Maximum segmentation solving method for relaxation optimization sampling based on re-parameterized graph neural network and related equipment

Abstract

The embodiment of the invention provides a maximum segmentation solving method for relaxation optimization sampling based on a re-parameterized graph neural network and related equipment. The method comprises the following steps: acquiring a maximum segmentation model; performing simplex relaxation conversion on one-hot vector parameters in the maximum segmentation model to obtain a relaxation continuous optimization model; the continuous parameters are converted into node embedding parameters, and an adjacent objective function of the relaxation continuous optimization model is converted into an embedding objective function based on the node embedding parameters; performing iterative solution on the relaxation continuous optimization model based on the embedding objective function, the node embedding parameters and the re-parameterized graph neural network to obtain a relaxation feasible solution; sampling is carried out based on the probability distribution of the relaxation feasible solution, a target feasible solution of the maximum segmentation model is obtained, the target feasible solution is used for segmenting the image data corresponding to the maximum segmentation model into a plurality of subset image data with the maximum total weight, and the solving efficiency and solving quality of the maximum segmentation model can be improved.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a maximum splitting solution method and related equipment based on relaxed optimization sampling of a reparameterized graph neural network. Background Art

[0002] The Max-k-Cut problem requires partitioning the vertices of image data into multiple non-overlapping subsets such that the total weight of the edges between the different subsets is maximized. This problem has important academic value in combinatorial optimization and has been widely applied in various practical fields, such as telecommunications networks, data clustering, and theoretical physics. Because it is a generalization of the classic Max-k-Cut problem, one of the 21 NP-complete problems proposed by Karp, the Max-k-Cut problem has also been proven to be NP-complete, meaning it is difficult to solve directly.

[0003] In related technologies, solving the model corresponding to the maximum split problem typically uses machine learning techniques to model the maximum split problem as a sequential decision problem, and then uses reinforcement learning to train a policy network to generate a feasible solution. However, when this reinforcement learning method is extended to the maximum split problem, the increased complexity of the action space and the need for a large number of samples significantly prolong the training and testing time, making the maximum split model less efficient. Summary of the Invention

[0004] The embodiments of the present application provide a maximum split solution method and related equipment based on relaxed optimization sampling of a reparameterized graph neural network, which can improve the solution efficiency of the maximum split model.

[0005] To achieve the above objectives, a first aspect of an embodiment of the present application proposes a maximum split solution method based on relaxed optimization sampling of a reparameterized graph neural network, the method comprising:

[0006] Obtaining a maximum segmentation model, the maximum segmentation model including an adjacency objective function and a one-hot vector parameter;

[0007] Performing simplex relaxation transformation on the one-hot vector parameters in the maximum segmentation model to obtain a relaxed continuous optimization model, wherein the relaxed continuous optimization model includes continuous parameters;

[0008] Converting the continuous parameters into node embedding parameters, and converting the adjacency objective function of the relaxed continuous optimization model into an embedding objective function based on the node embedding parameters;

[0009] Iteratively solving the relaxed continuous optimization model based on the embedding objective function, the node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution;

[0010] Sampling is performed based on the probability distribution of the relaxed feasible solution to obtain a target feasible solution of the maximum segmentation model.

[0011] In some embodiments, the iteratively solving the relaxed continuous optimization model based on the embedding objective function, the node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution includes:

[0012] Generate an iterative update function for each layer of the neural network in the reparameterized graph neural network based on the node embedding parameters, the embedding objective function, and the network parameters of the reparameterized graph neural network;

[0013] generating a loss function based on the network parameters and optimizing the embedding objective function;

[0014] Iteratively updating the network parameters and the node embedding parameters based on the iterative update function and the loss function;

[0015] The relaxed feasible solution is obtained based on the node embedding parameters after multiple iterations of updating.

[0016] In some embodiments, the network parameters include first network parameters and second network parameters, the embedding objective function includes adjacency matrix parameters, and generating an iterative update function for each layer of the neural network in the reparameterized graph neural network based on the node embedding parameters, the embedding objective function, and the network parameters of the reparameterized graph neural network includes:

[0017] obtaining a first iterative update part based on a product of the first network parameter and the node embedding parameter of the current node;

[0018] A second iterative update part is obtained by multiplying the accumulated value of the product of the node embedding parameter and the node weight of all other nodes by the second network parameter, where the node weight is a weight parameter between the current node and other nodes in the adjacency matrix parameter;

[0019] The iterative update function of the current node is obtained based on the accumulated value of the first iterative update part and the second iterative update part and multiplied by the activation function.

[0020] In some embodiments, the iteratively updating the network parameters and the node embedding parameters based on the iterative update function and the loss function includes:

[0021] generating a plurality of training loss functions based on a plurality of training adjacency matrices and the node embedding parameters;

[0022] Iteratively updating the network parameters and the node embedding parameters based on each of the training loss functions, and obtaining a training feasible solution corresponding to each of the training adjacency matrices based on the node embedding parameters after multiple iterative updates;

[0023] Based on the plurality of training adjacency matrices and the corresponding training feasible solutions, calculating and obtaining optimized initial network parameters;

[0024] The optimized initial network parameters are used as initial values ​​of the network parameters, and the network parameters and the node embedding parameters are iteratively updated based on the iterative update function and the loss function.

[0025] In some embodiments, the step of calculating and optimizing initial network parameters based on the plurality of training adjacency matrices and the corresponding training feasible solutions includes:

[0026] generating a parameter optimization function corresponding to the embedding objective function based on each of the training adjacency matrices and the corresponding training feasible solution;

[0027] Obtaining a training parameter optimization function based on an average processing of all the parameter optimization functions;

[0028] The training parameter optimization function is optimized to obtain the optimized initial network parameters.

[0029] In some embodiments, the reparameterized graph neural network includes a multi-layer neural network, and the iterative updating of the network parameters and the node embedding parameters based on the iterative update function and the loss function includes:

[0030] In each layer of the neural network, the network parameters are updated based on the node embedding parameters of each node output by the previous layer of the neural network and the loss function;

[0031] The node embedding parameters of each node are updated based on the updated network parameters, and the updated node embedding parameters are used as inputs for corresponding nodes in the next layer of neural network.

[0032] In some embodiments, the relaxed feasible solution includes multiple sub-relaxed feasible solutions, and sampling based on the probability distribution of the relaxed feasible solutions to obtain the target feasible solution of the maximum segmentation model includes:

[0033] Sampling based on the probability distribution of the relaxed feasible solution to obtain a single feasible solution of the maximum segmentation model;

[0034] Selecting the single feasible solution with the smallest adjacent objective function value from the multiple single feasible solutions as the sub-goal feasible solution;

[0035] Based on all the feasible solutions of the sub-goals, the feasible solution of the goal is obtained.

[0036] In some embodiments, performing a simplex relaxation transformation on the one-hot vector parameters in the maximum segmentation model to obtain a relaxed continuous optimization model includes:

[0037] generating a plurality of multidimensional Cartesian products based on the convex hull of the one-hot vector parameter;

[0038] Obtaining the continuous parameter for the one-hot vector parameter based on all the multidimensional Cartesian products;

[0039] Parameter conversion is performed on the maximum segmentation model based on the continuous parameters to obtain the relaxed continuous optimization model.

[0040] To achieve the above-mentioned purpose, a second aspect of an embodiment of the present application proposes a maximum split solving device based on relaxed optimization sampling of a reparameterized graph neural network, the device comprising:

[0041] An acquisition module, configured to acquire a maximum segmentation model, wherein the maximum segmentation model includes an adjacency objective function and a one-hot vector parameter;

[0042] a relaxation conversion module, configured to perform a simplex relaxation conversion on the one-hot vector parameters in the maximum segmentation model to obtain a relaxed continuous optimization model, wherein the relaxed continuous optimization model includes continuous parameters;

[0043] a model conversion module, configured to convert the continuous parameters into node embedding parameters, and convert the adjacency objective function of the relaxed continuous optimization model into an embedding objective function based on the node embedding parameters;

[0044] An iterative solution module, configured to iteratively solve the relaxed continuous optimization model based on the embedding objective function, the node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution;

[0045] A sampling processing module is used to perform sampling based on the probability distribution of the relaxed feasible solution to obtain a target feasible solution of the maximum segmentation model, wherein the target feasible solution is used to segment the image data corresponding to the maximum segmentation model into a plurality of subset image data with maximized total weight.

