2.1. Dual-tower recommendation models

The dual-tower architecture has become a standard paradigm for industrial-scale recommendation systems due to its balance between modeling power and inference efficiency. Early implementations such as; YouTube DNN [12] and DSSM [13] laid the foundation for industrial-grade dual-tower models. YouTube DNN proposed a user tower composed of multi-layer perceptrons (MLPs) to process user features such as search and watch history, and an item tower that processes content metadata. DSSM introduced the idea of learning semantic representations for query–document matching, which inspired many retrieval-based recommender systems. However, traditional dual-tower models adopt a pointwise training objective and often treat users and items as independent entities during representation learning. This independence assumption oversimplifies the intricate nature of user–item interactions. As a result, they may fail to model fine-grained relational signals, especially in personalized and cold-start scenarios where the interaction data is limited or noisy. To address this limitation, several enhanced variants of the dual-tower framework have been proposed. Multi-interest network with dynamic routing (MIND) [14] introduces a capsule routing mechanism to extract multiple interest vectors from user behavior sequences, allowing the model to capture diverse user intents. Deep interest network (DIN) and Deep interest evolution network (DIEN) [15] incorporate attention mechanisms over historical behaviors to compute dynamic user representations conditioned on candidate items, effectively modeling local user–item interactions. More recent works explore cross-tower interaction mechanisms. For example, DCN v2 [16] and DAML [17] introduce cross-feature fusion layers that allow signal propagation between user and item towers before computing similarity scores. However, these approaches typically increase online inference complexity, undermining one of the core advantages of the dual-tower structure—independent encoding and offline computation. Thus, the challenge remains to enhance inter-tower interaction without sacrificing efficiency [18].

Another common limitation is the use of static embedding representations. Most dual-tower models assume that user preferences remain stable and are fully reflected by past interactions, which is unrealistic in dynamic environments. For instance, a user’s interest may shift quickly due to contextual factors, recent events, or temporal trends. Static embeddings fail to account for this drift, leading to stale recommendations. Some efforts, such as TDM (Tree-based Deep Model) [19], attempt to incorporate hierarchical item structures for scalable long-term interest modeling, but they still lack temporal adaptability. Furthermore, dual-tower models often struggle with long-tail recommendation, where items or users have limited historical interactions. This data sparsity leads to poorly trained embeddings for cold-start entities, ultimately reducing retrieval diversity and personalization. While data augmentation techniques and side information have been explored, they provide limited improvements in capturing semantic relevance under sparse conditions [20].

In summary, while dual-tower architectures provide a scalable foundation for recommendation, key limitations persist in terms of user–item interaction modeling, adaptability to user interest dynamics, and robustness to data sparsity. These gaps motivate the design of enhanced frameworks that integrate sequential modeling, personalized feature interaction, and self-supervised representation learning—without compromising inference efficiency.

2.2. Sequential user modeling

Sequential modeling has been extensively explored to better capture temporal dynamics in user interactions. Early research in this direction focused on recurrent neural networks (RNNs), which naturally model sequential data. GRU4Rec [21] was among the first to apply gated recurrent units (GRU) to session-based recommendation, demonstrating that capturing short-term sequential dependencies can outperform traditional collaborative filtering. Subsequent variants such as neural attentive recommendation machine (NARM) [22] introduced attention mechanisms on top of RNNs to highlight important past interactions, further improving performance and interpretability. However, RNN-based models face inherent limitations in capturing long-range dependencies due to their sequential nature and vanishing gradient issues. To overcome these challenges, Transformer-based architectures have gained prominence. Self-attentive sequential recommendation (SASRec) [23] was a pioneering model that applied self-attention to sequence modeling, enabling the capture of both short-term fluctuations and long-term patterns in user behavior. BERT4Rec [24] later introduced bidirectional encoding using the BERT architecture, leveraging masked item prediction to learn high-quality sequential representations in a self-supervised manner. These approaches significantly advance the field by supporting parallel training, dynamic user interest modeling, and better generalization.

Building on these foundations, recent models have further incorporated multi-interest extraction, context-awareness, and temporal encoding. For example, FISMRec [25] represents users as a mixture of latent interests and aligns each interest with future items via attention. TiSASRec [26] enhances SASRec by incorporating explicit time interval modeling between interactions. ComiRec [27] applies capsule networks and contrastive objectives, respectively, to disentangle user preferences into multiple vectors for more diverse recommendations.

