An interpretable neural network structure proliferation method based on linear separable metrics

Abstract

The application discloses an interpretable neural network structure proliferation method based on linear separable metrics, belongs to the technical field of artificial intelligence, machine learning and deep learning, and realizes the method by taking the value of linear separable metrics as a criterion. First, a small-scale initial neural network is constructed as a structure growth starting point; second, structure proliferation target parameters are set; third, structure proliferation is performed layer by layer in the order from shallow to deep of a hidden layer, and the linear separable metrics of the output features of the current hidden layer to different categories of samples are calculated; then, when the layer reaches a preset target threshold, the structure proliferation of the layer is stopped, and the parameters of the layer are frozen, and structure proliferation of the next hidden layer is continued; finally, after all the hidden layers complete the structure proliferation, global super parameter optimization and overall fine-tuning training are performed on the whole network, and a final neural network model is obtained. The application dynamically adds neurons by explicitly measuring the task contribution rate, guarantees structure adaptability, and provides a new way for interpretable research.

Description

Technical Field

[0001] This invention belongs to the fields of artificial intelligence, machine learning and deep learning technology, and specifically relates to an adaptive optimization method for neural network structures, and more particularly to an interpretable neural network structure proliferation method based on linear separability metric, which can be applied to pattern recognition, classification prediction, medical auxiliary diagnosis, industrial intelligent detection, financial risk identification and adaptive intelligent decision-making. Background Technology

[0002] With the rapid development of artificial intelligence technology, machine learning methods, represented by deep neural networks, have achieved remarkable results in fields such as image recognition, speech processing, natural language understanding, industrial control, and medical diagnosis. Deep neural networks rely on multi-layer nonlinear mapping structures to achieve high-dimensional feature extraction and complex task modeling. Their performance largely depends on the network structure design, including the number of hidden layers, the number of hidden units in each layer, the connection method, and parameter configuration.

[0003] In existing technologies, most neural networks are built using a pre-designed fixed structure. This means that before training begins, researchers pre-determine the network depth, hidden node size, and network topology based on experience. Then, through extensive experimentation, hyperparameters such as learning rate, batch size, and number of iterations are repeatedly adjusted to obtain optimal model performance. However, this fixed-structure design method has the following drawbacks: (1) Structural design is highly dependent on experience. Network structures are usually set manually based on the experience of researchers, lacking clear theoretical guidance. Different tasks often require structural trials and parameter adjustments, resulting in high design costs. (2) Insufficient structural adaptability. Fixed structures are difficult to automatically adjust the network capacity according to the complexity of the task, which can easily lead to underfitting due to insufficient network size, or overfitting and parameter redundancy due to excessively large structures; (3) The model has weak interpretability. The formation process of existing deep neural network structures is usually generated by empirical design or black box optimization, which cannot explain why a certain layer structure is expanded, how much it is expanded, and the degree of contribution to the improvement of task performance after expansion, resulting in a lack of transparency in the structure learning process; (4) Insufficient training stability. For large-scale networks, simultaneous updates of global parameters can easily lead to problems such as gradient oscillations, local optima, and severe parameter coupling, which affect the training convergence stability.

[0004] To address the aforementioned issues, structurally growing neural network methods have emerged in recent years. These methods dynamically increase the number of hidden layer nodes or network layers during training, allowing the network complexity to gradually increase with task requirements. For example, the Cascade-Correlation method reduces residual error by adding new hidden neurons; some constructive networks use gradient descent strategies for dynamic structural expansion; and some neural architecture search methods utilize reinforcement learning or evolutionary algorithms to search for optimal structures. Although these methods improve structural adaptability to some extent, they still suffer from several drawbacks. Structural growth is typically driven by gradients, residual errors, or heuristic rules, lacking clear theoretical criteria; the improvement in hidden layer representational ability cannot be directly quantified during structural growth; the contribution of hidden layers to the task lacks explicit expression; redundant nodes and invalid connections are easily generated during structural expansion; and global parameter updates during training lead to a high degree of coupling between structural learning and parameter optimization, resulting in instability. Recent research has found that the linear separability of the output features of deep network hidden layers can effectively reflect the discriminative contribution of that layer to classification tasks. When the hidden layer output maps to a space that is more easily linearly separable, it indicates that the layer has formed a better class discriminative representation. Therefore, if the degree of improvement in the linear separability of the hidden layers can be used as the basis for structural growth, then the network structure expansion process can have a clear geometric meaning and a theoretical explanation.

