Search engine optimization method and system based on reformed graph neural network

Abstract

The invention belongs to the technical field of machine learning, and provides a search engine optimization method and system based on a reformed graph neural network, and the method comprises the steps: obtaining a search demand keyword of a user; performing user demand search according to the obtained search demand keyword and the search engine model; in a user demand search process, an optimal search result is obtained by searching an optimal parameter of the search engine model, and optimization of the search engine is completed; wherein the search engine model adopts a reformed graph neural network, in the process of searching the optimal parameters of the search engine model, stable fixed points of reformed group transformation are searched through reformed group flow analysis, and feedback adjustment of the parameters of the search engine model is carried out according to the parameters corresponding to the stable fixed points to obtain the optimal parameters; by accurately determining the optimal parameters of the search engine model, the search efficiency is greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of machine learning technology, specifically relating to a search engine optimization method and system based on renormalized graph neural networks. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of internet technology and the increasing abundance of online resources, users can enter keywords related to their search needs into search engines to obtain the information they require, thus receiving search results. Search engines then present these results, relevant to the user's entered keywords, in a specific order.

[0004] Matching and ranking search results with the user's search keywords based on their relevance can improve search efficiency. However, different search engine models can lead to significant differences in search results and efficiency. Furthermore, even within the same search engine model, different control parameters can result in variations in search results and efficiency.

[0005] Critical phenomena refer to the special physical properties exhibited by matter in its critical state and adjacent regions. They can manifest as continuous changes in order parameters during phase transitions, exhibiting characteristics such as specific heat divergence and critical opalescence. The critical index quantitatively describes its power-law behavior; its theoretical framework encompasses continuous phase transition mechanisms, scaling laws, and universality. Modern research has extended critical phenomena to complex systems (such as climate critical elements and stock market evolution) and the field of quantum phase transitions, achieving simulations of quantum multicritical phenomena.

[0006] The concept of criticality can be introduced into graph neural networks. When a graph neural network reaches a critical state, it exhibits optimal propagation and representation capabilities. The control parameters (such as temperature parameters) corresponding to this state are called critical temperatures. Accurately determining the critical temperature is crucial for optimizing the architecture design and training process of graph neural networks.

[0007] Neural networks are primarily used to process vector or sequential data, while graph neural networks (GNNs) can effectively handle unstructured graphical data but are not adept at active reasoning. The (non-trivial) fixed points of the renormalization equations correspond to phase transition points in critical systems. The coupling coefficient of the system is a temperature-like parameter that determines the strength of system interactions; the critical temperature of the system can be directly calculated. When the neural network structure is too small to be clearly seen, or too large to be fully understood, the renormalization group method is needed to continuously highlight the important features of the system and remove the unimportant ones. The renormalization group extracts key features of the system through continuous coarsening; shallower neural networks encode small-scale features, while deeper ones encode large-scale features. In multi-scale dynamic modeling, information at different scales does indeed play different roles: high-frequency information at small scales is helpful for short-term predictions, while low-frequency information at large scales plays a crucial role in long-term modeling; however, it is impossible to predict all the information in a graph neural network, only a simplified representation is needed.

[0008] Diffusion dynamics is a natural framework for describing the information propagation process in graph neural networks. By treating node features as particles, the propagation of information on the graph can be compared to the diffusion process of particles in the network structure. However, it has high computational complexity, low accuracy, and lacks certain spontaneous associative reasoning capabilities. Summary of the Invention

[0009] To address the aforementioned problems, this invention proposes a search engine optimization method and system based on renormalized graph neural networks, which significantly improves search efficiency by accurately determining the optimal parameters of the search engine model.

[0010] According to some embodiments, the first aspect of the present invention provides a search engine optimization method based on a renormalized graph neural network, employing the following technical solution: A search engine optimization method based on renormalized graph neural networks includes: Obtain the user's search keywords; Based on the obtained search keywords and search engine model, conduct user demand searches; In the process of user demand search, the optimal search results are obtained by finding the optimal parameters of the search engine model, thus completing the search engine optimization. The search engine model employs a renormalized graph neural network. In the process of finding the optimal parameters of the search engine model, the stable fixed point of the renormalized group transformation is found through renormalized group flow analysis. The parameters of the search engine model are adjusted based on the parameters corresponding to the stable fixed point to obtain the optimal parameters.

