Repeated Padding for Sequential Recommendation

Suppose we have user and item sets denoted by symbols $\mathcal{U}$ and $\mathcal{V}$, respectively. Each user $u\in\mathcal{U}$ is associated with a sequence of interacted items in chronological order $s_{u}=[v_{1},\ldots,v_{j},\ldots,v_{\left|s_{u}\right|}]$, where $v_{j}\in\mathcal{V}$ indicate the item that user $u$ has interacted with at time step $j$ and $\left|s_{u}\right|$ is the sequence length. The sequential recommendation task can be formulated as follows. Given the sequences of interacted items $s_{u}$, our task is to accurately predict the most possible item $v^{*}$ that user $u$ will interact with at time step $\left|s_{u}\right|+1$, formulated as follows:

This equation can be interpreted as calculating the probability of all candidate items and selecting the highest one for recommendation.

Padding is a common technique when training sequential models. The Batch Processing requires that the sequences in each batch have the same length. In addition, common CNN- or Transformer-based models can only handle fixed-length sequences and require model initialization and operations based on fixed sequence lengths. So, before training a recommendation model, we usually specify a maximum sequence length $N$. For sequences with an original length of more than $N$, the most recent $N$ items are usually chosen because they represent the user’s recent preferences. As shown in Figure1 (a) and (b), original sequences of length less than $N$ are padded with the special value 0 to reach the length $N$. The special value 0 contains no actual information and does not participate in model calculations. The above process can be formulated as follows:

where $ZeroPad(\cdot)$ indicates padding the 0 to the left side of the sequence until its length is $N$, and $Intercept(\cdot)$ indicates intercepting the nearest $N$ interactions. The $s_{u}^{f}$ is the final input to the model where $\small\left|s_{u}^{f}\right|=N$. Typically, the total number of sequences involved in model training is $\left|\mathcal{U}\right|$, i.e., one sequence for each user.

To alleviate the data sparsity problem, data augmentation is often used to augment the original data to increase the number of sequence involved in model training. Given an original sequence $s_{u}$, a data augmentation operation makes minor but appropriate changes to $s_{u}$ to generate a new sequence $s_{u}^{d}$. Both $s_{u}$ and $s_{u}^{d}$ are used for model training or self-supervised learning. For example, as shown in Figure1 (c), for an original sequence $s_{u}=[v_{5},v_{2},v_{6},v_{4},v_{1},v_{7},v_{9},v_{2}]$, we intercept a portion of the consecutive sequence to generate a new sequence data $s_{u}^{d}=[v_{6},v_{4},v_{1},v_{7},v_{9}]$. For original sequence $s_{u}=[v_{3},v_{7},v_{9}]$, we inert an item $v_{4}$ between $v_{7}$ and $v_{9}$ to generate sequence data $s_{u}^{d}=[v_{3},v_{7},v_{4},v_{9}]$. In each epoch, each sequence will be augmented at least once, so the total number of sequences involved in model training will be at least 2$\left|\mathcal{U}\right|$. The original and augmented sequences also need to apply function Eq. (2) before being fed into the model.

As illustrated in Figure 1 (b) and (c), a large amount of free space is filled with 0 regardless of whether data augmentation is performed. Also, due to the long-tail effect, the interaction sequences of the vast majority of users are usually short. Therefore, our idea is to utilize these free spaces further to improve the efficiency of model training and recommendation performance.

In order to achieve this objective, we propose a simple but effective padding strategy called Repeated Padding (RepPad). Specifically, we utilize the original sequence as padding content instead of the special value 0. As shown in Figure 1 (d), give the original sequence $s_{u}=[v_{1},v_{2},v_{3},v_{4}]$, and we pad the original sequence once on the left and get the padded sequence $s_{u}^{p}=[\underline{v_{1},v_{2},v_{3},v_{4}},v_{1},v_{2},v_{3},v_{4}]$. This operation can be formulated as:

where $m$ is padding times and $|$ indicates sequence concatenation. This operation can be performed only once or repeated several times until there is not enough space left to hold the original sequence. In other words, $m$ can be pre-specified or calculated based on the original sequence length $s_{u}$ and the maximum sequence length $N$. For example, when the maximum sequence length is 10, the remaining length of 2 is insufficient to accommodate the original sequence of length 4, so it still needs to apply function Eq. (2). The final input sequence $s_{u}^{f}=[0,0,\underline{v_{1},v_{2},v_{3},v_{4}},v_{1},v_{2},v_{3},v_{4}]$. In addition, given the original sequence $s_{u}=[v_{3},v_{7},v_{9}]$, the padding operation can be performed up to 3 times, and the final sequence $s_{u}^{f}=[0,0,\underline{v_{3},v_{7},v_{9}},\underline{v_{3},v_{7},v_{9}},v_{3},v_{7},v_{9}]$.

