A large-scale graph generation method based on persistent homology high-order interaction structure constraint

Abstract

The application discloses a large-scale graph generation method based on persistent homology high-order interaction structure constraint, and belongs to the technical field of graph data generation and topological data analysis. The application introduces zero-dimensional connected components and one-dimensional loop evolution features of persistent homology based on an asynchronous discrete diffusion model generation framework, constructs global whole-graph topological constraints and node-level local topological constraints through PersLay vectorization, reduces the persistent homology calculation overhead by adopting a sparse triggering strategy, and the generated target graph can match the node attribute distribution, edge structure distribution and multi-scale high-order topological features of a real graph, and is suitable for graph generation scenes such as social networks, academic citation networks and webpage hyperlink networks.

Description

Technical Field

[0001] This invention relates to the fields of graph data generation and topology data analysis, specifically a method for generating large-scale graphs based on continuous homology high-order interaction structure constraints. Background Technology

[0002] Graph generation models are core generative techniques in graph machine learning, widely applied in scenarios such as social network simulation, recommender system construction, knowledge graph completion, and biomolecular structure design. Their core objective is to generate new graph structures that are highly similar to the statistical characteristics of real graph data, effectively modeling node attributes, edge connections, and the overall graph distribution. In recent years, graph generation methods based on diffusion probability models and autoregressive models have become mainstream. However, these methods typically only model pairwise statistical features at the edge level, only depicting direct connections between nodes. They struggle to effectively represent higher-order interaction structures formed by three or more nodes, easily leading to situations where the generated graph has similar degree distribution and edge density to the real graph, but significant differences in connected component evolution, loop structures, and local closure patterns. Furthermore, modeling only the edge existence state and its statistical distribution is insufficient to guarantee that the generated graph maintains consistency with the real graph in terms of connected organization, loop structures, and local closure patterns. Even with the same node size and number of edges, different edge combinations may still correspond to significantly different higher-order topological structures.

[0003] Continuous cohomology, as a multi-scale topological characterization tool in the field of topological data analysis, can effectively characterize the high-order interaction features of graphs by tracking the evolution of topological structures under different filtering scales. Existing research has attempted to introduce it into graph generation tasks, but there are three limitations: First, traditional topological distance is based on predefined metrics to compress topological differences, which has limited expressive power and is difficult to adapt to the topological constraint requirements of different generation tasks; second, it can only generate global continuous features of the entire graph and cannot constrain the local high-order organizational structure around a single node at a fine-grained level; third, continuous barcodes are in the form of discrete sets, which are difficult to directly integrate into neural network optimization, and high-frequency continuous cohomology calculations will significantly increase the computational cost of training large-scale graphs. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention proposes a large-scale graph generation method based on continuous homology high-order interaction structure constraints. This method solves the problems that existing graph generation methods can only fit edge-level pairwise statistical features and are difficult to characterize multi-node high-order interaction structures. Traditional topological constraint metrics have limited expressive power and can only provide global constraints without fine-grained control over local high-order organization of nodes. The discrete form of continuous barcodes is difficult to directly integrate into neural network optimization, and the high computational cost of high-frequency continuous homology calculations makes it difficult to implement large-scale graph training. This invention achieves a deep integration of the asynchronous discrete diffusion generation framework and multi-scale continuous homology topological constraints, achieving efficient large-scale graph generation with node attributes, edge structure, global topology, and local high-order organization all highly matching the real graph.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for generating large-scale graphs based on continuous cohomology high-order interaction structure constraints includes the following steps: S1. Obtain real attribute graph data, and preprocess the real attribute graph data to obtain basic graph data containing node attribute encoding, edge existence state encoding, and real adjacency matrix. S2. Construct an asynchronous discrete diffusion graph generation module to perform forward noise addition and reverse noise reduction discrete diffusion modeling for the discrete attributes of nodes and the existence state of edges, respectively. S3. Construct a graph structure encoding module. Based on the node attribute state, edge existence state, and diffusion time step of the current diffusion step, output the node attribute recovery distribution and edge existence probability matrix. Construct a node distance matrix based on the true adjacency matrix and the predicted edge existence probability matrix respectively. Calculate the continuous cohomology features based on the node distance matrix and convert them into fixed-dimensional topological feature vectors. Construct a training loss function that includes node attribute recovery loss, edge structure recovery loss, and topological constraint loss. Jointly train the asynchronous discrete diffusion graph generation module and the graph structure encoding module. S4. Using the trained asynchronous discrete diffusion map generation module, starting from the random noise state, generate the target discrete attribute map through multi-step reverse denoising sampling.

[0006] Specifically, the asynchronous discrete diffusion graph generation module includes mutually independent node attribute diffusion submodules and edge structure diffusion submodules; The node attribute diffusion submodule performs forward noise addition and reverse noise reduction modeling on the discrete attributes of nodes. The forward noise addition process satisfies the following: ; in, For the first The preceding node attribute state of each diffusion step. For the first The node attribute noise state after each diffusion step and noise addition For the pre-configured fixed node attribute state transition matrix, Represents category distribution; The edge structure diffusion submodule performs forward denoising and reverse denoising modeling on the edge existence state. The forward denoising process satisfies: ; in, For the first The preceding edges of each diffusion step exist in a state. For the first The edges after each diffusion step with added noise have a noisy state. A state transition matrix exists for a pre-configured fixed edge; The forward noise addition process and reverse noise reduction process of the node attribute diffusion submodule and the edge structure diffusion submodule are independent of each other, and independently model the node attribute distribution and edge structure distribution respectively.

[0007] Specifically, the processing procedure of the graph structure encoding module includes: First, embedding mapping is performed on the input node attributes, conditional control variables, and diffusion time steps to obtain the initial node representation: ; in, For the first Nodes in each diffusion step Discrete attribute states, For nodes The corresponding conditional control variables include node category labels and graph category labels. Embed functions for node attributes. Embedding function for conditional control variables, For the diffusion time step embedding function, For nodes The initial node representation; The initial node representation is updated by aggregating neighborhood information through at least one graph messaging layer to obtain the final node representation: ; in, For the first After layer message passing, the node The expression, For nodes The set of neighboring nodes, For the first The edge exists in a state matrix or an edge exists in a probability matrix under each diffusion step. For the first Layered graph message passing functions; The final node represents the node attribute prediction branch and the edge structure prediction branch as inputs, respectively, and the output node attribute recovery distribution and edge existence probability matrix. The node attribute prediction branch outputs the node... Attribute recovery distribution satisfy: ; in The total number of message passing layers in the graph. A multilayer perceptron for predicting branches based on node attributes; The nodes of the edge structure prediction branch output With nodes The probability of the existence of an edge satisfy: ; in It is the Sigmoid activation function. Multilayer perceptron for predicting branches in edge structures. This is an element-wise multiplication operation.