[0011] As a further technical limitation, in the process of the renormalized group flow analysis, parameter space points are obtained through iterative renormalization transformation, and the evolution behavior of the obtained parameter space points under the renormalized flow is analyzed to find the stable fixed points of the renormalized group transformation.

[0012] Furthermore, the obtained parameter space points include space points corresponding to effective temperatures. Based on the effective temperatures corresponding to the stable fixed points of the found renormalization group transformation, the critical temperature is determined, and the control parameters corresponding to the critical temperature are the optimal parameters.

[0013] Furthermore, when the initial temperature near At that time, the renormalized flow hovers near the fixed point, and the correlation length is calculated. The divergent behavior is used to help determine the critical temperature, i.e. ,in, This represents the critical index.

[0014] Furthermore, during the feedback adjustment of the search engine model parameters, based on the critical temperature determined by the renormalization analysis, the parameters in the graph neural network, including the noise intensity in message passing, the threshold in the activation function, and the scaling factor in the attention mechanism, are adjusted in combination with the critical temperature adjustment. The initial temperature is then adjusted to be infinitely close to the determined critical temperature, thus completing the feedback adjustment of the graph neural network parameters.

[0015] As a further technical limitation, before the renormalization group flow analysis, the diffusion coefficient tensor of the graph neural network is obtained, and the obtained graph neural network diffusion coefficient tensor is renormalized to obtain a new graph structure of the graph neural network and its corresponding node feature matrix.

[0016] Furthermore, in the process of obtaining the diffusion coefficient tensor of the graph neural network, mass or energy transfer is simulated through a message-passing mechanism. The diffusion process can be expressed in the form of a partial differential equation, i.e. ;in, This represents the diffusion coefficient tensor of the graph neural network. Indicates time, Represents the node feature matrix; This represents the gradient operator, which is the total differential in all directions of space.

[0017] Furthermore, the graph structure of the graph neural network is coarsened. Based on the graph neural network diffusion coefficient tensor and the coarsened graph structure, node clustering or graph pooling operations are combined to obtain a new graph structure and its corresponding node feature matrix; the renormalization transformation satisfy ;in, Represents the node feature matrix, Representing the graph structure, This represents a new graph structure. The node feature matrix represents the new graph structure.

[0018] As a further technical limitation, when the activation degree of the nodes in the graph neural network exhibits a power-law distribution rather than an exponential distribution, the nodes in the graph neural network show long-range spatial correlations; the dynamics show a critical slowing phenomenon, that is, the relaxation time becomes significantly longer; at this point, the graph neural network truly reaches the critical state.

[0019] According to some embodiments, a second aspect of the present invention provides a search engine optimization system based on a renormalized graph neural network, employing the following technical solution: A search engine optimization system based on a renormalized graph neural network includes: The acquisition module is configured to acquire the user's search query keywords; The search module is configured to perform user-defined searches based on the obtained search query keywords and search engine model. The optimization module is configured to find the optimal parameters of the search engine model during the user's search process to obtain the optimal search results and complete the search engine optimization. The search engine model employs a renormalized graph neural network. In the process of finding the optimal parameters of the search engine model, the stable fixed point of the renormalized group transformation is found through renormalized group flow analysis. The parameters of the search engine model are adjusted based on the parameters corresponding to the stable fixed point to obtain the optimal parameters.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: The search engine model in this invention employs a renormalized graph neural network. The scale invariance is extracted through renormalization group transformation to describe the parameter space dynamics of the graph neural network. The method based on diffusion dynamics renormalization is used to reach the critical temperature of the graph neural network model. The renormalized flow method is used, with the help of the Laplace diffusion equation, to efficiently determine the critical temperature (i.e., the optimal parameters), which greatly improves the search efficiency. Attached Figure Description

[0021] The accompanying drawings, which form part of this embodiment, are used to provide a further understanding of this embodiment. The illustrative embodiments and their descriptions are used to explain this embodiment and do not constitute an improper limitation of this embodiment.

[0022] Figure 1 This is a flowchart of the search engine optimization method based on renormalized graph neural network in Embodiment 1 of the present invention; Figure 2 This is a structural block diagram of the search engine optimization system based on renormalized graph neural network in Embodiment 3 of the present invention. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0025] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0026] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0027] Example 1 Embodiment 1 of this invention introduces a search engine optimization method based on a renormalized graph neural network.

