Learning ID-free Item Representation with Token Crossing for Multimodal Recommendation

Due to the achievement in collaborative filtering (He et al., 2017), numerous early multimodal recommendation models aim to seamlessly blend visual or textual auxiliary data with entity ID embeddings, in order to effectively capture modality-augmented user-item interactions. For instance, VBPR (He and McAuley, 2016) enhances BPR-based recommendations by incorporating visual features. Meanwhile, Deepstyle (Liu et al., 2017) augments the representations of items with both visual and style features within the BPR framework. Recently, a new research direction introduces GNNs into multimodal recommendation systems. MMGCN (Wei et al., 2019) leverages modality-specific relational graphs, while DualGNN (Wang et al., 2021) incorporates a User-User graph. Certain studies have also addressed the semantic distinctions across modal domains. BM3 (Zhou et al., 2023a) and SLMRec (Tao et al., 2022) propose innovative self-supervised learning strategies for aligning modalities. AlignRec (Liu et al., 2024) breaks down the recommendation task into three alignment objective, with each governed by unique objective functions. Furthermore, DREAM (Zhang et al., 2024) addresses the issue of Modal Information Forgetting by introducing the similarity-supervised signal.

However, these ID-based models still heavily rely on the learning of item ID embeddings, which indicates that even with the integration of multimodal information, if ID embeddings are not adequately optimized, the model’s recommendation performance can decrease significantly. MOTOR does not focus on downstream multimodal recommendation models; instead, it employs a streamlined framework, using learnable Token Representations to replace the original ID embeddings, thereby transforming these ID-based recommenders into ID-free systems.

The current main methods of tokenization in recommendation focus mainly on the two dimensions: LLM-based Recommendation System and Generative Recommendation.

Tokens in LLM-based Recommendation. Due to the tremendous success of Large Language Models (LLMs) in the field of NLP, researchers are endeavoring to leverage the rich semantic knowledge and powerful reasoning capabilities of LLMs to improve recommendation systems (Lin et al., 2024b; Hou et al., 2023; Geng et al., 2023; Lin et al., 2024a). Early efforts such as VQRec (Hou et al., 2023) convert the text features encoded by BERT (Vaswani et al., 2017b) into discretized codes for transferable sequential recommenders. Recent studies explore using in-vocabulary tokens to characterize items in LLMs, where users and items are represented by token combinations. P5 (Geng et al., 2023) convert user-item interactions into natural language formats using numeric IDs constructed of in-vocabulary tokens of the T5 model (Raffel et al., 2023). Further, sequential ID and collaborative ID are developed to improve item information exchange (Hua et al., 2023).

Generative Recommendation. Within this paradigm, item sequences are transformed into token sequences, which are subsequently input into generative models to autoregressively predict the target item’s tokens. TIGER (Rajput et al., 2023) constructs IDs using hierarchical tokens through learnable RQ-VAE. LETTER (Wang et al., 2024) proposes aligning quantized embeddings in RQ-VAE with collaborative embeddings to leverage both collaborative and semantic information.

To our best knowledge, MOTOR is the first to consider leveraging the product quantization of multimodal features into ID-based multimodal recommenders, introducing an innovative Token Representation computed by Token Cross Network to replace original ID embeddings. Thus, our work remains orthogonal to the aforementioned LLM-based and Generative recommendation.

Consider a set of $M$ users denoted by $\mathcal{U}=\{u_{i}\}_{i=1}^{M}$, and a set of $N$ items denoted by $\mathcal{I}=\{i_{t}\}_{t=1}^{N}$. Each item is associated with multimodal features $f_{i}^{m}\in\mathbb{R}^{d_{m}}$, where $m\in\{V,T\}$. In this context, $V$ and $T$ correspond to the visual and textual modalities, respectively.

