture for dynamic link prediction. Key Specific Points: The first targeted application of state-space model in dynamic link prediction: The historical interaction sequence of nodes in a continuous-time dynamic graph is modeled as a discretized evolution process in state space. The linear complexity (O(L)) scan of historical sequences of arbitrary length is achieved through the recursive update of the state transition matrix, which fundamentally breaks through the O(L²) computation bottleneck of Transformer.

[0094] Input-dependent parameter selectivity mechanism: The state transition matrix, input matrix, and output projection matrix are all generated in real time from the current input signal through low-rank projection, enabling the model to adaptively adjust the balance between "remembering history" and "responding to new inputs" according to the differences in interaction content. Specifically, the inheritance gain of historical states is controlled by a time-varying step-size operator, preserving long-term information when interactions are sparse and quickly responding to new patterns when interactions are dense.

[0095] Structured design of spectral decay matrix: The state transition matrix is ​​designed in a structured diagonal form and combined with a predefined spectral decay matrix to ensure numerical stability in the recursive process of tens or even hundreds of steps, thus solving the gradient vanishing / exploding problem in the modeling of ultra-long sequences in state-space models.

[0096] Secondary key point: Meta-learning driven adaptive calendar semantic prompting mechanism Core Invention Idea: Utilizing a hypernetwork to generate feature modulation parameters based on calendar priors at interaction times, dynamically adjusting the model's evolutionary representation. Key Specific Points: Collaborative construction of multi-granularity calendar priors: The interaction time is simultaneously encoded as transient time interval (continuous value), weekly phase and monthly phase (discrete periodic value) and sudden event identifier (domain event marker). Through harmonic mapping and learnable lookup table, the heterogeneous granular temporal semantics are uniformly mapped to the latent space to form a calendar prior vector that comprehensively describes the macro-spatiotemporal background.

[0097] The hypernetwork parameter generation architecture uses a calendar prior vector as input and a meta-learning hypernetwork to generate scaling and translation vector pairs of Feature Linear Modulation (FiLM) in real time—rather than directly concatenating calendar features to the main network. The unique aspect of this design is that the hypernetwork's output "meta-cues" encapsulate the logic of how environmental semantics intervene in the dynamic system's state, essentially adjusting the model's "evolutionary strategy" in real time based on the external temporal context.

[0098] The two-way action of FiLM modulation: the scaling vector is responsible for recalibrating the importance of interactive features based on calendar context (determining which historical information is more worthy of attention in the current context), and the translation vector introduces environment-driven semantic offset (adding the macroscopic impact of holidays / emergencies as a system bias to the current state). The two work together to achieve feature reconstruction for environment perception.

[0099] Level 3 key point: Decoupling of structural and semantic duality in representation space Core Invention Idea: By using bi-branch projection and orthogonal constraints, the evolutionary representation of aliasing is decomposed into a long-term topological steady-state component and a short-term behavioral intention component. Key Specific Points: The dual-branch independent projection architecture: For the node representation matrix that integrates dynamic evolution and environmental modulation, two independent projection matrices are used to map it to the structural subspace and the semantic subspace respectively. The output of the structural branch reflects the inherent, slowly evolving topological relationships of the nodes (such as the social circles in which users have long been located); the output of the semantic branch reflects the instantaneous interaction tendencies driven by the current context (such as the interaction intentions temporarily generated by users).

[0100] F-norm-based orthogonality penalty constraint: A Frobenius norm orthogonality penalty term is introduced into the loss function between the structural representation matrix and the semantic representation matrix, geometrically forcing the two feature subspaces to be orthogonal (decorrelated). The strength of this constraint is adjustable through a decoupling balance factor λ. When λ=0.1, the model maintains sufficient separation between the two types of information while avoiding excessive stripping that could lead to semantic disconnect, enabling the model to achieve optimal performance on five public datasets.

