Denoising and Prompt-Tuning for Multi-Behavior Recommendation

In practice, user-side information could be well reflected by their co-interactions (Huang et al., 2021; Tao et al., 2022). Consequently, we utilize users’ co-interactive behaviors (e.g., co-view and co-purchase) to learn the complex patterns. Mathematically, there is an edge $\varepsilon^{U,*}_{uv}$ between user $u,v\in\mathcal{U}$ in the user relation graph $\mathcal{G}^{U}$ under the behavior $*$ iff $\mathcal{E}^{*}_{u\cdot}\cap\mathcal{E}^{*}_{v\cdot}\neq\emptyset\>\textrm{and}\>\mathcal{E}^{*}_{u\cdot}\cup\mathcal{E}^{*}_{v\cdot}\neq\emptyset.$ The weight $w^{U,*}_{uv}$ of $\varepsilon^{U,*}_{uv}$ is calculated by Jaccard similarity as $\frac{|\mathcal{E}^{*}_{u\cdot}\cap\mathcal{E}^{*}_{v\cdot}|}{|\mathcal{E}^{*}_{u\cdot}\cup\mathcal{E}^{*}_{v\cdot}|}$ to indicate the relevance strength between the users.

As suggested by previous studies (Xia et al., 2021a; Han et al., 2022), unlike user relations, items possess directed relations due to the existence of temporal information. Consequently, we construct a directed item relation graph for better representation learning. Specifically, we sort each user $u$’s interactions into a sequence $S_{u}$ according to interaction timestamps, and count the number of occurrences of each pair of items $(i,j)$ in a particular order (e.g., $i\xrightarrow{*}j$) from all sequences. Formally, there is an edge $\varepsilon^{I,*}_{ij}$ from item $i$ to $j$ in the item relation graph $\mathcal{G}^{I}$ under behavior $*$ iff $\text{Cnt}(i\xrightarrow{*}j)>0$, where $\text{Cnt}(\cdot)$ is a counter. The weight $w^{I,*}_{ij}$ of $\varepsilon^{I,*}_{ij}$ is calculated by Jaccard similarity as $\frac{\text{Cnt}(i\xrightarrow{*}j)}{\text{Cnt}(i\xrightarrow{*}j)+\text{Cnt}(j\xrightarrow{*}i)}$ to indicate the sequential strength.

Since the user relation graph $\mathcal{G}^{U}$ is an undirected graph, we encode such relations without distinguishing directions. Formally, for each user $u^{*}$, we aggregate the information from his/her neighbor’s information and himself/herself as per $\mathcal{G}^{U}$ to learn similar behavior patterns among users and generate layer-specific behavior-aware encoded vectors as follows

where $f^{U,(l)}_{u\rightarrow u}(\cdot)$ is the aggregation function to encode user relations, $l\in\mathbb{R}$ is the number of layer, $N^{U}_{u^{*}}$ is the neighbor of $u^{*}$ in $\mathcal{G}^{U,*}$ under behavior $*\in\{a,t\}$, and $\Theta^{(l)}_{U}$ is the set of trainable parameters. Motivated by (Nguyen et al., 2018; Han et al., 2022), which utilize a convolution operator to preserve dimension-wise information and effectively encode homogeneous relations, we implement $f^{U,(l)}(\cdot)$ and generate $\boldsymbol{e}^{U,(l)}_{u^{*}}$ via

where $\text{Conv}^{U,(l)}(\cdot)$ is a layer-specific convolution operator with stride 1 and filter size $2\times 1$, $w^{U,*}_{uu^{*}}$ is the normalized weight of edge $\varepsilon^{U,*}_{uu^{*}}$ in $\mathcal{G}^{U,*}$, $\|$ is the concatenation operation, and $\bar{\Theta}^{(l)}_{U}$ is the set of trainable weight parameters of the convolution operator.

