Filter enhanced dual-path mamba sequence recommendation method and system

Abstract

This invention discloses a filter-enhanced dual-path Mamba sequence recommendation method and system, belonging to the field of recommendation system technology. Addressing the noise propagation problem in current Mamba state-space modeling and the limitations of existing single-path Mamba modeling designs, the recommendation system of this invention includes a sequence encoding module, a filter enhancement module, a dual-path Mamba module, a dual-path fusion module, a candidate item prediction module, and an auxiliary loss module. The filter enhancement module of this invention achieves denoising from a frequency domain perspective by removing frequency components from the sequence representation. The dual-path Mamba module constructs two parameter-independent Mamba modeling paths, modeling the sequence from historical and future time perspectives respectively, and then uses the dual-path fusion module to fuse the sequence representations extracted from the two paths. Furthermore, this invention introduces an auxiliary loss module to fully leverage the advantages of the dual-path Mamba module, thereby further improving recommendation performance.

Description

Technical Field

[0001] This invention belongs to the field of recommendation system technology, specifically relating to a filter-enhanced dual-path Mamba sequence recommendation method and system. Background Technology

[0002] Recommendation systems (RSs) analyze users' interests and needs, filter and recommend content (such as information, services, items, etc.) that users are interested in from massive amounts of data, and have shown important application value in e-commerce, social media, news and information scenarios.

[0003] In recent years, with the rapid development of deep learning technology, significant progress has been made in recommender system research. Among them, Sequential Recommendations (SRs), by modeling users' interactions in chronological order, can effectively capture user interests and has therefore attracted widespread attention. Unlike traditional recommender systems (such as collaborative filtering and content-based recommendations) that model user interests statically, Sequential Recommendations (SRs) aim to dynamically capture user interests, thereby predicting content that users may be interested in in the future and achieving more accurate personalized recommendations. Existing Sequential Recommendations widely employ deep neural network technology to model user preferences, with models represented by Transformer becoming mainstream. For example, SASRec uses a multi-head self-attention mechanism to model user interaction sequences to capture users' short-term and long-term preferences; BERT uses a bidirectional Transformer to capture contextual information in the sequence. Currently, the Mamba architecture based on the State Space Model (SSM), with its efficient and powerful sequence modeling capabilities, has also been introduced into the field of Sequential Recommendations and is receiving increasing attention. Among them, Mamba4Rec pioneered the application of the Mamba architecture to sequence recommendation, achieving excellent recommendation results while realizing efficient sequence modeling; STAR-Rec further adaptively integrates Mamba and preference-aware attention mechanisms, which can not only capture more complex sequence patterns, but also further improve recommendation performance.

[0004] Although Mamba-based sequence recommendation methods have shown some effectiveness, they still face two key challenges: (1) the recursive state update mechanism of the state space model in Mamba is prone to noise propagation, which affects recommendation performance; (2) the single-path Mamba modeling design is difficult to fully capture temporal context dependencies and has insufficient ability to characterize user preferences in short sequence scenarios, which limits the further improvement of recommendation performance. Summary of the Invention

[0005] To address the noise propagation problem in current Mamba state-space modeling and the limitations of existing single-path Mamba modeling designs, this invention provides a filter-enhanced dual-path Mamba sequence recommendation method and system.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A filter-enhanced two-path Mamba sequence recommendation method includes the following steps:

[0008] Step 1: Encode the interactive sequence to obtain the initial sequence representation;

[0009] Step 2: Perform filter enhancement processing on the initial sequence representation to suppress noise in the sequence; the filter enhancement processing includes: mapping the sequence from the time domain to the frequency domain through one-dimensional fast Fourier transform, filtering the frequency domain sequence element by element using a learnable filter, and then restoring it to the time domain through one-dimensional fast Fourier inverse transform to obtain the denoised sequence representation.

[0010] Step 3: Using two parameter-independent Mamba paths, the denoised sequence representation is modeled from the historical time perspective and the future time perspective, respectively, to obtain the forward Mamba representation and the backward Mamba representation;

[0011] Step 4: Fuse the forward Mamba representation and the backward Mamba representation to obtain the dual-path fused representation;

[0012] Step 5: Based on the dual-path fusion representation, predict the candidate items to obtain the recommended prediction probability;

[0013] Step 6: Calculate the auxiliary prediction loss based on the forward Mamba representation and the backward Mamba representation respectively, and combine the auxiliary prediction loss with the main recommendation loss calculated based on the recommendation prediction probability as the overall training objective to optimize the model.