[0101] The temporal pooling strategy of cascading at the last time step: only the decoupled output of the last time step of the sequence is cascaded as the final representation of the node. The rationale for this design is that the recursive update mechanism of the state-space model has compressed all historical information into the hidden state of the current time step. Therefore, taking the features at the last time step not only preserves the complete temporal information, but also avoids redundant aggregation of features at each time step, thus improving computational efficiency.

[0102] System-level key points: The overall architecture of three modules working together The information flow and functional division of labor in the three stages are as follows: the causal dynamics operator is responsible for "converting historical sequences into state trajectories" (temporal compression); the meta-calendar prompting mechanism is responsible for "modulating state trajectories according to environmental context" (environmental adaptation); and the dual decoupling space is responsible for "decomposing aliased states into two types of heterogeneous features" (feature purification). The three are sequentially linked and have clear functional boundaries, forming a complete end-to-end prediction process.

[0103] Robustness verification of composite negative sampling for real-world scenarios: The model maintains superior performance under three negative sampling strategies: random, historical, and inductive. In particular, when historical negative samples severely interfere with the model's judgment (the AUC of EdgeBank drops from 0.913 to 0.521 under inductive sampling), the AUC of this invention only decreases by 5.5%. The root cause lies in the fact that the decoupling space geometrically separates the short-term semantics that are susceptible to historical interference from the long-term structure that reflects the essential relationship, providing a verifiable technical path for the model to resist interference from complex negative samples.

[0104] This invention can be directly deployed in financial risk control systems for real-time fraud transaction link identification. It can also be used in scenarios such as real-time friend recommendation on social networking platforms, user-product interaction prediction on e-commerce platforms, and congestion propagation prediction in intelligent traffic management. It has good platform versatility and domain portability.

[0105] This invention systematically solves the problem of synergistic optimization of computational efficiency, environmental adaptability and feature decoupling in dynamic link prediction by using a three-pronged approach of "selective state space architecture + meta-calendar semantic modulation + dual decoupling representation".

[0106] This invention proposes a dynamic link prediction method, Mamba-DD, based on selective state space and dual decoupling. Compared with existing technologies, it achieves significant advantages in multiple dimensions, including computational efficiency, prediction accuracy, anti-interference robustness, and module effectiveness. The following detailed explanation of the invention's effectiveness, combined with specific experimental data and theoretical analysis, further elaborates on its effectiveness.

[0107] First, the beneficial effect of computational efficiency. This invention uses the selective state-space model Mamba as the core evolution engine, replacing the Transformer architecture with a computational complexity of O(L²) in the prior art.

[0108] Theoretical Analysis of Effectiveness: The state-space model employed in this invention processes historical interaction sequences through recursive updates of a structured state transition matrix. Its computational complexity is linearly related to the sequence length L, i.e., O(L). When processing long sequence data (such as the Flight dataset where a single node's interaction sequence length can reach tens of thousands), the computational resource consumption growth rate of this invention is far lower than that of Transformer-based FATDyG and TFWaveFormer. This linear complexity advantage allows this invention to model complete sequences without truncating the historical window, effectively avoiding the loss of evolutionary information caused by forced truncation. This provides a feasible computational foundation for real-time link prediction in large-scale dynamic networks (such as global aviation networks and national-level financial transaction networks).

[0109] Table 1: Dataset Information

[0110] Table 2: Repeatability Analysis of Five Datasets

[0111] Second, the beneficial effect of prediction accuracy. Referring to Tables 1 and 2, the present invention underwent a comprehensive performance comparison with seven cutting-edge benchmark algorithms on five publicly available real-world dynamic graph datasets, covering three evaluation strategies: random negative sampling, historical negative sampling, and inductive negative sampling, using AUC (area under the curve) and AP (average precision) as evaluation metrics. The experimental results fully demonstrate the superiority of the present invention in prediction accuracy.

[0112] (1) Improved accuracy under random negative sampling strategy.