[0046] To achieve the above-mentioned purpose, the third aspect of an embodiment of the present application proposes an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the maximum segmentation solution method based on relaxed optimization sampling of a reparameterized graph neural network as described in the first aspect.

[0047] To achieve the above-mentioned purpose, the fourth aspect of an embodiment of the present application proposes a storage medium, which is a computer-readable storage medium and stores a computer program. When the computer program is executed by a processor, it implements the maximum split solution method based on relaxed optimization sampling of a reparameterized graph neural network described in the first aspect.

[0048] The embodiments of the present application propose a maximum segmentation solution method and related equipment based on relaxed optimization sampling of a reparameterized graph neural network. The method includes: first, obtaining a maximum segmentation model, which includes an adjacency objective function and one-hot vector parameters; then, performing a simplex relaxation transformation on the one-hot vector parameters in the maximum segmentation model to obtain a relaxed continuous optimization model, which includes continuous parameters; then, converting the continuous parameters into node embedding parameters, and converting the adjacency objective function of the relaxed continuous optimization model into an embedding objective function based on the node embedding parameters; next, iteratively solving the relaxed continuous optimization model based on the embedding objective function, the node embedding parameters and the reparameterized graph neural network to obtain a relaxed feasible solution; finally, sampling based on the probability distribution of the relaxed feasible solution to obtain a target feasible solution of the maximum segmentation model, which is used to divide the image data corresponding to the maximum segmentation model into multiple subset image data with maximized total weight. The embodiment of the present application converts the discrete one-hot vector parameters of the original maximum segmentation model into a more easily tractable continuous optimization problem by performing simplex relaxation, effectively reducing the difficulty of solving the problem, and uses a reparameterized graph neural network to efficiently iteratively solve the node embedding parameters and the embedding objective function, and finally obtains the target feasible solution through probability sampling. Compared with traditional reinforcement learning methods, through the innovative "relaxation-optimization-sampling" framework, especially by utilizing the powerful graph representation learning ability and end-to-end optimization method of the graph neural network, it can significantly improve the efficiency of solving large-scale maximum segmentation models and the quality of the solution, avoid the complex sequential decision-making process and long training time in the reinforcement learning method, and provide a faster, more accurate and easier to expand solution for the NP-complete maximum segmentation problem, thereby greatly improving the solution efficiency and accuracy of the maximum segmentation model, and providing an innovative and scalable technical solution for solving large-scale weighted maximum segmentation problems.

[0049] Other features and advantages of the present application will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present application. The purposes and other advantages of the present application can be achieved and obtained through the structures particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1This is a flowchart of a maximum split solution method based on relaxed optimization sampling of a reparameterized graph neural network provided by an embodiment of the present application.

[0051] Figure 2 yes Figure 1 Flowchart of step 102 in FIG.

[0052] Figure 3 yes Figure 1 Flowchart of step 104 in FIG.

[0053] Figure 4 yes Figure 3 Flowchart of step 301 in FIG.

[0054] Figure 5 yes Figure 3 Flowchart of step 304 in FIG.

[0055] Figure 6 yes Figure 5 Flowchart of step 503 in FIG.

[0056] Figure 7 yes Figure 5 Flowchart of step 504 in FIG.

[0057] Figure 8 yes Figure 1 Flowchart of step 105 in FIG.

[0058] Figure 9 This is a schematic diagram of a random sampling algorithm based on relaxed feasible solution category distribution provided by another embodiment of the present application.

[0059] Figure 10 This is a flowchart of solving a maximum segmentation model provided by another embodiment of the present application.

[0060] Figure 11 This is a performance simulation diagram of a maximum segmentation model solution provided by another embodiment of the present application.

[0061] Figure 12 It is a structural diagram of a maximum split solution device based on relaxed optimization sampling of a reparameterized graph neural network provided in one embodiment of the present application.

[0062] Figure 13 This is a schematic diagram of the hardware structure of an electronic device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0064] It should be noted that although the functional modules are divided in the device schematic and the logical order is shown in the flowchart, in some cases, the steps shown or described can be performed in a different order than the module division in the device or the order in the flowchart.

[0065] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application pertains. The terms used herein are for the purpose of describing the embodiments of this application only and are not intended to limit this application.

[0066] The Max-k-Cut problem requires partitioning the vertices of image data into multiple non-overlapping subsets such that the total weight of the edges between the different subsets is maximized. This problem has important academic value in combinatorial optimization and has been widely applied in various practical fields, such as telecommunications networks, data clustering, and theoretical physics. Because it is a generalization of the classic Max-k-Cut problem, one of the 21 NP-complete problems proposed by Karp, the Max-k-Cut problem has also been proven to be NP-complete, meaning it is difficult to solve directly.

[0067] In related technologies, solving the model corresponding to the maximum split problem typically uses machine learning techniques to model the maximum split problem as a sequential decision problem, and then uses reinforcement learning to train a policy network to generate a feasible solution. However, when this reinforcement learning method is extended to the maximum split problem, the increased complexity of the action space and the need for a large number of samples significantly prolong the training and testing time, making the maximum split model less efficient.

[0068] In order to improve the efficiency of solving the maximum segmentation model, the embodiment of the present application converts the discrete one-hot vector parameters of the original maximum segmentation model into a more easily handled continuous optimization problem by performing simplex relaxation, effectively reducing the difficulty of solving, and using a reparameterized graph neural network to efficiently iteratively solve the node embedding parameters and embedding objective function, and finally obtain the target feasible solution through probability sampling. Compared with traditional reinforcement learning methods, through the innovative "relaxation-optimization-sampling" framework, especially by utilizing the powerful graph representation learning ability and end-to-end optimization method of the graph neural network, it can significantly improve the efficiency of solving large-scale maximum segmentation models and the quality of the solution, avoiding the complex sequential decision process and long training time in the reinforcement learning method, and providing a faster, more accurate and easier to expand solution path for the NP-complete maximum segmentation problem, thereby greatly improving the solution efficiency and accuracy of the maximum segmentation model, and providing an innovative and scalable technical solution for solving large-scale weighted maximum segmentation problems.

[0069] The following describes a maximum split solution method and related equipment based on relaxed optimization sampling of a reparameterized graph neural network provided in an embodiment of the present application. The maximum split solution method based on relaxed optimization sampling of a reparameterized graph neural network provided in an embodiment of the present application can be applied to any server or computing processor with computing resources, etc.

[0070] The following is a detailed description of the maximum segmentation solution method based on the relaxed optimization sampling of the reparameterized graph neural network in the embodiment of the present application. Figure 1 , which is an optional flowchart of a maximum split solution method based on relaxed optimization sampling of a reparameterized graph neural network provided in an embodiment of the present application, Figure 1 The method may include but is not limited to steps 101 to 105. It is also understood that this embodiment is Figure 1 The order of step 101 to step 105 is not specifically limited, and the order of steps can be adjusted or some steps can be reduced or added according to actual needs.

[0071] Step 101: Obtain the maximum segmentation model.

[0072] Step 101 is described in detail below.

[0073] In some embodiments, the maximum segmentation model corresponding to the segmentation of the image data is used. Represents an undirected graph corresponding to image data, where is the vertex set, ε is the edge set. Each edge (i, j)∈ε is assigned an arbitrary weight It is the adjacency matrix, and the weights can be positive, zero, or negative. The partition in refers to the vertex set The goal of the maximum segmentation problem (i.e., the maximum k-cut problem) corresponding to image data is to find the vertex set A k-partition of The sum of the weights of the edges between vertices belonging to different partitions is maximized.

[0074] In order to represent this partition, a k-dimensional unique hot encoding method is used. Specifically, a k×N dimension matrix is ​​defined Each column is a one-hot vector parameter, so the maximum segmentation model for the input can be expressed as the following optimization problem formula (1).

[0075]

[0076] where X ·j represents the jth column of the matrix parameter X, the adjacency matrix W is a symmetric matrix with zero main diagonal elements, is a one-hot vector whose lth component is 1 and the rest are 0. The goal of the maximum partition model corresponding to the above formula (1) is to maximize the sum of the edge weights between different partitions while ensuring that each vertex is assigned to only one partition and represented by a one-hot encoding vector.

