Adaptive time-frequency fusion sequence recommendation method based on Mama architecture

Abstract

The invention provides an adaptive time-frequency fusion sequence recommendation method based on a Mama framework, and relates to the technical field of sequence recommendation. Comprising the following steps: S1, carrying out embedding expansion processing on a user behavior sequence, and constructing a unified sequence input representation containing user embedding, article embedding and position embedding; s2, sending the sequence input representation into a frequency kernel guided filtering module, and extracting periodic preference features in the frequency domain representation; s3, inputting the extracted features into a selective state space module, constructing frequency modulation parameters, completing frequency domain state modeling, and generating frequency domain feature representation; s4, the sequence input representation is input into a Mamba module, time sequence modeling operation is executed, and time domain feature representation is generated; and S5, inputting the time-frequency feature representations obtained in S3 and S4 into an adaptive fusion module, calculating a fusion weight, completing feature fusion, and inputting the fused features into a prediction layer to generate a final recommendation result. The frequency domain and time domain features are modeled in a combined mode, and the accuracy of recommendation results is improved.

Description

Technical Field

[0001] The present invention relates to the field of recommendation systems, and in particular to an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture. Background Art

[0002] With the widespread application of recommendation systems in personalized services, intelligent push notifications, information retrieval, and other fields, accurately predicting users' potential interests based on their historical behavior has become a key issue in improving user experience and system performance. User interests are often dynamic, with their behavior sequences encompassing both immediate feedback on short-term interests and periodic preference patterns that recur over time. Simultaneously modeling the temporal dependencies and cyclical regularities of user behavior is a major challenge facing current recommendation systems.

[0003] Currently, mainstream sequence recommendation methods mostly use temporal modeling approaches based on recurrent neural networks (RNNs) or Transformer architectures, achieving some success in capturing the temporal dependencies of user behavior. However, these methods generally suffer from low inference efficiency and weak ability to model cyclical interests when processing long behavior sequences. In recent years, the Mamba architecture, a modeling framework based on selective state-space models, has demonstrated advantages in balancing modeling capabilities and computational efficiency by introducing input dependency mechanisms, becoming a research hotspot in sequence modeling. However, existing Mamba-based methods still primarily focus on modeling temporal features and lack the ability to model multi-scale cyclical behaviors. Furthermore, their modeling strategies are relatively fixed, making it difficult to dynamically adjust to differences in user behavior, resulting in certain limitations in modeling diverse interests.

[0004] The difference proposed by the present invention is that it integrates the modeling advantages of the time domain and the frequency domain, and introduces an adaptive feature fusion mechanism to improve the ability to express complex preference patterns in user behavior sequences. Unlike methods that rely solely on time series modeling or static frequency domain enhancement, the present invention effectively captures the multi-scale periodic preferences of users in different behavior cycles through frequency domain analysis, and at the same time combines time series modeling to explore the dynamic evolution of user interests, thereby enhancing the modeling ability of variable behavior patterns. Among them, the adaptive feature fusion mechanism is based on time-frequency features, and dynamically allocates the fusion weights of time domain features and frequency domain features to avoid redundancy and imbalance in information utilization of static fusion strategies. The present invention can achieve more accurate personalized recommendations based on the periodic behaviors and interest migrations exhibited by users at different time granularities, and effectively improve the model's adaptability to complex behavior patterns and recommendation performance. Summary of the Invention

[0005] The technical problem solved by the present invention is to address the deficiencies of the existing technology and propose an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture to improve the accuracy of the recommendation system.

[0006] In order to achieve the above object, the present invention provides an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture, which is performed according to the following steps:

[0007] Step 1: Perform embedding expansion on the user behavior sequence to construct a unified sequence input representation that includes user embedding, item embedding, and location embedding. The basic steps are as follows:

[0008] Assign a learnable embedding vector u to each user i , reflecting the static features of the user as user embedding; each item in the user interaction sequence is mapped to a vector representation v k , as item embedding; introduce position embedding vector p for each item position k , enhances the model's ability to perceive the interaction order as position embedding. The above three types of embedding are fused to obtain the final input representation h k =u i +v k +p, where k = 1, 2, ..., L, h k It is a unified input for subsequent modeling.