[0113] In a typical prediction scenario (random negative sampling), the overall performance of this invention is as follows: On the Wikipedia dataset, this invention achieved the best results with an AUC of 0.920 and an AP of 0.916. Compared with the second-best algorithm CoDCL (AUC: 0.919, AP: 0.915), the AUC is improved by about 0.11% and the AP is improved by about 0.11%.

[0114] On the MOOC dataset, this invention achieved the best results with an AUC of 0.860 and an AP of 0.846. Compared with the second-best algorithm TFWaveFormer (AUC: 0.826, AP: 0.804), the AUC is improved by about 4.1% and the AP is improved by about 5.2%. Compared with FATDyG (AUC: 0.797, AP: 0.774), the improvements are 7.9% and 9.3%, respectively.

[0115] On the LastFM dataset, this invention achieved the best performance with an AP of 0.901 (on par with CAWN) and an AUC of 0.908, outperforming most of the comparison algorithms.

[0116] On the Flight large-scale dataset, this invention achieved a second-best performance with an AUC of 0.922 and an AP of 0.919, which is close to the performance of the optimal algorithm EdgeBank (AUC: 0.925, AP: 0.922). However, EdgeBank is only a simple memory lookup mechanism and does not have the ability to predict unseen edges.

[0117] On the Reddit dataset, this invention achieved a near-optimal score of 0.922 AUC and 0.914 AP, with a very small performance gap compared to the optimal algorithm CoDCL (AUC: 0.923, AP: 0.922).

[0118] Overall evaluation: Under the random negative sampling strategy, the present invention improves the AUC index by an average of 1.24% and the AP index by an average of 1.09% compared with the suboptimal algorithm.

[0119] (2) Improved accuracy under historical negative sampling strategy.

[0120] The performance advantage of this invention is even more significant under the more challenging historical negative sampling strategy (negative samples are real edges that have appeared in historical moments, which constitute a stronger disturbance to the model): On the Reddit dataset, this invention achieved the best results with an AUC of 0.880 and an AP of 0.859. Compared with the second-best algorithm CAWN (AUC: 0.867, AP: 0.846), the AUC is improved by about 1.5% and the AP is improved by about 1.5%.

[0121] On the MOOC dataset, this invention achieved the best results with an AUC of 0.805 and an AP of 0.782. Compared with the second-best algorithm TFWaveFormer (AUC: 0.777, AP: 0.755), the AUC is improved by about 3.6% and the AP is improved by about 3.6%.

[0122] On the Flight dataset, this invention achieved the best results with an AUC of 0.890 and an AP of 0.875. Compared with the second-best algorithm TFWaveFormer (AUC: 0.870, AP: 0.850), the AUC is improved by about 2.3% and the AP is improved by about 2.9%.

[0123] On the Wikipedia dataset, this invention achieved a near-optimal score of 0.869 AUC and 0.848 AP, which is only slightly lower than the performance of the optimal algorithm CAWN (AUC: 0.875, AP: 0.861).

[0124] On the LastFM dataset, this invention achieved a second-best result with an AUC of 0.858 and an AP of 0.843.

[0125] Overall evaluation: Under the historical negative sampling strategy, the present invention improves the AUC index by an average of 2.47% and the AP index by an average of 2.68% compared with the suboptimal algorithm.

[0126] (3) Improvement of accuracy under the negative sampling strategy.

[0127] The performance advantage of this invention is most prominent under the most challenging inductive negative sampling strategy (negative samples contain entirely new nodes that have not appeared during the training phase, testing the model's generalization ability): On the Wikipedia dataset, this invention achieved the best results with an AUC of 0.875 and an AP of 0.861. Compared with the second-best algorithm CoDCL (AUC: 0.848, AP: 0.831), the AUC is improved by about 3.2% and the AP is improved by about 3.6%.