[0028] Methods for parameter optimization based on empirical tuning or grid search are inefficient and lack theoretical guidance; Monte Carlo simulations and molecular dynamics methods, while applicable to critical behavior, are computationally expensive and difficult to apply directly to large-scale graph neural networks. Existing renormalization group methods are primarily designed for regular lattice systems and lack adaptability to irregular graph structures; diffusion dynamics is a natural framework for describing the information propagation process in graph neural networks. By treating node features as particles, the propagation of information on the graph can be analogized to the diffusion process of particles in the network structure.

[0029] The renormalization group is a powerful theoretical framework used to handle systems with multiple degrees of freedom. It can transform the configuration description and associated model node parameters at different resolution levels. The renormalization group also provides a method for identifying phase transition critical points and studying the behavior of systems around them. This embodiment extends the concept of the renormalization group to complex graph neural networks. The renormalization group is a mathematical tool for examining system changes at different scales; changes in scale are called "scale transformations." The renormalization group is closely related to "scale invariance" and "conformal invariance," both of which are related to self-similarity. In renormalization theory, a system at a certain temperature is self-similar to a smaller temperature, but the parameter values ​​describing their composition are different. The system's variables are described by the interconnection parameters between the system's components.

[0030] During renormalization, the complex details of adjusting numerous parameters in the model often disappear; the parameters remain but do not affect the overall image. After appropriate scaling, the coarse-grained system can be described by a Hamiltonian of the same form as the initial model and a set of renormalized parameters. The transformation of parameters from finer to coarser scales constitutes the renormalization group. Repeatedly applying this coarsening process to the model produces a so-called parameter flow, which has fixed points (i.e., special values ​​that remain unchanged under renormalization). These parameters correspond to the critical points of the universal scaling law followed by the model.

[0031] Renormalization groups utilize this multi-level, multi-scale approach. Specifically, at each level, the model simplifies and reprocesses the results from the previous level (e.g., merging certain pixels into a block or discretizing continuous speech signals into several notes), forming a higher-level, more abstract description. Even the largest datasets are "compressed" layer by layer into simple elements and relationships, significantly reducing the computational burden. Simultaneously, these higher-level "concepts" or "states" can be computed across time and space, allowing the model to make effective inferences without getting bogged down in every minute dimension.

[0032] After renormalization, the model generalizes the results through active learning; that is, during the learning process, it selects some data from a large number of images for training by optimizing its parameters (such as the compression method and the chosen block transformation method). Then, the model calculates how to compress this data (i.e., through block transformation) to find the most efficient compression method, so that the compressed image still retains as much key information as possible. This active learning ensures a scale-invariant mapping from pixels to object or digit categories, preserving mutual information between pixels.

[0033] Graph Neural Networks (GNNs) are deep learning models specifically designed for processing graph data. While traditional neural networks primarily handle vector or sequential data, GNNs can effectively process unstructured graphical data. GNNs capture information propagation and interactions within graph data by learning connection patterns and topological structures between nodes. They achieve representation learning for the entire graph by aggregating and updating the features of each node and its neighbors.

[0034] In graph neural networks (Graph Neural Networks), node and edge representations are typically defined to better represent the relationships and features between nodes. The fundamental principle of Graph Neural Networks is to progressively propagate and update node feature information through a multi-layered neural network structure, thereby learning and representing global information about the entire graph. This approach helps Graph Neural Networks retain local structural information while also considering the topological structure and relationships between features of the global graph, thus improving their ability to model graph data.

[0035] Graph neural networks can be based on neighborhood aggregation (or message passing) strategies, where each node updates its representation by aggregating and transforming information from its neighbors, including the following steps: Message aggregation, which is the collection of information from the neighbors of a given node, involves aggregation operations on the feature vectors of neighboring nodes, such as summation, averaging, or maximization.

[0036] An update is a process of combining the features of the current node with information from its neighbors to update the node's representation. This update process is usually implemented through a neural network (such as a fully connected layer).

[0037] Repetition, meaning that the above process can be repeated multiple times, allows information to be transmitted over a greater distance with each iteration, thereby capturing graph structure features over a wider range.