Since items typically have directed patterns, we perform an attention-based message passing scheme (Velickovic et al., 2018) (i.e., $f^{I,(l)}_{i\rightarrow i}(\cdot)$) for adaptively encoding. For each item $i^{*}$ in the item relation graph $\mathcal{G}^{I,*}$ under behavior $*$, we first assign a $2$-dimensional attention vector $\boldsymbol{\alpha}^{*}$ to weight $i^{*}$’s incoming (i.e., $i\in N^{I,\text{IN}}_{i^{*}}$) and outgoing (i.e., $j\in N^{I,\text{OUT}}_{i^{*}}$) neighbors. Formally, we implement $f^{I,(l)}_{i\rightarrow i}(\cdot)$ and generate $\boldsymbol{e}^{I,(l)}_{i^{*}}$ as follows

where $\text{Conv}^{U,(l)}(\cdot)$ is a similar convolution used in Eq. (3) with different parameters, $w^{I,*}_{ii^{*}},w^{I,*}_{i^{*}j}$ are the normalized weights of edge in $\mathcal{G}^{I,*}$, and $\Theta^{(l)}_{I}$ is the set of trainable parameters, including attention matrices $W^{(l)}_{I,n}\in\mathbb{R}^{d\times d}$ and the convolutional filter $\bar{\Theta}^{(l)}_{I}$ .

For each user $u^{*}$ and item $i^{*}$, we formally present a lightweight message passing scheme based on LightGCN (He et al., 2020) as follows

To encoder multiple patterns from different graphs into embeddings, we design a gating operator, which could adaptively balance and fuse the different views generated from the $(l)$- to $(l+1)$-th layers. More specifically, we generate the pattern-enhanced user/item embedddings $\boldsymbol{e}^{(l+1)}_{u^{*}}$ and $\boldsymbol{e}^{(l+1)}_{i^{*}}$ under the type of behavior $*$ via

where $\sigma(\cdot)$ is the sigmoid function, $\beta^{*}_{u},\beta^{*}_{i}\in\mathbb{R}$ are weight scalars, and $\boldsymbol{W}^{(l)}_{UU},\boldsymbol{W}^{(l)}_{II}\in\mathbb{R}^{2d\times 1}$ are trainable parameters. Accordingly, we generate multi-behavior embeddings in the $(l+1)$-th layer via

We concatenate user/item embeddings across each layer to generate the final behavior-aware (i.e., $\boldsymbol{h}^{*}_{u},\boldsymbol{h}^{*}_{i}\in\mathbb{R}^{d}$) and multi-behavior (i.e., $\boldsymbol{h}_{u},\boldsymbol{h}_{i}\in\mathbb{R}^{d}$) representations:

where $f_{U}$ and $f_{I}$ are feedforward layers activated by the ReLU function with different trainable parameters $\boldsymbol{W}_{U},\boldsymbol{W}_{I}\in\mathbb{R}^{(L\times d)\times d}$.

We design a behavior-aware graph decoder as a discriminator to perform information reconstruction. It takes the learned behavior-aware representations as input and generates the probability graph via

where $\boldsymbol{h}_{\mathcal{G}^{*}}\in[0,1]^{|\mathcal{U}|\times|\mathcal{I}|}$ is the parameterized graph under behavior $*$, $\boldsymbol{H}^{*}_{U}\in\mathbb{R}^{|\mathcal{U}|\times d},\boldsymbol{H}^{*}_{I}\in\mathbb{R}^{|\mathcal{I}|\times d}$ are the learned representations of the user/item set, and $\boldsymbol{e}_{b^{*}}\in\mathbb{R}^{d}$ is the behavior embedding. Thus, we formulate the information reconstruction task as a binary classification task to predict user-item interactions in graph $\mathcal{G}$:

Note that we also enhance the decoder (i.e., Eq. (9)) to reconstruct the target behavior graph since target behavior (e.g., purchase) is more reliable than auxiliary behaviors (e.g., click) in real-world scenarios and can help avoid incorrect noise identification. Moreover, it is reasonable to assume that most interactions should be noiseless. Therefore, we could gradually learn informative interactions’ distribution by minimizing Eq. (10). In this case, interactions with higher loss scores can be identified as noisy interactions.