Moreover, most sequential models focus exclusively on user-side modeling, assuming that item representations are static and unaffected by evolving user contexts. This assumption limits performance in cold-start and long-tail scenarios, where items with sparse interactions lack semantic reinforcement [28]. As a result, recommendations tend to favor popular items, exacerbating popularity bias and neglecting personalized intent.

In light of these limitations, recent studies have started exploring lightweight sequence encoders for retrieval tasks and joint user–item temporal modeling. However, there is still a lack of scalable frameworks that integrate sequential signals into dual-tower architectures while maintaining low latency and offline item indexing capabilities. Addressing this gap is critical for enhancing the personalization and generalization capacity of retrieval-stage models.

2.3. Self-supervised learning in recommendation

A prominent line of work in this domain leverages contrastive learning, which aims to maximize agreement between positive pairs (e.g., user–item pairs with known interactions) while minimizing agreement between negative pairs. This principle has been successfully applied in several recommendation settings. For instance, self-supervised sequential recommendation (S3Rec) [29] introduces multiple SSL objectives, including masked item prediction, attribute prediction, and segment reconstruction, to enrich item and user embeddings in sequential models. CL4Rec [30] employs InfoNCE-based contrastive loss to distinguish between augmented views of user sequences, enhancing the robustness and generalization of learned representations. Similarly, SelfCF [31] and SimCLR-inspired models [32] construct contrastive views of the user–item graph via dropout or node perturbations to facilitate representation learning under cold-start settings.

Beyond sequence modeling, SSL has also been applied to graph-based recommendation. Models such as SSLRec [33] and CmclRec [34] generate structural or semantic augmentations of user–item graphs, enabling contrastive learning over neighborhood or global graph contexts. These approaches significantly improve discriminative capacity, particularly for items with sparse interactions or users with limited history. Despite their success, most existing SSL-enhanced recommendation models are designed as standalone architectures that focus on sequence-based or graph-based modeling, with limited attention to dual-tower frameworks. The dual-tower structure poses unique challenges for integrating SSL: First, the independent encoding of users and items limits the ability to generate coherent, cross-view augmentations. Second, the global contrastive objectives used in prior work often fail to capture fine-grained, personalized matching signals that are essential in retrieval scenarios. Third, most methods introduce computationally intensive augmentations or graph convolutions, which are incompatible with the low-latency requirements of industrial retrieval systems.

In this context, our work seeks to bridge the gap between SSL and dual-tower retrieval architectures. We incorporate a lightweight contrastive learning strategy directly into the dual-tower framework, enabling the model to learn personalized, structure-aware representations for both users and items. Unlike prior work, our approach does not rely on expensive augmentations or graph modeling, and maintains the efficiency and modularity of the dual-tower paradigm. By doing so, we enhance the model’s capacity to handle long-tail item retrieval and cold-start user scenarios, while remaining scalable for large-scale recommendation systems. The differences between CL-EPIDTN and relevant model variants is detailed in Table 1.

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Table 1. The differences between CL-EPIDTN and relevant model variants.

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3.1. Problem definition

In the recall stage of a recommendation system, the goal is to efficiently retrieve a small subset of items from a large-scale candidate pool I for each user u. This subset, typically containing only thousands of items, should align closely with the user’s interests and preferences. Doing so enables faster and more effective computation in the subsequent ranking stage. To train the recall model, the system leverages users’ historical interaction data.

Specifically, each training sample can be represented as a tuple , where: denotes the set of items the user u has interacted with (also referred to as the user behavior sequence), denotes the user feature vector (e.g., gender, age, interests), denotes the feature vector of the target item (e.g., item ID, category). The core task of the recommendation model is to learn mapping functions that project the raw user and item features into their respective embedding vectors. The user embedding function can be simply denoted as Eq. (1).

(1)

where represents the user embedding vector, and denotes the user tower’s neural network architecture. Similarly, the embedding function for the target item i is formulated as Eq. (2).

(2)

where denotes the item embedding vector, and represents the item tower’s neural network structure. After learning the embedding vectors for users and items, the model applies a scoring function to measure their similarity and retrieve the top-K most relevant items, where K is a predefined number of candidates for recall. This scoring function quantifies the similarity between a user and an item, and is typically defined as Eq. (3).

(3)

where denotes the similarity score between the user embedding vector and the item embedding vector , which is typically computed using either cosine similarity or inner product.

The central challenge for Transformer-based dual-tower models lies in how to effectively learn the embedding functions and , which are responsible for generating expressive representations of users and items, respectively. This will be elaborated in detail in the following section.