[0008] Specifically, the distance matrix between nodes is constructed using at least one of the following: adjacency distance, resistance distance, and thermal core response distance. When adjacency distance is used, nodes With nodes The distance satisfies: ; in, For nodes With nodes The probability of an edge existing between them is given by the real graph. Take the corresponding values ​​from the actual adjacency matrix for the generated graph. Take the corresponding value of the edge existence probability matrix. For nodes With nodes The adjacency distance; When using resistive distance, nodes With nodes The distance satisfies: ; in, The graph Laplacian matrix is ​​constructed based on the true adjacency matrix or the edge existence probability matrix. for Moore-Penrose generalized inverse matrix, , They are nodes ,node The corresponding unit basis vectors, For nodes With nodes The resistivity distance; When using thermonuclear response distance, nodes With nodes The distance satisfies: ; ; in, For thermonuclear scale parameters, For the heat core matrix, For nodes ,node The corresponding thermonuclear response vector, For L2 norm operations, For nodes With nodes The thermonuclear response distance.

[0009] Specifically, the process of calculating the persistent homology feature based on the distance matrix between nodes is as follows: A Vietoris-Rips filtering complex is constructed based on the inter-node distance matrix, and the topological evolution at different filtering scales is tracked to obtain a zero-dimensional complex. Continuous features of connected components and one-dimensional Graph-level persistent barcodes with loop persistence features: ; in, For the first The birth scale of each topological feature corresponds to the filtering threshold for the first occurrence of that topological feature. For the first The death scale of a topological feature corresponds to the filtering threshold for the disappearance of that topological feature; This represents the total number of topological features. The zero dimension The connectivity component persistence feature is used to characterize the multi-scale connectivity organization evolution process of a graph, the one-dimensional Loop persistence features are used to characterize the evolution of closed paths and multi-node interaction structures in a graph.

[0010] Specifically, the process of converting persistently homogeneous features into fixed-dimensional topological feature vectors is as follows: Each duration interval Convert to point features : ; in, The duration of this topological feature is the length of its duration; the longer the duration, the higher the stability of the topological feature. Based on the PersLay vectorization layer, all point features are mapped and aggregated to obtain a fixed-dimensional topological feature vector: ; in, It is a learnable weighting function used to assign higher weights to topological features with longer durations; This is a learnable feature mapping function used to map point features to a high-dimensional feature space; It is a substitution-invariant aggregation function; The output is a fixed-dimensional topological feature vector, including a global topological feature vector and node-level local topological feature vectors.

[0011] Specifically, the process of constructing the node-level local topological feature vector is as follows: Obtain the paired simplex information corresponding to each topological feature during the continuous homology calculation process, and determine the first... The duration interval of each topological feature The set of associated nodes ; Each persistent interval is assigned to the local persistent barcodes corresponding to all nodes in its associated node set, resulting in the node-level local persistent barcodes for each node: ; in, For the first The duration interval of each topological feature is assigned to a node. The weights are either uniform weights or weighted weights based on the degree of participation of nodes in the simplex that constitutes the topological feature. Perform PersLay vectorization on the node-level local persistent barcode of each node to obtain the node. The corresponding node-level local topological feature vector: ; in, As a continuous homology vectorization layer, its parameter configuration is set independently of the PersLay layer used for global topological feature vector calculation.

[0012] Specifically, the topology constraint loss includes global topology constraint loss and node-level local topology constraint loss; The global topological constraint loss is used to constrain the consistency of the multi-scale topological structure of the generated graph and the real graph, and the formula is: ; in, For real images The corresponding global topological feature vector, Generate a graph for the current prediction The corresponding global topological feature vector; The node-level local topological constraint loss is used to constrain the consistency of the generated graph with the local high-order interaction structure around the corresponding node in the real graph. The formula is as follows: ; in, For the set of valid nodes, For real images Middle node The corresponding node-level local topological feature vector, Generate a graph for the current prediction In and nodes Aligned node-level local topological feature vectors.

[0013] Specifically, the overall calculation formula for the training loss function is as follows: ; in, To recover the loss for node attributes, For edge structure recovery loss, For pre-configured topology constraint loss weights, For topology constraint trigger indicator, For the currently enabled topology constraint loss, including , At least one of them; Topology constraint trigger indicator The value is determined by a preset sparse triggering rule: when the current training batch number satisfy hour, ,otherwise ,in The pre-configured topology constraint trigger interval; The global topology constraint loss and the node-level local topology constraint loss are independent configurable branches, which can be enabled, disabled, have their loss weights set, and trigger intervals configured independently.

[0014] Specifically, the multi-step reverse denoising sampling process is as follows: With total diffusion step size The corresponding completely random node attribute noise state and completely random edge noise state are used as the initial reverse sampling state. from arrive Successive reverse denoising update: update the node attribute noise state of the current diffusion step. Noise exists on the edge. diffusion time step The graph structure encoding module, after training, is input with conditional control variables to obtain the node attribute recovery distribution. The probability matrix of the existence of edges The first step is to update the discrete diffusion back transfer rule to obtain the second step. Step node attribute state With edge existence state The reverse transfer process satisfies: ; ; When iterates to At that time, the final set of node attributes and edge adjacency matrix are output to obtain the target discrete attribute graph.

[0015] In summary, the beneficial technical effects of the present invention are as follows: 1. Quantifiable and Constraintible High-Order Interaction Structures: This invention concretizes the difficult-to-quantify multi-node high-order interaction structures as the evolution characteristics of zero-dimensional connected components and one-dimensional loops under continuous homology, enabling high-order interaction relationships to have clear topological data analysis meanings. This solves the problem that existing graph generation methods can only fit edge-level paired features and cannot characterize complex interaction structures across scales.

[0016] 2. Strong adaptability of multiple distance metrics: This invention supports three types of node distance calculation methods: adjacency distance, resistance distance, and thermal core response distance, which respectively represent direct connection relationships, multi-path redundancy relationships, and diffusion propagation associations. Different distances do not simply change the numerical scale, but rather introduce different structural inductive biases into topological constraints. The appropriate distance metric can be flexibly selected based on the structural characteristics of the graph data and the constraint requirements of the generation task, solving the problems of limited expressive power and poor adaptability of traditional topological distance metrics.

[0017] 3. Two-level topological constraints cover the entire structure: This invention designs two independent and configurable branches: global topological constraints and node-level local topological constraints. It constrains the consistency of the topological structure of the whole graph across scales through global persistent homology features, and allocates local persistent barcodes through paired simplex information in the persistent homology calculation. It finely constrains the local high-order structures such as closed organizations and participating loops around individual nodes, which solves the problem that traditional topological constraints can only control the features of the whole graph and cannot cover the node-level local structures.