As shown in Figure 2(a), DPT takes the constructed relation graphs as input and encodes patterns into embeddings, which helps pinpoint noise. Specifically, we generate base embeddings by Eq. (1) and input them to the pattern-enhanced graph encoder (i.e., Section 3.3) to encode multi-view patterns so as to generate behavior-aware and multi-behavior representations by Eq. (8). We leverage the obtained behavior-aware representations to guide the denoising module to learn parameterized graph $\boldsymbol{h}_{\mathcal{G}^{*}}$ by Eq. (9) and calculate reconstruction loss $\mathcal{L}_{\text{REC}}$ by Eq. (10). We convert $\boldsymbol{h}_{\mathcal{G}^{a}}$ into a hard-coding binary (i.e., 0 vs. 1) distribution, which indicates whether the interaction under auxiliary behaviors is noisy or not, to generate the denoised multi-behavior graph $\mathcal{G}^{\prime}$. Here we could adopt differentiable methods (e.g., Gumbel-softmax function (Wang et al., 2019b; Yu et al., 2019; Zhao et al., 2021; Qin et al., 2021)) to binarize the real-valued graph $\boldsymbol{h}_{\mathcal{G}^{a}}$ in each training iteration. However, reconstructing and generating such a large-scale graph according to Eq. (9) and Eq. (10) leads to large computational costs. Motivated by sub-graph sampling (Xia et al., 2021a; Zheng et al., 2021) and hyper-parameter optimizing (Liu et al., 2019; Yao et al., 2021) strategies, we first sample a mini-batch $\mathcal{B}$ of user/item interactions to optimize Eq. (10), thus endowing the denoising module with the ability of handling large-scale graphs. Then we leverage the optimized parameters to generate the probability graph instead of generating it iteratively. Specifically, we adopt a simple threshold strategy (i.e., $\boldsymbol{h}_{\mathcal{G}^{a}_{ui}}=0$ if $\boldsymbol{h}_{\mathcal{G}^{a}_{ui}}<0.5-\delta$, $\boldsymbol{h}_{\mathcal{G}^{a}_{ui}}=1$ otherwise) to binarize $\boldsymbol{h}_{\mathcal{G}^{a}}$, where $\delta$ is a disturber to control reliability of the denoising discriminator. Note that $\delta\rightarrow 0^{+}$ and $\delta\rightarrow 0.5^{-}$ lead to more and less identified noise, respectively. After that, we can generate $\mathcal{G}^{\prime}=\{\mathcal{G}^{a}\odot\boldsymbol{h}_{\mathcal{G}^{a}},\mathcal{G}^{t}\}$ for the following stages of DPT, where $\odot$ is the element-wise dot product operator.

However, noise identification highly depends on the reliability of the graph encoder. A pure unsupervised task for denoising may make the optimization process irrelevant to multi-behavior recommendation. Inspired by the co-guided learning scheme (Zhang et al., 2022b), we incorporate a multi-behavior recommendation task into the first stage, and thus can avoid unreliable learning (e.g., false noise identification) in the early stage of the training process. Specifically, we formulate the multi-behavior recommendation task as minimizing the Bayesian Personalized Ranking (BPR) objective function:

where $\text{sim}(\cdot)$ is a similarity function (e.g., inner product or a neural network), $u\in\mathcal{U}$, $i^{*}\in\mathcal{I}$, $\mathcal{G}^{*}_{ui^{*}}=1$, and $j^{*}$ is a randomly sampled item from $\mathcal{I}$ with $\mathcal{G}^{*}_{uj^{*}}=0$ in each mini-batch $\mathcal{B}$.

While representations learned in the first stage are informative, noise still inevitably affects the learned model parameters (e.g., the embedding layer) because the representation-based denoising module can capture only reliable, but not all, noise. Intuitively, we could leverage $\mathcal{G}^{\prime}$ to retrain (e.g., full-tuning) the entire model. However, it is less desirable due to the large additional computational costs of model re-training. In addition, the optimized parameters in the embedding layer are informative enough to reflect pattern information, and thus there is no need to encode relation graphs in the second stage. Accordingly, we can fine-tune a few parameters instead of full-tuning the entire model to further attenuate noise’s influence. Due to the disentangled design choice of aggregation layers, we can efficiently aggregate user-item interactions (i.e., by Eq. (5) and Eq. (7)) without repeatedly encoding patterns. More specifically, as shown in Figure 2(b), we freeze the parameters of the embedding layer to generate the base embeddings for users and items. Then, we input them to the user-item interaction aggregation layer (i.e., Eq. (5) and Eq. (7)) to iteratively generate multi-behavior embeddings, and learn the final multi-behavior representations (i.e., $\boldsymbol{h}^{\prime}_{u}$ and $\boldsymbol{h}^{\prime}_{i}$) by Eq. (8) with re-initialized parameters (i.e., $\boldsymbol{W}_{U},\boldsymbol{W}_{I}\in\mathbb{R}^{Ld\times d}$). According to the learned representations, we rewrite the BPR loss based on the noiseless graph as follows