However, there is a problem with the above padding strategy: there may be cases where the end of the original sequence is used to predict the head. Using $[0,0,\underline{v_{1},v_{2},v_{3},v_{4}},\underline{v_{1}},v_{2},v_{3},v_{4}]$ as training data, there will be cases where $v_{1},v_{2},v_{3},v_{4}$ is used to predict $v_{1}$. To solve this problem, we add the special value 0 between each repeated padding to prevent this from happening. This operation can be formulated as:

As shown in Figure 1 (e), given original sequence $s_{u}=[v_{1},v_{2},v_{3},v_{4}]$, the final sequence after Eq. (4) and (2) is $[0,v_{1},v_{2},v_{3},v_{4},0,v_{1},v_{2},v_{3},v_{4}]$. We give the possible values of $m$ and their interpretation in Table 1.

Our method has no trainable parameters or hyper-parameters that need to be manually tuned. It is a model-agnostic plug-and-play data augmentation approach. In the Experiments section, we will explore and analyze several variants of RepPad, including different times of padding and whether to add the delimiter 0. The best-performing variant is The best-performing variant is randomly selected in the range from one to the maximum number of times. Our method is very easy to implement, and we present its Python procedure in Algorithm 1. So far, we have introduced the basic idea of our RepPad. It is worth emphasizing that the repeated padding sequences still need to apply function Eq. (2) operation before they can be fed into the model:

The experiments are conducted on six datasets:

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  Toys, Beauty, Sports, and Home: Four datasets obtained from Amazon (McAuley et al., 2015) and correspond to the ”Toys and Games”, ”Beauty”, ”Sports and Outdoors”, and ”Home” categories, respectively.

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  Yelp¹¹1https://www.yelp.com/dataset: It is the second version of the Yelp dataset released in 2020. We utilize the records after January 1st, 2019.

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  MovieLens-1M²²2https://grouplens.org/datasets/movielens/ (ML-1M for short): This dataset comprises rating behaviors gathered from a movie review website.

The Amazon and Yelp datasets contain mainly short user sequences. The MovieLens-1M contains mainly long user sequences. Following (Liu et al., 2021a; Dang et al., 2023a; Tian et al., 2023), we reduce the data by extracting the 5-core. The maximum sequence length $N$ is set to 200 for the MovieLens-1M dataset and 50 for other datasets. The detailed statistics are summarized in Table 3.

In order to conduct a comprehensive evaluation of the effectiveness and superiority of RepPad, the baselines consist of three main categories:

Following (Liu et al., 2021a; Dang et al., 2023a; Tian et al., 2023), we adopt the leave-one-out strategy, wherein the last item of each user sequence serves as the test data, the items preceding it as validation data, and the remaining data as training data. We rank the prediction over the whole item set rather than negative sampling, otherwise leading to biased discoveries (Krichene and Rendle, 2020). The evaluation metrics include Hit Ratio@K (denoted by HR@K), and Normalized Discounted Cumulative Gain@K (NDCG@K). We report results with K $\in\{5,10,20\}$. Generally, greater values imply better ranking accuracy.

For all baselines, we adopt the implementation provided by the authors. We set the embedding size to 64 and the batch size to 256. To ensure fair comparisons, we carefully set and tune all other hyper-parameters of each method as reported and suggested in the original papers. We use the Adam (Kingma and Ba, 2014) optimizer with the learning rate 0.001, $\beta_{1}=0.9$, $\beta_{2}=0.999$. For all methods, we adopt early stopping on the validation set if the performance does not improve for 20 epochs and report results on the test set.

The experimental results of original sequential recommendation models and adding our RepPad are presented in Table 4 and Table 5. These tables show that our method can significantly improve the performance of recommendation models on short-sequence datasets, but our method may become ineffective for long-sequence datasets. These results validate our conjecture in Section 2.5.2.

(1) As a whole, the RNN- and CNN-based models perform comparably. NARM is usually the best performer, which verifies the effectiveness of combining attention mechanisms and RNN architectures. The Transformer-based models perform better overall, especially SASRec and STOSA. This shows the ability of the Transformer architecture to model user sequence patterns. FMLP-Rec performs slightly less well, which we believe may be related to the fact that the pure MLP architecture cannot accurately capture the fine-grained relationship between each user interaction and historical behavior as the Transformer does.