[0018] 4. Topological features can directly participate in end-to-end training: This invention converts discrete continuous barcodes into trainable feature vectors of fixed dimensions through the PersLay vectorization layer, and supports automatically assigning higher weights to stable topological features with longer continuity lengths. This solves the problem that the discrete form of continuous barcodes cannot be directly connected to neural network training. Topological constraints can directly participate in the end-to-end optimization of the model without the need for additional predefined topological distance metric rules.

[0019] 5. Low training overhead and adaptability to large-scale graph scenarios: This invention adopts a sparse triggering strategy to control the computation frequency of topology constraints, eliminating the need to perform continuous cohomology computation in each training round. Furthermore, the two topology constraint branches can be enabled and their trigger intervals can be configured independently, significantly reducing computational overhead compared to full round-by-round computation of topology constraints. This invention is suitable for large-scale graph generation training with hundreds of thousands of nodes.

[0020] 6. Strong scene adaptability: The asynchronous discrete diffusion basic framework adopted in this invention supports independent modeling of node attributes and edge structure, and is compatible with generation scenarios with conditional control. The generated graph structure matches the distribution of node attributes, edge structure, global topological features and local high-order structure. It can be directly applied to various scenarios such as social network propagation simulation, academic citation pattern analysis, web page hyperlink structure design, and biomolecular network construction without additional secondary adaptation. Attached Figure Description

[0021] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the training process of the asynchronous discrete diffusion graph generation model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the calculation of global continuous homology layer and node-level local barcode topology constraints in an embodiment of the present invention. Detailed Implementation

[0022] To make the technical means, creative features, objectives and effects of this invention clearer and easier to understand, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0023] Example This embodiment focuses on the discrete attribute graph generation task. The higher-order interaction structure mentioned in this embodiment specifically refers to the topological evolution characteristics of the graph during multi-scale filtering, including zero-dimensional... Evolutionary characteristics of connected components and one-dimensional Loop evolution characteristics: Among them Features are used to characterize the process by which a group of nodes gradually connects and merges from an isolated state to form a unified connected organization at different filtering scales. Features are used to characterize loops, closed paths, and multi-path connectivity structures formed by multiple nodes. These features cannot be completely determined by a single edge or a single pair of connections, and therefore serve as the core high-order interaction structure representation of constraints in this embodiment.

[0024] This embodiment uses an asynchronous discrete diffusion process as the basis for generating the framework, and the overall process is as follows: Figure 1As shown, it includes eight core steps: data preprocessing, asynchronous diffusion module construction, graph structure encoding module construction, distance matrix calculation, continuous homology feature extraction, topological constraint loss construction, joint training, and backsampling generation.

[0025] S1. Preprocessing of real attribute map data; The system acquires real attribute graph data for the target scene and performs standardized preprocessing to obtain basic graph data containing node attribute encoding, edge existence state encoding, and a real adjacency matrix, which serves as input for subsequent modules. In this embodiment, the real attribute graph data includes at least a set of nodes, a set of edges, and discrete node attributes; in the conditional generation scenario, it also includes conditional control variables such as node category labels and graph category labels.

[0026] The specific preprocessing procedure for this step is as follows: S11. Edge Existence State Encoding: Extract the real edge index from the edge set of the real attribute graph, construct the edge existence state matrix based on the real edge index, and perform one-hot encoding on the edge existence state matrix to obtain the one-hot encoding matrix of the edge existence state. The edge existence state matrix is ​​directly used as the real adjacency matrix for subsequent construction of the distance matrix between nodes and calculation of topological loss. The one-hot encoding matrix of the edge existence state is used for discrete diffusion modeling of edge structure.

[0027] S12. Node attribute encoding: The discrete attributes of nodes in the real attribute graph are digitally encoded to obtain the discrete attribute encoding of nodes; if it is a condition generation scenario, the node category label and graph category label also need to be encoded to obtain the corresponding condition control variable encoding.

[0028] S13. Empirical Distribution Statistics: The empirical marginal distribution of the discrete attributes of statistical nodes and the empirical marginal distribution of the edge existence state serve as the benchmark distribution for the noise addition process of the asynchronous discrete diffusion module, ensuring that the forward noise addition process conforms to the distribution characteristics of the real data.

[0029] S2. Construct an asynchronous discrete diffusion map generation module; This step constructs two independent sub-modules: a node attribute diffusion sub-module and an edge structure diffusion sub-module. These sub-modules perform discrete diffusion modeling by adding noise forward and denoising backward, respectively, for the discrete attributes of nodes and the existence state of edges. The forward noise addition process and the backward noise denoising process of the two sub-modules are completely independent and do not interfere with each other, thus completing the independent modeling of the distribution of node attributes and the distribution of edge structures.

[0030] S21, Construction of the node attribute diffusion submodule; The node attribute diffusion submodule is used to perform forward noise addition and backward noise reduction modeling on the discrete attributes of nodes. The forward noise addition process follows predefined fixed rules, requires no training, and satisfies the following: ; in, For the first The preceding node attribute state of each diffusion step. For the first The node attribute noise state after each diffusion step and noise addition For the pre-configured fixed node attribute state transition matrix, Represents the category distribution; during the forward noise addition process, the discrete attributes of the nodes are arranged according to... The transition probability is gradually perturbed by random perturbations, eventually reaching the [transition probability] on the [first] [time]. T Each diffusion step degenerates into a completely random noise state.

[0031] The reverse denoising process is the mapping relationship that the model needs to learn. Based on the node attribute distribution output by the subsequent graph structure encoding module, the distribution is restored, and the process is completed from the noise state to the true attribute state.

[0032] S22, Construction of the edge structure diffusion submodule; The edge structure diffusion submodule is used to perform forward denoising and reverse denoising modeling on the edge existence state. The forward denoising process follows predefined fixed rules, requires no training, and satisfies the following: ; in, For the first The preceding edges of each diffusion step exist in a state. For the first The edges after each diffusion step with added noise have a noisy state. A pre-configured fixed edge existence state transition matrix is ​​used; during the forward noise addition process, the edge existence state follows... The transition probability is gradually perturbed by random perturbations, eventually reaching the [transition probability] on the [first] [time]. T Each diffusion step degenerates into a completely random noisy edge state.

[0033] The reverse denoising process is the mapping relationship that the model needs to learn. Based on the edge existence probability matrix output by the subsequent graph structure encoding module, it completes the gradual restoration from the noisy edge state to the real edge existence state.