[0038] The output, i.e. the final embedding of the nodes, can be utilized in various ways, such as directly for node-level tasks, or by aggregating the representations of all nodes for graph-level tasks.

[0039] Graph Neural Networks (GNNs) have become the primary tool for processing graph-structured data, and are widely used in fields such as social network analysis, recommender systems, prediction of chemical molecular properties, and knowledge graphs. However, GNNs face many challenges during training and inference, particularly issues such as over-smoothing, over-squashing, and vanishing / exploding gradients, which severely impact the performance and stability of deep GNNs.

[0040] The renormalization group method, introduced by Wilson in 1971 to the study of critical phenomena, provides a powerful tool for solving this problem. Its core idea is to eliminate detailed degrees of freedom through scaling transformations, preserving the key physical characteristics of the system, thereby analyzing the universal properties of phase transition points. Traditional real-space renormalization methods include Kadanoff's block spin transformation and the Migdal-Kadanoff approximation scheme. While these methods have achieved some success, they often suffer from insufficient accuracy or excessive computational complexity when dealing with complex systems.

[0041] Therefore, this embodiment uses a graph neural network based on diffusion dynamics and renormalization group theory to optimize the search engine, specifically as follows: Figure 1 The illustrated search engine optimization method based on a renormalized graph neural network includes: Obtain the user's search keywords; Based on the obtained search keywords and search engine model, conduct user demand searches; In the process of user demand search, the optimal search results are obtained by finding the optimal parameters of the search engine model, thus completing the search engine optimization. The search engine model employs a renormalized graph neural network. In the process of finding the optimal parameters of the search engine model, the stable fixed point of the renormalized group transformation is found through renormalized group flow analysis. The parameters of the search engine model are adjusted based on the parameters corresponding to the stable fixed point to obtain the optimal parameters.

[0042] It should be noted that the specific process for obtaining the optimal parameters of the renormalized graph neural network is as follows: Obtain the graph structure and node feature matrix; Based on the obtained node feature matrix, the graph neural network diffusion coefficient tensor is obtained; The graph structure and the graph neural network diffusion coefficient tensor are renormalized to obtain a new graph structure and its corresponding node feature matrix. Renormalized group flow analysis is performed on the obtained new graph structure and its corresponding node characteristic matrix to find the stable fixed point of the renormalized group transformation and determine the critical temperature. Based on the critical temperature determined by the renormalization group analysis, the feedback adjustment of the graph neural network parameters is completed. By combining the adjusted graph neural network parameters, the critical temperature (i.e. the optimal parameters) based on the renormalized graph neural network is determined.

[0043] As one or more implementation methods, the graph neural network is initialized based on the obtained graph structure and node feature matrix to obtain the initial state and interaction topology of the graph neural network.

[0044] Given a graph structure G=(V,E), where graph G consists of a vertex set V and an edge set E, denoted as G=(V, E), where V(G) represents the finite non-empty set of vertices in graph G; and E(G) represents the set of relationships (edges) between vertices in graph G.

[0045] Based on the graph structure, obtain the node feature matrix X corresponding to the graph result, initialize the graph neural network parameters, that is, define the initial state and interaction topology of the graph neural network, and provide a basis for the subsequent diffusion dynamics process.

[0046] In graph neural networks (GNNs), feature extraction is a crucial step when processing graph-structured data. By calculating and analyzing the attributes of the nodes, edges, and the overall graph, useful feature information can be extracted for direct use in model training or as a feature enhancement method for GNN models.

[0047] In this embodiment, during the graph structure feature extraction process, node features are obtained by capturing the importance and structural information of nodes, edge features including distance features, local neighborhood overlap features, and global neighborhood overlap features are obtained by extracting features between two node pairs, and graph features are obtained by extracting the feature vector of the entire graph structure.

[0048] As one or more implementation methods, in the process of obtaining the diffusion coefficient tensor of the graph neural network based on the acquired node feature matrix, a message passing mechanism is used to simulate mass or energy transfer. The diffusion process can be expressed in the form of a partial differential equation, i.e. ;in, This represents the diffusion coefficient tensor of the graph neural network. Indicates time, Represents the node feature matrix; This represents the gradient operator, i.e., the total differential in all directions of space. In this embodiment, the diffusion intensity between nodes can be adjusted through attention mechanisms or gating mechanisms, making the diffusion process anisotropic and better adapting to the non-uniformity of the graph structure.