[0128] On the MOOC dataset, this invention achieved the best results with an AUC of 0.822 and an AP of 0.801. Compared with the second-best algorithm TFWaveFormer (AUC: 0.774, AP: 0.749), the AUC is improved by about 6.2% and the AP is improved by about 6.9%. Compared with CoDCL (AUC: 0.791, AP: 0.766), the improvements are 3.9% and 4.6%, respectively.

[0129] On the LastFM dataset, this invention achieved the best results with an AUC of 0.858 and an AP of 0.846. Compared with the second-best algorithm CAWN (AUC: 0.848, AP: 0.831), the AUC is improved by about 1.2% and the AP is improved by about 1.8%.

[0130] On the Flight dataset, this invention achieved the best results with an AUC of 0.875 and an AP of 0.862. Compared with the second-best algorithm TFWaveFormer (AUC: 0.838, AP: 0.824), the AUC is improved by about 4.4% and the AP is improved by about 4.6%.

[0131] On the Reddit dataset, this invention achieved a second-best result with an AUC of 0.864 and an AP of 0.844.

[0132] Overall evaluation: Under the inductive negative sampling strategy, the present invention improves the AUC index by an average of 2.57% and the AP index by an average of 3.12% compared to the suboptimal algorithm.

[0133] Third, the beneficial effects of anti-interference and robustness.

[0134] This invention exhibits excellent and stable anti-interference performance under three negative sampling strategies with increasing difficulty, which is a remarkable effect that existing technologies do not possess.

[0135] Horizontal comparison: When shifting from random negative sampling to more perturbative historical negative sampling, the performance of benchmark algorithms generally drops significantly. For example, on the Wikipedia dataset, the AUC of EdgeBank plummeted from 0.913 to 0.654, a decrease of 28.4%; CAWN dropped from 0.918 to 0.875, a decrease of 4.7%; and CoDCL dropped from 0.919 to 0.849, a decrease of 7.6%. In contrast, this invention only decreased from 0.920 to 0.869, a decrease of only 5.5%, the smallest decrease among similar models.

[0136] Longitudinal Comparison: When transitioning from historical negative sampling to inductive negative sampling, the performance of this invention remains largely consistent or even improves across multiple datasets. On the Reddit dataset, the AUC of this invention even improves by 1.8% under inductive sampling compared to historical sampling, while CoDCL decreases by 2.6% under the same transformation. On the LastFM dataset, the AUC of EdgeBank drops from 0.641 to 0.512, a significant decrease of 20.1%, while the AUC of this invention only slightly decreases from 0.858 to 0.858 (remaining consistent), demonstrating excellent stability.

[0137] The above data fully demonstrates that the present invention, through the structure-semantic dual decoupling space, geometrically forces the decorrelation of long-term topological stability and short-term behavioral intent, enabling the model to maintain high discrimination accuracy when facing different distributional shifts and strongly disturbed negative samples, and possessing robustness unmatched by existing technologies.

[0138] Fourth, the effectiveness of each module verified by the ablation experiment.

[0139] This invention verifies the beneficial contributions of each core module through systematic ablation experiments: Experimental conditions: Under the random negative sampling strategy, four variant models were set up for comparison: Model 0 (only basic interaction embedding and causal dynamics operator are retained), Model 1 (adaptive meta-calendar semantic cue mechanism is removed), Model 2 (structural and semantic dual decoupling space is removed), Model 3 (decoupling framework is retained but orthogonal constraint loss is removed), and the complete model Mamba-DD is used as a control.

[0140] Data-driven impact of each module's contribution: The effect of the causal dynamics foundation module: Compared to Model 0, the complete model improves the AUC and AP metrics by an average of 3.2% and 3.8% on the five datasets, respectively. This indicates that the Mamba-based evolutionary engine can provide effective time-series modeling capabilities for dynamic link prediction.