[0005] To address the aforementioned issues, this invention proposes an interpretable neural network structure proliferation method based on linear separability metrics. This method provides a neural network structure proliferation method that uses the linear separability of hidden layers as the core criterion, can explicitly measure the task contribution rate, and has good training stability and structural interpretability. Summary of the Invention

[0006] To address the problems of existing technologies, this invention provides an interpretable neural network structure proliferation method based on linear separability metrics. The neural network of this invention dynamically adds neurons layer by layer by explicitly measuring the task contribution rate, providing a new perspective for interpretability research while ensuring structural adaptability. Existing neural network structure proliferation techniques suffer from problems such as reliance on experience in neural network structure design, lack of theoretical basis for structure growth, insufficient interpretability, and poor training stability.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: An interpretable neural network structure proliferation method based on a linear separability metric, wherein the interpretable neural network structure proliferation method uses a linear separability metric ( The value of ) is used as the criterion. This includes the following steps: S1: Construct a small-scale initial neural network as the starting point for structural growth; specifically: S1-1: Construct an input layer, multiple hidden layers, and an output layer in the neural network as the initial neural network. The number of hidden layers is preset according to the actual task. Each hidden layer is initially set with a small number of hidden neurons to form a compact network structure.

[0008] S1-2: The initial neural network adopts a fully connected interlayer approach, that is, all neurons in two adjacent hidden layers are connected in pairs.

[0009] The hidden layer uses a non-linear activation function for mapping, and the ReLU activation function is preferred. (1) Where x is the input of the hidden layer; f(x) is the output of the hidden layer; max(0,x) is the maximum value between 0 and x; The output layer uses the Sigmoid activation function to output the binary classification probability result; the Sigmoid activation function is: (2) Where x is the input of the hidden layer; σ(x) is the output of the hidden layer; Meanwhile, the network weight parameters and bias parameters are randomly initialized to break the parameter symmetry between neurons.

[0010] S2: Set the target parameters for structural proliferation, including the target linear separability threshold, the maximum allowed number of neurons, and the preset number of neurons added during each structural proliferation. Also, set the loss function for neural network training. Specifically: The target linear separability threshold is T. l Where l = 1,2,…,L represents the l-th hidden layer, and L is the number of hidden layers; the target linear separability threshold is set according to the actual task situation.

[0011] The maximum allowed number of neurons is N. l max , used to limit the unlimited expansion of structures; The preset number of neurons added during each structural proliferation is Δn, where 0 < Δn < 100 is a natural number; The structural proliferation target parameters are set according to the task complexity, training sample size, and computational resource conditions. The loss function during the training of the neural network is: (3) in, This is a measure of linear separability; the goal is to maximize the linear separability measure for each layer during training.

[0012] S3: Perform structural proliferation layer by layer on the hidden layers of the initial neural network constructed in S1, from shallow to deep. During the proliferation process of each layer, add a predetermined number of new neurons, and calculate the linear separability measure of the output features of the current hidden layer for samples of different categories. Specifically: S3-1: For the current hidden layer to be multiplied, obtain its output feature H. l For binary classification problems, the output features of the current hidden layer are divided into two sets of points based on the two different sample class labels. The first set of points is A, where A = {a1, ..., a2}. I} R N The second type of point set is B, B = {b1, ..., b}. J} R N The Minkowski difference between the two types of point sets is constructed as follows: (4) Where MD(A,B) denotes the Minkowski difference set; m ij Let a represent an element in MD(A,B). i Let b represent a point in the first type of point set A. j R represents a point in the second type of point set B; N Let represent an n-dimensional vector space in Euclidean space.

[0013] S3-2: Based on the Minkowski difference in S3-1, the linear separability of two point sets A and B is transformed into the Minkowski difference set MD(A,B) and a hyperplane passing through the origin. T The relative positional relationships between m=0 are then used to calculate the linear separability metric. : (5) in: = / , ∈R N It is a hyperplane T The normal vector when m=0; This represents the sum of the elements in MD(A,B). := m ij This represents an element in MD(A,B).

[0014] In formula (5), the numerator is all points in the set MD(A,B) that are connected to the hyperplane. TThe absolute value of the sum of directed distances when m=0; the denominator is the sum of the distances from all points in the set MD(A,B) to the hyperplane. T The sum of the absolute values ​​of directed distances where m=0; S3-3: The linear separability metric of the current hidden layer output features obtained from formula (5).