[0014] Step 1.1: Obtain the item embeddings of the sequence through the embedding matrix of the embedding layer. The calculation formula is as follows:

[0015]

[0016] in, For the first in the sequence Embedding of an item; Represents the embedding matrix of items The operation of searching for the corresponding item in the middle; For the first in the sequence One item; This is the item embedding matrix, used to map item IDs in the dataset to vectors;

[0017] Step 1.2: Embed and concatenate the items into an initial sequence representation. The calculation formula is shown below:

[0018]

[0019] in, This represents the initial sequence.

[0020] Furthermore, step 2 specifically includes the following steps:

[0021] Step 2.1: Using the initial sequence representation obtained in Step 1 as input, the initial sequence representation is first mapped from the time domain to the frequency domain using a one-dimensional fast Fourier transform. The calculation formula is shown below:

[0022]

[0023] in, It is represented as a frequency domain sequence; This represents a one-dimensional Fast Fourier Transform; This represents the initial sequence.

[0024] Step 2.2: Filter the frequency domain sequence using a set of learnable filters to obtain the denoised frequency domain sequence representation. The calculation formula is shown below:

[0025]

[0026] in, This is the denoised frequency domain sequence representation. For learnable filters, This represents element-wise multiplication; during model training, optimization is performed by multiplying element-wise with the frequency domain sequence representation to enhance or suppress different frequency components in the sequence representation, thereby achieving adaptive denoising of the sequence.

[0027] Step 2.3: The denoised frequency domain sequence representation is mapped from the frequency domain to the time domain using a one-dimensional inverse fast Fourier transform to obtain the filter-enhanced sequence representation. The calculation formula is shown below:

[0028] ;

[0029] in, A sequence representation enhanced by a filter; This represents the one-dimensional inverse fast Fourier transform.

[0030] Furthermore, step 3 specifically includes the following steps:

[0031] Step 3.1: Construct a forward Mamba architecture. The time-order sequence is modeled using a parameter-independent Mamba architecture, and the calculation formula is shown below:

[0032] ;

[0033] in, For the first The forward Mamba representation of the layer; This indicates Mamba modeling; For the first The filter-enhanced sequence representation of the layer;

[0034] Step 3.2: Construct a reversed Mamba sequence. First, reverse the sequence, then model the reversed sequence using a parameter-independent Mamba architecture, and finally restore the modeled reversed sequence. The calculation formula is shown below:

[0035] ;

[0036] in, For the first Backward Mamba representation of the layer; Indicates the reverse operation; This indicates Mamba modeling; For the first The filter-enhanced sequence representation of the layer.

[0037] Furthermore, step 4, fusing the sequence representations in the dual-path Mamba module, specifically includes the following steps:

[0038] Step 4.1: Concatenate the forward Mamba representation and the reverse Mamba representation, and then fuse them using a linear transformation mapping. The calculation formula is shown below:

[0039] ;

[0040] in, This represents a dual-path fusion representation; These are the final forward Mamba representation and the reverse Mamba representation, respectively; The weight matrix is ​​a learnable matrix; This represents the total number of stacking layers for dual-path Mamba modules.

[0041] Furthermore, step 5 specifically includes the following steps:

[0042] Step 5.1: Calculate the similarity between the dual-path fusion representation obtained in Step 4 and the item embedding in Step 1, and generate the predicted probabilities of all candidate items using the Softmax activation function, thereby predicting potential interactive items for the user. The calculation formula is shown below:

[0043] ;

[0044] in, This is the predicted probability vector; Use the Softmax activation function; Embedded into items; This is a transpose operation; This represents the dual-path fusion representation.