[0141] The effect of the adaptive meta-calendar semantic prompting mechanism: Compared with Model 1, the full model improved the AUC and AP metrics by an average of 1.40% and 1.5%, respectively. This shows that the meta-calendar prompting mechanism effectively supplements the environmental context information missing by relying solely on local interaction sequences by injecting macro-time priors such as weekly phase and monthly phase into the representation process, enabling the model to adaptively adjust the representation strategy according to the temporal context.

[0142] The effect of decoupling the structural and semantic dual space: Compared with Model 2, the complete model improved the AUC and AP metrics by an average of 1.8% and 1.8%, respectively, with particularly significant improvements on the MOOC dataset. This indicates that separating structural and semantic information through bi-branch projection effectively eliminates the mutual interference between the two types of heterogeneous features, significantly improving the model's discriminative and expressive capabilities.

[0143] The effect of orthogonal constraint loss: Compared with Model 3, the full model improved the AUC and AP by an average of 0.5% and 0.3%, respectively. This indicates that the Frobenius norm orthogonal penalty term, by forcing the structural subspace and semantic subspace to remain geometrically orthogonal, further reduces the covariance crossover between different subspaces and achieves deep decorrelation of the representation space. Although the improvement is relatively small, it shows a consistent positive gain across all metrics.

[0144] Fifth, the beneficial effects of parameter robustness This invention demonstrates, through sensitivity analysis of key parameters, that it maintains stable and excellent performance under different configurations: Robustness of historical sequence window length: When the historical window L is expanded from 10 to 80, the prediction accuracy of this invention steadily increases across all datasets, without performance degradation due to excessively long sequences. On the Wikipedia dataset, the AUC reaches 0.922 when L=80, a 1.5% improvement over 0.908 when L=10. This trend demonstrates that the linear complexity mechanism of this invention enables it to effectively utilize longer historical information to improve prediction accuracy, without being limited by the quadratic complexity bottleneck of the Transformer architecture.

[0145] Controllability of the decoupling balance factor: When λ=0.1, this invention achieves peak performance on all datasets. When λ is too small (0.01), long-term topological genes and short-term behavioral intentions produce semantic aliasing; when λ is too large (5), excessive decoupling causes the AUC of some datasets (such as MOOCs) to drop to 0.823. When λ=0.1, the optimal balance between structural and semantic information can be achieved, ensuring effective separation of the two types of features while avoiding the destruction of semantic associations by excessive decoupling.

[0146] Scalability of latent space dimension: The performance of this invention continues to improve as the latent space dimension increases from 64 to 256; however, the performance gain begins to converge when it is further increased to 512. This indicates that 256 dimensions is the optimal configuration for balancing computational cost and representation efficiency, and the model can fully capture the complex evolutionary features in dynamic networks at 256 dimensions.

[0147] In summary, the beneficial effects achieved by this invention can be systematically summarized as follows: Table 3: Technical Effects and Data Support of the Mamba-DD Method

[0148] Final Conclusion: This invention, through a three-pronged technical solution of "selective state-space architecture + meta-calendar semantic modulation + dual decoupling representation," significantly improves the accuracy, anti-interference ability, and generalization capability of dynamic link prediction while maintaining linear computational complexity. In a total of 30 comparative experiments (5 datasets (details in Tables 2 and 3) × 3 sampling strategies × 2 evaluation metrics), this invention achieved optimal performance on 19 datasets and suboptimal performance on the remaining 11, fully demonstrating the comprehensive superiority and practical application value of the technical solution. This invention can be widely deployed in practical business scenarios such as social network friend recommendation, real-time financial risk control early warning, intelligent traffic flow prediction, and e-commerce personalized recommendation, showing promising industrial application prospects.

[0149] Table S1: Performance Comparison of Mamba-DD and Benchmark Algorithms under Random Negative Sampling Strategy

[0150] Table S2 Performance Comparison of Mamba-DD and Benchmark Algorithms under Historical Negative Sampling Strategy

[0151] Table S3 summarizes the performance comparison between Mamba-DD and benchmark algorithms under the inductive negative sampling strategy.