3.2. Structure of EPIDTN

Fig 1 presents the overall architecture of EPIDTN, which is designed based on a Transformer-based encoder framework. The model consists of three main components: the embedding layer, encoding layer, and interaction layer, each serving a distinct function:

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Fig 1. Schematic diagram of the enhanced personalized interaction dual tower network.

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Embedding layer: This layer handles high-dimensional sparse input features such as user IDs and item IDs, which are typically one-hot encoded. To avoid the computational burden of high-dimensional inputs, the model uses embedding dictionaries to project these sparse vectors into a lower-dimensional dense space. This not only reduces parameter size and training complexity but also enables efficient feature representation.

Encoding Layer: The encoding layer transforms input embeddings into expressive user and item representations. It incorporates deep neural components, including multilayer perceptrons (MLPs), Transformer blocks, and a personalized dual-enhanced module. The personalized module is specifically designed to strengthen cross-tower representation interactions in a user-specific manner, improving the model’s ability to capture nuanced preferences.

Interaction Layer: This layer matches the final user and item embeddings generated by their respective towers. It computes a preference score for each item based on its similarity with the user embedding. These scores are then used to rank candidate items during the recall phase.

The following subsections provide a detailed explanation of each component within the EPIDTN framework.

3.2.2. Encoding layer.

The role of the encoding layer is to further learn the representation of users and items. For EPIDTN, in order to solve the problem of lack of information interaction between the two towers in the traditional dual-tower model. This paper adopts the DAT structure proposed by Yu et al. [27], and in view of the lack of personalization of the augmented vector in the DAT structure, this paper designs a personalized augmented vector structure (hereinafter referred to as PAV structure), which realizes that different users/items correspond to different augmented vectors. This architecture is referred to as the personalized dual-augmented structure throughout this paper.

The DAT structure assigns a corresponding augmented vector and to each user and item to capture the information from the other tower, and splices it with other Embeddings on the same side, which is regarded as the input feature of one tower and input to the subsequent encoding layer together. Therefore, the input of one tower of the DAT model carries valuable information of the other tower, implicitly realizing the information interaction between the two towers.

In order to estimate the augmented vectors and , the DAT structure designs an adaptive mimic mechanism (AMM), which aims to use the augmented vectors to fit the input vectors of all positive interactions in the other tower belonging to the corresponding user or item. Specifically, AMM defines the simulation loss as the mean square error between the augmented vector and the user/item embedding and for each sample with a label equal to 1, are the loss is denoted as Eqs (4) and (5).

(4)(5)

where B represents the number of samples in the batch, and is the label. It can be seen that if the label , and are close to the user embedding or the item embedding . if the label , the loss is equal to 0. The augmented vectors and summarize the high-level information about the user or item that may match the other towers, and participate in the feature crossover of this tower, implicitly realizing the information interaction between the two towers.

However, the dual augmented vectors and in the DAT model are randomly initialized and are high-order comprehensive representations of all possible matching positive sample information of users or items, so they are not personalized. To solve the augmented vector personalization problem, this paper designs a personalized augmented vector structure (hereinafter referred to as PAV structure). The personalized augmented vector structure is shown in Fig 2. The PAV structure selects user personalized features (such as user id and user activity) and item personalized features (such as item id and item category) as input. These features and user/item pass through the embedding layer, and we get the embedding representations and . To reduce the complexity of the model, and in the PAV structure share the embedding layer with the model input features , and . With the embedding representations and as input, the PAV structure uses the MLP network to obtain the final output and , which are calculated by Eqs (6) and (7).

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Fig 2. Personalized augmented vector structure.

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(6)(7)

Through the PAV structure, we obtain personalized augmented vectors and . Similar to the DAT structure, this paper connects the augmented vectors and with other feature embedding vectors on the same side to obtain the augmented input vectors , and of the two towers, and the vectors are calculated using Eqs (8)–(10).

(8)(9)(10)

where indicates that the two vectors are concatenated in the same dimension. The enhanced input vectors z_u, and z_i contain not only the information of the current user and item, but also the information of historical positive interactions with the user and item.

Next, this paper further encodes the augmented input vector z_u, and z_i. The encoding layer of the item tower takes the item feature augmented vector z_i as input, and after a layer of MLP network, the output of the item tower is obtained , which is described in Eq. (11).