where $u\in\mathcal{U}$, $i^{*},j^{*}\in\mathcal{I}$, $\mathcal{G}^{\prime}_{ui^{*}}=1$, and $\mathcal{G}^{\prime}_{uj^{*}}=0$. By minimizing Eq. (12), we denote the parameter set as $\Theta_{2}=\{\boldsymbol{W}_{U},\boldsymbol{W}_{I}\}$, which contains $2Ld\times d$ parameters. It can be seen that we only tune a small amount of parameters $2Ld\times d\ll(|\mathcal{U}|+|\mathcal{I}|)\times d$, instead of tuning the embedding layer.

After the above stages, we can generate noiseless auxiliary behaviors and informative knowledge. However, bridging the semantic gap among multi-typed behaviors is still challenging because it requires transferring sufficient target-specific semantics without jeopardizing learned multi-behavioral knowledge. Inspired by the effectiveness of the prompt-tuning paradigm (Jia et al., 2022; Xin et al., 2022; Geng et al., 2022; Wu et al., 2022c; Sun et al., 2022), we adopt a deep continuous prompt-tuning approach in the third stage to alleviate the semantic gap between auxiliary and target behaviors. Specifically, as illustrated in Figure 2(c), we utilize the aggregation of multi-typed behavior embeddings (i.e., $\boldsymbol{e}_{b^{a}}$ and $\boldsymbol{e}_{b^{t}}$) to generate a prompt embedding $\boldsymbol{e}_{p}\in\mathbb{R}^{d}$, instead of initializing it randomly, to better understand prompt semantics (Sun et al., 2022). Note that, during the initializing process, we freeze auxiliary behaviors’ embedding parameters (i.e., $\boldsymbol{W}_{b^{a}}$) and update the target behavior’s parameters (i.e., $\boldsymbol{W}_{b^{t}}\in\mathbb{R}^{d}$). Therefore, to adopt prompt-tuning in the third stage, we freeze not only the parameters of the embedding layer (except $\boldsymbol{W}_{b^{t}}$) but also the parameter set $\Theta_{2}$ learned in the second stage. More specifically, to generate embeddings of the graph encoder’s $(l)$-th layer, we only adopt prompt under the target behavior via

where we can leverage various ways to adopt the prompt, e.g., add, concatenate, and projection operators. Inspired by VPT (Jia et al., 2022), we use the simple yet effective add operator to adopt the prompt in each layer. We further conduct experiments in Section 4.3 over these variants to justify our design choice. We formulate the above process via

We can leverage the identical process to learn the final multi-behavior representations by Eq. (8) and rewrite the BPR loss based on the noiseless graph for the target behavior via

We only optimize the objective function under the target behavior, and the prompt only has $d\ll 2L\times d\times d$ trainable parameters.

We analyze the size of the trainable parameters in DPT at each stage. In this first stage, we update all parameters of the embedding layer and the pattern-enhanced graph encoder, which are denoted by $\Theta_{1}$. We have $|\Theta_{1}|=(|\mathcal{U}|+|\mathcal{I}|)\times d+4L\times(d\times d+1)$. In the second stage, we only train a small amount of parameters, which are denoted by $\Theta_{2}$. We have $|\Theta_{2}|=2L\times(d\times d)$. In the third stage, we train the parameters of the prompt, denoted by $\Theta_{3}$. Its size is $|\Theta_{3}|=d$. In conclusion, the proposed DPT can achieve comparable space complexity with state-of-the-art multi-behavior recommendation methods (e.g., CML (Wei et al., 2022)). The adopted lightweight approaches (i.e., the second and third stages of DPT) only tune/add a small number of parameters compared with the ones in the embedding layer for encoding users and items (i.e., $\mathcal{U}$ and $\mathcal{I}$ are typically of large sizes).