[0009] Step 2: Feed the sequence input representation into the frequency kernel guided filtering module to extract the periodic preference features in the frequency domain representation. The steps are as follows:

[0010] The sequence input representation is input to the frequency kernel guided filtering module to obtain a frequency domain representation that characterizes multi-scale periodic preferences. The frequency kernel guided filtering module is built based on the kernel integral operator. It uses the kernel function to perform weighted calculations on the user-item interaction sequence on the time axis to extract the periodic preference components and enhance the modeling ability of user periodic behavior. The kernel integral operator is defined as:

[0011]

[0012] where x s is the embedding representation of the interaction sequence at time point s, is a parameterized learnable kernel function used to model periodic correlations under different time differences; in discrete implementation, the operation can be equivalent to a weighted summation form On this basis, the above output is mapped to the frequency domain using Fourier transform, and combined with the learnable frequency kernel weight matrix Perform frequency component weighting, and the final frequency domain feature calculation formula is: Where F(e(n)) represents the Fourier transform result of the input sequence, is the frequency domain representation after frequency-guided filtering.

[0013] Step 3: Input the extracted features into the selective state space module, construct the frequency modulation parameters and complete the frequency domain state modeling to generate the frequency domain feature representation. The basic steps are as follows:

[0014] Step 3.1: Input the frequency domain feature representation output by the frequency kernel guided filtering module into the selective state space module to generate state modeling parameters that integrate the user's periodic preference characteristics. The calculation process is as follows:

[0015]

[0016] In the formula is the frequency domain feature representation of the jth channel at the fth frequency point, L is the total number of frequency components, and n is the position index in the behavior sequence. This inverse transform operation can map the periodic features extracted by the frequency kernel back to the time domain to generate the modulation factor Δ that can be used by the state modeling module. F , to enhance the model's ability to express periodic behavior patterns.

[0017] Step 3.2: Based on this factor, further construct the periodic modulation parameter A of the state space model F With B F , calculated as follows:

[0018] A F =exp(Δ F A)

[0019] B F =Δ F ·A -1 ·(I-exp(Δ F ))·B

[0020] Here, A and B are the original trainable matrices in the state-space model, I is the identity matrix, and exp(·) represents the element-by-element exponential operation. This construction process achieves a deep fusion of frequency-domain features and state transitions, enabling the state update mechanism to perceive periodic dynamic patterns at different scales.

[0021] Step 3.3: Input the constructed periodic modulation parameters into the state space module to perform dynamic state update operations based on frequency modulation. This module uses a discrete state space structure for modeling, and its core calculation process is as follows:

[0022] H fre =SSM(A F ,B F ,C)(H)

[0023] Where C is the learnable state mapping matrix, and H represents the sequence representation output by the frequency kernel-guided filtering module. This structure guides the state update process by using a periodic modulation matrix to achieve dynamic modeling of user periodic behavior.

[0024] Step 3.4: To improve the feature interaction capability, the state output is gated and enhanced. The calculation method is:

[0025]

[0026] in Represents element-by-element multiplication, SiLU is the activation function, and the final output is H freq as the final representation of the frequency modeling path.

[0027] Step 4: Input the sequence input representation into the Mamba module, perform the time series modeling operation, and generate the time domain feature representation. The basic steps are as follows:

[0028] Step 4.1: Represent the input feature sequence Input state parameter construction process. First, perform combined feature transformation on H, and then perform linear mapping, local convolution and nonlinear activation operations to extract context information and enhance modeling capabilities to obtain intermediate feature representation. and the gated component H z , which are used for subsequent state modeling and gate fusion operations respectively. The calculation process is as follows:

[0029] H x ,H z =Linear(H)

[0030]

[0031] Among them, H x represents the characteristic component used for main channel state modeling, H z is the auxiliary feature used for the gated enhancement path, Model input representation for the sequence after extracting context.

[0032] Step 4.2: Input linear transformation layer and add learnable bias H z , the output is controlled to be non-negative through the Softplus activation function, and the state discrete factor Δ is generated. The specific calculation process is as follows:

[0033] The formula for calculating the weight of the connection between words in the lth layer is as follows.