(11)

Different from the item tower, in order to capture the changes in user interests, this paper introduces the user’s positive historical behavior information in the user tower. Since the transformer structure has achieved good results in the field of machine translation, more and more researchers have tried to apply the transformer structure to other machine learning fields, including Sun et al. [28] who applied the transformer structure in the NLP field to the sequence recommendation model and achieved good recommendation results. Inspired by the work of Sun et al., the EPIDTN model applies the transformer structure to the dual tower structure to process the user’s positive historical behavior information. As shown in Fig 3, after the user behavior sequence feature passes through L layers of transformers, the encoding result of each item in the sequence is obtained, , where . represents the calculation of the transformer structure. The EPIDTN designed in this paper uses two methods to represent sequence information:

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Fig 3. User sequence feature processing.

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• The embedding representation of the most recent item in the behavior sequence after encoding: this information focuses on real-time interest.
• The embeddings of all items after encoding are averaged and pooled: this information focuses on global interest. Then they are concatenated with the output results of user feature information to form user-side features and obtain the user embedding representation , and the calculation process is shown in Eq. (12).

(12)

where pool (T_u) represents the average pooling of the embeddings after encoding all items. represents the encoding result of the most recent item. The cancat function represents the concatenation of all inputs.

3.2.3. Connection layer.

After the encoding layer, we get the representation vector of user features and the representation vector of item features. The final user and item representations, obtained from their respective towers, are used to compute the user’s interest score for each item through the matching layer. This layer typically adopts cosine similarity as the matching function, where the similarity between the user embedding and the item embedding is calculated as the cosine of the angle between the two vectors. This score serves as the model’s final output and reflects the user’s preference for the item. Specifically, for the output vector of the user tower is , and the output vector of the item tower is , their cosine similarity is shown in Eq. (13).

(13)

where represents the L₂ norm of the vector, and the similarity is the predicted interest level .

3.3. Model training

The above model calculates the cosine similarity of the output vectors of the user and the item, and the similarity is the predicted interest level . Generally, we regard the recall problem as a binary classification problem and use cross entropy loss as the loss function of the EPIDTN model. The parameters of the model are updated by minimizing the loss function. Specifically, if the actual interest level of user u in item i is y_i and the predicted interest level is , the cross-entropy loss can be expressed as Eq. (14).

(14)

where T represents the number of samples in the batch. In order to allow the personalized augmented vector structure network parameters to be updated synchronously during model training, similar to the DAT model, this paper adds in Eq. (4) and in Eq. (5) to , and the final model loss function is expressed as Eq. (15).

(15)

where , are regularization parameters. and are used to update and . In order not to affect the learning of and , this paper adopts a stop gradient strategy to prevent the gradients of and from flowing back to and . In addition, the input features of the personalized augmented vector structure network share the embedding layer with other features. In order not to affect the learning of the embedding dictionary, a system strategy is adopted to prevent the gradients of and from flowing back to the update of the embedding layer parameters.

We optimize the model parameters by minimizing the loss function through stochastic gradient descent (SGD). During training, we divide the data into mini-batches and iteratively update model parameters for each batch. For each mini-batch, we first compute the output from the matching layer, then evaluate the loss using a predefined loss function. Next, we apply backpropagation to compute the gradients of all parameters and update them using gradient descent. Specifically, let W denote the model parameters, L the loss function, and the learning rate. The parameter update rule is shown in Eq. (16).

(16)

where represents the gradient of L to W.

4.1. Self-supervised learning

We begin by introducing the general framework of SSL, as illustrated in Fig 4. The core idea consists of two main components: (1) Applying various data augmentation strategies to each training sample to generate multiple views, enabling the model to learn richer representations. (2) Utilizing a contrastive loss function to ensure that representations derived from different views of the same instance are close in the embedding space, while those from different instances remain distant. For a batch of N items, , where represents a set of features for item i. Suppose there is a pair of transformation functions that augment to and respectively, and the process is formulated as Eq. (17).

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Fig 4. Self-supervised learning.

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(17)

Given the same input item i, it is hoped that different representations and are learned after augmentation to ensure that the model can still recognize that and represent the same input i. In other words, the contrastive loss learns to minimize the difference between and . At the same time, for different examples i and j, the contrastive loss maximizes the difference between the representations and learned after data augmentation. Let and represent the representation vectors of and respectively. and are encoded by two neural networks , and the calculation process is presented in Eq. (18).

(18)

Due to , contrastive learning generally regards as a positive pair and as a negative pair. To encourage the self-supervised loss for similar samples to be minimized and that for dissimilar samples to be maximized, we define the contrastive loss over a batch of N samples as Eq. (19).