[0049] As one or more implementation methods, in this embodiment, during the renormalization transformation process, the acquired graph structure is coarsened. Based on the graph neural network diffusion coefficient tensor and the coarsened graph structure, node clustering or graph pooling operations are combined to obtain a new graph structure and its corresponding node feature matrix; the renormalization transformation satisfy ;in, Represents the node feature matrix, Representing the graph structure, This represents a new graph structure. The node characteristic matrix represents the new graph structure; and it is necessary to maintain certain key invariants of the system (such as free energy). This process simulates the idea in statistical physics of integrating out short-range degrees of freedom and focusing on long-range behavior, and reveals the effective theory of the system at different scales through scale transformation.

[0050] As one or more implementation methods, this embodiment obtains a series of points in the parameter space through iterative renormalization transformation during the renormalization group flow analysis process. (including effective temperature) (Equal parameters), analyze the evolution behavior of the obtained parameter space points under the renormalization flow, and find the stable fixed points of the renormalization group transformation.

[0051] It should be noted that the obtained parameter space points include space points corresponding to the effective temperature. The critical temperature is determined based on the effective temperature corresponding to the stable fixed point of the renormalization group transformation.

[0052] In this embodiment, when the initial temperature near At that time, the renormalized flow hovers near the fixed point, and the correlation length is calculated. The divergent behavior is used to help determine the critical temperature, i.e. ,in, This represents the critical index.

[0053] This embodiment adjusts the graph neural network parameters to a critical state, specifically: The critical temperature determined by renormalization analysis By combining parameters in the critical temperature regulation graph neural network, including noise intensity in message passing, threshold in the activation function, and scaling factor in the attention mechanism, the initial temperature is adjusted to be infinitely close to the determined critical temperature (i.e., This completes the feedback adjustment of the graph neural network parameters.

[0054] As one or more implementation methods, this embodiment further verifies the critical behavior, specifically: (1) Verification of power-law distribution Calculate the absolute value distribution of logits of the final layer output nodes in the critical state (Dropout=0.3). Plot the distribution histogram and observe it on a double logarithmic coordinate system. If it shows a linear trend, it indicates that it conforms to a power-law distribution, which is a sign of the critical state.

[0055] (2) Long-range correlation verification Calculate the correlation of node pairs at different distances in the hidden layer representation. In the critical state, the correlation should decay more slowly with node distance than in the non-critical state (e.g., Dropout=0.1 or 0.8), indicating the existence of long-range associations.

[0056] (3) Performance evaluation In the node classification task, the test accuracy was compared between critical states (T=0.6) and non-critical states (T=0.3, T=0.9). It is expected that the model under critical states will achieve optimal or near-optimal classification performance.

[0057] This embodiment fully considers the diffusion process of graph neural networks. Real-world networks are finite in size and shrink in each coarsening step, so renormalization always flows to trivial solutions—single, isolated nodes. The set of nodes with significant probability flow during the diffusion process is called a block. The probability vector evolves according to the heat equation and is controlled by the Laplace matrix, which is the discrete counterpart of the Laplace operator used for vector computation. Like the traditional Laplace operator, the Laplace operator of graph neural networks is tightly coupled in time and space. The eigenvectors of the network's Laplace operator are like standing waves oscillating in an elastic medium, which will converge or disperse energy in the graph neural network, thereby efficiently changing the node temperature. When each layer of the neural network reaches a critical temperature, it will trigger the similar distribution of nodes in each layer, thereby triggering the spontaneous associative reasoning of the neural network.

[0058] It should be noted that the renormalized graph neural network in this embodiment is not only used for search engine optimization, but can also be applied to concepts with certain coupling relationships, such as: network search nodes, keyword-based network search, company ownership relationship search, determination of company equity ratio, and construction of network perspectives between companies.

[0059] This embodiment innovatively proposes a systematic scheme for reaching the critical temperature (i.e., optimal parameters) based on the diffusion kinetics renormalization method. It utilizes the diffusion process to explore the system configuration space and extracts scale invariance through renormalization group transformation, thereby accurately determining the critical temperature point. Compared with traditional methods, this embodiment effectively overcomes the critical slowing problem, significantly improves computational efficiency, and is applicable to various phase transition systems.