[0034]

[0035] Softplus(x)=ln(1+e x)

[0036] Step 4.3: Combine the basic state matrix A and the input mapping matrix B to construct dynamic adjustment parameters based on state space theory:

[0037] A t =exp(Δ·A)

[0038] B t =Δ·A -1 ·(I-exp(Δ))·B

[0039] Where I represents the identity matrix and exp(·) is the element-by-element exponential operation.

[0040] Step 4.4: Represent the context using a differentiable selective state-space model To make dynamic updates:

[0041]

[0042] Among them, C is the state output mapping matrix, H y is the state output representation of the current time step.

[0043] Step 4.5: To enhance the representation capability of the frequency modeling path, the state output H y The gated component H obtained in step 4.1 z Perform fusion processing:

[0044] H time =H y ⊙SiLU(H z )

[0045] Here, ⊙ represents element-wise multiplication, and SiLU is a nonlinear activation function. This gating mechanism can dynamically adjust the effectiveness of each channel, improving the model's adaptability to behavioral changes.

[0046] Step 5: Input the frequency domain features and time domain features into the adaptive fusion module, calculate the fusion weights and complete the feature fusion, and input the fused features into the prediction layer to generate the final recommendation results. The basic steps are as follows:

[0047] Step 5.1: To jointly model user behavior features in the frequency and time domains, an adaptive fusion module based on radial basis functions and local residual feedback is introduced. This module dynamically generates fusion weights by calculating the nonlinear similarity between frequency and time domain features. The specific process is as follows:

[0048]

[0049] Among them, σ is a learnable scaling hyperparameter. The first fusion is performed based on the initial weight α to obtain the initial fusion feature:

[0050]

[0051] By initially fusion feature M (0) Extract local residual information and correct the initial fusion weights. The correction process includes:

[0052] Δα=MLP(M (0) )

[0053] α′=α+Δα

[0054] Among them, MLP represents a multi-layer perceptron, which is used for nonlinear modeling of local residuals. Based on the modified weight α′, fine-grained fusion is performed to obtain the final fusion feature:

[0055]

[0056] Step 5.2: The final fusion M fusion It is sent to the subsequent residual connection and normalization module and is calculated as follows:

[0057] H (l) =LN(H (l-1) +Dpt(Linear(M fusion )))

[0058] Among them, H (l) is the output result after fusion, LN is the layer normalization operation, and Dpt is the Dropout operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solution of the present invention, a brief introduction is given to the drawings required for the present invention.

[0060] Figure 1 This is a flowchart of an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture provided in an embodiment of this specification;

[0061] Figure 2 This is a framework diagram of an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture provided in an embodiment of this specification;

[0062] Figure 3 This is a frequency-aware Mamba module structure diagram of an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture provided in an embodiment of this specification. DETAILED DESCRIPTION

[0063] The invention is further described below:

[0064] The purpose of this paper is to propose an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture. This method jointly models the time domain features and frequency domain features in user behavior sequences to simultaneously capture users' dynamic interest changes and multi-scale periodic preferences.

[0065] Combine Figure 1-3 The present invention provides an adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture, which is performed in the following steps:

[0066] Step 1: Perform embedding expansion on the user behavior sequence to construct a unified sequence input representation that includes user embedding, item embedding, and location embedding. The basic steps are as follows:

[0067] Assign a learnable embedding vector u to each user i , reflecting the static features of the user as user embedding; each item in the user interaction sequence is mapped to a vector representation v k , as item embedding; introduce position embedding vector p for each item position k , enhances the model's ability to perceive the interaction order as position embedding. The above three types of embedding are fused to obtain the final input representation h k =u i +v k +p, where k = 1, 2, ..., L, h k It is a unified input for subsequent modeling.

[0068] Step 2: Feed the sequence input representation into the frequency kernel guided filtering module to extract the periodic preference features in the frequency domain representation. The steps are as follows:

[0069] The sequence input representation is input to the frequency kernel guided filtering module to obtain a frequency domain representation that characterizes multi-scale periodic preferences. The frequency kernel guided filtering module is built based on the kernel integral operator. It uses the kernel function to perform weighted calculations on the user-item interaction sequence on the time axis to extract the periodic preference components and enhance the modeling ability of user periodic behavior. The kernel integral operator is defined as:

[0070]

[0071] where x s is the embedding representation of the interaction sequence at time point s, is a parameterized learnable kernel function used to model periodic correlations under different time differences; in discrete implementation, the operation can be equivalent to a weighted summation form On this basis, the above output is mapped to the frequency domain using Fourier transform, and combined with the learnable frequency kernel weight matrix Perform frequency component weighting, and the final frequency domain feature calculation formula is: Where F(e(n)) represents the Fourier transform result of the input sequence, is the frequency domain representation after frequency-guided filtering.