The user behavior history is represented as $R\in\mathbb{R}^{M\times N}$, where $R_{ui}=1$ signifies that user $u$ has interacted with item $i$, and $R_{ui}=0$ otherwise. Essentially, $R$ can be viewed as a sparse behavior graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, with $\mathcal{V}=\mathcal{U}\cup\mathcal{I}$ representing the vertices, and $\mathcal{E}=\{(u,i)\mid u\in\mathcal{U},i\in\mathcal{I},R_{ui}=1\}$ representing the edges. The set of items that a user $u$ has interacted with is denoted by $\mathcal{I}_{u}=\{i\mid(u,i)\in\mathcal{E}\}$.

The aim of ID-based multimodal recommendation is to precisely estimate user preferences by ranking items for each user, utilizing the predicted preference scores $y_{ui}=f_{\theta}(e_{u},e_{i},f_{i}^{m})$. In this function, $\theta$ represents the model’s parameters, $e_{u}$ and $e_{i}$ stand for the ID embeddings, and $f_{i}^{m}$ denotes the modal features for the item $i$. In MOTOR, we attempt to learn a novel Item Token Representation $r_{i}$, to replace the item’s ID embedding, $e_{i}$. The preference function of ID-free recommendation can be denoted as $y_{ui}=f_{\theta}(e_{u},r_{i},f_{i}^{m})$²²2In this work, we use lowercase letters with subscripts to denote the vector corresponding to a specific item, and uppercase letters to represent the feature matrix of all items. For example, $r_{i}\in\mathbb{R}^{d}$ denotes the final Token Representation of item $i$, while $R\in\mathbb{R}^{N\times d}$ represents the final Token Representations of all items..

The structure of MOTOR is illustrated in Figure 2. The core objective of MOTOR is to effectively learn $r_{i}$. This learning process can be divided into two steps. Firstly, by applying Product Quantization to the raw multimodal features of items, we obtain items’ unique multimodal Token IDs $T^{m}$ in modality $m$. Based on the learned Token IDs, we can retrieve the token embeddings for specific items by looking them up in the Token Embedding Table. Here, each item corresponds to multiple token embeddings. Secondly, we treat the token embeddings obtained for each item as its implicit feature vectors. Through a lightweight Token Cross Network, we perform one-order, second-order, and high-order feature interactions on these implicit feature vectors, ultimately generating the Token Representation $r_{i}$. Please note that the parameters in MOTOR (e.g. Token Embedding Tables, Token Cross Network) is trained end-to-end with downstream multimodal models, rather than through separate learning. Next, we present the MOTOR in detail.

The initial textual and visual information of items can be compressed into specific feature vectors $F^{t}$ and $F^{v}$ using various text encoders (Vaswani et al., 2017b; Radford et al., 2019; Reimers and Gurevych, 2019; Raffel et al., 2023) and visual encoders (Simonyan and Zisserman, 2014; He et al., 2016; Dosovitskiy et al., 2020), respectively. Within the MOTOR framework, we do not rely on specific encoders, nor do we require semantic alignment between image features and text features such as CLIP (Radford et al., 2021).

Next, based on Product Quantization (Jegou et al., 2010), we consider mapping the modal features into discretized tokens. Taking the visual feature $F^{v}$ as an example, a similar approach is applied to the text feature $F^{t}$. We begin by partitioning each visual feature vector $F^{v}\in\mathbb{R}^{N\times d_{v}}$ into $D$ subvectors, each of dimensionality $N\times\frac{d_{v}}{D}$. This can be expressed as:

For each subvector $F_{x}^{v}$, we apply the K-means clustering algorithm to generate $K$ cluster centroids, constructing a codebook $C_{x}^{v}\in\mathbb{R}^{K\times\frac{d_{v}}{D}}$. This step can be mathematically formulated as:

where $c_{x,j}^{v}\in\mathbb{R}^{\frac{d_{v}}{D}}$ represents the $j$-th centroid in the $x$-th subvector’s codebook. To acquire these PQ centroid embeddings, we employ a well-known technique called Optimized Product Quantization (OPQ) (Ge et al., 2013). We then optimize these centroid embeddings by utilizing the visual features of the items from the entire training dataset. Each subvector matrix $F^{v}_{x}$ is then quantized by finding the nearest centroid in the corresponding codebook $C_{x}^{v}$. The index of this centroid acts as the Token IDs. This assignment is expressed as:

where $t_{x,i}^{v}$ is the Token ID of item $i$ for the $x$-th subvector in vision modality. $t_{i}^{v}$ is the visual token ids for item $i$. Finally, the discrete Token IDs $T^{v}\in\mathbb{R}^{N\times D}$ of all items are represented as a concatenation of $t_{i}^{v}$:

In summary, through the process of vector quantization and clustering, visual features $F^{v}$ is transformed into a set of discrete Token IDs $T^{v}$. A similar procedure can be applied to convert text features $F^{t}$ into their Token IDs $T^{t}$. Although the original multimodal features are transformed into discretized token IDs, they still retain significant semantic information (e.g., semantically similar items share the certain token IDs). We further demonstrate the result about semantic analysis of token ids in Appendix 6.3.

Given the learned discrete token IDs in multimodals, we can directly perform the embedding lookup to get the token embeddings.

Considering the visual tokens $T^{v}\in\mathbb{R}^{N\times D}$, which comprise $D$ specific indexed token IDs, we construct $D$ Token Embedding Tables for lookup, each corresponding to a particular dimension of the Token IDs. For a given dimension $x$ in the visual modality, all items share the same Token Embedding Table $E^{v}_{x}\in\mathbb{R}^{K\times d}$, where $K$ corresponds to the number of cluster centers as specified in Section 3.3 and also represents the range of index values, and $d$ denotes the dimension of token embeddings and Token Representations. In MOTOR, the Token Representation replaces the original ID Embedding, thereby ensuring that $d$ is consistent with the dimension of the original model’s ID Embedding.

Considering the visual tokens of item $i$, $t_{i}^{v}=[t_{1,i}^{v},\ldots,t_{D,i}^{v}]$, we can obtain the token embeddings by embedding lookup as $[e_{t_{1},i}^{v},\ldots,e_{t_{D},i}^{v}]$, where $e_{t_{x},i}^{v}$ is the $t_{x}$-th row of embedding tables $E^{v}_{x}$. Note that the token embedding $e_{t_{x},i}^{v}$ is different from the corresponding PQ centroid center $c_{x,t_{x}}^{v}$. Similar to the ID Embeddings, we initialize the token embedding tables randomly and update them throughout the learning process alongside downstream multimodal recommendation models in an end-to-end fashion. Analogous to the visual modality, we obtain the token embeddings for text modality in the same manner. Therefore, the overall token embeddings of item $i$ correspond to $\{e_{1,i}^{v},\ldots,e_{D,i}^{v},e_{1,i}^{t},\ldots,e_{D,i}^{t}\}$.

In multimodal recommendation, we assume that items do not have content-related features such as titles or categories, but only multiple modal-related features. Within the MOTOR framework, we regard all obtained token embeddings as implicit features of these item and apply them to the Token Cross Network. An intuitive explanation is that the similarity between item’s multimodal features implies content and semantic similarity. When both items share the same token embeddings, it is analogous to sharing the same category features (e.g., the same category: technology).

In traditional CTR tasks, a core issue is the effective utilization of feature interactions (Cheng et al., 2016; Guo et al., 2017; Wang et al., 2017). In MOTOR, we regard the Token Embeddings of items as the corresponding implicit features and use a lightweight Token Cross Network to compute the feature interactions. Inspired by DeepFM (Guo et al., 2017), in the Token Cross Network, we focus on modeling the one-, second-, and high-order components between token embeddings.

Considering that an item comprises token embeddings from multiple modalities, in MOTOR, we design two mechanisms for Token interactions, namely, the Modal-specific Token Cross Network and the Modal-agnostic Token Cross Network. The Modal-specific Token Cross Network implies that we separately interact with the token embeddings under different modalities and ultimately combine the representations from multiple modalities. Conversely, the Modal-agnostic Token Cross Network performs holistic interactions with all tokens of an item, directly generating the final Token Representation.