(19)

where is an adjustable hyperparameter. , represents the similarity degree of and . The loss function used in Eq. (19) is the infoNCE loss function commonly used in contrastive learning.

4.2. CL-EPIDTN model structure

The CL-EPIDTN model integrates contrastive learning into the dual-tower architecture and applies it to both the user and item dimensions. For the user dimension, it distinguishes between sequence features and attribute features, and performs contrastive learning separately on these two types of features. In particular, for sequence features, the model constructs positive and negative pairs by augmenting the user’s original interaction sequence. Specifically, it treats the original positive sequence as the anchor and generates negative samples by perturbing the sequence (e.g., using randomly sampled subsequences), thereby enhancing the discriminative power of learned representations.

The CL-EPIDTN model addresses both the long-tail item sparsity and the cold-start problem of low-activity users, thereby significantly enhancing recommendation performance. Fig 5 illustrates the detailed architecture of CL-EPIDTN. As shown, the model first applies masking and dropout to enhance user-side features, including sequence features, attribute features, and item features. These enhanced features are then passed through the shared embedding and encoding layers to generate three corresponding representation vectors. Based on these representations, the model constructs self-supervised loss functions for each feature type. To ensure that SSL benefits the primary recommendation task, CL-EPIDTN adopts a joint training strategy. Specifically, it shares model parameters between the SSL framework and the main task, and optimizes both objectives simultaneously using a multi-task learning approach. This design allows the auxiliary SSL task to guide and regularize the learning of the main supervised task, such as click-through rate prediction or item ranking. Assume that represents a batch of user-item pairs taken from the training data, represents a batch of items taken from the item set, and represents a batch of users taken from the user set. The total loss function is expressed as Eq. (20).

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Fig 5. Contrastive learning-enhanced personalized interaction dual tower network.

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(20)

where represents the loss function of the main task, represents the contrast loss function of the user attribute feature, represents the contrast loss function of the user sequence feature, and represents the contrast loss function of the item. Weight coefficient controls the relative importance of the contrastive losses for sequence, attribute, and item features.

4.2.2. Contrastive learning loss function.

The proposed CL-EPIDTN model categorizes input features into three types: user behavior sequence features, user attribute features, and item features. For each feature category, a dedicated contrastive loss function is designed to serve as an auxiliary self-supervised objective, reinforcing the model’s ability to learn robust and discriminative representations.

Among these, user behavior sequences play a central role in capturing dynamic user preferences. To enhance the expressiveness of sequence encoding, CL-EPIDTN introduces self-supervised signals that explicitly optimize the sequence encoder by contrasting positive and negative behavior patterns. This contrastive mechanism allows the model to distinguish between relevant (positive) and irrelevant (negative) user interests.

The construction of sample pairs for contrastive learning in the sequence feature space is as follows:

Positive samples. two independently augmented versions of the user’s original behavior sequence, generated using random masking. Negative samples, augmented behavior sequences from other users in the same mini-batch. A negatively sampled subsequence from the same user’s historical interactions, intended to represent a dissimilar or irrelevant interest. This setup encourages the encoder to bring positive samples closer in the embedding space while pushing apart negative samples. Formally, the contrastive loss for the user i’s behavior sequence features is defined as Eq. (21).

(21)(22)

where and represent the model outputs of samples generated by the same user through data enhancement, which constitute the positive example pairs of contrastive learning. and represent the model outputs of samples generated by different users through data enhancement, which constitute the negative example pairs of contrastive learning. and represent the model outputs of samples generated by data enhancement for the positive and negative sequence features of the same user, respectively, which constitute the negative example pairs of contrastive learning. N represents the number of negative example samples.

For user attribute features and item features, CL-EPIDTN employs a two-stage data augmentation strategy—random masking followed by dropout—to generate diverse views of the input and construct positive and negative sample pairs for contrastive learning. This approach helps the model capture the underlying semantics of sparse or static features and promotes robustness against noise and missing data. For user i, the contrast loss function constructed by its attribute features is defined as Eq. (23).

(23)

where and represent the model outputs of samples generated by the same user through data enhancement, which constitute the positive example pairs of contrastive learning. and represent the model outputs of samples generated by different users through data enhancement, which constitute the negative example pairs of contrastive learning. N represents the number of negative example samples.

For item i, the contrast loss function of its feature construction is defined as Eq. (24).