[0045] Furthermore, step 6 specifically includes the following steps:

[0046] Step 6.1: Calculate the similarity between the forward Mamba representation and the reverse Mamba representation obtained in Step 3 and the item embedding in Step 1 to obtain the corresponding predicted probabilities. The calculation formula is shown below:

[0047] ;

[0048] in, This is the predicted probability vector of the forward Mamba; This is the predicted probability vector for backward Mamba; Use the Softmax activation function; Embedded into items; This is a transpose operation; Forward Mamba representation; Reverse Mamba representation;

[0049] Step 6.2: Construct an auxiliary loss based on the predicted probabilities of forward and reverse Mamba to guide the two paths in learning more discriminative sequence representations. The calculation formula is shown below:

[0050] ;

[0051] in, To mitigate losses; For users to view items Real-world interactive tags; Indicates forward Mamba on items The predicted probability; Backward Mamba on items The predicted probability;

[0052] Step 6.3: Combine the auxiliary loss and the recommendation loss to form the final training objective, calculated as follows:

[0053] ;

[0054] in, Recommended loss; These are hyperparameters used to control the weights of the auxiliary loss; For dual-path fusion representation of items The predicted probability.

[0055] A filter-enhanced dual-path Mamba sequence recommendation system includes a sequence encoding module, a filter enhancement module, a dual-path Mamba module, a dual-path fusion module, a candidate item prediction module, and an auxiliary loss module.

[0056] The sequence encoding module uses the user's historical interaction sequence as input to encode the sequence;

[0057] The filter enhancement module first maps the sequence from the time domain to the frequency domain through a one-dimensional fast Fourier transform, and then filters the sequence through a set of learnable filters.

[0058] The dual-path Mamba module constructs two parameter-independent Mamba modeling paths to model sequences from historical and future time perspectives, respectively.

[0059] The dual-path fusion module fuses the sequences obtained from the dual-path Mamba module;

[0060] The candidate item prediction module calculates the similarity between the sequence representation generated by the dual-path fusion module and the item embedding, and generates the predicted probability of the candidate item.

[0061] The auxiliary loss module performs item prediction on the two independent Mamba modules in the dual-path Mamba module, calculates the corresponding loss, and combines it with the recommendation loss to further improve the system's recommendation performance.

[0062] An electronic device includes at least one processor and at least one memory communicatively connected to the processor, the memory storing instructions executable by the at least one processor to enable the at least one processor to perform the aforementioned filter-enhanced dual-path Mamba sequence recommendation method.

[0063] A non-transitory computer-readable storage medium storing computer instructions, wherein a computer program is stored thereon, the computer program being executed by a processor of the aforementioned filter-enhanced dual-path Mamba sequence recommendation method.

[0064] Compared with the prior art, the present invention has the following advantages:

[0065] (1) This invention proposes a filter-enhanced dual-path Mamba sequence recommendation method and system. In view of the noise propagation problem when Mamba is applied to sequence recommendation, a filter enhancement module is introduced to denoise the interactive sequence, which effectively reduces the impact of noise on state space modeling.

[0066] (2) The dual-path Mamba modeling module proposed in this invention achieves richer temporal context modeling through two Mamba models with independent parameters, effectively solving the limitations of existing single-path Mamba models.

[0067] (3) This invention proposes a dual-path fusion module for fusing the sequence representation of dual-path Mamba modules, which shows good performance in short sequence scenarios.

[0068] (4) This invention proposes an auxiliary loss function, which, combined with the recommendation loss, can further improve recommendation performance. Attached Figure Description

[0069] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0070] Figure 1 This is an overall architecture diagram of a filter-enhanced dual-path Mamba sequence recommendation method provided in an embodiment of the present invention;

[0071] Figure 2 This is a structural diagram of the sequence encoding module of the present invention;

[0072] Figure 3 This is a structural diagram of the filter enhancement module of the present invention;

[0073] Figure 4 This is a structural diagram of the dual-path Mamba module of the present invention;

[0074] Figure 5 This is a structural diagram of the dual-path fusion module of the present invention;

[0075] Figure 6 This is a structural diagram of the item prediction module of the present invention;

[0076] Figure 7 This is a structural diagram of the auxiliary loss module of the present invention;

[0077] Figure 8This is a data example used in this invention;

[0078] Figure 9 This is the input sequence for the present invention;

[0079] Figure 10 This invention provides an overall architecture diagram of a filter-enhanced dual-path Mamba sequence recommendation system.