[0034] Preferably, the asynchronous discrete diffusion module in this embodiment can be implemented using the GraphMaker asynchronous diffusion graph generation framework, or it can be implemented using other discrete diffusion graph generation frameworks that can model the discrete attributes of nodes and the existence state of edges respectively.

[0035] S3, Construct the graph structure encoding module; This step, based on the node attribute state, edge existence state, diffusion time step, and optional conditional control variables of the current diffusion step, outputs the node attribute recovery distribution and edge existence probability matrix. The module's input includes the node attribute noise state, edge existence noise state, diffusion time step, and optional conditional control variables of the current diffusion step. The module's internal processing flow is as follows: S31, The initial node represents the embedding; First, embedding mapping is performed on the input node attributes, conditional control variables, and diffusion time steps to obtain the initial node representation for each node: ; in, For the first Nodes in each diffusion step Discrete attribute states, For nodes The corresponding conditional control variables include node category labels and graph category labels. Embed functions for node attributes. Embedding function for conditional control variables, For the diffusion time step embedding function, For nodes The initial node representation. If the scene is generated unconditionally, then... The value is 0.

[0036] S32, Graph message passing updates node representation; The initial node representation is aggregated with neighborhood information through at least one layer of Graph Message Passing (MPNN) to iteratively update and obtain the final node representation: ; in, For the first After layer message passing, the node The expression, For nodes The set of neighboring nodes, For the first The edge exists in a state matrix or an edge exists in a probability matrix under each diffusion step. For the first The graph message passing function of the layer can be implemented using mainstream graph neural network layers such as GCN, GAT, and GIN.

[0037] S33, Dual-branch output prediction results; go through The final node representation obtained after layer graph message passing is used as input for node attribute prediction branches and edge structure prediction branches, and the corresponding prediction results are output: (1) Node attribute prediction branch output node Attribute recovery distribution ,satisfy: ; in The total number of message passing layers in the graph. Multilayer perceptron for predicting branches based on node attributes For nodes The probability distribution of each attribute category; (2) Edge structure prediction branch output node With nodes The probability of the existence of an edge ,satisfy: ; in It is the Sigmoid activation function. Multilayer perceptron for predicting branches in edge structures. This is an element-wise multiplication operation. For nodes With nodes There is a probability value between the two edges, which ranges from [0,1].

[0038] S4. Construct the distance matrix between nodes; This step constructs a node distance matrix based on the actual adjacency matrix and the predicted edge existence probability matrix, respectively. This matrix serves as the input for subsequent continuous homology feature extraction and topological constraint loss calculation. The complete process of global continuous homology calculation, node-level local barcode construction, and topological constraints is as follows: Figure 3 As shown. This invention supports three distance calculation methods: adjacency distance, resistance distance, and thermal core response distance, which can be flexibly selected according to the characteristics of the graph data and the requirements of the generation task. These three types of distances characterize the structural relationships between nodes from three levels: direct connectivity, global diffusion association, and multi-path connectivity. Based on this, filtering metrics with different structural representation capabilities are constructed, enabling the continuous cohomology module to extract multi-scale topological features under local adjacency, global propagation, and path redundancy conditions. The specific calculation methods for the three types of distances are as follows: (1) Adjacency distance; Adjacency distance is the most lightweight distance calculation method, suitable for small-scale graphs with simple structures and nodes. With nodes The adjacent distance satisfies: ; in, For nodes With nodes The probability of an edge existing between them is given by the real graph. Take the corresponding values ​​from the actual adjacency matrix (1 if an edge exists, 0 if no edge exists) for the generated graph. The corresponding values ​​of the edge existence probability matrix , For nodes With nodes The adjacency distance of is in the range of [0,1]. (2) Resistance distance; Resistive distance treats a graph as an equivalent circuit, characterizing the density of multipath connectivity between nodes. It is suitable for graph structures with a large number of indirect connections. With nodes The resistance distance satisfies: ; in, The graph Laplacian matrix is ​​constructed based on the true adjacency matrix or the edge existence probability matrix. for Moore-Penrose generalized inverse matrix, , They are nodes ,node The corresponding unit basis vectors, For nodes With nodes The resistivity distance; S43, thermonuclear response distance; The thermonuclear response distance is used to calculate the structural relationships between nodes based on the graph thermal diffusion process. It can reflect global structural relationships over a larger range and is suitable for large-scale graphs with complex structures. With nodes The thermonuclear response distance satisfies: ; ; in, These are thermonuclear scale parameters, supporting single-scale or multi-scale configuration. For the heat core matrix, For nodes ,node The corresponding thermonuclear response vector, For L2 norm operations, For nodes With nodes The thermonuclear response distance.

[0039] After the distance calculation is completed, the initial distance matrix between nodes is normalized: first, symmetry is performed to ensure that the nodes... arrive distance and arrive First, the distances between nodes are kept consistent. Second, the diagonal elements are set to zero, meaning that the distance from each node to itself is 0. Finally, all distance values ​​are normalized to the interval [0,1] to obtain the normalized distance matrix between nodes, which is used for subsequent continuous homology calculations.

[0040] S5. Calculate the persistent homology feature; This step constructs a filtered complex based on the normalized inter-node distance matrix, tracks the evolution of the topology at multiple scales, and obtains continuous homology features.

[0041] This embodiment uses Vietoris-Rips (VR) filtering complexes for topological feature extraction. The specific process is as follows: S51. Using a distance threshold as the filtering metric, from Start to gradually increase The value of is determined when the distance between node pairs is less than or equal to the current filtering scale. When, connect the node with an edge; when k The distance between any two nodes is less than or equal to 1. At that time, build k -The simplex, from which the following forms... Increase the progressively expanding VR-filtered complex sequence.

[0042] S52. Track the birth and death events of the topology as the filtering scale gradually increases: Zero-dimensional Connectivity component characteristics: When an isolated node first connects with other nodes to form a new connected component, the birth scale of that component is recorded. When two connected components merge, record the death scale of the smaller connected component. This type of feature is used to characterize the multi-scale connectivity organization and evolution process of a graph, corresponding to the complete process of a group of nodes gradually connecting and merging from isolation.

[0043] One-dimensional Loop characteristics: When multiple nodes form a closed loop and there are no smaller-scale edge fillers within the loop, record the birth scale of the loop. When a loop is split by subsequently added edges, record the dead phase of that loop. This type of feature is used to characterize the evolution process of closed paths and multi-node interaction structures in a graph, corresponding to higher-order interaction structures formed by three or more nodes.