[0152] Table S4 Experimental results of Mamba-DD ablation under random negative sampling strategy

[0153] Table S5 Historical sequence window of Mamba-DD under random negative sampling strategy Parameter Analysis

[0154] Table S6 Decoupling Balance Factors of Mamba-DD under Random Negative Sampling Strategy Parameter Analysis

[0155] Table S7 Latent space of Mamba-DD under random negative sampling strategy Parameter Analysis

[0156] Next, referring to the accompanying drawings, a dynamic link prediction system based on selective state space and dual decoupling proposed according to an embodiment of the present invention is described, which is used to implement the dynamic link prediction method based on selective state space and dual decoupling as described in any of the above schemes.

[0157] Figure 3 This is a structural diagram of a dynamic link prediction system based on selective state space and dual decoupling according to an embodiment of the present invention.

[0158] like Figure 3 As shown, the dynamic link prediction system based on selective state space and dual decoupling includes: a historical interaction sequence construction module 100, a state space evolution module 200, a calendar semantic modulation module 300, and a structural semantic decoupling prediction module 400.

[0159] Specifically, the historical interaction sequence construction module 100 is used to obtain the historical interaction events of each node in the node pair to be predicted before the target time, construct the initial embedding of each of the historical interaction events, and arrange the initial embeddings in chronological order as the historical interaction sequence of each node in the node pair to be predicted. The state space evolution module 200 is used to sequentially input each of the initial embeddings in the historical interaction sequence of each node into the selective state space model, recursively update the hidden state of the corresponding node through the selective state space model, and generate the stimulated representation of the corresponding historical interaction moment according to the updated hidden state, so as to obtain the stimulated representation sequence of each node. The calendar semantic modulation module 300 is used to extract the calendar prior information corresponding to each of the historical interaction events, generate feature modulation parameters based on the calendar prior information through a meta-learning supernetwork, and use the feature modulation parameters to perform feature modulation on the stimulated representation at the corresponding time in the stimulated representation sequence to obtain the environment perception representation matrix of each node fused with calendar semantics. The structural-semantic decoupling prediction module 400 is used to perform bi-branch projection of the environment perception representation matrix of each node into the structural subspace and the semantic subspace respectively to obtain the structural components and semantic components of the corresponding node. The structural components and semantic components of the source node in the node pair to be predicted are aggregated with the structural components and semantic components of the target node, and the aggregation result is input into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time.

[0160] Figure 4 A structural diagram of a device provided in an embodiment of the present invention. The device may include: The memory 501, the processor 502, and the computer program stored on the memory 501 and capable of running on the processor 502.

[0161] When the processor 502 executes the program, it implements the dynamic link prediction method based on selective state space and dual decoupling provided in the above embodiments.

[0162] Furthermore, the equipment also includes: Communication interface 503 is used for communication between memory 501 and processor 502.

[0163] The memory 501 is used to store computer programs that can run on the processor 502.

[0164] Memory 501 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0165] If the memory 501, processor 502, and communication interface 503 are implemented independently, then the communication interface 503, memory 501, and processor 502 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EIS) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 4 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0166] Optionally, in a specific implementation, if the memory 501, processor 502, and communication interface 503 are integrated on a single chip, then the memory 501, processor 502, and communication interface 503 can communicate with each other through an internal interface.

[0167] Processor 502 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention.

[0168] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described dynamic link prediction method based on selective state space and dual decoupling.

[0169] One embodiment of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the present invention. Figure 1 The corresponding embodiments provide a dynamic link prediction method based on selective state space and dual decoupling.