To evaluate the effectiveness of the proposed DPT model, we conduct experiments on two public recommendation datasets: (1) Tmall that is collected from the Tmall E-commerce platform, and (2) IJCAI-Contest that is adopted in IJCAI15 Challenge from a business-to-customer retail system (referred to as IJCAI for short). These datasets have same types of behaviors, including click,add-to-favorite,add-to-cart, and purchase. Identical to previous studies (Jin et al., 2020; Xia et al., 2020; Wei et al., 2022), we set the purchase behavior as the target behavior, and others are considered as auxiliary behaviors. Then we filter out users whose interactions are less than 3 under the purchase behavior. Moreover, we adopt the widely used leave-one-out strategy by leaving users’ last interacted items under the purchase behavior as the test set. Two evaluation metrics, HR (Hit Ratio) and NDCG (Normalized Discounted Cumulative Gain, N for short) @ 10, are used for performance evaluation. The statistics of the two datasets are summarized in Table 1.

We compare DPT with various representative recommendation methods, including single- and multi-behavior recommendation models. Single-behavior recommendation: (1) BPR (Rendle et al., 2009) is a matrix factorization model with the BPR optimization objective. (2) PinSage (Ying et al., 2018) uses an importance-based method to pass the message on paths constructed by a random walk. (3) NGCF (Wang et al., 2019a) utilizes a standard convolutional message passing method to learn representations. (4) LightGCN (He et al., 2020) is a lightweight yet effective graph convolution network for representation learning. (5) SGL (Wu et al., 2021) performs a self-supervised learning paradigm with multi-view graph augmentation and discrimination. Multi-behavior recommendation: (1) NMTR (Gao et al., 2019) integrates prior knowledge of behavior relations into a multi-task learning framework. (2) MATN (Xia et al., 2020) uses memory-enhanced self-attention mechanism for multi-behavior recommendation. (3) MBGCN (Jin et al., 2020) leverages convolutional graph neural network to learn high-order multi-behavioral patterns. (4) EHCF (Chen et al., 2020) conducts knowledge transferring among heterogeneous behaviors and uses a new positive-only loss for model optimization. (5) KHGT (Xia et al., 2021a) incorporates temporal information and item-side knowledge into the multi-behavior modeling. (6) CML (Wei et al., 2022) adopts meta-learning and contrastive learning paradigms to learn distinguishable behavior representations. In addition, we compare DPT with two state-of-the-art lightweight methods by applying them in multi-behavior recommendation: (1) ADT (Wang et al., 2021a) adaptively prunes noisy interactions for implicit feedback denoising. (2) NoisyTune (Wu et al., 2022a) uses a matrix-wise perturbing method to empower the traditional fine-tuning paradigm.

Identical to the previous study (Wei et al., 2022), we initialize the trainable parameters with Xavier (Glorot and Bengio, 2010). The AdamW optimizer (Loshchilov and Hutter, 2017) and the Cyclical Learning Rate (CLR) strategy (Smith, 2017) are adopted with a default base learning rate of $1e^{-3}$ and a max learning rate of $5e^{-3}$. We set the default mini-batch size to $8192$. The dimension $d$ of trainable parameters is set to $16$ and $32$ for IJCAI and Tmall, respectively. The $L_{2}$ regularization coefficient is searched in $\{1e^{-4},1e^{-3},1e^{-2}\}$. As suggested by CML (Wei et al., 2022), we adopt the dropout operation with a default ratio of $0.8$, and set the maximum layer of the graph encoder to $L=3$ to learn high-order information without falling into over-fitting and over-smoothing issues. Inspired by NoisyTune (Wu et al., 2022a), we set the default disturber $\delta=0.2$ to control noise identification reliability. The hyper-parameters of all competing models either follow the suggestions from the original papers or are carefully tuned, and the best performances are reported. We implement DPT in PyTorch 1.7.1, Python 3.8.3 on a workstation with an Intel Xeon Platinum 2.40GHz CPU, an NVIDIA Quadro RTX 8000 GPU, and 754GB RAM.