[0044] S53. Integrate the birth and death scales of all topological features into a graph-level persistent barcode: ; in, For the first The birth scale of each topological feature corresponds to the filtering threshold for the first occurrence of that topological feature. For the first The death scale of a topological feature corresponds to the filtering threshold for the disappearance of that topological feature; This represents the total number of topological features. If there are infinitely long topological features that do not disappear within the current filtering scale, their death scale is truncated according to the preset maximum filtering scale to ensure that the subsequent vectorization process can be executed normally.

[0045] S6, Continuous Homogeneity Eigenvectorization; This step converts the discrete continuous barcode into a fixed-dimensional topological feature vector for subsequent loss calculation, including two types: global topological feature vector and node-level local topological feature vector.

[0046] S61, General PersLay Vectorization Process; This embodiment uses the PersLay persistent homology vectorization layer to convert discrete persistent barcodes into fixed-dimensional vectors. Unlike fixed summaries that only count the number of barcodes, average persistence length, or maximum persistence length, PersLay can learn the weights and combinations of different persistence intervals during training, enabling the model to automatically identify topological features that are more discriminative for the current graph generation task. The general processing flow is as follows: (1) Point feature transformation: transform each continuous interval Convert to point features : ; in, The duration of this topological feature is the length of its duration. The longer the duration, the higher the stability of the topological feature, which corresponds to a more stable high-order interaction structure in the graph. (2) Weight and Feature Mapping: Perform weight assignment and high-dimensional mapping on each feature point: ; in, It is a learnable weighting function used to assign higher weights to topological features with longer durations; This is a learnable feature mapping function used to map point features to a high-dimensional feature space; (3) Permutation-invariant aggregation: Perform permutation-invariant aggregation on the mapping results of all point features to obtain a fixed-dimensional topological feature vector: ; in, To achieve a permutation-invariant aggregation function, at least one of the following methods can be used: summation, mean, max pooling, or attention aggregation. The aggregation process is independent of the order of the persistence intervals, thus ensuring the stability of the topological features. The output is a fixed-dimensional topological feature vector, including a global topological feature vector and node-level local topological feature vectors.

[0047] S62, Calculation of global topological feature vector; Full-image-level continuous barcodes for real and predicted generated images By performing the PersLay vectorization process described above, the global topological feature vectors of the real graph are obtained respectively. With the global topological feature vector of the predicted generated graph This vector represents the multi-scale, multi-level topological structure features of the entire graph.

[0048] S63, Calculation of node-level local topological feature vectors; Based on the paired simplex information output during the continuous homology calculation process, node-level local topological feature vectors are constructed. The specific process is as follows: S631. Obtain the paired simplex information corresponding to each topological feature during the continuous homology calculation process, and determine the first... The duration interval of each topological feature The set of associated nodes :for Connected component characteristics: associated nodes are all nodes contained in the connected component; for Loop characteristics: associated nodes are all nodes that make up the loop.

[0049] S632. Assign each persistent interval to its associated node set. By analyzing the local persistent barcodes corresponding to all nodes, we can obtain the node-level local persistent barcodes for each node: ; in, For the first The duration interval of each topological feature is assigned to a node. The weights are uniform (i.e., all associated nodes have the same weight) or weighted based on the degree of participation of the node in the simplex constituting the topological feature (the more simplexes the node participates in, the higher the weight); the node-level local persistence barcode is used to characterize the evolution of connected components, loop structure, local closure structure and higher-order interaction relationship in which the target node participates or is associated. S633. Perform PersLay vectorization processing on the node-level local persistent barcode of each node to obtain the node... The corresponding node-level local topological feature vector: ; in, This is a continuously coherent vectorization layer. The parameter configuration of the PersLay layer used for local barcode vectorization can be independently set with respect to the PersLay layer used for global topological feature vector calculation, allowing for adaptation to different distribution characteristics of global and local topological features.

[0050] S7. Construct the training loss function and perform joint training; This step constructs a training loss function that includes node attribute recovery loss, edge structure recovery loss, and topological constraint loss. The asynchronous discrete diffusion graph generation module and the graph structure encoding module are then jointly trained. The overall training process is as follows: Figure 2 As shown.

[0051] S71, Basic Loss Calculation; Node attribute recovery loss The node attribute generation accuracy is calculated based on the difference between the node attribute recovery distribution output by the graph structure encoding module and the actual node attributes. Class cross-entropy loss is used to constrain the accuracy of the generated node attributes. ; in, This represents the total number of nodes. This represents the total number of categories for node attributes. For nodes The true attributes Class tags, For nodes The attribute recovery distribution of the first The predicted probability of a class.

[0052] Edge structure recovery loss The edge existence probability matrix is ​​calculated based on the difference between the edge existence probability matrix output by the graph structure encoding module and the actual edge existence state. A binary cross-entropy loss is used to constrain the accuracy of edge structure generation. ; in, For nodes in the true adjacency matrix With nodes The edge exists in a state. The probability of the predicted edge existing.

[0053] S72, Calculation of topological constraint loss; The topological constraint loss includes global topological constraint loss and node-level local topological constraint loss. These two types of constraints are independent configurable branches, supporting independent enabling, disabling, setting loss weights, and configuring trigger intervals. Node attribute recovery loss and edge structure recovery loss ensure the feasibility of the local generation process. Topological loss, as a structure correction term, is used to suppress candidate structures with good edge-level fitting but distorted overall organization, without replacing the basic generation target. (1) Global topology constraint loss : Used to constrain the consistency of the multi-scale topological structure of the generated graph and the real graph, calculating the L2 norm squared difference of the global topological eigenvectors of the real and generated graphs: ; in, For real images The corresponding global topological feature vector, Generate a graph for the current prediction The corresponding global topological feature vector; during calculation, gradient truncation is performed on the global topological features of the real graph to block gradient backpropagation of the real graph topological features and avoid model training collapse.

[0054] (2) Node-level local topology constraint loss : Used to constrain the consistency of the local higher-order interaction structure around the corresponding nodes in the real graph, and calculate the average of the squared differences of the L2 norm of the local topological eigenvectors of all valid nodes: ; in, The effective set of nodes consists of non-isolated nodes participating in the calculation of topological features. For real images Middle node The corresponding node-level local topological feature vector, Generate a graph for the current prediction In and nodes Aligned node-level local topological feature vectors; gradient truncation is performed on the local topological features of the real graph during computation to block gradient backpropagation of the real graph's topological features and avoid model training collapse.

[0055] S73, Total Loss and Sparse Triggering Strategy; The overall formula for calculating the training loss function is: ; in, The pre-configured topology constraint loss weights can be adjusted according to task requirements; This is a topology constraint trigger indicator; For the currently enabled topology constraint loss, including , At least one of the following: when only global topology constraints are enabled When only local topology constraints are enabled When both types of constraints are enabled simultaneously ,in , These are independent weights for global and local constraints, respectively.