[0170] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0171] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0172] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

[0173] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable storage medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable storage medium could be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0174] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any of the following techniques known in the art, or a combination thereof: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0175] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0176] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0177] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0178] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

[0179] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic link prediction method based on selective state space and dual decoupling, characterized in that, The dynamic link prediction method based on selective state space and dual decoupling includes: Obtain the historical interaction events of each node in the node pair to be predicted before the target time, construct the initial embedding of each historical interaction event, and arrange the initial embeddings in chronological order as the historical interaction sequence of each node in the node pair to be predicted. Each initial embedding in the historical interaction sequence of each node is sequentially input into the selective state space model. The hidden state of the corresponding node is recursively updated through the selective state space model. Based on the updated hidden state, the stimulated representation of the corresponding historical interaction moment is generated to obtain the stimulated representation sequence of each node. Extract the calendar prior information corresponding to each of the historical interaction events, generate feature modulation parameters based on the calendar prior information through a meta-learning supernetwork, and use the feature modulation parameters to perform feature modulation on the stimulated representation at the corresponding time in the stimulated representation sequence to obtain the environment-aware representation matrix of each node fused with calendar semantics. The environmental perception representation matrix of each node is projected into the structural subspace and the semantic subspace in a two-branch manner to obtain the structural components and semantic components of the corresponding node. The structural components and semantic components of the source node in the node pair to be predicted are aggregated with the structural components and semantic components of the target node, and the aggregation result is input into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time. The calendar prior information includes weekly phase information, monthly phase information, and sudden event identifiers; the feature modulation parameters include scaling vectors and translation vectors. The process of extracting calendar prior information corresponding to each of the historical interaction events, generating feature modulation parameters based on the calendar prior information through a meta-learning supernetwork, and using the feature modulation parameters to modulate the stimulated representations at corresponding times in the stimulated representation sequence to obtain an environment-aware representation matrix fused with calendar semantics for each node, specifically includes: For any historical interaction event, obtain the weekly phase information, monthly phase information, and sudden event identifier corresponding to the historical interaction time of the historical interaction event, and encode the weekly phase information, monthly phase information, and sudden event identifier to obtain a calendar prior vector; The calendar prior vector is input into the meta-learning supernetwork, and the meta-learning supernetwork maps and generates the scaling vector and translation vector corresponding to the historical interaction event. Using the scaling vector and the translation vector, feature linear modulation is performed on the excited representations in the excited representation sequence that are at the same time as the historical interaction event to obtain the environmental perception representations corresponding to the historical interaction event. By combining the environmental perception representations corresponding to each historical interaction event in chronological order, an environmental perception representation matrix fused with calendar semantics for the corresponding node is obtained. The environmental perception representation matrix of each node is projected into both the structural subspace and the semantic subspace in a two-branch manner to obtain the structural and semantic components of the corresponding node, specifically including: The environmental perception representation matrix is ​​input into the structure projection layer and mapped to the structure subspace through the structure projection layer to obtain the structure representation matrix; The environmental perception representation matrix is ​​input into the semantic projection layer and mapped to the semantic subspace through the semantic projection layer to obtain the semantic representation matrix; Extract the state corresponding to the last moment from the structural representation matrix, and use it as the structural component of the corresponding node; Extract the state corresponding to the last moment from the semantic representation matrix, and use it as the semantic component of the corresponding node.

2. The dynamic link prediction method based on selective state space and dual decoupling according to claim 1, characterized in that, The initial embedding of each of the aforementioned historical interaction events specifically includes: For any historical interaction event, obtain the first feature of the current node participating in the historical interaction event, the second feature of the interacting peer node, and the attribute feature of the interacting edge. Aggregate the first feature, the second feature, and the attribute feature to obtain the interaction context feature. Obtain the global index of the current node, and construct the node identifier representation of the current node by fusing the position encoding with the learnable node identifier vector; Obtain the relative time span between the historical interaction time of the historical interaction event and the target time, and encode the relative time span as a time embedding; The interaction context features, the node identifier representation, and the time embedding are fused and projected to generate the initial embedding of the historical interaction event.