[0077] It should be noted that the maximum cut model shown in formula (1) is a generalized form of the classical maximum cut problem, which is a weighted maximum k-cut problem with arbitrary weights. It is widely used in many important fields, including telecommunications networks, data clustering, theoretical physics, data clustering, combinatorial optimization, and mixed integer programming. In other words, the maximum cut solution method based on relaxed optimization sampling of reparameterized graph neural networks proposed in this application is not only applicable to the field of image data processing, but can also be used in other technical fields.

[0078] Next, the maximum segmentation model shown in formula (1) is simplified by removing the constant term and inverting the objective function, and the simplified equivalent form of the maximum segmentation model is obtained as shown in the following formula (2).

[0079]

[0080] in, is the adjacency objective function, X is the one-hot vector parameter, that is That is, the one-hot vector parameter X is a discrete parameter. It should be noted that since the diagonal elements of the adjacency matrix W are set to zero, the matrix W is an unshaped matrix.

[0081] Step 102: Perform simplex relaxation transformation on the one-hot vector parameters in the maximum partitioning model to obtain a relaxed continuous optimization model.

[0082] Step 102 is described in detail below.

[0083] In some embodiments, since the variables in the discrete maximum split model corresponding to formula (2) are discrete, its solution faces great challenges. In order to be able to solve it, the one-hot vector parameter X in the maximum split model will be further transformed into a simplex relaxation to obtain a relaxed continuous optimization model to convert the discrete one-hot vector parameter X into a continuous parameter, so that subsequent solution can be performed, as described below.

[0084] Reference Figure 2 , performing simplex relaxation transformation on the one-hot vector parameters in the maximum partitioning model to obtain a relaxed continuous optimization model, including the following steps 201 to 203.

[0085] Step 201: Generate multiple multi-dimensional Cartesian products based on the convex hull of the one-hot vector parameters.

[0086] Step 202: Based on all multi-dimensional Cartesian products, perform relaxation transformation on the one-hot vector parameters to obtain continuous parameters.

[0087] Step 203: Perform parameter conversion on the maximum segmentation model based on the continuous parameters to obtain a relaxed continuous optimization model.

[0088] Steps 201 to 203 are described in detail below.

[0089] For each node, the convex hull of its one-hot vector is a K-dimensional simplex. For example, when K=3, the convex hull is a triangle consisting of three vertices (1,0,0), (0,1,0) and (0,0,1). In this embodiment, the one-hot vector parameter is The convex hull of is represented as the Cartesian product of N k-dimensional probability simplexes, denoted as Then based on all these multidimensional Cartesian products Perform a relaxation transformation on the one-hot vector parameters to obtain continuous parameters, i.e. Thus, the original one-hot vector parameter, which can only take K discrete values, is converted into a continuous vector that can take values ​​within the K-dimensional simplex.

[0090] Afterwards, the maximum segmentation model (2) is parameter-converted based on the continuous parameters to obtain a relaxed continuous optimization model as shown in the following formula (3).

[0091]

[0092] Through the above steps 201 to 203, the discrete category assignment problem that is difficult to directly optimize in the original maximum segmentation model is transformed into an optimization problem that can be solved in a continuous space, so that mature and efficient continuous optimization algorithms such as gradient descent can be applied to find the optimal solution or high-quality approximate solution of the model, greatly improving the solution efficiency and stability, and avoiding the computational complexity brought about by combinatorial search in a huge discrete solution space.

[0093] The maximum k-cut problem (i.e., the maximum partitioning problem) is an NP-hard combinatorial optimization problem. Although traditional optimization methods (such as semi-definite relaxation, heuristic algorithms, etc.) can provide approximate solutions, they are often computationally intensive and take a long time to solve. Especially when faced with large-scale graphs, traditional methods often take hours or even longer to calculate a sufficiently good solution. In order to solve the maximum partitioning problem corresponding to the relaxed continuous optimization model shown in the above formula (3), this application proposes an efficient learning optimization method based on graph neural network parameterization. This method greatly reduces the large number of iterative processes usually required in classical optimization methods (such as mirror descent) by utilizing the powerful representation ability of the graph neural network model on graph structure data. In addition, a "pre-training + fine-tuning" optimization strategy is introduced to inject graph structure prior knowledge into the model during the pre-training stage, thereby significantly reducing the computation time required to optimize the relaxed continuous optimization model (3), as described below.

[0094] Step 103: Convert the continuous parameters into node embedding parameters, and convert the adjacency objective function of the relaxed continuous optimization model into an embedding objective function based on the node embedding parameters.

[0095] Step 103 is described in detail below.

[0096] In some embodiments, when solving the above relaxed continuous optimization model (3) using a graph neural network, the maximum partitioning problem can be modeled as a node classification task, so that the graph neural network can be used to aggregate node features and obtain high-quality solutions. Therefore, it is necessary to convert the continuous parameters Converted into node embedding parameters And based on the node embedding parameters The adjacency objective function f(X;W) of the relaxed continuous optimization model is transformed into an embedding objective function f(H;W).

[0097] Step 104: Iteratively solve the relaxed continuous optimization model based on the embedded objective function, node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution.

[0098] Step 104 is described in detail below.

[0099] In some embodiments, after obtaining the embedding objective function f(H; W), the embedding objective function f(H; W), the node embedding parameters The relaxed continuous optimization model is iteratively solved by a reparameterized graph neural network to obtain a relaxed feasible solution, as described below.

[0100] First, for the figure Each node i in is randomly assigned an initial node embedding parameter

[0101] Reference Figure 3 , based on the embedded objective function, the node embedding parameters and the reparameterized graph neural network, the relaxed continuous optimization model is iteratively solved to obtain a relaxed feasible solution, including the following steps 301 to 304.

[0102] Step 301: Generate an iterative update function for each layer of the neural network in the reparameterized graph neural network based on the node embedding parameters, the embedding objective function, and the network parameters of the reparameterized graph neural network.

[0103] Step 301 is described in detail below.

[0104] In some embodiments, in order to obtain the optimal relaxed feasible solution in the iterative update of the reparameterized graph neural network, it is first necessary to firstly embed the node parameters Embedding objective function f(H;W) and network parameters of reparameterized graph neural network Generate an iterative update function for each layer of the neural network in the reparameterized graph neural network, where l is the index of the neural network layer, as described below.

[0105] Reference Figure 4 , based on the node embedding parameters, the embedding objective function and the network parameters of the reparameterized graph neural network, an iterative update function of each layer of the neural network in the reparameterized graph neural network is generated, including the following steps 401 to 403.

[0106] Step 401: Obtain a first iterative update part based on the product of a first network parameter and a node embedding parameter of a current node.

[0107] Step 402: The second iterative update part is obtained by multiplying the accumulated value of the product of the node embedding parameters and the node weights of all other nodes by the second network parameter.

[0108] Step 403: Based on the accumulated value of the first iterative update part and the second iterative update part, and multiplied by the activation function, an iterative update function of the current node is obtained.

[0109] Steps 401 to 403 are described in detail below.

[0110] In some embodiments, first based on network parameters The first network parameter in and the node embedding parameters of the input of the current node (i.e. the node embedding parameter of the current node output by the upper neural network layer) to obtain the first iterative update part and node embedding parameters based on the inputs of all other nodes (i.e., the node embedding parameters of the other nodes output by the upper neural network layer) and the node weights W between the other nodes and the current node ji The accumulated value of the product, multiplied by the network parameter The second network parameter in Get the second iteration update part Among them, the node weight W ji is the weight parameter between the current node i and other nodes j in the adjacency matrix parameter W.

[0111] Then, based on the accumulated values ​​of the first iterative update part and the second iterative update part, and multiplied by the activation function σ, the iterative update function corresponding to the output of the node embedding parameter of the current neural network for the current node (i.e., the input of the next layer of neural network) and the input (i.e., the output of the previous layer of neural network) is obtained as shown in the following formula (4).

[0112]

[0113] where X (l) is the continuous parameter of the lth layer The node embedding vector for iterative update, l∈{0,1,L,L-1}, and are the trainable parameters of the k-th layer neural network, which are used to adjust the self-update of node embedding and the interaction with the adjacency matrix. W is the adjacency matrix parameter of the graph, which includes the connection relationship between nodes and the weight of the edge. σ represents the nonlinear activation function. is a learnable embedding for nodes. Through this design, the model can effectively learn high-dimensional representations of nodes and fully utilize node features and their associated graph structures.

[0114] Step 302: Generate a loss function based on the network parameters and the optimized embedding objective function.

[0115] Step 303: Iteratively update the network parameters and node embedding parameters based on the iterative update function and the loss function.