(2) As demonstrated in Table 4, after adding our RepPad to the original model, the performance of all models is significantly improved. The average recommendation performance improvement is up to 60.3% on GRU4Rec, 24.3% on SASRec, and 22.8% on STOSA. In particular, Our method gives GRU4Rec a boost of up to 110.00% Hit@5 and 122.22% for NDCG@5 on the Home dataset. The above experimental results validate the effectiveness of our method on short-sequence datasets. It also shows that RepPad can be applied to various types of sequential models. Considering that in real-world scenarios, the vast majority of user history records are short sequences (Liu et al., 2021b; Jiang et al., 2021), our approach has great potential for application.

(3) From Table 5, we can observe that RepPad can only achieve less improvement on some models for the long-sequence dataset and even cause performance degradation on some methods. These results verify our conjecture in Section 2.5.2. Even though we have set the maximum sequence length to 200 for long-sequence datasets, most user sequences still do not have enough space left for repeated padding. At the same time, repeated padding may interfere with the model’s ability to capture long-term user preferences and impair recommendation performance. We also note that the Transformer-based model still outperforms other types of models overall, further demonstrating the power of its architecture.

In this subsection, we compare RepPad with different data augmentation methods. For the heuristic methods, we choose the two representative models, SASRec and GRU4Rec, as the backbone network. For methods that require training, we chose the most versatile SASRec since different methods have different restrictions on the type of backbone network.

From Table 6, we observe that RepPad outperforms existing heuristic data augmentation methods in most cases. CMRSI performs the best among the baselines, thanks to the five well-designed data augmentation operators that help discover more preference information while mitigating data sparsity. Ran-S also achieves competitive performance in some examples due to its augmentation using items in the original sequence. We also observe that in some cases, the model performance degraded after using data augmentation methods, which may be related to the fact that these methods introduce too much noise that destroys the integrity of the original sequence. RepPad utilizes the free data space and uses the original sequences for padding, which improves model performance while retaining the user’s complete preference knowledge. From Table 7, RepPad still achieves satisfactory results in the face of data augmentation methods that require training. Among the baseline methods, DiffuASR and CL4SRec leverage the diffusion model and sequence-level augmentation with contrastive learning to achieve competitive performance in some cases. Surprisingly, RepPad achieves the best or second-best performance in all cases without including any parameters and training process.

Overall, RepPad proved its superiority by achieving highly competitive results without including any parameters or training processes. Also, our approach is not limited by the backbone network and can be seamlessly inserted into most existing sequential recommendation models.

In this section, we conduct an ablation study to explore the different variants of RepPad. Based on the padding times $m$ in Table 1 and whether or not to add the delimiter 0, we compare the performance of the following variants: 1) RP-Fix: Performing repeated padding with a fixed number of times, we report the best results for times in range $\{1,2,3\}$. 2) RP-Max: Performing repeated padding until the remaining space is insufficient (i.e., maximum padding times). 3) RP(0, Max): When performing repeated padding each time, randomly select between 0 and the maximum number of times. 4) RP(1, Max): When performing repeated padding each time, randomly select between 1 and the maximum number of times. Figure 2 presents the results. We report the performance of each of the four variants with and without adding the delimiter 0.

For performance between different variants, in most results, the performance of RP(0, Max) and RP(1, Max) can come with considerable improvements. RP-Fix and RP-Max bring limited performance improvement compared to RP(0, Max) and RP(1, Max). For PR-Fix, RepPad is executed with a fixed number of times, so it does not utilize the idle input space. For RP-Max, we observe that it not only does not bring improvement in some cases but also leads to a significant decrease in model performance. If every sequence performs RepPad to the maximum number of times, it may make the representation learned by the model unbalanced. Because the repeated padding time tends to be large for short sequences, multiple iterations of short behavioral sequences may interfere with the model’s ability for long-sequence and long-term preferences modeling, which in turn impairs recommendation performance. For RP(0, Max) and RP(1, Max), they avoid the imbalance problem caused by RP-Max while utilizing the free input space. Meanwhile, RP(1, Max) performs better than RP(0, Max), indicating that executing RepPad at least once is essential.

For whether or not to add the delimiter 0, we observe that this factor is related to the type of recommendation model. For GRU4Rec, there are more examples of better performance when no delimiter is added. In contrast, for SASRec, there are more examples that models perform better when the delimiter is added. In other words, RNN-based models are less susceptible to the interference of ”predicting the tail with the head”. The self-attention module of Transformer-based models pays attention to the effect of each historical interaction on the following action, so the negative effect of ”predicting the tail with the head” can be minimized by adding the delimiter 0. We leave the theoretical explanation of this phenomenon to the future work.