MOTOR replaces the original Item ID Embeddings with Token Representations and transforms the original ID-based models into ID-free recommerder. During model training, the primary parameters in the MOTOR module (Token Embedding Tables, Token Cross Network) undergo end-to-end training and optimization, analogous to ID Embeddings. Specifically, for a downstream multimodal recommendation model, to generate item recommendations for a specific user $u$, we first predict the interaction scores between the user and the candidate items. Then we rank the candidate items based on the predicted interaction scores in descending order and select the top $K$ items as recommendations for $u$. The interaction score is calculated as:

where $h_{u}$ and $h_{i}$ are the final user and item representations, derived from the output of the multimodal recommendation models as shown in Figure 2.

We conduct experiments on three public Amazon review datasets (Ni et al., 2019): (a) Musical Instruments, (b) Baby and (c) Office Products. For simplicity, we denote them as Music, Baby, and Office, respectively. To ensure a fair comparison with previous work (Zhou et al., 2023b, a; Zhou and Shen, 2023; Yu et al., 2023), we have adopted their feature processing methodologies: For image features, we directly use the 4,096-dimensional visual features extracted by pre-trained CNN (Ni et al., 2019). For textual features, we concatenate textual information such as the title, descriptions, categories, and brands of each item, and extract 384-dimensional textual features using the Sentence transformer (Reimers and Gurevych, 2019). To further illustrate the impact of MOTOR on the recommendation capability for items with various interaction records (e.g., long-tail items, popular items), we apply a 1-core filtering on the original dataset, ensuring that each user and item has at least one interaction record in the training datatset. The filtering results are presented in Table 1.

Given that MOTOR is compatible with various ID-based multimodal recommendation models, we integrate MOTOR into nine representative recommendation models. These include three General Recommendation models (e.g., BPR (Rendle et al., 2012), LightGCN (He et al., 2020), LayerGCN (Zhou et al., 2022)), which do not utilize multimodal features as additional supervison signal, and six Multimodal Recommendation models (e.g., VBPR (He and McAuley, 2016), GRCN (Wei et al., 2020), SLMRec (Tao et al., 2022), BM3 (Zhou et al., 2023a), FREEDOM (Zhou and Shen, 2023), MGCN (Yu et al., 2023)), which incorporate multimodal features for learning user and item representations. The detailed description about backbone models is in Appendix 6.1.

For a fair comparison, we adhere to the evaluation settings used in [31, 39], employing a random data split of 8: 1: 1 for training, validation and testing of each user’s interaction history. Furthermore, we assess the top-$K$ recommendation performance of various methods using Recall@$K$ and NDCG@$K$. During the recommendation phase, all items that the user did not previously interact with are considered candidate items. In our experiments, the results are empirically reported for $K$ values of 10 and 20, and we abbreviate Recall@$K$ and NDCG@$K$ as R@$K$ and N@$K$, respectively.

First, we implement Optimized Product Quantization based on the Faiss ANNS (Johnson et al., 2017) and integrate MOTOR into ID-based recommendation models via the MMRec (Zhou et al., 2023b) framework. The vector quantization process needs to be performed only once and can then be utilized by multiple downstream models. Similar to other existing work (Zhou et al., 2023a; Zhou and Shen, 2023; Yu et al., 2023), we fix the embedding sizes of users, items, and token to 64 for all models, initialize embedding parameters using the Xavier method (Glorot and Bengio, 2010), and employ Adam (Kingma and Ba, 2014) as the optimizer with learning rate of 0.001. For a fair comparison, we meticulously tune the parameters of each model according to their respective published papers. The parameter tuning for MOTOR is exceptionally straightforward, only involving a search for the number of tokens among $\{2,4,8,16\}$. We fix the number of cluster centers $K$ as 256. We implement the Token Cross Network in both modal-specific and modal-agnostic manners.