[0015] S4: The linear separability measure obtained from S3 To achieve the target linear separability threshold T preset by S2 l When l = 1, 2, ..., L, stop the structural proliferation of the current hidden layer and freeze the parameters of the current hidden layer, then continue with the structural proliferation of the next hidden layer to obtain the final network structure; specifically: S4-1: Starting from the first hidden layer, determine the current hidden layer (i.e., the first hidden layer). Does it meet the requirements? ≥T l If this condition is met, it means that the current hidden layer has formed a feature representation with sufficient discriminative power, and the proliferation of the current hidden layer structure is stopped. S4-2: If not satisfied, perform hidden node expansion operation: add Δn new neurons to the current hidden layer; and re-randomly initialize the relevant weight parameters and bias parameters of the newly added neurons, then retrain the current proliferating part parameters, and recalculate the new parameters. If the target linear separability threshold is still not reached, the next round of proliferation continues until the following condition is met: ≥T l (l = 1,2,…,L) or N l ≥N l max Up to now, where N l max This represents the maximum allowed number of neurons.

[0016] S4-3: After structural proliferation is completed in a certain hidden layer, all parameters of the hidden layer obtained in S4-2 are frozen, meaning that the parameters of this hidden layer will not be updated in subsequent training. Only newly added node parameters, downstream connection parameters, and parameters of deeper hidden layers are allowed to participate in subsequent optimization.

[0017] S4-4: Proceed to the next hidden layer and repeat S3 to S4. Proceed layer by layer in the order from shallow to deep until all hidden layers have completed structural proliferation, and the final network structure is obtained.

[0018] S5: Optimize and fine-tune the global hyperparameters of the entire neural network after all hidden layers have multiplied, to obtain the final neural network model; specifically: S5-1: Based on the final network structure obtained in S4, a grid search method is used to perform a global hyperparameter combination traversal to finally determine the optimal learning rate and the optimal number of training rounds that maximize the classification accuracy of the final network structure. The global hyperparameters include the learning rate and the number of training rounds. S5-2: After determining the optimal learning rate and the optimal number of training rounds in S5-1, perform global fine-tuning training on the entire final network structure to further optimize the parameter coordination relationship, improve the overall classification performance of the model, and output the final neural network model.

[0019] The beneficial effects of this invention are: (1) The optimal learning rate and the optimal number of training rounds will be used as explicit mathematical indicators to measure linear separability. As a basis for structural growth, it enhances model interpretability while improving classification performance, and realizes the transformation of structural growth from experience-driven to measurement-driven. (2) The optimal learning rate and optimal number of training rounds adopt a layer-by-layer increment and parameter freezing update mechanism, which effectively reduces the coupling of parameters between layers and improves training stability; (3) The optimal learning rate and the optimal number of training rounds can automatically adjust the network size according to the task complexity, thereby improving the adaptive capability of the structure. Attached Figure Description

[0020] Figure 1 This is a curve showing how the linear separability metric of this invention changes with the number of training rounds and layers after propagation on a specific dataset. Figure 2 This is a curve showing the changes in training and testing errors as a function of the number of training rounds after amplification on a specific dataset according to the present invention; Figure 3 This is a flowchart of the method of the present invention. Detailed Implementation

[0021] To make the technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with specific embodiments.

[0022] This invention addresses the shortcomings of existing proliferation methods by proposing a method based on linear separability measurement in the fields of artificial intelligence, machine learning, and deep learning. This paper presents an interpretable neural network structure proliferation method. This embodiment uses the spambase data from the UCI dataset for neural network structure proliferation. First, an initial neural network with four hidden layers, each with two neurons, is constructed as the starting point for structure growth. Second, the target parameters for structure proliferation are set as follows: target linear separability threshold = [0.92, 0.96, 0.99, 0.999], maximum allowed number of neurons = 100, and a preset number of neurons added each time for structure proliferation = 3. Third, structure proliferation is performed layer by layer from shallow to deep, with 3 new neurons added each time. The linear separability metric of the current hidden layer's output feature for different categories of samples is calculated. Then, when the layer outputs features... When a preset target threshold is reached, the proliferation of that layer's structure is stopped and its parameters are frozen, then the proliferation of the next hidden layer continues. Finally, after all hidden layers have completed their proliferation, global hyperparameter optimization and overall fine-tuning training are performed on the entire network to obtain the final neural network model. The method includes the following steps: S1: Construct a small-scale neural network as the starting point for structural growth; specifically: S1-1: Construct an initial neural network consisting of an input layer, four hidden layers, and an output layer, with each hidden layer having two initial neural units as the starting point for structural growth.