In Figure 3, we illustrate the loss convergence of different methods during training. We also compare the epoch time consumption of different methods in Table 8. From the figures and tables, we can observe that RepPad’s losses converge slightly faster than the original model. For CMRSI, the heuristic data augmentation introduces more different training sequences along with more noise, resulting in more epochs for the model to converge. The contrastive learning task of CL4SRec also imposes additional computational overhead and convergence burden. Also, RepPad only adds a small amount of epoch elapsed time compared to the original model. While CMSRI and CL4SRec add extra training sequences and auxiliary tasks, resulting in a substantial increase in training elapsed time. Comparing RP-Fix and RP(1, Max), the former can only be performed repeated padding a fixed and smaller number of times. At the same time, the latter randomly chooses between one time and the maximum number of times, which slightly increases the elapsed time but improves the speed of loss convergence and model performance.

Research has shown that more stable or smooth gradients are more helpful for model training (Li et al., 2019; Reddi et al., 2019; Xu et al., 2019), thus improving model robustness and performance. In Figure 4, we illustrate the average gradient of item embeddings throughout the training process with and without our RepPad. We show the frequency of the gradient values as histograms. We can observe that the average gradient values are more centralized with the addition of our method. While the gradient is more likely to have large or small values during the original model training, RepPad mitigates this phenomenon, making the gradient more stable during the training process. Smooth updating of the gradient allows training to converge stably and improves the model’s recommendation performance

RepPad can make the gradient update of the model more stable without increasing the total number of training sequences. Unlike existing methods, our method augments short sequences to a length comparable to that of long sequences in a nearly lossless manner. Existing methods inevitably generate noise or compromise the integrity of the original data when perform augmentation. From another perspective, RepPad enables the model to focus fairly on short and long sequences, giving more attention to long-tail items and users. In this way, the model can better learn the representation of cold-start users and items. We also speculate that RepPad acts as some kind of regularization, which mitigates the negative effects of the uneven distribution of original dataset.

Sequential recommendation (SR) is an emerging topic in the field of recommender systems (Qu et al., 2022). An early solution is to treat the item sequence as a Markov Chain (Rendle et al., 2010; Shani et al., 2005; He and McAuley, 2016), where the next item to predict is closely related to the latest few interactions. The limitation lies in the inability to learn the dependency in a relatively large time step. Hence, a better solution based on recurrent neural networks (RNNs) (Schuster and Paliwal, 1997) emerges since it can capture long- and short-term preferences. A pioneering work GRU4Rec (Hidasi et al., 2015a) introduced RNN into the field of recommender systems. It trained a Gated Recurrent Unit (GRU) architecture to model the evolution of user interests. Following this idea, CmnRec (Qu et al., 2022) proposed to divide proximal information units into chunks, whereby the number of memory operations can be significantly reduced. More recently, transformer-based approaches have attracted much attention because of their convenience for parallelization and carefully designed self-attention architecture (Vaswani et al., 2017; Devlin et al., 2018). SASRec (Kang and McAuley, 2018) employed unidirectional Transformers to fulfill the next-item prediction task in the sequential recommendation. Some works further optimized the Transformer’s architecture to make it more suitable for recommendation scenarios, such as reducing computational complexity (Fan et al., 2021) and stochastic self-attention (Fan et al., 2022). Furthermore, FMLP-Rec (Zhou et al., 2022) proposes an all-MLP architecture with learnable filters to enhance recommendation performance.

Data augmentation has been established as a standard technique to train more robust models in many domains. In recommender systems, Slide Windows is an early work (Tan et al., 2016b), which modified the original click sequence by splitting it into many sub-sequences or randomly discarding a certain number of items. Inspired by counterfactual thinking, CASR (Wang et al., 2021) revised the sequence of user behaviors by substituting some previously purchased items with other unknown items. Some researchers proposed to leverage bi-directional transformers (Liu et al., 2021b; Jiang et al., 2021) and diffusion models (Liu et al., 2023) for sequence data augmentation. With the rise of self-supervised techniques (e.g., contrastive learning), many researchers used it as an auxiliary task to further improve model performance (Qin et al., 2023; Xie et al., 2022). For example, CL4SRec (Xie et al., 2020) developed three data augmentation operators for pre-training recommendation tasks equipped with a contrastive learning framework. Based on CL4SRec, CoSeRec (Liu et al., 2021a) integrated item similarity information for data augmentation with a contrastive learning objective, aiming to maximize the agreement of augmented sequences. Unlike existing methods, we are the first to explore the use of idle padding space for data augmentation. In terms of simplicity and applicability, our method does not contain any parameters or training processes and can be plugged into most existing sequential models.