[0116] Step 304: Based on the node embedding parameters updated after multiple iterations, a relaxed feasible solution is obtained.

[0117] Steps 302 to 304 are described in detail below.

[0118] Next, based on the network parameters And the embedded objective function is optimized to obtain the loss function of each layer of the neural network as shown in the following formula (5).

[0119]

[0120] Then, in the reparameterized graph neural network, a multi-layer neural network connected step by step is used to update the network parameters of the reparameterized graph neural network based on the iterative update function (4) and the loss function (5). and the node embedding parameters for each node Perform iterative updates, and after iterative updates of the L-layer GNN, the final output is obtained Then, the last layer passes the softmax activation function to output Convert to The relaxed feasible solution in the solution can be directly applied to optimize the relaxed continuous optimization model (3).

[0121] The following further describes how to iteratively update the network parameters and node embedding parameters.

[0122] Reference Figure 5 , iteratively updating the network parameters and node embedding parameters based on the iterative update function and the loss function, including the following steps 501 to 504.

[0123] Step 501: Generate multiple training loss functions based on multiple training adjacency matrices and node embedding parameters.

[0124] Step 502: Iteratively update the network parameters and node embedding parameters based on each training loss function, and obtain a training feasible solution corresponding to each training adjacency matrix based on the node embedding parameters after multiple iterative updates.

[0125] Step 503: Based on the multiple training adjacency matrices and the corresponding training feasible solutions, the optimized initial network parameters are calculated.

[0126] Steps 501 to 503 are described in detail below.

[0127] In some embodiments, in order to further improve the efficiency and accuracy of iteratively updating network parameters and node embedding parameters in a reparameterized graph neural network, thereby further improving the accuracy of the output training feasible solution. Based on the reparameterized graph neural network, this application proposes a "pre-training + fine-tuning" framework for optimizing the trainable weights in each neural network layer in the graph neural network model. The framework first trains the model on a series of pre-collected datasets to obtain a pre-trained model; it is then fine-tuned on each specific problem instance. By incorporating prior knowledge of the graph structure, the pre-training phase significantly reduces the computation time required for subsequent optimization problem instances. Furthermore, the fine-tuning phase enhances the model's generalization capabilities, enabling it to adapt to out-of-distribution optimization problem instances.

[0128] Based on this, firstly based on the pre-acquired pre-training dataset Multiple training adjacency matrices and node embedding parameter H, generating the adjacency matrix for each training The corresponding training loss function is shown in the following formula (6).

[0129]

[0130] Then, the Adam optimizer is used for optimization, and the above iterative update function (4) and training loss function (6) are used to embed the randomly initialized node parameters in the reparameterized graph neural network. The starting point for the trainable weights Perform update training and update the trainable weights during the update training process Then, based on the node embedding parameters updated after multiple iterations, each training adjacency matrix is ​​obtained The corresponding training feasible solution Then, based on multiple training adjacency matrices and corresponding training feasible solutions, the trainable weights are further Update to take advantage of the final updated trainable weights As the optimized initial network parameters, so that the optimized initial network parameters can be used in the subsequent iterative solution of the relaxed continuous optimization model. As the initial network parameters of each neural network layer in the reparameterized graph neural network Therefore, when using the optimized initial network parameters in the reparameterized graph neural network to iteratively solve the relaxed continuous optimization model, the prior knowledge of the graph structure introduced in the pre-training stage can effectively improve the computing time and accuracy required for the optimization problem instance.

[0131] The following will further describe how to train the trainable weights based on multiple training adjacency matrices and corresponding training feasible solutions. to update.

[0132] Reference Figure 6 , based on multiple training adjacency matrices and corresponding training feasible solutions, the optimized initial network parameters are calculated, including the following steps 601 to 603.

[0133] Step 601: Based on each training adjacency matrix and the corresponding training feasible solution, generate a parameter optimization function corresponding to the embedding objective function.

[0134] Step 602: Based on the average processing of all parameter optimization functions, a training parameter optimization function is obtained.

[0135] Step 603: Optimize the training parameter optimization function to obtain optimized initial network parameters.

[0136] Steps 601 to 603 are described in detail below.

[0137] In some embodiments, after obtaining each training adjacency matrix and the corresponding training feasible solution After that, a parameter optimization function corresponding to the embedded objective function f(H;W) is generated Then optimize the function based on all parameters The training parameter optimization function is obtained by averaging the training parameter optimization function, and the training parameter optimization function is further optimized to obtain the optimized initial network parameter function as shown in the following formula (7).

[0138]

[0139] Use the above optimization function to optimize the initial network parameters and the training parameter optimization function Perform optimization processing to obtain the optimized initial network parameters

[0140] Step 504: The optimized initial network parameters are used as the initial values ​​of the network parameters, and the network parameters and node embedding parameters are iteratively updated based on the iterative update function and the loss function.

[0141] Steps 501 to 504 are described in detail below.

[0142] In some embodiments, after obtaining the optimized initial network parameters Afterwards, when performing the actual relaxation continuous optimization model iteration in the reparameterized graph neural network, the initial network parameters will be optimized. As the initial network parameters of each neural network layer in the reparameterized graph neural network Therefore, when using the optimized initial network parameters in the reparameterized graph neural network to iteratively solve the relaxed continuous optimization model, the prior knowledge of the graph structure introduced in the pre-training stage can be used to effectively improve the computational time and accuracy required for the optimization problem instance.

[0143] Reference Figure 7 , iteratively updating the network parameters and node embedding parameters based on the iterative update function and the loss function, including the following steps 701 to 702.

[0144] Step 701: In each layer of the neural network, the network parameters are updated based on the node embedding parameters and loss function of each node output by the previous layer of the neural network.

[0145] Step 702: Update the node embedding parameters of each node based on the updated network parameters, and use the updated node embedding parameters as input to the corresponding node in the next layer of the neural network.

[0146] Steps 701 to 702 are described in detail below.

[0147] In some embodiments, for the actual W test The problem instance represented by corresponds to the relaxed continuous optimization model (3) as shown in the following formula (8).

[0148]

[0149] When the optimized initial network parameters are used in the reparameterized graph neural network to iteratively solve the above example model (8), the Adam optimizer is used for solution optimization. In each layer of the reparameterized graph neural network (such as the i-th layer), the nodes output by the previous layer of the neural network are embedded in the parameters Input the loss function (5) to get the loss value of the neural network layer, and then use the loss value to adjust the network parameters of the current neural network layer. Update and then use the updated network parameters The node embedding parameters are updated in combination with the iterative update function (4), and the updated node embedding parameters are used as the input parameters of the next layer of neural network, so as to perform iterative updates until all neural network layers are iteratively updated, and the node embedding parameters output by the last layer of neural network are used as the relaxed feasible solution.

[0150] Furthermore, to fully adapt the graph neural network model to a specific problem instance, the pre-training phase can be omitted, and the model can be trained and tested directly on the problem instance. Although this direct training approach may require longer computation time, it generally provides better performance on the objective function. Therefore, users can decide whether to include the pre-training phase based on the needs of their specific application scenario to achieve a balance between performance and efficiency.

[0151] Through the above steps 301 to 304, 501 to 504, 601 to 603, and 701 to 702, by clarifying the specific steps of iteratively solving the relaxed continuous optimization model (including generating an iterative update function, a loss function, and iteratively updating the network parameters and node embedding parameters based on this), a clear algorithm flow is provided for how the core reparameterized graph neural network learns and approximates the relaxed feasible solution; secondly, by distinguishing and processing the node's own information (the first iterative update part) and the adjacent node aggregation information (the second iterative update part, and considering the weights in the adjacency matrix), and combining the activation function, the network can more accurately capture and fuse the local structural features and mutual influences of the nodes in the graph, thereby learning node representations that are more discriminative for the maximum segmentation problem; and, an advanced network parameter initialization strategy is introduced by utilizing multiple training adjacency matrices and their corresponding The model uses the feasible solution of training to pre-calculate and optimize the initial network parameters. This "meta-learning" or "pre-training" method enables the model to iterate from an optimized parameter starting point that is closer to the optimal solution space when processing a new target graph, thereby significantly accelerating the convergence speed, improving the quality of the final solution, and enhancing the model's generalization ability for different graph structures, avoiding the problem of local optimality or low training efficiency that may be encountered when training from random parameters; finally, the refined learning mechanism of layer-by-layer and alternating update of network parameters and node embedding parameters in multi-layer reparameterized graph neural networks is clarified. In each layer of the network, the network parameters of the layer are first updated according to the node embedding and loss function output by the previous layer, and then the updated network parameters are used to optimize the node embedding of the layer. This layer-by-layer refinement method enables the network to learn deeper and more complex graph feature representations, thereby gradually improving the understanding and solution accuracy of the maximum segmentation problem.