[0080] Figure 11 This is a schematic diagram of the overall structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0081] To gain a deeper understanding of this invention, we will provide a comprehensive and detailed description. However, this invention has various implementations and is not limited to the specific examples listed herein. These examples are presented to enhance a full understanding of the disclosure of this invention.

[0082] like Figure 10 As shown in the structural diagram, this invention provides a filter-enhanced dual-path Mamba sequence recommendation system, including a sequence encoding module, a filter enhancement module, a dual-path Mamba module, a dual-path fusion module, a candidate item prediction module, and an auxiliary loss module.

[0083] The sequence encoding module takes the user's historical interaction sequence as input, encodes the sequence, and obtains the item embedding and the initial sequence representation;

[0084] The filter enhancement module takes the initial sequence representation as input, first maps the initial sequence representation from the time domain to the frequency domain through a one-dimensional fast Fourier transform, and then filters it through a set of learnable filters to obtain the filter-enhanced sequence representation.

[0085] The dual-path Mamba module constructs two parameter-independent Mamba modeling paths to model the filter-enhanced sequence representation from historical and future time perspectives, respectively, in order to better capture the global context information of the sequence.

[0086] The dual-path fusion module fuses the sequence representations obtained from the dual-path Mamba module to obtain the final sequence representation.

[0087] The candidate item prediction module calculates the similarity between the sequence representation generated by the dual-path fusion module and the item embedding, and generates the prediction probability of the candidate item, thereby realizing the prediction of the user's potential interactive items.

[0088] The auxiliary loss module performs item prediction and calculates the corresponding loss for the two independent Mamba modules in the dual-path Mamba module, and combines the recommendation loss to further improve the recommendation performance of the present invention.

[0089] Example 1

[0090] Figure 8 This is an example of an Amazon Beauty sequence recommendation dataset. The dataset contains 22,363 users, 12,101 items (beauty products), and 198,502 user-item interactions, with an average interaction length of 8.9 seconds per user. Preprocessing this dataset yields the following results: Figure 9 The interaction sequence shown meets the requirements.

[0091] Figure 1 The following is a diagram illustrating the overall architecture of a filter-enhanced dual-path Mamba sequence recommendation method provided in this embodiment of the invention. The method will be further described in detail below with reference to the accompanying drawings:

[0092] Step 1: Encode the items in the sequence using the embedding layer of the sequence encoding module to obtain the item embeddings and the initial sequence representation. Figure 2 Here is a diagram of the module's structure. The calculation formula is shown below:

[0093] ;

[0094] in, It is the item embedding matrix, used to map item IDs in the dataset to vectors; No. 1 in the sequence One item; Represents the embedding matrix of items The operation of searching for the corresponding item in the middle; It is the first in the sequence Embedding of an item; This represents the initial sequence.

[0095] Step 2 involves using a filter enhancement module to denoise the interaction sequence, effectively mitigating the propagation of noise in subsequent Mamba state space modeling. Figure 3 The diagram below shows the module's structure. Specifically, using the initial sequence representation obtained in step 1 as input, this module first maps the sequence representation from the time domain to the frequency domain using a one-dimensional fast Fourier transform, and then processes the sequence through a set of learnable filters to obtain a filter-enhanced sequence representation. The calculation formula is shown below:

[0096] ;

[0097] in, This represents the initial sequence. This represents a one-dimensional Fast Fourier Transform; It is represented as a frequency domain sequence; A learnable filter; This represents element-wise multiplication; For the denoised frequency domain sequence representation, a learnable filter Optimization is performed during model training by enhancing or suppressing different frequency components in the sequence representation through element-wise multiplication with the frequency domain sequence representation, thereby achieving adaptive denoising of the sequence. This represents the one-dimensional inverse fast Fourier transform. A sequence representation for filter enhancement.

[0098] Step 3: Utilize the dual-path Mamba module to model the filtered sequence from both historical and future time perspectives to better capture the global contextual information of the sequence. Figure 4 The diagram below shows the module's structure. Specifically, the dual-path Mamba module constructs two parameter-independent Mamba modeling paths: a forward Mamba path, used to model sequences in chronological order, learning dynamic changes in user interests from historical behavior; and a reverse Mamba path, used to reverse the sequence and model the reversed sequence to uncover potential contextual information. The calculation formula is shown below:

[0099] ;

[0100] in, For the first The filter-enhanced sequence representation of the layer; This indicates Mamba modeling; For the first The forward Mamba representation of the layer; Indicates the reverse operation; For the first Backward Mamba representation of the layer.