(24)

where and represent the model outputs of samples generated by data augmentation for the same item, which constitute the positive example pairs for contrastive learning. and represent the model outputs of samples generated by data augmentation for different items, which constitute the negative example pairs for contrastive learning. N represents the number of negative example samples. The training procedure of CL-EPIDTN is presented in Algorithm 1.

Algorithm 1 Training procedure of CL-EPIDTN

Input: User-item interaction data D, batch size B, temperature τ, learning rate η

Output: Trained model parameters θ

 1.Initialize model parameters θ

 2.for each training epoch do

 3.Sample mini-batch

 4.Apply data augmentation (masking, dropout) to user and item features

 5.Generate embeddings using shared encoder

 6.Compute the loss of main task

 7.Compute contrast losses , and

 8.Total loss

 9.Update

End for

4.3. Model training

In order to enable SSL learned representations to help improve the learning of the main supervised task (such as regression or classification), this paper uses a multi-task training strategy to jointly optimize the main supervised task and the auxiliary SSL task. Assume that represents a batch of user-item pairs taken from the training data, represents a batch of items taken from the item set, and represents a batch of users taken from the user set. The joint loss function is expressed as shown in Eq. (20). For the CL-EPIDTN model, its main loss function is aligned with the construction method of the auxiliary SSL loss function, and both use the infoNCE loss function. Specifically, and are the vector representations of users and items of the user and item examples . Then for a batch of sample pairs , the infoNCE loss function of the main model can be expressed as Eq. (25).

(25)

where represents positive sample pairs, and represents negative sample pairs.

4.4. Algorithmic workflow of the CL-EPIDTN

The algorithmic workflow of the CL-EPIDTN is illustrated in Fig 6. It can be divided into the following key steps:

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Fig 6. Algorithm flow based on CL-EPIDTN.

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Raw data collection: The platform collects historical user-item interaction data through data logging mechanisms. The collected data includes users’ basic attributes, items’ basic attributes, and users’ behavioral interactions with items.

Input data generation: The raw data undergoes preprocessing, including data cleaning and feature extraction, to generate structured input suitable for model training.

Model computation and training: The processed data is fed into the CL-EPIDTN model for forward computation. A joint loss function is constructed, incorporating both the main task and contrastive learning objectives. SGD is then used to optimize the model parameters.

Recommendation list generation: Once training is complete, the optimized CL-EPIDTN model is used to score candidate items. The top-k items with the highest predicted scores are selected and recommended to the user.

5.1. Datasets

To evaluate the effectiveness of the proposed CL-EPIDTN model, two real-world publicly available datasets are utilized: the Amazon Books dataset and the TmallData dataset. Below, we briefly introduce these two datasets along with the data preprocessing steps applied in this study.

5.1.3. Dataset statistics.

All experiments in this paper are conducted on the two datasets described above: Amazon Books and TmallData. These datasets differ significantly in both data volume and structural characteristics. This diversity provides a robust evaluation environment that highlights the effectiveness and generalizability of the proposed CL-EPIDTN model. The differences in data structure and scale also help better demonstrate the model’s adaptability and performance under various conditions. Table 2 shows the statistics of the two datasets, Amazon Books and TmallData.

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Table 2. Summarizes the statistical information of the datasets used in this study.

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5.2. Experimental setup

5.2.1. Experimental environment.

The software and hardware environment used in this study is detailed in Table 3. All experiments were implemented using the Python programming language. The proposed CL-EPIDTN model was built using TensorFlow, an open-source Python-based machine learning library developed by Google.

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Table 3. Experimental hardware and software environment.

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TensorFlow is currently one of the most widely used machine learning frameworks, offering a rich ecosystem of open-source tools and components required to build and deploy various machine learning architectures.

5.2.2. Evaluation metrics.

To comprehensively evaluate the performance of the proposed model, two widely adopted metrics in recommendation systems are used in this study: Hit Rate (HR) and Recall.

Hit Rate (HR) measures the ability of the recommendation system to correctly include the desired item(s) in the recommended list, reflecting the accuracy of the predictions. In this study, we use HR@N, a standard metric in Top-N recommendation tasks, which calculates the proportion of test samples (i.e., ground-truth positive items) that appear in the Top-N predicted items.

The formula for HR@N is defined as:

(26)

More specifically, the denominator corresponds to the total number of test items, while the numerator denotes the total number of items in the Top-N recommendation list that match the ground-truth items across all users.