[0023] S1-2: The initial neural network constructed in S1-1 adopts a fully connected interlayer approach, that is, all neurons in two adjacent hidden layers are connected in pairs.

[0024] The hidden layer uses a non-linear activation function for mapping, and the ReLU activation function is preferred. (1) Where x is the input of the hidden layer; f(x) is the output of the hidden layer; max(0,x) is the maximum value between 0 and x; The output layer uses the Sigmoid activation function to output the binary classification probability result; the Sigmoid activation function is: (2) Here, x is the input of the hidden layer; σ(x) is the output of the hidden layer; at the same time, the network weight parameters and bias parameters are randomly initialized to break the parameter symmetry between neurons.

[0025] S2: Set the target parameters for structural proliferation, including the target linear separability threshold, the maximum allowed number of neurons, and the preset number of neurons added during each structural proliferation. Also, set the loss function for neural network training. Specifically: The target linear separability threshold is T.l , where: l = 1,2,…,L, representing the l-th hidden layer; according to this task, the target linear separability threshold of the hidden layer is set to [0.92, 0.96, 0.99, 0.999], that is, T1=0.92, T2=0.96, T3=0.99, T4=0.999.

[0026] The maximum allowed number of neurons is N. l max =100, used to limit the infinite expansion of the structure; The preset number of neurons added during each structural proliferation is: Δn=3, where: 0<Δn<100 is a natural number; The loss function during the training of the neural network is: (3) in, This is a measure of linear separability; the goal is to maximize the linear separability measure for each layer during training.

[0027] S3: Perform structural proliferation layer by layer on the hidden layers of the initial neural network constructed in S1, from shallow to deep. During the proliferation process of each layer, 3 new neurons are proliferated each time, and the linear separability measure of the output features of the current hidden layer for samples of different classes is calculated. Specifically: S3-1: For the current hidden layer to be multiplied, obtain its output feature H. l For binary classification problems, the output features of the current hidden layer are divided into two sets of points based on the two different sample class labels. The first set of points is A, where A = {a1, ..., a2}. I} R N The second type of point set is B, B = {b1, ..., b}. J} R N The Minkowski difference between the two types of point sets is constructed as follows: (4) Where MD(A,B) denotes the Minkowski difference set; m ij Let a represent an element in MD(A,B). i Let b represent a point in the first type of point set A. j R represents a point in the second type of point set B; N Let represent an n-dimensional vector space in Euclidean space.

[0028] S3-2: Based on the Minkowski difference in S3-1, the linear separability of two point sets A and B is transformed into the Minkowski difference set MD(A,B) and a hyperplane passing through the origin. T The relative positional relationship between m=0 Calculate the linear separability metric : (5) in: = / , ∈R N It is a hyperplane T The normal vector when m=0; This represents the sum of the elements in MD(A,B). := m ij Represents the elements in MD(A,B) In formula (5), the numerator is all points in the set MD(A,B) that are connected to the hyperplane. T The absolute value of the sum of directed distances when m=0; the denominator is the sum of the distances from all points in the set MD(A,B) to the hyperplane. T The sum of the absolute values ​​of directed distances where m=0; S3-3: The linear separability metric of the current hidden layer output features obtained from formula (5).

[0029] S4: The linear separability measure obtained from S3 To achieve the target linear separability threshold T preset by S2 i When i=1,2,3,4, stop the structural proliferation of the current hidden layer and freeze the parameters of the current hidden layer, then continue with the structural proliferation of the next hidden layer to obtain the final network structure; specifically: S4-1: Starting from the first hidden layer, determine the current hidden layer (i.e., the first hidden layer). Does it meet the requirements? If the value is ≥0.92, it means that the current hidden layer has formed a feature representation with sufficient discriminative power, and the proliferation of the current hidden layer structure is stopped. S4-2: If not satisfied, perform hidden node expansion operation: add Δn=3 new neurons to the current hidden layer; and re-randomly initialize the relevant weight parameters and bias parameters of the newly added neurons, then retrain the current proliferating part parameters, and calculate the new parameters again using formula (4). If the target linear separability threshold is still not reached, the next round of proliferation continues until the following condition is met: ≥T i (i=1,2,3,4) or N l ≥Nl max Up to now, where N l max This represents the maximum allowed number of neurons.