[0072] Step 3: Input the extracted features into the selective state space module, construct the frequency modulation parameters and complete the frequency domain state modeling to generate the frequency domain feature representation. The basic steps are as follows:

[0073] Step 3.1: Input the frequency domain feature representation output by the frequency kernel guided filtering module into the selective state space module to generate state modeling parameters that integrate the user's periodic preference characteristics. The calculation process is as follows:

[0074]

[0075] In the formula is the frequency domain feature representation of the jth channel at the fth frequency point, L is the total number of frequency components, and n is the position index in the behavior sequence. This inverse transform operation can map the periodic features extracted by the frequency kernel back to the time domain to generate the modulation factor Δ that can be used by the state modeling module. F , to enhance the model's ability to express periodic behavior patterns.

[0076] Step 3.2: Based on this factor, further construct the periodic modulation parameter A of the state space model F With B F , calculated as follows:

[0077] A F =exp(Δ F A)

[0078] B F =Δ F ·A -1 ·(I-exp(Δ F ))·B

[0079] Here, A and B are the original trainable matrices in the state-space model, I is the identity matrix, and exp(·) represents the element-by-element exponential operation. This construction process achieves a deep fusion of frequency-domain features and state transition processes, enabling the state update mechanism to perceive periodic dynamic patterns at different scales.

[0080] Step 3.3: Input the constructed periodic modulation parameters into the state space module to perform dynamic state update operations based on frequency modulation. This module uses a discrete state space structure for modeling, and its core calculation process is as follows:

[0081] H fre =SSM(A F,B F ,C)(H)

[0082] Where C is the learnable state mapping matrix, and H represents the sequence representation output by the frequency kernel-guided filtering module. This structure guides the state update process by using a periodic modulation matrix to achieve dynamic modeling of user periodic behavior.

[0083] Step 3.4: To improve the feature interaction capability, the state output is gated and enhanced as follows:

[0084]

[0085] in Represents element-by-element multiplication, SiLU is the activation function, and the final output is H freq as the final representation of the frequency modeling path.

[0086] Step 4: Input the sequence input representation into the Mamba module, perform the time series modeling operation, and generate the time domain feature representation. The basic steps are as follows:

[0087] Step 4.1: Represent the input feature sequence Input state parameter construction process. First, perform combined feature transformation on H, and then perform linear mapping, local convolution and nonlinear activation operations to extract context information and enhance modeling capabilities to obtain intermediate feature representation. and the gated component H z , which are used for subsequent state modeling and gate fusion operations respectively. The calculation process is as follows:

[0088] H x ,H z =Linear(H)

[0089]

[0090] Among them, H x represents the characteristic component used for main channel state modeling, H z is the auxiliary feature used for the gated enhancement path, Model input representation for the sequence after extracting context.

[0091] Step 4.2: Input linear transformation layer and add learnable bias H z , the output is controlled to be non-negative through the Softplus activation function, and the state discrete factor Δ is generated. The specific calculation process is as follows:

[0092] The formula for calculating the weight of the connection between words in the lth layer is as follows.

[0093]

[0094] Softplus(x)=ln(1+e x )

[0095] Step 4.3: Combine the basic state matrix A and the input mapping matrix B to construct dynamic adjustment parameters based on state space theory:

[0096] A t =exp(Δ·A)

[0097] B t =Δ·A -1 ·(I-exp(Δ))·B

[0098] Where I represents the identity matrix and exp(·) is the element-by-element exponential operation.

[0099] Step 4.4: Represent the context using a differentiable selective state-space model To make dynamic updates:

[0100]

[0101] Among them, C is the state output mapping matrix, H y Output representation of the state at the current time step.