We perform comprehensive experiments on the Music, Baby, and Office datasets, showcasing performance comparisons with various backbone models in Table 2. From the table, we can have the following three observations:

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  MOTOR consistently boosts the performance of recommendation models by a considerable margin, independent of the backbone model. The modal-related item-item graph in FREEDOM and MGCN exhibits exceptional capability in leveraging multimodal information. MOTOR-enhanced FREEDOM achieves optimal performance on the Music and Baby datasets, while MOTOR-enhanced MGCN performs best on the Office dataset.

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  MOTOR’s performance improvement is particularly significant for General Recommendation Models (e.g., MOTOR-enhanced BPR exceeds the original BPR model by more than 100% in recall@20 metrics on the Music and Office datasets. Similarly, the recommendation performance of LightGCN and LayerGCN also improves by over 50%). General Recommendation Models do not incorporate multimodal information as additional supervision signals during training. It is important to note that MOTOR does not explicitly introduce multi-modal features into these models. Instead, by tokenizing multimodal features and transform the ID-based model into ID-free, it mitigates multiple issues (e.g., Information Isolation, Cold-Start) within the ID-based paradigm and implicitly incorporates the semantic information contained in the token IDs (e.g., Items with similar multimodal features also share similar token IDs). Although Original Multimodal Models generally outperform General Models, after enhancement with MOTOR, specific General Models can achieve outstanding performance on certain datasets (e.g., on the Music dataset, MOTOR-enhanced LayerGCN achieves results that are surpassed only by MOTOR-enhanced FREEDOM).

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  We systematically compared the performance of two types of Token Cross Networks (TCN): Modal-Agnostic (MA) and Modal-Specific (MS). In general, both TCN networks effectively uncover the interaction pattern between multimodal tokens. Their relative performance depends on the specific backbone model and the particular data distribution. (e.g., for BPR, MGCN, Modal-agnostic consistently outperforms Modal-specific; similarly, for GRCN, SLMRec, and FREEDOM, Modal-agnostic consistently surpasses Modal-specific. For other backbone models, the performance of Modal-specific and Modal-agnostic TCN is comparable.

In this section, we specifically examine the recommendation performance of MOTOR-enhanced recommenders (e.g., LightGCN, VBPR, SLMRec, FREEDOM) for items with varying interaction counts. Specifically, we choose the Baby dataset and divide the test items into five buckets based on their interaction counts in the training set: $[0-5]$, $[6-10]$, $[11-20]$, $[20-50]$, $[50,\infty)$. We then analyze the performance of the trained recommenders for each of these buckets. The distribution of item division by interaction records is shown in Table 3. The performance of four models with/without MOTOR is demonstrate in Fig 3. From the figure, we can derive the following observations:

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  Both MOTOR-enhanced and Original Models exhibit significantly higher recommendation capabilities for popular items (¿50) compared to long-tail items ([0-5]); The recommendation performance of these models improves as the number of item interaction counts increases.

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  MOTOR consistently enhances model recommendation performance across various interaction ranges. Notably, due to the heavy reliance on ID embeddings, the Recall@20 metric for original models, such as LightGCN and SLMRec, on long-tail items ([0-5]) drops to nearly zero (0.0007 for LightGCN and 0.0010 for SLMRec), leading to a significant loss in recommendation capability. MOTOR mitigates this dependency through ID-free learning scheme, thereby achieving superior recommendation performance even for long-tail items (0.0171 for MOTOR-enhanced LightGCN, 0.0025 for MOTOR-enhanced SLMRec).

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  For items with high popularity (¿ 50), the original ID-based recommendation models demonstrated impressive results (e.g., Recall@20 for LightGCN, VBPR, SLMRec, and FREEDOM are 0.1023, 0.1086, 0.1409, and 0.1333, respectively). Under the MOTOR-enhanced paradigm, despite eliminating the models’ reliance on ID embeddings, ID-free recommenders still outperform the original models (e.g., Recall@20 for MOTOR-enhanced LightGCN, VBPR, SLMRec, and FREEDOM are 0.1146, 0.1156, 0.1536, and 0.1516, respectively).