[0101] Step 4: The forward Mamba representation and the backward Mamba representation are fused using the dual-path fusion module to obtain the final sequence representation. Figure 5 This is a diagram of the module's structure. Specifically, the forward Mamba representation and the reverse Mamba representation are concatenated, and then mapped using a linear transformation. The calculation formula is shown below:

[0102] ;

[0103] in, The weight matrix is ​​a learnable matrix; These are the final forward Mamba representation and the reverse Mamba representation, respectively; This represents the total stacking level of dual-path Mamba modules; This represents the dual-path fusion representation.

[0104] Step 5: Using the item prediction module, predict items that the user might be interested in. Figure 6 This is a structural diagram of the module. Specifically, the similarity between the dual-path fusion representation obtained in step 4 and the item embedding in step 1 is calculated, and the predicted probabilities of all candidate items are generated using the Softmax activation function, thereby achieving the prediction of potential interactive items for the user. The calculation formula is shown below:

[0105] ;

[0106] in, This represents the dual-path fusion representation in step 4; Embed the items from step 1; This is a transpose operation; Use the Softmax activation function; This is the predicted probability vector.

[0107] Step 6: Using the auxiliary loss module, perform item prediction operations on the forward and backward Mamba methods of the dual-path Mamba module respectively, calculate their respective prediction probabilities, and calculate the auxiliary loss based on these probabilities. Then, combine the auxiliary loss with the main recommendation loss, and control the weight of the auxiliary loss through hyperparameters to form the final training objective. Figure 7 This is a diagram of the module's structure. Specifically, the corresponding prediction probabilities are calculated based on the final forward and backward Mamba representations, using the following formula:

[0108] ;

[0109] in, These are the final forward Mamba representation and the reverse Mamba representation, respectively; Embedded into items; This is a transpose operation; Use the Softmax activation function; These are the predicted probability vectors for the forward and backward Mamba sequences, respectively. The auxiliary loss, constructed based on the predicted probabilities of the forward and backward Mamba sequences, guides the two paths to learn a more discriminative sequence representation. The calculation formula is shown below:

[0110] ;

[0111] in, These represent forward Mamba and backward Mamba, respectively, representing the relationship between items. The predicted probability; For users to view items Real-world interactive tags; This is used as an auxiliary loss. The auxiliary loss is combined with the main recommendation loss, and the weights of the auxiliary loss are controlled by hyperparameters to form the final training objective. The calculation formula is shown below:

[0112] ;

[0113] in, For hyperparameters; Recommended loss; The dual-path fusion representation obtained in step 4 represents the items The predicted probability.

[0114] Example 2

[0115] This invention provides a filter-enhanced dual-path Mamba sequence recommendation device, which specifically executes the process of the above-described filter-enhanced dual-path Mamba sequence recommendation method embodiment. For details, please refer to the content of the above-described filter-enhanced dual-path Mamba sequence recommendation method embodiment, which will not be repeated here.

[0116] The model proposed in this invention was tested on the Amazon Beauty public dataset, and Recall and NDCG were selected as evaluation metrics. The experiments show that the model of this invention achieves better results than existing models. The comparison of experimental results is shown in the table below:

[0117]

[0118] The model of this invention was compared with existing models, and it can be seen that the method of this invention has the best performance than other methods. Among them, FreqRec is from the literature "Exploiting Inter-Session Information with Frequency-enhanced Dual-Path Networks for Sequential Recommendation", and Mamba4Rec is from the literature "Mamba4Rec: Towards Efficient Sequential Recommendation with Selective StateSpace Models".

[0119] This embodiment provides an electronic device. Figure 11This is a schematic diagram of the overall structure of an electronic device provided in an embodiment of the present invention. The device includes a processor, a memory, a communication bus, and a communication interface. The processor, communication interface, and memory communicate with each other via the communication bus. The memory stores program instructions executable by the processor. The processor can execute the methods provided in the above-described method embodiments by calling the program instructions. These methods include, for example: encoding a sequence using a sequence encoding module; denoising the sequence using a filter enhancement module; modeling the filtered sequence from historical and future time perspectives using a dual-path Mamba module; fusing the sequences using a dual-path fusion module; and predicting items using an item prediction module and an auxiliary loss module.