Recall, also known as true positive rate or sensitivity, measures the proportion of relevant items that are successfully recommended. In the context of information retrieval and recommendation systems, Recall is an important metric to assess how well the model captures all relevant results. It is defined as:

(27)

A perfect recall score of 1.0 indicates that all relevant items have been successfully retrieved, although it does not account for how many irrelevant items were also included. In contrast, Precision (not the focus of this study) evaluates the relevance among retrieved results, and Specificity reflects true negative rate.

In our experiments, we adopt a value of K = 50 for evaluating Top-K performance, meaning the model is tested on its ability to recommend the top 50 items for each user. The corresponding HR@50 and Recall@50 are computed and analyzed in the subsequent sections.

5.3. Effectiveness analysis of the proposed CL-EPIDTN

To validate the effectiveness of the proposed CL-EPIDTN in recommendation tasks, we compare it with several widely adopted and well-established baseline models. The comparison models are described as follows:

WALS (Weighted alternating least squares): A classical matrix factorization method that decomposes the user-item interaction matrix into latent factors of users and items. Recommendations are made based on the compatibility between the user and item latent representations.

YouTube DNN: One of the most successful deep learning models applied in industrial recommendation systems, designed to learn user embeddings for large-scale retrieval.

DSSM (Deep structured semantic model): A category of deep representation learning models that aim to capture semantic similarities between items and users through neural architectures.

MIND (Multi-interest network with dynamic routing): A multi-interest recall model that models diverse user interests during the recall stage, addressing limitations in traditional user representation and enhancing performance in large-scale industrial recommendation systems.

SASRec (Self-attentive sequential recommendation): A sequential recommendation model that captures long-term dependencies in user behavior using self-attention mechanisms, making it suitable for prediction tasks with relatively sparse data.

All models are implemented using TensorFlow, and Faiss is employed to retrieve the Top-N items from a large-scale candidate set. For consistency and fairness across all experiments, the following settings are applied:

Embedding dimension: 128. Batch size: 32. Optimizer: Adam. Dropout rate: 0.3 (applied after each network layer to prevent overfitting). Top-N values for evaluation (N): 10 and 50. For CL-EPIDTN, the dimension of the augmentation vector is set to 32, the number of Transformer layers (L) is set to 5, and the regularization strength is set to 1.

To ensure a fair comparison, all baseline models are tuned to their optimal hyperparameter configurations. The evaluation metrics HR@K and Recall@K are used to compare the performance of the proposed model against the five baselines on both the Amazon Books and TmallData datasets. Different values of N correspond to different lengths of the recommended list. A larger N implies a broader recommendation list, which may lead to higher recall but potentially lower precision. To ensure robustness, each experiment was repeated five times with different random seeds, and we report the mean performance ± standard deviation across these runs in Table 4 and Fig 7.

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Table 4. Comparison of seven models based on two datasets.

https://doi.org/10.1371/journal.pone.0332894.t004

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Fig 7. Performance comparison on Amazon Books and TmallData.

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Table 4 presents the performance comparison of CL-EPIDTN and the five baseline models under different N values. Performance comparison on Amazon Books and TmallData are illustrated in Fig 7. The results clearly demonstrate that the CL-EPIDTN model consistently achieves the highest scores in both Hit Rate (HR) and Recall, for both N = 10 and N = 50 scenarios. These results (highlighted in bold in the table) strongly support the superior effectiveness of the proposed approach.

To further evaluate the performance advantage of the proposed CL-EPIDTN method, HR@10 was adopted as the primary evaluation metric. A two-sample t-test was conducted to assess whether the differences in recommendation performance between CL-EPIDTN and the baseline models on two real-world datasets—Amazon Books and TmallData—are statistically significant. The test results are presented in Table 5.

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Table 5. Statistical significance analysis of CL-EPIDTN and baseline models in terms of HR@10.

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As shown in Table 5, CL-EPIDTN achieved statistically significant or highly significant improvements (p < 0.01) in HR@10 over all baseline models on the Amazon Books dataset. In particular, the differences with mainstream models such as WALS, DSSM, and SASRec were highly significant (p < 0.001). Similarly, on the TmallData dataset, CL-EPIDTN also demonstrated a clear performance advantage, with p-values below 0.01 for most baseline comparisons. Notably, the improvements over YouTube DNN and DSSM were highly significant, with p-values of 2.89e-05 and 4.65e-05, respectively. From a numerical perspective, CL-EPIDTN improved HR@10 by 41.3% compared to WALS and by 23.7% compared to YouTube DNN on the Amazon Books dataset. On the TmallData dataset, the gains reached 36.1% over WALS and 21.9% over DSSM. These results underscore the proposed method’s strong generalization ability and robustness across diverse recommendation scenarios. In summary, CL-EPIDTN not only achieves substantial improvements in HR@10 but also significantly outperforms existing state-of-the-art recommendation models in terms of statistical significance. These findings validate the effectiveness of the proposed contrastive learning mechanism and the enhanced cross-attention module.