[0102] Step 4.5: To enhance the representation capability of the frequency modeling path, the state output H y The gated component H obtained in step 4.1 z Perform fusion processing:

[0103] H time =H y ⊙SiLU(H z )

[0104] Here, ⊙ represents element-wise multiplication, and SiLU is a nonlinear activation function. This gating mechanism can dynamically adjust the effectiveness of each channel, improving the model's adaptability to behavioral changes.

[0105] Step 5: Input the frequency domain features and time domain features into the adaptive fusion module, calculate the fusion weight and complete the feature fusion, and input the fused features into the prediction layer to generate the final recommendation results. The steps are as follows:

[0106] Step 5.1: To jointly model user behavior features in the frequency and time domains, an adaptive fusion module based on radial basis functions and local residual feedback is introduced. This module dynamically generates fusion weights by calculating the nonlinear similarity between frequency and time domain features. The specific process is as follows:

[0107]

[0108] Among them, σ is a learnable scaling hyperparameter. The first fusion is performed based on the initial weight α to obtain the initial fusion features:

[0109]

[0110] Extract local residual information through preliminary fusion features and correct the preliminary fusion weights. The correction process is as follows:

[0111] Δα=MLP(M (0) )

[0112] α′=α+Δα

[0113] Among them, MLP represents a multi-layer perceptron, which is used for nonlinear modeling of local residuals. Based on the modified weight α′, fine-grained fusion is performed to obtain the final fusion feature:

[0114]

[0115] Step 5.2: The final fusion M fusion It is fed into the subsequent residual connection and normalization modules as follows:

[0116] H (l) =LN(H (l-1) +Dpt(Linear(M fusion )))

[0117] Among them, H (l) is the output result after fusion, LN is the layer normalization operation, and Dpt is the Dropout operation.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. An adaptive time-frequency fusion sequence recommendation method based on Mamba architecture, characterized by include: Step 1: Perform embedding expansion on the user behavior sequence to construct a unified sequence input representation that includes user embedding, item embedding, and location embedding; Step 2: Feed the sequence input representation into the frequency kernel guided filtering module to extract the periodic preference features in the frequency domain representation; Step 3: Input the feature representation output by the frequency kernel guided filtering module into the selective state space module to construct the frequency modulation parameters and complete the frequency domain state modeling to generate the frequency domain feature representation; Step 4: Input the sequence input representation into the Mamba module, perform the time series modeling operation, and generate the time domain feature representation; Step 5: Input the frequency domain features and time domain features into the adaptive fusion module, calculate the preliminary fusion weights through the radial basis function and perform weighted fusion, and correct the weights based on the fusion residual to complete the fine-grained feature fusion.

2. According to claim 1, the adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture is characterized in that Step 1 includes: Assign a learnable embedding vector u to each user i , used to characterize the static features of the user; each item in the interaction sequence is mapped to an item embedding vector v k ; and introduce a position embedding vector p for each item position k , enhancing the ability to perceive the interaction order. The above three types of embeddings are fused to obtain the fusion of the kth time step represented as h k =u i +v k +p k , the fused representation serves as a unified input for subsequent modeling.

3. The method for adaptive time-frequency fusion sequence recommendation based on Mamba architecture according to claim 1, characterized in that: The frequency kernel guided filtering module in step 2 is constructed as follows: The frequency kernel guided filtering module is built based on the kernel integral operator. It uses the kernel function to perform weighted calculation on the user-item interaction sequence on the time axis to extract the periodic preference components and enhance the modeling ability of user periodic behavior. The kernel integral operator is defined as: where x s is the embedding representation of the interaction sequence at time point s, is a parameterized learnable kernel function used to model periodic correlations under different time differences. In discrete implementation, the operation can be equivalent to a weighted summation:

4. The method for adaptive time-frequency fusion sequence recommendation based on Mamba architecture according to claim 1, characterized in that: The specific process of the frequency kernel guided filtering in claim 3 is as follows: The above output is mapped to the frequency domain using Fourier transform, and a learnable frequency kernel weight matrix is ​​introduced Perform element-by-element weighting operation on each frequency component to adjust the importance of each frequency component. The formula for calculating the weighted frequency domain feature is: Where F(e(n)) represents the Fourier transform result of the input sequence, is the frequency domain representation after frequency-guided filtering. The frequency kernel weight matrix During the training process of the sequential recommendation model, it is used as a learnable parameter. The back-propagation gradient of the prediction loss function is updated end-to-end together with other model parameters to achieve dynamic adjustment of the importance of different frequency components. Its initial value is set to a random variable that obeys a uniform distribution.