[0120] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), and random access memory (RAM).

[0121] This embodiment provides a non-transitory computer-readable storage medium that stores computer instructions. The computer instructions cause the computer to execute the methods provided in the above-described method embodiments, such as: encoding a sequence using a sequence encoding module; denoising the sequence using a filter enhancement module; modeling the filtered sequence from historical and future time perspectives using a dual-path Mamba module; fusing the sequences using a dual-path fusion module; and predicting items using an item prediction module and an auxiliary loss module.

[0122] Contents not described in detail in this specification are prior art known to those skilled in the art. Although illustrative specific embodiments of the invention have been described above to facilitate understanding by those skilled in the art, it should be understood that the invention is not limited to the scope of the specific embodiments. Various modifications are readily apparent to those skilled in the art as long as they fall within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.

Claims

1. A filter-enhanced dual-path Mamba sequence recommendation method, characterized in that: Includes the following steps: Step 1: Encode the interactive sequence to obtain the initial sequence representation; Step 2: Perform filter enhancement processing on the initial sequence representation to suppress noise in the sequence; The filter enhancement process includes: mapping the sequence from the time domain to the frequency domain through a one-dimensional fast Fourier transform, filtering the frequency domain sequence element by element using a learnable filter, and then restoring it to the time domain through a one-dimensional fast Fourier inverse transform to obtain a denoised sequence representation. Step 3: Using two parameter-independent Mamba paths, the denoised sequence representation is modeled from the historical time perspective and the future time perspective, respectively, to obtain the forward Mamba representation and the backward Mamba representation; Step 4: Fuse the forward Mamba representation and the backward Mamba representation to obtain the dual-path fused representation; Step 5: Based on the dual-path fusion representation, predict the candidate items to obtain the recommended prediction probability; Step 6: Calculate the auxiliary prediction loss based on the forward Mamba representation and the backward Mamba representation respectively, and combine the auxiliary prediction loss with the main recommendation loss calculated based on the recommendation prediction probability as the overall training objective to optimize the model.

2. The filter-enhanced dual-path Mamba sequence recommendation method according to claim 1, characterized in that: Step 1 specifically includes the following steps: Step 1.1: Obtain the item embeddings of the sequence through the embedding matrix of the embedding layer. The calculation formula is as follows: ； in, For the first in the sequence Embedding of an item; Represents the embedding matrix of items The operation of searching for the corresponding item in the middle; For the first in the sequence One item; This is the item embedding matrix, used to map item IDs in the dataset to vectors; Step 1.2: Embed the items sequentially to form an initial sequence representation. The calculation formula is shown below: ； in, This represents the initial sequence.

3. The filter-enhanced dual-path Mamba sequence recommendation method according to claim 1, characterized in that: Step 2 specifically includes the following steps: Step 2.1: Using the initial sequence representation obtained in Step 1 as input, the initial sequence representation is first mapped from the time domain to the frequency domain using a one-dimensional fast Fourier transform. The calculation formula is shown below: ； in, It is represented as a frequency domain sequence; This represents a one-dimensional Fast Fourier Transform; This represents the initial sequence. Step 2.2: Filter the frequency domain sequence using a set of learnable filters to obtain the denoised frequency domain sequence representation. The calculation formula is shown below: ； in, This is the denoised frequency domain sequence representation. For learnable filters, This represents element-wise multiplication; during model training, optimization is performed by multiplying element-wise with the frequency domain sequence representation to enhance or suppress different frequency components in the sequence representation, thereby achieving adaptive denoising of the sequence. Step 2.3: The denoised frequency domain sequence representation is mapped from the frequency domain to the time domain using a one-dimensional inverse fast Fourier transform to obtain the filter-enhanced sequence representation. The calculation formula is shown below: ； in, A sequence representation enhanced by a filter; This represents the one-dimensional inverse fast Fourier transform.