[0152] Step 105: Sampling is performed based on the probability distribution of the relaxed feasible solution to obtain the target feasible solution of the maximum segmentation model.

[0153] Step 105 is described in detail below.

[0154] In some embodiments, after obtaining a high-quality continuous feasible solution to the relaxed continuous optimization model (3), After that, since the original goal is to construct a discrete feasible solution of the maximum partition model (3) of the original problem At the same time, it is necessary to ensure that the objective function value is equal to the objective value of the solution to the relaxed problem.

[0155] Therefore, in this embodiment, based on the relaxed feasible solution The probability distribution of is sampled to obtain a high-quality target feasible solution corresponding to the maximum segmentation model (2) When this target feasible solution is applied to the field of image data processing, it can be used to divide the image data corresponding to the maximum segmentation model into multiple subset image data with maximized total weights; similarly, when applied to other technical fields, similar effects can also be achieved. It only requires the existence of an optimization problem form such as formula (1) or (2) corresponding to the maximum segmentation model, that is, the maximum segmentation solution method based on relaxed optimization sampling of a reparameterized graph neural network provided in the embodiment of the present application can be implemented to obtain a high-quality feasible solution at high speed.

[0156] The following will further describe how to solve the problem based on the relaxed feasible solution. The probability distribution of is sampled to obtain a high-quality target feasible solution corresponding to the maximum segmentation model (2)

[0157] Reference Figure 8 , sampling is performed based on the probability distribution of the relaxed feasible solution to obtain the target feasible solution of the maximum segmentation model, including the following steps 801 to 803.

[0158] Step 801: Sampling is performed based on the probability distribution of each sub-relaxed feasible solution to obtain a sub-goal feasible solution.

[0159] Step 802: Select the single feasible solution with the smallest value of the adjacent objective function from multiple single feasible solutions as the sub-goal feasible solution.

[0160] Step 803: Based on all sub-goal feasible solutions, obtain the goal feasible solution.

[0161] Steps 801 to 803 are described in detail below.

[0162] Reference Figure 9 , is a schematic diagram of a random sampling algorithm based on a relaxed feasible solution category distribution provided in an embodiment of the present application. Figure 9 As shown in the example, in this embodiment, the target feasible solution Consistent, relaxed feasible solution Is a matrix data, so it includes multiple columns of data, each column of data is a sub-relaxed feasible solution. Therefore, from a sub-relaxed feasible solution Sampling from a categorical distribution of event probabilities (e.g. Figure 9 As shown in step 3 of the algorithm in , it is expressed as Where Cat() is the probability distribution processing) to obtain the target feasible solution Each column of data, that is, the feasible solution of the sub-goal X ·i Then based on all sub-goals, a feasible solution X ·i Combine to obtain the final feasible solution corresponding to the maximum segmentation model (2)

[0163] This randomized approach yields a feasible solution to the maximum partitioning model (2) However, due to Figure 7 The algorithm 1 shown in arrive Randomness is introduced in the generation process of the objective function value Therefore, it becomes a random variable. In this embodiment, it can be proved by theory This shows that The expectation is equal to This means that the random sampling method can generate a maximum k-cut feasible solution with the same objective function value in a probabilistic sense based on the continuous solution. This means that the random sampling method can generate a maximum k-cut feasible solution with the same objective function value in a probabilistic sense based on the continuous solution.

[0164] In some embodiments, based on the probability distribution of the relaxed feasible solution obtained in the previous step, a sampling is performed to obtain a single feasible solution of the maximum segmentation model. The sampling process here can be understood as randomly assigning a segmentation label to each node based on the probability of each node belonging to different segmentation regions. For example, if a node has an 80% probability of belonging to region A and a 20% probability of belonging to region B, then when sampling, there is an 80% probability of assigning it to region A and a 20% probability of assigning it to region B.

[0165] Next, the maximum segmentation model is processed multiple times, each time using the iterative solution and probabilistic sampling process described above, to obtain multiple single-shot feasible solutions. Alternatively, different random sampling methods can be used to generate different segmentation schemes. This increases the diversity of segmentation results for subsequent selection. This allows for a broader exploration of the solution space and avoids being trapped in local optima.

[0166] Finally, the best single-shot feasible solution is selected as the final target feasible solution. The selection criterion is the value of the adjacency objective function, which is used to evaluate the quality of the segmentation result, such as the smoothness and connectivity of the segmented region. By comparing the adjacency objective function values ​​corresponding to different single-shot feasible solutions and selecting the solution with the smallest value, we have found a solution that best meets the segmentation goal based on the current relaxed feasible solution. This is similar to a local search process, searching for the optimal discrete solution within the neighborhood of the current probability distribution.

[0167] Through the above steps 801 to 803, the continuous solution obtained by the relaxed optimization can be converted into a practical discrete segmentation result, and the probability distribution is used for sampling to generate multiple different segmentation schemes, thereby providing more flexible choices and possibly finding the best segmentation scheme that better meets actual needs. At the same time, the sampling process can be regarded as a "refinement" of the relaxed solution, which helps to eliminate the errors introduced by the relaxation and improve the accuracy of the segmentation results. Multiple different feasible solutions are then generated by repeated sampling, which effectively explores the probability space defined by the relaxed solution, increases the possibility of finding high-quality solutions, and avoids the suboptimal results that may be caused by single random sampling. The adjacency objective function is then used as an evaluation criterion to select the best one from multiple candidate solutions to ensure that the final output target feasible solution not only conforms to the probability distribution, but also performs best in actual segmentation quality (such as regional smoothness, boundary clarity, and other indicators defined by the adjacency objective function), thereby improving the accuracy and reliability of the final image segmentation result.

[0168] Reference Figure 10 , is a flowchart of a maximum segmentation model solution provided by an embodiment of the present application. Figure 9 As shown in , first, the adjacency matrix W of the image data G is input, which describes the relationship between nodes (or nodes). Next, the "probabilistic simplex relaxation" (corresponding to steps 201-203 above) is performed to convert the original discrete assignment problem (such as the one-hot vector representation) into a continuous probability distribution representation, and obtain a relaxed continuous optimization model. Then, the core step is to use the "reparameterized graph neural network optimization" (corresponding to steps 301-304 and steps 501-504 above). The network learns the optimization parameters through "unsupervised loss training" in the "training" stage and outputs the optimized continuous parameters (relaxed feasible solution) in the "inference" stage. Finally, through "category distribution sampling" (corresponding to steps 801-803 above), sampling is performed from the relaxed feasible solution (probability distribution) output by the neural network to obtain the final discrete "node allocation of graph G" result (target feasible solution) as output.

[0169] It can be understood that the target feasible solution to the maximum segmentation problem obtained by the solution of the present application can be used to divide the vertices of image data into multiple non-overlapping subsets so as to maximize the total weight of the edges between different subsets. It can also be applied to a wide range of fields such as telecommunication networks, data clustering, and theoretical physics.

[0170] In order to further verify the reliability of the maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks proposed in this application, this embodiment also conducts simulation experiments on the performance of this scheme and other algorithms in solving the maximum split model.

[0171] Reference Figure 10, is a performance simulation diagram of a maximum segmentation model solution provided by an embodiment of the present application. Figure 10 As shown in , this embodiment compares the performance of the maximum segmentation model solving method (relaxation-optimization-sampling algorithm) proposed in this application with five other existing algorithms (semi-positive definite relaxation algorithm, local search algorithm, genetic algorithm, mirror gradient descent algorithm, and physical driven graph neural network algorithm) under different problem scales. Each column in the table represents a different experimental setting, specifically a combination of the number of nodes N (with a value of 100, 1000, 10000) and the number of categories k (with a value of 2, 3). The rows of the table correspond to different solving algorithms. The value in the cell (usually in the format of mean ± standard deviation) represents the objective function value or other performance index obtained by each algorithm to solve the maximum segmentation model under the corresponding setting, where the smaller the value, the better the performance. Some cells are marked "N / A" or "-", indicating that the algorithm is not applicable, has not been tested, or has not been successfully solved under this setting. This table aims to demonstrate, through quantitative comparison, the effectiveness and scalability of the method proposed in this application compared to existing technologies in segmentation problems of different scales and complexities. In particular, when dealing with large-scale problems (such as N = 10,000), the solution provided by this application brings significant overall beneficial effects through a refined reparameterized graph neural network iterative solution relaxation model, a specifically designed network layer update function, a training-based optimization strategy for initial network parameters, and a layer-by-layer optimized multi-layer network learning mechanism. These effects are reflected in the fact that this solution can not only obtain high-quality maximum segmentation solutions under various graph scales and numbers of segmentations, but more importantly, it exhibits superior scalability and robustness on large-scale graphs, thus providing a new approach to solving the maximum segmentation problem with high efficiency and excellent performance.