3. The dynamic link prediction method based on selective state space and dual decoupling according to claim 1, characterized in that, The step of sequentially inputting each initial embedding from the historical interaction sequence of each node into a selective state space model, and recursively updating the hidden state of the corresponding node through the selective state space model, specifically includes: Each of the initial embeddings in the historical interaction sequence is sequentially input into the selective state space model, and for the currently input initial embedding, an input-dependent state transition matrix and an input matrix are generated; Based on the state transition matrix and the time-varying step size operator corresponding to the initial embedding of the current input, a discretized state transition matrix is ​​generated, and based on the input matrix and the time-varying step size operator, a discretized input matrix is ​​generated. Based on the discretized state transition matrix, the discretized input matrix, and the hidden state at the previous time step, the hidden state is recursively updated to obtain the hidden state at the current time step.

4. The dynamic link prediction method based on selective state space and dual decoupling according to claim 1, characterized in that, The aggregation result is a joint characterization; The step of aggregating the structural and semantic components of the source node and the target node in the node pair to be predicted, and inputting the aggregation result into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time, specifically includes: Obtain the structural components and semantic components of the source node, and the structural components and semantic components of the target node; The structural components of the source node, the semantic components of the source node, the structural components of the target node, and the semantic components of the target node are concatenated to obtain a joint representation; The joint representation is input into the prediction network, and after being mapped by the prediction network, the predicted probability of the interaction relationship between the nodes to be predicted at the target time is output.

5. The dynamic link prediction method based on selective state space and dual decoupling according to claim 3, characterized in that, The state transition matrix is ​​a structured diagonal matrix, and the selective state space model is configured with a predefined spectral decay matrix. The spectral decay matrix is ​​a diagonal matrix, and the diagonal elements of the spectral decay matrix are located in the interval (0,1), which is used to constrain the spectral radius of the hidden state during the recursive update process.

6. A dynamic link prediction system based on selective state space and dual decoupling, characterized in that, The dynamic link prediction system based on selective state space and dual decoupling is used to implement the dynamic link prediction method based on selective state space and dual decoupling as described in any one of claims 1-5. The dynamic link prediction system based on selective state space and dual decoupling includes: The historical interaction sequence construction module is used to obtain the historical interaction events of each node in the node pair to be predicted before the target time, construct the initial embedding of each historical interaction event, and arrange the initial embeddings in chronological order as the historical interaction sequence of each node in the node pair to be predicted. The state space evolution module is used to sequentially input the initial embeddings in the historical interaction sequence of each node into the selective state space model, recursively update the hidden state of the corresponding node through the selective state space model, and generate the stimulated representation of the corresponding historical interaction moment according to the updated hidden state, so as to obtain the stimulated representation sequence of each node. The calendar semantic modulation module is used to extract the calendar prior information corresponding to each of the historical interaction events, generate feature modulation parameters based on the calendar prior information through a meta-learning supernetwork, and use the feature modulation parameters to perform feature modulation on the stimulated representation at the corresponding time in the stimulated representation sequence to obtain the environment perception representation matrix of each node fused with calendar semantics. The structural-semantic decoupling prediction module is used to project the environment perception representation matrix of each node into the structural subspace and the semantic subspace in a two-branch manner to obtain the structural components and semantic components of the corresponding node. The structural components and semantic components of the source node in the node pair to be predicted are aggregated with the structural components and semantic components of the target node, and the aggregation result is input into the prediction network to obtain the prediction probability that the node pair to be predicted has an interaction relationship at the target time.

7. A device, characterized in that, The device includes: a memory, a processor, and a dynamic link prediction program based on selective state space and dual decoupling stored in the memory and executable on the processor. When the dynamic link prediction program based on selective state space and dual decoupling is executed by the processor, it implements the steps of the dynamic link prediction method based on selective state space and dual decoupling as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a dynamic link prediction program based on selective state space and dual decoupling, which, when executed by a processor, implements the steps of the dynamic link prediction method based on selective state space and dual decoupling as described in any one of claims 1-5.

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