[0060] The search engine model employs a renormalized graph neural network. By extracting scale invariance through renormalization group transformation, it describes the parameter space dynamics of the graph neural network. The method based on diffusion dynamics renormalization is used to reach the critical temperature of the graph neural network model. The renormalized flow method is adopted, and with the help of the Laplace diffusion equation, the critical temperature (i.e., the optimal parameters) is determined efficiently, which greatly improves the search efficiency.

[0061] Example 2 This second embodiment of the invention builds upon the renormalized graph neural network in the search engine optimization method based on the renormalized graph neural network introduced in the first embodiment, and takes a molecular graph prediction task (such as toxicity prediction) based on the renormalized graph neural network as an example to illustrate its practicality.

[0062] Molecular map prediction tasks can be divided into the following steps: (1) Graph construction and initialization This embodiment uses the Tox21 dataset from MoleculeNet, where nodes represent atoms and edges represent chemical bonds; node features include atom type, degree, etc.; and graph-level labels indicate whether the molecule has a certain toxicity.

[0063] (2) Diffusion kinetics and renormalization This embodiment uses the graph isomorphic network GIN, which has strong discriminative power for graph structures, as the basic model for related research; the renormalization transformation adopts the edge contraction method to merge strongly correlated atom pairs (such as double bonds and conjugated structures) into supernodes, so as to better preserve the functional group information of molecules.

[0064] (3) Renormalization flow analysis and determination of critical temperature Will with temperature T The relevant control parameters are specifically defined as the standard deviation of the Gaussian noise added during message passing. s ;make s = T (Or associated through a constant ratio). After message aggregation at each layer, the aggregated message is injected with a distribution N(0, s 2 I The noise vector is calculated; the analysis process is the same as in Example 1. An initial noise intensity is set. s 0 (i.e., initial temperature) T 0), in the original molecular diagram G Running the GIN model on 0 yields a graph-level representation Φ0; coarsening the graph results in... G 1. Then find an effective new noise intensity. s 1, making G 1 in s The graph representations Φ1 and Φ0 under condition 1 are most similar, which results in a renormalization group transformation: s 0→ s 1; in ( σn , σn +1) Draw the renormalized flow on the plane; when the initial... s When the size is small, after transformation σn +1< σn (Flowing towards the ordered phase); when initially s When the value is large, after transformation σn +1> σn (Flowing towards disordered phase), unstable fixed point σc That is, streamlines and diagonals σn +1= σn The points where they intersect and the streamlines are directed away from that point; here... σc That is, the critical temperature of the system. Tc .

[0065] (4) Results and Comparison The graph isomorphic network was adjusted to a critical state (Gaussian noise with σ=0.1 was added), and compared with the unadjusted model. It is expected that the model at the critical state will improve metrics such as ROC-AUC, and the uncertainty in the model's predictions will exhibit specific scaling behavior at the critical state.

[0066] This embodiment verifies the high efficiency of the method described in Embodiment 1.

[0067] The detailed steps are the same as those of the search engine optimization method based on renormalized graph neural networks provided in Example 1, and will not be repeated here.

[0068] Example 3 Embodiment 3 of this invention introduces a search engine optimization system based on a renormalized graph neural network.

[0069] like Figure 2 The illustrated search engine optimization system based on a renormalized graph neural network includes: The acquisition module is configured to acquire the user's search query keywords; The search module is configured to perform user-defined searches based on the obtained search query keywords and search engine model. The optimization module is configured to find the optimal parameters of the search engine model during the user's search process to obtain the optimal search results and complete the search engine optimization. The search engine model employs a renormalized graph neural network. In the process of finding the optimal parameters of the search engine model, the stable fixed point of the renormalized group transformation is found through renormalized group flow analysis. The parameters of the search engine model are adjusted based on the parameters corresponding to the stable fixed point to obtain the optimal parameters.

[0070] The detailed steps are the same as those of the search engine optimization method based on renormalized graph neural networks provided in Example 1, and will not be repeated here.

[0071] The above description is merely a preferred embodiment of this practice and is not intended to limit the scope of this practice. Various modifications and variations can be made to this practice by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this practice should be included within the protection scope of this practice.