5.4. Ablation study

To investigate the rationality and contribution of each sub-module in the proposed CL-EPIDTN model, we conducted three ablation experiments focusing on the multi-layer Transformer structure, the dual personalized augmentation module, and the contrastive learning strategy. The ablated variants are defined as follows: EPIDTN: The model without contrastive learning. CLTD: The model without the personalized dual augmentation module. CL-DSSM: The model without the multi-layer Transformer structure. The results of the ablation experiments are presented in Table 6 and Fig 8.

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Table 6. Ablation experiment results.

https://doi.org/10.1371/journal.pone.0332894.t006

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Fig 8. Ablation study results on Amazon Books and TmallData.

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For fairness and consistency, the experiments were conducted on both Amazon Books and TmallData datasets using the same optimal hyperparameter settings across all models. Two evaluation metrics, HR and Recall, were used to assess model performance. From the results in Table 6, it is evident that the proposed CL-EPIDTN model, which integrates all three components—multi-layer Transformer architecture, dual personalized augmentation, and contrastive learning—achieves the best performance. Specifically: CL-EPIDTN outperforms EPIDTN (without contrastive learning), demonstrating the effectiveness of incorporating contrastive learning EPIDTN performs better than CLTD (without the dual augmentation module), indicating the importance of personalized augmentation strategies. CLTD also surpasses CL-DSSM (without multi-layer Transformer structure), which further validates the significance of deep sequence modeling via Transformers. These results clearly show that each component—multi-layer Transformer, dual augmentation, and contrastive learning—contributes meaningfully to the overall performance. The ablation study thus reinforces the validity and effectiveness of the CL-EPIDTN design for recommendation tasks.

5.5. Parameter setting analysis

To further investigate the architecture of the CL-EPIDTN model, this section conducts a sensitivity analysis on three critical hyperparameters: the number of Transformer layers L, the output embedding dimension M, and the regularization strength (denoted as ). The effects of varying these hyperparameters on model performance are examined on both datasets. The ranges of the hyperparameters considered are summarized in Table 7.

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Table 7. Range of hyperparameter settings.

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As shown in Fig 9, the impact of the number of Transformer layers L on the experimental results is evident. When L is set to 5, the model achieves the best performance on both datasets. Increasing the number of Transformer layers beyond 5 yields a negative impact on model performance, suggesting that increased complexity does not necessarily lead to more accurate feature extraction. Similarly, when L is set to 1, the performance on both datasets deviates from that observed with other settings.

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Fig 9. Impact of Transformer layer number L on experimental results.

(a) Impact of Transformer layer number L on HR. (b) Impact of Transformer layer number L on recall.

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Fig 10 shows the impact of embedding size M on experimental results. It can be seen that when the embedding size M is 128, the CL-DSSM model designed in this paper has the best effect on the two datasets, followed by 256, and the worst when M is 32. These results demonstrate that increasing the embedding layer depth does not linearly enhance the model’s capacity and may lead to diminishing returns.

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Fig 10. The impact of output embedding size M on experimental results.

(a) The impact of output embedding size M on HR (b) The impact of output embedding size M on recall.

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For the impact of regularization strength on experimental results in Fig 11, we still found that the best performance of the model on both datasets is still when =1, followed by =2, and =0.1 is the worst. The difference is that the impact of changing the hyperparameter on the model is slightly greater than the first three parameters, and the height difference of the tree diagram can confirm this point.

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Fig 11. Effect of regularization strength on experimental results.

(a) Effect of regularization strength on HR (b) Effect of regularization strength on recall.

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This paper conducts hyperparameter sensitivity analysis on the number of Transformer layers L, output embedding size M, and regularization strength on two datasets, and finds that these hyperparameters have a certain impact on the model effect. On this basis, the hyperparameters that can show the best effect of the model on the two datasets are selected, namely, the number of Transformer layers L is selected as 5, the output embedding size M is selected as 128, and the regularization strength is selected as 1.