[0056] Topology constraint trigger indicator The value is determined by a preset sparse triggering rule: when the current training batch number satisfy hour, Calculate the corresponding topological constraint loss and participate in parameter updates; otherwise... The current batch only uses node attribute recovery loss and edge structure recovery loss for training, where The pre-configured topology constraint trigger interval can be adjusted according to the graph size: 5~20 for small-scale graphs and 20~100 for large-scale graphs, to balance the constraint effect and training cost.

[0057] The triggering intervals for the two types of topological constraint branches can be configured independently, further reducing the computational overhead of training large-scale graphs.

[0058] S74, Joint Training Process; The following steps are executed iteratively according to the preset training batches until the loss converges or the preset training rounds are reached: 1. Randomly select training samples and, through the forward noise addition process of the asynchronous discrete diffusion map generation module, obtain the first... Noise state of node attributes in each diffusion step With noisy states on the edges ; 2. , diffusion time step The optional conditional control variables are input into the graph structure encoding module to obtain the node attribute recovery distribution and edge existence probability matrix; 3. Calculate the corresponding training loss based on whether the current batch meets the triggering conditions; 4. Update the trainable parameters of the asynchronous discrete diffusion graph generation module and the graph structure encoding module based on loss backpropagation, including the graph message passing layer parameters, the prediction branch multilayer perceptron parameters, and the PersLay vectorization layer parameters.

[0059] S8. Reverse denoising sampling generates a discrete attribute map of the target; This step utilizes the trained asynchronous discrete diffusion map generation module to generate the target discrete attribute map by starting from the random noise state and performing multi-step reverse denoising sampling.

[0060] S81, Initial state settings; With total diffusion step size The corresponding completely random node attribute noise state and completely random edge noise state are used as the initial reverse sampling state. S82, progressive reverse noise reduction; from arrive Perform reverse denoising updates sequentially: 1. Set the node attribute noise state for the current diffusion step. Noise exists on the edge. diffusion time step The graph structure encoding module, after training, is input with conditional control variables to obtain the node attribute recovery distribution. The probability matrix of the existence of edges ; 2. The first step is to update the discrete diffusion reverse transfer rule to obtain the... Step node attribute state With edge existence state The reverse transfer process satisfies: ; ; S83, Generate and output the results; When iterates to At that time, the final set of node attributes and edge adjacency matrix are output to obtain the target discrete attribute graph.

[0061] This embodiment uses structural and topological indices to experimentally and quantitatively evaluate the effectiveness of the generated graph. The experiment does not evaluate all structural properties through a single overall score, but rather examines the technical effects of basic generation, global / local topological constraints, and different distance constructions on graph size, local closure, connectivity organization, loop structure, and distribution matching. The evaluation indices include: 1. Basic structural statistical indicators: number of nodes, number of edges, and number of triangles, which respectively represent the overall scale of the generated graph, the density of edges, and the retention level of local ternary closed structures; 2. Topological structure metric: Zero-dimensional homology number (Number of connected components), one-dimensional homology number (Number of independent loops) respectively measures the restoration effect of the overall macroscopic connectivity organization structure and the high-order loop structure of the graph; 3. Distribution difference index: Degree MMD and Spectral MMD quantify the differences in node degree distribution and spectral feature distribution between the generated graph and the real graph, respectively. The lower the value, the higher the distribution matching degree.

[0062] The experimental parameters are consistent with the configuration of the project source code. The definitions, values, and descriptions of each parameter are shown in Table 1 below: Table 1 - Unified Hyperparameter Configuration Table for Experiments

[0063] This embodiment sets up multiple comparison schemes: a basic unconstrained asynchronous diffusion scheme (Base), a scheme with global persistent cohomology constraints (GlobalPH, abbreviated G), and a scheme with node-level local persistent cohomology constraints (LocalPH, abbreviated L). GlobalPH and LocalPH are respectively paired with adjacency distance, thermal core response distance, and resistivity distance, resulting in six topology constraint schemes: G-Adj, G-Heat, G-Res, L-Adj, L-Heat, and L-Res. The above comparisons are performed within the same basic generation framework to isolate the technical contributions of the topology constraint hierarchy and the distance construction itself.

[0064] (a) Wisconsin university website hyperlink network verification; The Wisconsin hyperlink network was used as the training dataset. This dataset contains 251 webpage nodes and 450 hyperlink edges. The node attributes are discrete features of the webpage text content, and it can be used for scenarios such as university website structure design and webpage navigation path simulation. The quantitative results of the generation effect are shown in Table 2 below: Table 2 - Summary of representative validation results for the Wisconsin dataset

[0065] The verification results show that: ① After introducing GlobalPersLay and LocalPersLay, the consistency of the node degree distribution in the generated graph is significantly improved. The Degree MMD of the Base method is 2.662, while the Degree MMD of each PersLay configuration is reduced to 0.518-0.646, indicating that the continuous homology feature can provide an effective topological constraint signal for the graph generation process, making the node connection distribution of the generated graph closer to the original graph.

[0066] ② G-Heat has the lowest Degree MMD at 0.518, which is about 80.5% lower than Base; its Spectral MMD is 0.133, which is also the best result among all PersLay configurations, indicating that GlobalPersLay based on thermal diffusion distance can simultaneously improve node degree distribution and maintain good spectral structure consistency. G-Adj generates 103.5 edges, 160.3 connected components, and 12.8 independent loops, achieving good overall structure recovery results in the PersLay configuration, indicating that adjacency distance can directly preserve edge connectivity and loop information.

[0067] ③ Comparing GlobalPersLay and LocalPersLay reveals that GlobalPersLay performs more stably in Degree MMD, Spectral MMD, and connectivity structure metrics, indicating that the global persistent homology vector can effectively characterize the overall connectivity pattern of small-scale graphs. This result validates the feasibility of constructing persistent homology features by different distances and using GlobalPersLay to impose global structural constraints on the graph generation model.

[0068] In summary, on the Wisconsin dataset, GlobalPersLay can significantly improve the consistency of node degree distribution. Among them, G-Heat performs best in degree distribution and spectral structure, while G-Adj performs well in edge structure, connected components and loop recovery. This shows that different distance constructions can adjust the generated graph structure from the perspectives of probabilistic connectivity, diffusion propagation and multi-path connectivity.