Claims

1. A search engine optimization method based on a renormalized graph neural network, characterized in that, include: Obtain the user's search keywords; Based on the obtained search keywords and search engine model, conduct user demand searches; In the process of user demand search, the optimal search results are obtained by finding the optimal parameters of the search engine model, thus completing the search engine optimization. The search engine model employs a renormalized graph neural network. In the process of finding the optimal parameters of the search engine model, the stable fixed point of the renormalized group transformation is found through renormalized group flow analysis. The parameters of the search engine model are adjusted based on the parameters corresponding to the stable fixed point to obtain the optimal parameters.

2. The search engine optimization method based on a renormalized graph neural network as described in claim 1, characterized in that, In the process of renormalized group flow analysis, parameter space points are obtained through iterative renormalization transformation. The evolution behavior of the obtained parameter space points under renormalized flow is analyzed to find the stable fixed points of renormalized group transformation.

3. The search engine optimization method based on a renormalized graph neural network as described in claim 2, characterized in that, The obtained parameter space points include space points corresponding to effective temperatures. Based on the effective temperatures corresponding to the stable fixed points of the found renormalization group transformation, the critical temperature is determined, and the control parameters corresponding to the critical temperature are the optimal parameters.

4. The search engine optimization method based on a renormalized graph neural network as described in claim 3, characterized in that, When the initial temperature near At that time, the renormalized flow hovers near the fixed point, and the correlation length is calculated. The divergent behavior is used to help determine the critical temperature, i.e. ,in, This represents the critical index.

5. The search engine optimization method based on a renormalized graph neural network as described in claim 3, characterized in that, During the feedback adjustment of the search engine model parameters, based on the critical temperature determined by the renormalization analysis, the parameters in the graph neural network, including the noise intensity in message passing, the threshold in the activation function, and the scaling factor in the attention mechanism, are adjusted in combination with the critical temperature adjustment. The initial temperature is then adjusted to be infinitely close to the determined critical temperature, thus completing the feedback adjustment of the graph neural network parameters.

6. The search engine optimization method based on a renormalized graph neural network as described in claim 1, characterized in that, Before the renormalized group flow analysis, the diffusion coefficient tensor of the graph neural network is obtained, and the obtained graph neural network diffusion coefficient tensor is renormalized to obtain a new graph structure of the graph neural network and its corresponding node feature matrix.

7. The search engine optimization method based on a renormalized graph neural network as described in claim 6, characterized in that, In obtaining the diffusion coefficient tensor of a graph neural network, a message-passing mechanism is used to simulate mass or energy transfer. The diffusion process can be represented as a partial differential equation, i.e. ;in, This represents the diffusion coefficient tensor of the graph neural network. Indicates time, Represents the node feature matrix; This represents the gradient operator, which is the total differential in all directions of space.

8. The search engine optimization method based on a renormalized graph neural network as described in claim 6, characterized in that, The graph structure of the graph neural network is coarsened. Based on the graph neural network diffusion coefficient tensor and the coarsened graph structure, node clustering or graph pooling operations are combined to obtain a new graph structure and its corresponding node feature matrix; the renormalization transformation... satisfy ;in, Represents the node feature matrix, Representing the graph structure, This represents a new graph structure. The node feature matrix represents the new graph structure.

9. The search engine optimization method based on a renormalized graph neural network as described in claim 1, characterized in that, When the activation of nodes in a graph neural network exhibits a power-law distribution rather than an exponential distribution, long-range spatial correlations are observed between the node states. The dynamics show a critical slowdown phenomenon, i.e., the relaxation time becomes significantly longer. At this point, the graph neural network truly reaches a critical state.

10. A search engine optimization system based on a renormalized graph neural network, characterized in that, include: The acquisition module is configured to acquire the user's search query keywords; The search module is configured to perform user-defined searches based on the obtained search query keywords and search engine model. The optimization module is configured to find the optimal parameters of the search engine model during the user's search process to obtain the optimal search results and complete the search engine optimization. The search engine model employs a renormalized graph neural network. In the process of finding the optimal parameters of the search engine model, the stable fixed point of the renormalized group transformation is found through renormalized group flow analysis. The parameters of the search engine model are adjusted based on the parameters corresponding to the stable fixed point to obtain the optimal parameters.

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