[0172] The embodiment of the present application proposes a maximum split solution method and related equipment based on relaxed optimization sampling of a reparameterized graph neural network. The method includes: first, obtaining a maximum split model, which includes an adjacency objective function and a one-hot vector parameter; then, sampling is performed based on the probability distribution of the relaxed feasible solution to obtain a single feasible solution of the maximum split model, and a single feasible solution with the smallest value of the adjacency objective function is selected from multiple single feasible solutions as a sub-target feasible solution. Based on all sub-target feasible solutions, a target feasible solution is obtained, and the relaxed continuous optimization model includes continuous parameters; then, the continuous parameters are converted into node embedding parameters, and the relaxed continuous optimization model is converted into node embedding parameters based on the node embedding parameters. The adjacency objective function is converted into an embedding objective function; next, based on the product of the first network parameter and the node embedding parameter of the current node, the first iterative update part is obtained, based on the cumulative value of the product of the node embedding parameters and the node weight of all other nodes, and then multiplied by the second network parameter, the second iterative update part is obtained, the node weight is the weight parameter between the current node and other nodes in the adjacency matrix parameter, based on the cumulative value of the first iterative update part and the second iterative update part, and multiplied by the activation function, the iterative update function of the current node is obtained, the loss function is generated based on the network parameters and the optimized embedding objective function, and multiple training adjacency matrices and node embedding parameters are generated. Training loss function, iteratively updating network parameters and node embedding parameters based on each training loss function, and obtaining the training feasible solution corresponding to each training adjacency matrix based on the node embedding parameters after multiple iterative updates, generating parameter optimization function corresponding to the embedding objective function based on each training adjacency matrix and the corresponding training feasible solution, obtaining the training parameter optimization function based on the average processing of all parameter optimization functions, optimizing the training parameter optimization function, obtaining the optimized initial network parameters, and using the optimized initial network parameters as the initial values ​​of the network parameters, in each layer of the neural network, the node embedding parameters and loss function of each node based on the output of the previous layer of the neural network are used. number, update the network parameters, update the node embedding parameters of each node based on the updated network parameters, and use the updated node embedding parameters as the input of the corresponding node in the next layer of neural network, and obtain a relaxed feasible solution based on the node embedding parameters after multiple iterations; finally, sample based on the probability distribution of the relaxed feasible solution to obtain a single feasible solution of the maximum segmentation model, select the single feasible solution with the smallest value of the adjacency objective function from multiple single feasible solutions as the sub-target feasible solution, and obtain the target feasible solution based on all sub-target feasible solutions. The target feasible solution is used to segment the image data corresponding to the maximum segmentation model into multiple subset image data with maximized total weight.

[0173] The embodiment of the present application converts the discrete one-hot vector parameters of the original maximum segmentation model into a more easily tractable continuous optimization problem by performing simplex relaxation, effectively reducing the difficulty of solving the problem, and uses a reparameterized graph neural network to efficiently iteratively solve the node embedding parameters and the embedding objective function, and finally obtains the target feasible solution through probability sampling. Compared with traditional reinforcement learning methods, the innovative "relaxation-optimization-sampling" framework, especially the use of the powerful graph representation learning ability and end-to-end optimization method of the graph neural network, can significantly improve the efficiency of solving large-scale maximum segmentation models and the quality of the solution, and avoid the complex sequence decision-making in the reinforcement learning method. The process and long training time provide a faster, more accurate and more scalable solution to the NP-complete maximum split problem, which can greatly improve the solution efficiency and accuracy of the maximum split model, and provide an innovative and scalable technical solution for solving large-scale weighted maximum split problems. Moreover, the discrete category assignment problem that is difficult to directly optimize in the original maximum split model is converted into an optimization problem that can be solved in a continuous space, making it possible to apply mature and efficient continuous optimization algorithms such as gradient descent to find the optimal solution or high-quality approximate solution of the model, greatly improving the solution efficiency and stability, and avoiding the problem of The computational complexity brought by combinatorial search in a huge discrete solution space; in addition, by clarifying the specific steps of iteratively solving the relaxed continuous optimization model (including generating iterative update functions, loss functions, and iteratively updating network parameters and node embedding parameters based on this), a clear algorithm flow is provided for how the core reparameterized graph neural network learns and approximates the relaxed feasible solution; secondly, by distinguishing between processing node information itself (the first iterative update part) and adjacent node aggregation information (the second iterative update part, and considering the weights in the adjacency matrix), and combining the activation function, the network can more accurately capture and fuse the local structural features of the nodes in the graph and interact with each other, thereby learning node representations that are more discriminative for the maximum segmentation problem; and, introducing an advanced network parameter initialization strategy, which pre-calculates and optimizes the initial network parameters by utilizing multiple training adjacency matrices and their corresponding training feasible solutions. This "meta-learning" or "pre-training" approach enables the model to iterate from an optimized parameter starting point that is closer to the optimal solution space when processing a new target graph, thereby significantly accelerating convergence, improving the quality of the final solution, and enhancing the model's generalization ability to different graph structures, avoiding the problems of local optimality or low training efficiency that may occur when training from random parameters.Finally, the refined learning mechanism of layer-by-layer and alternating updates of network parameters and node embedding parameters in multi-layer reparameterized graph neural networks is clarified. In each layer of the network, the network parameters of the layer are first updated according to the node embedding and loss function output by the previous layer, and then the node embedding of the layer is optimized with the updated network parameters. This layer-by-layer refinement method enables the network to learn deeper and more complex graph feature representations, thereby gradually improving the understanding and solution accuracy of the maximum segmentation problem; in addition, the continuous solution obtained by relaxed optimization can be converted into a practical discrete segmentation result, and sampling using probability distribution can generate multiple different segmentation schemes, thereby providing more flexible choices and possibly finding the best one that better meets actual needs. The optimal segmentation scheme is obtained. At the same time, the sampling process can be regarded as a "refinement" of the relaxed solution, which helps to eliminate the errors introduced by relaxation and improve the accuracy of the segmentation results. Repeated sampling generates multiple different feasible solutions, effectively exploring the probability space defined by the relaxed solution, increasing the possibility of finding a high-quality solution, and avoiding the suboptimal results that may be caused by single random sampling. The adjacency objective function is then used as an evaluation criterion to select the best one from multiple candidate solutions, ensuring that the final output target feasible solution not only conforms to the probability distribution but also performs best in terms of actual segmentation quality (such as regional smoothness, boundary clarity, and other indicators defined by the adjacency objective function), thereby improving the accuracy and reliability of the final image segmentation result.

[0174] The embodiment of the present application also provides a maximum split solution device based on relaxation optimization sampling of reparameterized graph neural network, which can realize the maximum split solution method based on relaxation optimization sampling of reparameterized graph neural network. Figure 11 , the apparatus 1200 comprises:

[0175] An acquisition module 1210 is configured to acquire a maximum segmentation model, the maximum segmentation model including an adjacency objective function and a one-hot vector parameter;

[0176] A relaxation transformation module 1220 is used to perform a simplex relaxation transformation on the one-hot vector parameters in the maximum partitioning model to obtain a relaxed continuous optimization model, wherein the relaxed continuous optimization model includes continuous parameters;

[0177] a model conversion module 1230 for converting continuous parameters into node embedding parameters, and converting the adjacency objective function of the relaxed continuous optimization model into an embedding objective function based on the node embedding parameters;

[0178] An iterative solution module 1240 is configured to iteratively solve the relaxed continuous optimization model based on the embedded objective function, the node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution;

[0179] The sampling processing module 1250 is used to perform sampling based on the probability distribution of the relaxed feasible solution to obtain the target feasible solution of the maximum segmentation model. The target feasible solution is used to segment the image data corresponding to the maximum segmentation model into multiple subset image data with maximized total weight.