[0069] (ii) Cora academic citation network verification; The Cora academic citation network was used as the training dataset. This dataset contains 2708 paper nodes and 5278 citation edges. The node attributes are binary bag-of-words features of paper keywords, which can be used for citation pattern analysis, academic network evolution simulation, and other scenarios. The quantitative results of the generation effect of the selected representative schemes are shown in Table 3 below: Table 3 - Summary of representative validation results for the Cora dataset

[0070] The verification results show that: ① On the Cora dataset, the introduction of GlobalPersLay or LocalPersLay significantly improved both the Degree MMD and Clustering MMD of the generated graph. The Degree MMD of the Base method was 0.993, while the Degree MMD of each PersLay configuration decreased to 0.0296–0.0766; the Clustering MMD of the Base method was 3.2091, while the Clustering MMD of each PersLay configuration decreased to 0.219–1.235, indicating that this method can simultaneously improve the node degree distribution and local clustering structure of the generated graph.

[0071] ② In the GlobalPersLay configuration, G-Heat has the lowest Degree MMD at 0.0296, a decrease of approximately 97.0% compared to Base, indicating that the continuous cohomology feature constructed based on thermal diffusion distance can effectively capture multi-scale propagation relationships between nodes. G-Res has a Degree MMD of 0.0303 and a Clustering MMD of 1.094, yielding 724 connected components and 1500 independent loops, demonstrating good overall structure preservation capability in the global configuration. These results demonstrate that resistive distance can utilize multi-path connectivity information between nodes to provide a stable structural representation for global topology constraints.

[0072] ③ In the LocalPersLay configuration, L-Res achieved good overall results. It generated 3527 edges and 1578 triangles, with the number of triangles approaching the original image's 1630; The value is 1587, the Degree MMD is 0.0325, and the Clustering MMD is 1.003. Compared with Base, L-Res improves on multiple metrics such as number of edges, number of triangles, number of connected components, number of loops, degree distribution, and clustering distribution, indicating that LocalPersLay based on resistive distance can effectively constrain the local connectivity structure and higher-order closure relationships around nodes.

[0073] L-Heat achieved a Clustering MMD of 0.219, the lowest among all configurations, indicating that local topological constraints based on thermal diffusion distance can significantly enhance the characterization of node neighborhood clustering patterns and local closed structures. Different LocalPersLay configurations exhibited different structural adjustment characteristics, verifying that this method can selectively control local connectivity, triangles, and loop structures by choosing the distance type.

[0074] In another set of Cora Native verifications, the historical G-Res configuration generated 4224 edges and 1671 triangles, achieving 80.0% of the original image's edge count and 102.5% of its triangle count, respectively. and The values ​​are 613 and 2129, respectively. This result further demonstrates that GlobalPersLay based on resistive distance can effectively recover the edge size, triangle structure, and number of independent loops in the graph, and has good global high-order structure preservation capability.

[0075] In summary, Cora's validation results show that both GlobalPersLay and LocalPersLay can effectively improve the structural consistency of the generated graph. G-Heat performs best in restoring the node degree distribution, while L-Heat performs best in restoring the clustering coefficient distribution. G-Res can better maintain the global edge structure, the number of triangles, and loops, while L-Res achieves a good overall effect in balancing local closed structures and global distribution indices. This demonstrates that our method can configurably adjust the multi-scale connectivity and high-order interaction structure of the generated graph through global or local PersLay constraints and different distance constructions.

[0076] Therefore, this invention provides a large-scale graph generation method based on continuous cohomology high-order interactive structure constraints. By adopting asynchronous discrete diffusion node-edge dual independent modeling, multi-type node distances are used to characterize the structural relationships between nodes at different levels. Based on continuous cohomology, a global and node-level local two-layer topological constraint is constructed. PersLay is used to perform learnable weighting, mapping, and aggregation on continuous intervals to achieve end-to-end optimization of continuous cohomology features. At the same time, a sparse triggering strategy is adopted to reduce the computation frequency and training overhead of continuous cohomology. Based on this, a complete discrete attribute graph generation system is constructed, consisting of "data preprocessing - diffusion framework construction - topological feature extraction - joint constraint training - backsampling generation". This system solves the pain points of existing graph generation methods, such as difficulty in fitting multi-node high-order interaction structures, traditional topological constraints only controlling global topology and failing to constrain fine-grained local node organization, and difficulty in integrating continuously homogeneous discrete features into neural networks and excessive high-frequency computational overhead. It effectively improves the matching degree between generated graphs and real graphs in multiple dimensions such as node attributes, edge structure, global topology, and local high-order organization, enhances the adaptability of different types of graph data, reduces the computational cost of large-scale graph training, and ultimately provides an efficient and reliable technical solution for simulated graph generation needs, which can support the simulation, analysis, and optimization design of various graph structure data.

[0077] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for generating large-scale graphs based on continuous homology high-order interaction structure constraints, characterized in that, Includes the following steps: S1. Obtain real attribute graph data, and preprocess the real attribute graph data to obtain basic graph data containing node attribute encoding, edge existence state encoding, and real adjacency matrix. S2. Construct an asynchronous discrete diffusion graph generation module to perform forward noise addition and reverse noise reduction discrete diffusion modeling for the discrete attributes of nodes and the existence state of edges, respectively. S3. Construct a graph structure encoding module. Based on the node attribute state, edge existence state, and diffusion time step of the current diffusion step, output the node attribute recovery distribution and edge existence probability matrix. Construct a node distance matrix based on the true adjacency matrix and the predicted edge existence probability matrix respectively. Calculate the continuous cohomology features based on the node distance matrix and convert them into fixed-dimensional topological feature vectors. Construct a training loss function that includes node attribute recovery loss, edge structure recovery loss, and topological constraint loss. Jointly train the asynchronous discrete diffusion graph generation module and the graph structure encoding module. S4. Using the trained asynchronous discrete diffusion map generation module, starting from the random noise state, generate the target discrete attribute map through multi-step reverse denoising sampling.

2. The large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 1, characterized in that, The asynchronous discrete diffusion graph generation module includes mutually independent node attribute diffusion submodules and edge structure diffusion submodules. The node attribute diffusion submodule performs forward noise addition and reverse noise reduction modeling on the discrete attributes of nodes. The forward noise addition process satisfies the following: ； in, For the first The preceding node attribute state of each diffusion step. For the first The node attribute noise state after each diffusion step and noise addition For the pre-configured fixed node attribute state transition matrix, Represents category distribution; The edge structure diffusion submodule performs forward denoising and reverse denoising modeling on the edge existence state. The forward denoising process satisfies: ； in, For the first The preceding edges of each diffusion step exist in a state. For the first The edges after each diffusion step with added noise have a noisy state. A state transition matrix exists for a pre-configured fixed edge; The forward noise addition process and reverse noise reduction process of the node attribute diffusion submodule and the edge structure diffusion submodule are independent of each other, and independently model the node attribute distribution and edge structure distribution respectively.