[0030] S4-3: After structural proliferation is completed in a certain hidden layer, all parameters of the hidden layer obtained in S4-2 are frozen, meaning that the parameters of this hidden layer will not be updated in subsequent training. Only newly added node parameters, downstream connection parameters, and parameters of deeper hidden layers are allowed to participate in subsequent optimization.

[0031] S4-4: Proceed to the next hidden layer and repeat S3 to S4. Proceed layer by layer in the order from shallow to deep until all hidden layers have completed structural proliferation, and the final network structure is obtained.

[0032] S5: Optimize and fine-tune the global hyperparameters of the entire neural network after all hidden layers have multiplied, to obtain the final neural network model; specifically: S5-1: Based on the final network structure obtained in S4, a grid search method is used to perform a global hyperparameter combination traversal to finally determine the optimal learning rate and the optimal number of training rounds that maximize the classification accuracy of the final network structure. In this embodiment, the optimal learning rate is 0.01 and the optimal number of training rounds is 15. The global hyperparameters include the learning rate and the number of training rounds. S5-2: After determining the optimal learning rate and the optimal number of training rounds in S5-1, perform global fine-tuning training on the entire final network structure to further optimize the parameter coordination relationship, improve the overall classification performance of the model, and output the final neural network model.

[0033] In this embodiment, an interpretable neural network structure proliferation method based on linear separability metric is proposed. The neural network dynamically adds neurons by explicitly measuring the task contribution rate, which provides a new perspective for interpretability research while ensuring structural adaptability.

[0034] As an application example, we conducted experiments on datasets with different data scales, feature dimensions, and class distributions. Numerical experiments on binary classification tasks were performed on three classic UCI datasets: Spambase, Heart Disease, and Beed. In these experiments, the networks proliferated using our proposed method achieved higher prediction accuracy in the final tasks and exhibited better interpretability. Traditional methods primarily rely on heuristic or implicit gradient-driven structural adaptation, while our proposed method introduces an explicit representation quality criterion in structural proliferation. Each increase in network complexity is demonstrated through a measurable improvement in hidden layer separability, providing a clear geometric explanation for the cause of structural growth. This explicit coupling between representational separability and architectural adaptation not only improves prediction performance but also significantly enhances the interpretability of the network construction process. Therefore, the proposed framework provides a principled direction for adaptive, efficient, and interpretable neural network design.

[0035] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for the proliferation of interpretable neural network structures based on a linearly separable metric, characterized in that, The explained neural network structure proliferation method uses linear separability as a metric. The value is used as the criterion. Includes the following steps: S1: Construct a small-scale initial neural network as the starting point for structural growth; S2: Set the target parameters for structural proliferation, including the target linear separability threshold, the maximum allowed number of neurons, and the preset number of neurons added during each structural proliferation. Also, set the loss function for neural network training. Specifically: The loss function is: （3） in, This is a measure of linear separability; the goal is to maximize the linear separability measure for each layer during training. S3: Perform structural proliferation layer by layer on the hidden layers of the initial neural network constructed in S1, from shallow to deep. During the proliferation process of each layer, add a predetermined number of new neurons, and calculate the linear separability measure of the output features of the current hidden layer for samples of different categories. Specifically: S3-1: For binary classification problems, based on the two different sample class labels, the output features of the current hidden layer are divided into two sets of points, the first set of points being A, A={a1, ..., a2}. I } R N The second type of point set is B, B = {b1, ..., b}. J } R N The Minkowski difference between the two types of point sets is constructed as follows: （4） Where MD(A,B) denotes the Minkowski difference set; m ij Let a represent an element in MD(A,B). i Let b represent a point in the first type of point set A. j R represents a point in the second type of point set B; N Represents an n-dimensional vector space in Euclidean space; S3-2: Based on the Minkowski difference in S3-1, the linear separability of two point sets A and B is transformed into the Minkowski difference set MD(A,B) and a hyperplane passing through the origin. T Calculate the linear separability measure based on the relative positional relationships between m=0. : （5） in: = / , ∈R N It is a hyperplane T The normal vector when m=0; This represents the sum of the elements in MD(A,B). := m ij This represents the elements in MD(A,B); S3-3: The linear separability metric of the current hidden layer output features obtained by formula (5); S4: The linear separability measure obtained from S3 To achieve the target linear separability threshold T preset by S2 l When l = 1,2,…,L, stop the structural proliferation of the current hidden layer and freeze the parameters of the current hidden layer, and continue the structural proliferation of the next hidden layer to obtain the final network structure; S5: Optimize the global hyperparameters and fine-tune the overall training of the entire neural network after all hidden layers have been multiplied to obtain the final neural network model.