[0180] In some embodiments, the relaxation conversion module 1220 is further configured to:

[0181] Generate multiple multidimensional Cartesian products based on the convex hull of the one-hot vector parameters;

[0182] Based on all multidimensional Cartesian products, the one-hot vector parameters are relaxed to obtain continuous parameters;

[0183] The parameters of the maximum split model are transformed based on the continuous parameters to obtain a relaxed continuous optimization model.

[0184] In some embodiments, the iterative solution module 1240 is further configured to:

[0185] Generate an iterative update function for each layer of the reparameterized graph neural network based on the node embedding parameters, the embedding objective function, and the network parameters of the reparameterized graph neural network;

[0186] Generate a loss function based on the network parameters and the optimized embedding objective function;

[0187] Iteratively update network parameters and node embedding parameters based on iterative update function and loss function;

[0188] Based on the node embedding parameters updated after multiple iterations, a relaxed feasible solution is obtained.

[0189] In some embodiments, the iterative solution module 1240 is further configured to:

[0190] obtaining a first iterative update portion based on a product of the first network parameter and a node embedding parameter of the current node;

[0191] The second iterative update part is obtained by multiplying the accumulated value of the product of the node embedding parameters and the node weights of all other nodes by the second network parameter, where the node weight is the weight parameter between the current node and other nodes in the adjacency matrix parameter;

[0192] Based on the accumulated value of the first iterative update part and the second iterative update part, and multiplied by the activation function, the iterative update function of the current node is obtained.

[0193] In some embodiments, the iterative solution module 1240 is further configured to:

[0194] Generate multiple training loss functions based on multiple training adjacency matrices and node embedding parameters;

[0195] Iteratively update the network parameters and node embedding parameters based on each training loss function, and obtain the training feasible solution corresponding to each training adjacency matrix based on the node embedding parameters after multiple iterations of updates;

[0196] Based on multiple training adjacency matrices and corresponding training feasible solutions, the optimized initial network parameters are calculated;

[0197] The optimized initial network parameters are used as the initial values ​​of the network parameters, and then the network parameters and node embedding parameters are iteratively updated based on the iterative update function and loss function.

[0198] In some embodiments, the iterative solution module 1240 is further configured to:

[0199] Based on each training adjacency matrix and the corresponding training feasible solution, a parameter optimization function corresponding to the embedding objective function is generated;

[0200] Based on the average processing of all parameter optimization functions, the training parameter optimization function is obtained;

[0201] The training parameter optimization function is optimized to obtain the optimized initial network parameters.

[0202] In some embodiments, the iterative solution module 1240 is further configured to:

[0203] In each layer of the neural network, the network parameters are updated based on the node embedding parameters and loss function of each node output by the previous layer of the neural network;

[0204] The node embedding parameters of each node are updated based on the updated network parameters, and the updated node embedding parameters are used as the input of the corresponding node in the next layer of neural network.

[0205] In some embodiments, the sampling processing module 1250 is further configured to:

[0206] Sampling is performed based on the probability distribution of the relaxed feasible solution to obtain a single feasible solution of the maximum partitioning model;

[0207] Select the single feasible solution with the smallest value of the adjacent objective function from multiple single feasible solutions as the sub-goal feasible solution;

[0208] Based on all feasible solutions of sub-goals, the feasible solution of the goal is obtained.

[0209] In the above embodiments, the description of each embodiment has its own focus. For the part that is not described in detail in a certain embodiment, the specific implementation of the maximum split solution device based on relaxed optimization sampling of reparameterized graph neural network is basically consistent with the specific implementation of the maximum split solution method based on relaxed optimization sampling of reparameterized graph neural network mentioned above, and will not be repeated here.

[0210] In the embodiment of the present application, the maximum split solution device based on relaxation optimization sampling of reparameterized graph neural network converts the discrete one-hot vector parameters of the original maximum split model into a more easily handled continuous optimization problem by performing simplex relaxation, effectively reducing the difficulty of solution, and using the reparameterized graph neural network to efficiently iteratively solve the node embedding parameters and the embedding objective function, and finally obtains the target feasible solution through probability sampling. Compared with the traditional reinforcement learning method, through the innovative "relaxation-optimization-sampling" framework, especially by utilizing the powerful graph representation learning ability and end-to-end optimization method of the graph neural network, it can significantly improve the efficiency and The quality of the solution is improved, avoiding the complex sequential decision-making process and long training time in the reinforcement learning method, and providing a faster, more accurate and more easily scalable solution to the NP-complete maximum split problem, thereby greatly improving the solution efficiency and accuracy of the maximum split model, and providing an innovative and scalable technical solution for solving large-scale weighted maximum split problems; and, converting the discrete category assignment problem that is difficult to directly optimize in the original maximum split model into an optimization problem that can be solved in a continuous space, making it possible to apply mature and efficient continuous optimization algorithms such as gradient descent to find the optimal solution or high-quality approximate solution of the model, greatly improving The efficiency and stability of the solution are improved, and the computational complexity brought by the combinatorial search in the huge discrete solution space is avoided. In addition, by clarifying the specific steps of iteratively solving the relaxed continuous optimization model (including generating the iterative update function, the loss function, and updating the network parameters and node embedding parameters based on this iterative process), a clear algorithm flow is provided for how the core reparameterized graph neural network learns and approximates the relaxed feasible solution. Secondly, by distinguishing between processing the node's own information (the first iterative update part) and the aggregated information of the adjacent nodes (the second iterative update part, and considering the weights in the adjacency matrix), and combining the activation function, the network can more accurately capture and fuse the nodes in the graph. The method uses the local structural features and mutual influence of the network to learn node representations that are more discriminative for the maximum segmentation problem; and introduces an advanced network parameter initialization strategy that pre-calculates and optimizes the initial network parameters by utilizing multiple training adjacency matrices and their corresponding training feasible solutions. This "meta-learning" or "pre-training" approach enables the model to iterate from an optimized parameter starting point that is closer to the optimal solution space when processing a new target graph, thereby significantly accelerating convergence, improving the quality of the final solution, and enhancing the model's generalization ability to different graph structures, avoiding the problems of local optimality or low training efficiency that may occur when training with random parameters.Finally, the refined learning mechanism of layer-by-layer and alternating updates of network parameters and node embedding parameters in multi-layer reparameterized graph neural networks is clarified. In each layer of the network, the network parameters of the layer are first updated according to the node embedding and loss function output by the previous layer, and then the node embedding of the layer is optimized with the updated network parameters. This layer-by-layer refinement method enables the network to learn deeper and more complex graph feature representations, thereby gradually improving the understanding and solution accuracy of the maximum segmentation problem; in addition, the continuous solution obtained by relaxed optimization can be converted into a practical discrete segmentation result, and sampling using probability distribution can generate multiple different segmentation schemes, thereby providing more flexible choices and possibly finding the best one that better meets actual needs. The optimal segmentation scheme is obtained. At the same time, the sampling process can be regarded as a "refinement" of the relaxed solution, which helps to eliminate the errors introduced by relaxation and improve the accuracy of the segmentation results. Repeated sampling generates multiple different feasible solutions, effectively exploring the probability space defined by the relaxed solution, increasing the possibility of finding a high-quality solution, and avoiding the suboptimal results that may be caused by single random sampling. The adjacency objective function is then used as an evaluation criterion to select the best one from multiple candidate solutions, ensuring that the final output target feasible solution not only conforms to the probability distribution but also performs best in terms of actual segmentation quality (such as regional smoothness, boundary clarity, and other indicators defined by the adjacency objective function), thereby improving the accuracy and reliability of the final image segmentation result.

[0211] An embodiment of the present application further provides an electronic device, including:

[0212] at least one memory;

[0213] at least one processor;

[0214] at least one program;

[0215] The program is stored in the memory, and the processor executes the at least one program to implement the maximum split solution method based on relaxed optimization sampling of a reparameterized graph neural network implemented in this application. The electronic device can be any smart terminal including a mobile phone, a tablet computer, a personal digital assistant (PDA), an in-vehicle computer, etc.