3. The large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 1, characterized in that, The processing steps of the graph structure encoding module include: First, embedding mapping is performed on the input node attributes, conditional control variables, and diffusion time steps to obtain the initial node representation: ； in, For the first Nodes in each diffusion step Discrete attribute states, For nodes The corresponding conditional control variables include node category labels and graph category labels. Embed functions for node attributes. Embedding function for conditional control variables, For the diffusion time step embedding function, For nodes The initial node representation; The initial node representation is updated by aggregating neighborhood information through at least one graph messaging layer to obtain the final node representation: ； in, For the first After layer message passing, the node The expression, For nodes The set of neighboring nodes, For the first The edge exists in a state matrix or an edge exists in a probability matrix under each diffusion step. For the first Layered graph message passing functions; The final node represents the node attribute prediction branch and the edge structure prediction branch as inputs, respectively, and the output node attribute recovery distribution and edge existence probability matrix. The node attribute prediction branch outputs the node... Attribute recovery distribution satisfy: ； in The total number of message passing layers in the graph. A multilayer perceptron for predicting branches based on node attributes; The nodes of the edge structure prediction branch output With nodes The probability of the existence of an edge satisfy: ； in It is the Sigmoid activation function. Multilayer perceptron for predicting branches in edge structures. This is an element-wise multiplication operation.

4. The large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 1, characterized in that, The distance matrix between nodes is constructed using at least one of the following: adjacency distance, resistance distance, and thermonuclear response distance. When adjacency distance is used, nodes With nodes The distance satisfies: ； in, For nodes With nodes The probability of an edge existing between them is given by the real graph. Take the corresponding values ​​from the actual adjacency matrix for the generated graph. Take the corresponding value of the edge existence probability matrix. For nodes With nodes The adjacency distance; When using resistive distance, nodes With nodes The distance satisfies: ； in, The graph Laplacian matrix is ​​constructed based on the true adjacency matrix or the edge existence probability matrix. for Moore-Penrose generalized inverse matrix, , They are nodes ,node The corresponding unit basis vectors, For nodes With nodes The resistivity distance; When using thermonuclear response distance, nodes With nodes The distance satisfies: ； ； in, For thermonuclear scale parameters, For the heat core matrix, For nodes ,node The corresponding thermonuclear response vector, For L2 norm operations, For nodes With nodes The thermonuclear response distance.

5. The large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 1, characterized in that, The specific process of calculating the persistent homology feature based on the distance matrix between nodes is as follows: A Vietoris-Rips filtering complex is constructed based on the inter-node distance matrix, and the topological evolution at different filtering scales is tracked to obtain a zero-dimensional complex. Continuous features of connected components and one-dimensional Graph-level persistent barcodes with loop persistence features: ； in, For the first The birth scale of each topological feature corresponds to the filtering threshold for the first occurrence of that topological feature. For the first The death scale of a topological feature corresponds to the filtering threshold for the disappearance of that topological feature; This represents the total number of topological features. The zero dimension The connectivity component persistence feature is used to characterize the multi-scale connectivity organization evolution process of a graph, the one-dimensional Loop persistence features are used to characterize the evolution of closed paths and multi-node interaction structures in a graph.

6. The large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 5, characterized in that, The process of converting persistent homology features into fixed-dimensional topological feature vectors is as follows: Each duration interval Convert to point features : ； in, The duration of this topological feature is the length of its duration; the longer the duration, the higher the stability of the topological feature. Based on the PersLay vectorization layer, all point features are mapped and aggregated to obtain a fixed-dimensional topological feature vector: ； in, It is a learnable weighting function used to assign higher weights to topological features with longer durations; This is a learnable feature mapping function used to map point features to a high-dimensional feature space; It is a substitution-invariant aggregation function; The output is a fixed-dimensional topological feature vector, including a global topological feature vector and node-level local topological feature vectors.

7. A large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 6, characterized in that, The specific process for constructing the node-level local topological feature vector is as follows: Obtain the paired simplex information corresponding to each topological feature during the continuous homology calculation process, and determine the first... The duration interval of each topological feature The set of associated nodes ; Each persistent interval is assigned to the local persistent barcodes corresponding to all nodes in its associated node set, resulting in the node-level local persistent barcodes for each node: ； in, For the first The duration interval of each topological feature is assigned to a node. The weights are either uniform weights or weighted weights based on the degree of participation of nodes in the simplex that constitutes the topological feature. Perform PersLay vectorization on the node-level local persistent barcode of each node to obtain the node. The corresponding node-level local topological feature vector: ； in, As a continuous homology vectorization layer, its parameter configuration is set independently of the PersLay layer used for global topological feature vector calculation.

8. The large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 1, characterized in that, The topology constraint loss includes global topology constraint loss and node-level local topology constraint loss; The global topological constraint loss is used to constrain the consistency of the multi-scale topological structure of the generated graph and the real graph, and the formula is: ； in, For real images The corresponding global topological feature vector, Generate a graph for the current prediction The corresponding global topological feature vector; The node-level local topological constraint loss is used to constrain the consistency of the generated graph with the local high-order interaction structure around the corresponding node in the real graph. The formula is as follows: ； in, For the set of valid nodes, For real images Middle node The corresponding node-level local topological feature vector, Generate a graph for the current prediction In and nodes Aligned node-level local topological feature vectors.

9. A large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 7, characterized in that, The overall formula for calculating the training loss function is as follows: ； in, To recover the loss for node attributes, For edge structure recovery loss, For pre-configured topology constraint loss weights, For topology constraint trigger indicator, For the currently enabled topology constraint loss, including , At least one of them; Topology constraint trigger indicator The value is determined by a preset sparse triggering rule: when the current training batch number satisfy hour, ,otherwise ,in The pre-configured topology constraint trigger interval; The global topology constraint loss and the node-level local topology constraint loss are independent configurable branches, which can be enabled, disabled, have their loss weights set, and trigger intervals configured independently.

10. A large-scale graph generation method based on continuous homology high-order interaction structure constraints according to claim 2, characterized in that, The multi-step reverse denoising sampling process is specifically as follows: With total diffusion step size The corresponding completely random node attribute noise state and completely random edge noise state are used as the initial reverse sampling state. from arrive Successive reverse denoising update: update the node attribute noise state of the current diffusion step. Noise exists on the edge. diffusion time step The graph structure encoding module, after training, is input with conditional control variables to obtain the node attribute recovery distribution. The probability matrix of the existence of edges The first step is to update the discrete diffusion back transfer rule to obtain the second step. Step node attribute state With edge existence state The reverse transfer process satisfies: ； ； When iterates to At that time, the final set of node attributes and edge adjacency matrix are output to obtain the target discrete attribute graph.

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