4. The filter-enhanced dual-path Mamba sequence recommendation method according to claim 1, characterized in that: Step 3 specifically includes the following steps: Step 3.1: Construct a forward Mamba architecture. The time-order sequence is modeled using a parameter-independent Mamba architecture, and the calculation formula is shown below: ； in, For the first The forward Mamba representation of the layer; This indicates Mamba modeling; For the first The filter-enhanced sequence representation of the layer; Step 3.2: Construct a reversed Mamba sequence. First, reverse the sequence, then model the reversed sequence using a parameter-independent Mamba architecture, and finally restore the modeled reversed sequence. The calculation formula is shown below: ； in, For the first Backward Mamba representation of the layer; Indicates the reverse operation; This indicates Mamba modeling; For the first The filter-enhanced sequence representation of the layer.

5. The filter-enhanced dual-path Mamba sequence recommendation method according to claim 1, characterized in that: Step 4 specifically involves concatenating the forward Mamba representation and the reverse Mamba representation, and then fusing them through a linear transformation mapping to obtain the dual-path fused representation. The calculation formula is shown below: ； in, This represents a dual-path fusion representation; These are the final forward Mamba representation and the reverse Mamba representation, respectively; The weight matrix is ​​a learnable matrix; This represents the total number of stacking layers for dual-path Mamba modules.

6. The filter-enhanced dual-path Mamba sequence recommendation method according to claim 1, characterized in that: Step 5 specifically includes the following steps: Step 5.1: Calculate the similarity between the dual-path fusion representation and the item embedding, and generate the predicted probabilities of all candidate items using the Softmax activation function, thereby predicting potential interactive items for the user. The calculation formula is shown below: ； in, This is the predicted probability vector; Use the Softmax activation function; Embedded into items; This is a transpose operation; This represents the dual-path fusion representation.

7. The filter-enhanced dual-path Mamba sequence recommendation method according to claim 1, characterized in that: Step 6 specifically includes the following steps: Step 6.1: Calculate the similarity between the forward Mamba representation and the backward Mamba representation and the item embedding, and obtain the forward prediction probability and the backward prediction probability using the Softmax function. The calculation formula is shown below: ； in, This is the predicted probability vector of the forward Mamba; This is the predicted probability vector for backward Mamba; Use the Softmax activation function; Embedded into items; This is a transpose operation; Forward Mamba representation; Reverse Mamba representation; Step 6.2: Construct an auxiliary loss based on the predicted probabilities of forward and reverse Mamba to guide the two paths in learning more discriminative sequence representations. The calculation formula is shown below: ； in, To mitigate losses; For users to view items Real-world interactive tags; Indicates forward Mamba on items The predicted probability; Backward Mamba on items The predicted probability; Step 6.3: Combine the auxiliary loss and the recommendation loss to form the final training objective, calculated as follows: ； in, Recommended loss; These are hyperparameters used to control the weights of the auxiliary loss; For dual-path fusion representation of items The predicted probability.

8. A filter-enhanced dual-path Mamba sequence recommendation system, characterized in that: It includes a sequence encoding module, a filter enhancement module, a dual-path Mamba module, a dual-path fusion module, a candidate item prediction module, and an auxiliary loss module; The sequence encoding module uses the user's historical interaction sequence as input to encode the sequence; The filter enhancement module first maps the sequence from the time domain to the frequency domain through a one-dimensional fast Fourier transform, and then filters the sequence through a set of learnable filters. The dual-path Mamba module constructs two parameter-independent Mamba modeling paths to model sequences from historical and future time perspectives, respectively. The dual-path fusion module fuses the sequences obtained from the dual-path Mamba module; The candidate item prediction module calculates the similarity between the sequence representation generated by the dual-path fusion module and the item embedding, and generates the predicted probability of the candidate item. The auxiliary loss module performs item prediction on the two independent Mamba modules in the dual-path Mamba module, calculates the corresponding loss, and combines it with the recommendation loss to further improve the system's recommendation performance.

9. An electronic device, characterized in that: It includes at least one processor and at least one memory communicatively connected to the processor, the memory storing instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the filter-enhanced dual-path Mamba sequence recommendation method according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that: It stores a computer program that is executed by a processor using the filter-enhanced dual-path Mamba sequence recommendation method according to any one of claims 1 to 7.

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