[0216] See also Figure 13 , Figure 13 The hardware structure of an electronic device according to another embodiment is shown. The electronic device includes:

[0217] The processor 1301 can be implemented as a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present application;

[0218] The memory 1302 can be implemented in the form of ROM (Read Only Memory), static storage device, dynamic storage device or RAM (Random Access Memory). The memory 1302 can store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program codes are stored in the memory 1302, and the processor 1301 calls and executes the maximum segmentation solution method based on relaxed optimization sampling of a reparameterized graph neural network in the embodiments of this application;

[0219] Input / output interface 1303, used to implement information input and output;

[0220] Communication interface 1304, used to implement communication interaction between this device and other devices, which can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WiFi, Bluetooth, etc.);

[0221] Bus 1305 , which transmits information between various components of the device (e.g., processor 1301 , memory 1302 , input / output interface 1303 , and communication interface 1304 );

[0222] The processor 1301 , the memory 1302 , the input / output interface 1303 and the communication interface 1304 are connected to each other in communication within the device via a bus 1305 .

[0223] An embodiment of the present application also provides a storage medium, which is a computer-readable storage medium. The storage medium stores a computer program, which, when executed by a processor, implements the maximum segmentation solution method based on relaxed optimization sampling of a reparameterized graph neural network.

[0224] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0225] The embodiments described in the embodiments of this application are intended to more clearly illustrate the technical solutions of the embodiments of this application and do not constitute a limitation on the technical solutions provided by the embodiments of this application. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in the embodiments of this application are also applicable to similar technical problems.

[0226] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present application, and may include more or fewer steps than shown in the figures, or a combination of certain steps, or different steps.

[0227] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, i.e., they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of this embodiment.

[0228] Those skilled in the art will appreciate that all or some of the steps in the methods, systems, and functional modules / units in the devices disclosed above may be implemented as software, firmware, hardware, or appropriate combinations thereof.

[0229] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0230] It should be understood that in this application, "at least one (item)" means one or more, and "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following items" or similar expressions refers to any combination of these items, including any combination of single items or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0231] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the above-mentioned units is only a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. The mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0232] The units described above as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0233] In addition, the functional units in the various embodiments of the present application may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0234] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes multiple instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of the present application. The aforementioned storage medium includes: various media that can store programs, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0235] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present invention should be within the scope of the present invention.

Claims

1. A maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks, characterized by: The method comprises: Obtaining a maximum segmentation model, the maximum segmentation model including an adjacency objective function and a one-hot vector parameter; Performing simplex relaxation transformation on the one-hot vector parameters in the maximum segmentation model to obtain a relaxed continuous optimization model, wherein the relaxed continuous optimization model includes continuous parameters; Converting the continuous parameters into node embedding parameters, and converting the adjacency objective function of the relaxed continuous optimization model into an embedding objective function based on the node embedding parameters; Iteratively solving the relaxed continuous optimization model based on the embedding objective function, the node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution; Sampling is performed based on the probability distribution of the relaxed feasible solution to obtain a target feasible solution of the maximum segmentation model.

2. The maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks according to claim 1 is characterized in that: The iteratively solving the relaxed continuous optimization model based on the embedding objective function, the node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution includes: Generate an iterative update function for each layer of the neural network in the reparameterized graph neural network based on the node embedding parameters, the embedding objective function, and the network parameters of the reparameterized graph neural network; generating a loss function based on the network parameters and optimizing the embedding objective function; Iteratively updating the network parameters and the node embedding parameters based on the iterative update function and the loss function; The relaxed feasible solution is obtained based on the node embedding parameters after multiple iterations of updating.

3. The maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks according to claim 2 is characterized in that: The network parameters include first network parameters and second network parameters, the embedding objective function includes adjacency matrix parameters, and generating an iterative update function for each layer of the neural network in the reparameterized graph neural network based on the node embedding parameters, the embedding objective function, and the network parameters of the reparameterized graph neural network includes: obtaining a first iterative update part based on a product of the first network parameter and the node embedding parameter of the current node; A second iterative update part is obtained by multiplying the accumulated value of the product of the node embedding parameter and the node weight of all other nodes by the second network parameter, wherein the node weight is a weight parameter between the current node and other nodes in the adjacency matrix parameter; The iterative update function of the current node is obtained based on the accumulated value of the first iterative update part and the second iterative update part and multiplied by the activation function.

4. The maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks according to claim 3 is characterized in that: The iteratively updating the network parameters and the node embedding parameters based on the iterative update function and the loss function includes: generating a plurality of training loss functions based on a plurality of training adjacency matrices and the node embedding parameters; Iteratively updating the network parameters and the node embedding parameters based on each of the training loss functions, and obtaining a training feasible solution corresponding to each of the training adjacency matrices based on the node embedding parameters after multiple iterative updates; Based on the plurality of training adjacency matrices and the corresponding training feasible solutions, calculating and obtaining optimized initial network parameters; The optimized initial network parameters are used as initial values ​​of the network parameters, and the network parameters and the node embedding parameters are iteratively updated based on the iterative update function and the loss function.

5. The maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks according to claim 4 is characterized in that: The step of calculating and optimizing initial network parameters based on the plurality of training adjacency matrices and the corresponding training feasible solutions includes: generating a parameter optimization function corresponding to the embedding objective function based on each of the training adjacency matrices and the corresponding training feasible solution; Obtaining a training parameter optimization function based on an average processing of all the parameter optimization functions; The training parameter optimization function is optimized to obtain the optimized initial network parameters.

6. The maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks according to claim 4 is characterized in that: The reparameterized graph neural network includes a multi-layer neural network, and the iterative updating of the network parameters and the node embedding parameters based on the iterative update function and the loss function includes: In each layer of the neural network, the network parameters are updated based on the node embedding parameters of each node output by the previous layer of the neural network and the loss function; The node embedding parameters of each node are updated based on the updated network parameters, and the updated node embedding parameters are used as inputs for corresponding nodes in the next layer of neural network.

7. The maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks according to claim 1 is characterized in that: The relaxed feasible solution includes a plurality of sub-relaxed feasible solutions, and the sampling based on the probability distribution of the relaxed feasible solutions to obtain the target feasible solution of the maximum segmentation model includes: Sampling based on the probability distribution of the relaxed feasible solution to obtain a single feasible solution of the maximum segmentation model; Selecting the single feasible solution with the smallest adjacent objective function value from the multiple single feasible solutions as the sub-goal feasible solution; Based on all the feasible solutions of the sub-goals, the feasible solution of the goal is obtained.

8. The maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks according to claim 1 is characterized in that: The step of performing simplex relaxation transformation on the one-hot vector parameters in the maximum segmentation model to obtain a relaxed continuous optimization model comprises: generating a plurality of multidimensional Cartesian products based on the convex hull of the one-hot vector parameter; Obtaining the continuous parameter for the one-hot vector parameter based on all the multidimensional Cartesian products; Parameter conversion is performed on the maximum segmentation model based on the continuous parameters to obtain the relaxed continuous optimization model.

9. A maximum split solving device based on relaxed optimization sampling of reparameterized graph neural networks, characterized in that: The device comprises: An acquisition module, configured to acquire a maximum segmentation model, wherein the maximum segmentation model includes an adjacency objective function and a one-hot vector parameter; a relaxation conversion module, configured to perform a simplex relaxation conversion on the one-hot vector parameters in the maximum segmentation model to obtain a relaxed continuous optimization model, wherein the relaxed continuous optimization model includes continuous parameters; a model conversion module, configured to convert the continuous parameters into node embedding parameters, and convert the adjacency objective function of the relaxed continuous optimization model into an embedding objective function based on the node embedding parameters; An iterative solution module, configured to iteratively solve the relaxed continuous optimization model based on the embedding objective function, the node embedding parameters, and the reparameterized graph neural network to obtain a relaxed feasible solution; A sampling processing module is used to perform sampling based on the probability distribution of the relaxed feasible solution to obtain a target feasible solution of the maximum segmentation model, wherein the target feasible solution is used to segment the image data corresponding to the maximum segmentation model into a plurality of subset image data with maximized total weight.

10. An electronic device, characterized in that: It includes a memory and a processor, the memory stores a computer program, and is characterized in that when the processor executes the computer program, it implements the maximum split solution method based on relaxed optimization sampling of reparameterized graph neural networks as described in any one of claims 1 to 8.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the maximum split solution method based on relaxed optimization sampling of a reparameterized graph neural network according to any one of claims 1 to 8 is implemented.

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