5. The adaptive time-frequency fusion sequence recommendation method based on the Mamba architecture according to claim 1 is characterized in that Step 3 includes: Step 3.1: Input the frequency domain feature representation output by the frequency kernel guided filtering module into the selective state space module to generate state modeling parameters that integrate the user's periodic preference characteristics. The specific calculation process is as follows: Step 3.2: Based on this factor, further construct the periodic modulation parameter A of the state space model F With B F , calculated as follows: A F =exp(Δ F ·A) B F =Δ F ·A -1 ·(I-exp(Δ F ))·B Where A and B are the original trainable matrices in the state-space model, I is the identity matrix, and exp(·) represents the element-by-element exponential operation. Step 3.3: The constructed periodic modulation parameter A F 、B F Input to the state space module to perform dynamic state update operations based on frequency modulation. The core calculation process is as follows: H fre =SSM(A F ,B F ,C)(H) Where C is the learnable state mapping matrix, and H represents the sequence representation output by the frequency kernel guided filtering module. Step 3.4: Perform gated enhancement on the state output. The calculation method is: in represents element-by-element multiplication, SiLU is the activation function, H x represents the original sequence input representation.

6. The adaptive time-frequency fusion sequence recommendation method based on Mamba architecture according to claim 1 is characterized in that Step 4 includes: Step 4.1: The input feature sequence is represented as H, which is the input state parameter construction process. First, it is subjected to a combined feature transformation, which is sequentially subjected to linear mapping, local convolution and nonlinear activation operations to extract context information and enhance modeling capabilities to obtain an intermediate feature representation. and the gated component H′ y =H y ⊙SiLU(H z ), which are used for subsequent state modeling and gate fusion operations respectively. The specific calculation process is as follows: H x ,H z =Linear(H) Among them, H x represents the characteristic component used for main channel state modeling, H z is the auxiliary feature used for the gated enhancement path, Model input representation for the sequence after extracting context. Step 4.2: Input the linear transformation layer and add the learnable bias θ, control the output to be non-negative through the Softplus activation function, and generate the state discrete factor Δ: Softplus(x)=ln(1+e x ) Step 4.3: Combine the basic state matrix A and the input mapping matrix B to construct dynamic adjustment parameters based on state space theory: A t =exp(Δ·A) B t =Δ·A -1 ·(I-exp(Δ))·B Where I represents the identity matrix and exp(·) is the element-by-element exponential operation. Step 4.4: Represent the context using a differentiable selective state-space model To make dynamic updates: Among them, C is the state output mapping matrix, H y is the state output representation of the current time step. Step 4.5: To enhance the representation capability of the frequency modeling path, the state output H y The gated component H obtained in step 2.1 z Perform fusion processing: H time =H y ⊙SiLU(H z ) Here, ⊙ represents element-wise multiplication, and SiLU is a nonlinear activation function. This gating mechanism can dynamically adjust the effectiveness of each channel, improving the model's adaptability to behavioral changes.

7. The adaptive time-frequency fusion sequence recommendation method based on Mamba architecture according to claim 1 is characterized in that Step 5 includes: Step 5.1: To jointly model user behavior features in the frequency and time domains, an adaptive fusion module based on radial basis functions and local residual feedback is introduced. This module dynamically generates fusion weights by calculating the nonlinear similarity between frequency and time domain features. The specific process is as follows: Among them, σ is a learnable scaling hyperparameter. The first fusion is performed based on the initial weight α to obtain the initial fusion feature: By initially fusion feature M (0) Extract local residual information and correct the initial fusion weights. The correction process includes: Δα=MLP(M (0) ) α′=α+Δα Among them, MLP represents a multi-layer perceptron, which is used for nonlinear modeling of local residuals. Based on the modified weight α′, fine-grained fusion is performed to obtain the final fusion feature: Step 5.2: The final fusion M fusion It is sent to the subsequent residual connection and normalization module and is calculated as follows: H (l) =LN(H (l-1) +Dpt(Linear(M fusion ))) Among them, H (l) is the output result after fusion, LN is the layer normalization operation, and Dpt is the Dropout operation.

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