2. The method for propagating interpretable neural network structures based on linearly separable metrics according to claim 1, characterized in that, Specifically, S1 is: S1-1: Construct an input layer, multiple hidden layers, and an output layer in a neural network as the initial neural network; S1-2: The initial neural network adopts a fully connected interlayer approach, that is, all neurons in two adjacent hidden layers are connected in pairs.

3. The method for propagating interpretable neural network structures based on linearly separable metrics according to claim 2, characterized in that, In S1: The number of hidden layers is preset according to the actual task. Each hidden layer is initially set with a small number of hidden neurons to form a compact network structure. The hidden layer uses a non-linear activation function for mapping, and the ReLU activation function is preferred. （1） Where x is the input of the hidden layer; f(x) is the output of the hidden layer; max(0,x) is the maximum value between 0 and x; The output layer uses the Sigmoid activation function to output the binary classification probability result; the Sigmoid activation function is: （2） Where x is the input of the hidden layer; σ(x) is the output of the hidden layer; At the same time, the network weight parameters and bias parameters are randomly initialized.

4. The method for propagating interpretable neural network structures based on linearly separable metrics according to claim 3, characterized in that, In S2, the structural proliferation target parameters are set according to the task complexity, training sample size, and computational resource conditions.

5. The method for propagating interpretable neural network structures based on linearly separable metrics according to claim 4, characterized in that, In S2: The target linear separability threshold is T. l Where l = 1,2,…,L represents the l-th hidden layer, and L is the number of hidden layers; the target linear separability threshold is set according to the actual task situation. The maximum allowed number of neurons is N. l max , used to limit the unlimited expansion of structures; The preset number of neurons added during each structural proliferation is Δn, where 0 < Δn < 100 is a natural number.

6. The method for increasing the exponential structure of an interpretable neural network based on a linearly separable metric according to claim 5, characterized in that, In step S3-1, for the hidden layer to be propagated, its output feature H is obtained. l .

7. The method for propagating interpretable neural network structures based on linearly separable metrics according to claim 6, characterized in that, In formula (5) of S3, the numerator is all points in the set MD(A,B) to the hyperplane. T The absolute value of the sum of directed distances when m=0; the denominator is the sum of the distances from all points in the set MD(A,B) to the hyperplane. T The sum of the absolute values ​​of directed distances where m=0.

8. The method for increasing the structure of an interpretable neural network based on a linearly separable metric according to claim 7, characterized in that, Specifically, S4 includes: S4-1: Starting from the first hidden layer, determine the current hidden layer. Does it meet the requirements? ≥T l If this condition is met, it means that the current hidden layer has formed a feature representation with sufficient discriminative power, and the proliferation of the current hidden layer structure is stopped. S4-2: If not satisfied, perform hidden node expansion operation: add Δn new neurons to the current hidden layer; and re-randomly initialize the relevant weight parameters and bias parameters of the newly added neurons, then retrain the current proliferating part parameters, and recalculate the new parameters. If the target linear separability threshold is still not reached, the next round of proliferation continues until the following condition is met: ≥T l or N l ≥N l max Up to now, where N l max This represents the maximum allowed number of neurons. S4-3: After structural proliferation is completed in a certain hidden layer, all parameters of the hidden layer obtained in S4-2 are frozen, that is, the parameters of the hidden layer are not updated in subsequent training; only newly added node parameters, downstream connection parameters, and parameters of deeper hidden layers are allowed to participate in subsequent optimization. S4-4: Enter the next hidden layer and repeat S3 to S4; proceed layer by layer in the order from shallow to deep until all hidden layers have completed structural proliferation and the final network structure is obtained.

9. The method for propagating interpretable neural network structures based on linearly separable metrics according to claim 8, characterized in that, Specifically, S5 includes: S5-1: Based on the final network structure obtained in S4, a grid search method is used to perform a global hyperparameter combination traversal to finally determine the optimal learning rate and the optimal number of training rounds that maximize the classification accuracy of the final network structure. S5-2: After determining the optimal learning rate and the optimal number of training rounds in S5-1, perform global fine-tuning training on the entire final network structure to further optimize the parameter coordination relationship, improve the overall classification performance of the model, and output the final neural network model.

10. The method for propagating interpretable neural network structures based on a linearly separable metric according to claim 9, characterized in that, In S5, the global hyperparameters include the learning rate and the number of training epochs.

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