We analyze how each of the proposed components affects the performance of MOTOR. We select three backbone models (e.g., LightGCN (He et al., 2020), VBPR (He and McAuley, 2016) and SLMRec (Tao et al., 2022)) and the experimental results are shown in Table 4. To investigate the impact of multimodal tokens, we attempt to mask the tokens corresponding to a specific modality and explore the effects of another modality tokens. (e.g., “Image Tokens” means removing the text tokens and just utilizing the image-domain tokens to generate the Token Representations.) To examine the effect of the Token Cross Network (TCN) in MOTOR, we replace the TCN with mean or a simple linear layer (“Mean” denotes a straightforward average aggregation of all token embeddings for an item, while Linear represents a linear mapping of the concatenated token embeddings). From Table 4, we make the following observations: (i) The performance of Token Representation consistently exceeds original models, even when Tokens are removed from a specific modality or substituted for TCN with Mean or Linear; (ii) Removing Tokens from either the Image or Text domain leads to a decrease in model performance. Comparatively, “Text Tokens” generally achieves better results, which suggests that the semantic information in text features is more conducive to model learning; This phenomenon is consistent with previous works (Zhou et al., 2023a; Yu et al., 2023; Zhang et al., 2024). Furthermore, we examine the distribution of tokens in the text and vision modalities in Appendix 6.2. Compared to image tokens, text tokens produce a more uniform distribution; (iii) Replacing the Token Cross Network with Mean or Linear also results in a notable performance decrease, with Linear slightly outperforming Mean in VBPR and SLMRec.

In the ID-free framework, we replace the ID embedding table of any backbone model with learnable Token Representation. In Figure 4, we illustrate the overall trainable parameters of the model under different token number settings and the resulting performance improvements. In general, within a reasonable range of token numbers ($\{2,4,8,16\}$), ID-free models generally outperform the original ID-based models, and there is a significant reduction in trainable parameters (e.g., When the uni-modal token numbers are 4, the ID-free LightGCN, VBPR, and SLMRec reduce the overall trainable parameters by 27.9%, 16.0%, and 26.3% compared to their original models, with corresponding performance improvements of 52.6%, 49.2%, and 12.6%, respectively.)

The influence of Token Numbers. In MOTOR, we set the number of tokens per modality to $\{2,4,8,16\}$, resulting in total number of tokens for items of $\{4,8,16,32\}$. The optimal performance of these backbone models (e.g. LightGCN, VBPR, SLMRec) is achieved when the number of unimodal tokens is 4 or 8. Reducing the number of tokens limits the embedding solution space for specific items, increasing the likelihood of token collisions with other items. While expanding the number of tokens enhances MOTOR’s expressive capacity, it simultaneously introduces additional modality-related noise. As a result, items that were initially unrelated in interaction records can negatively impact each other because they share token IDs, arising from partially similar original multimodal features. This phenomenon underscores the delicate balance between improving model expressiveness and managing noise and unintended associations in token assignments.

General Recommendation Models:

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  BPR (Rendle et al., 2012) optimizes for pairwise rankings between observed (interacted) and unobserved (noninteracted) items. The core idea of BPR is to maximize the posterior probability that a user prefers an interacted item over a noninteracted one by using a stochastic gradient descent approach.

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  LightGCN (He et al., 2020) removes feature transformation and non-linear activation, focusing solely on neighborhood aggregation. It iteratively propagates embeddings of users and items through the graph to capture higher-order connectivity

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  LayerGCN (Zhou et al., 2022) is a layer-refined GCN model, which refines layer representations during information propagation and node updating of GCN. Further, LayerGCN prunes the edges of the user-item interaction graph following a degree-sensitive probability instead of the uniform distribution.

Multimodal Recommendation Models

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  VBPR (He and McAuley, 2016) integrates visual features into the matrix factorization (MF) framework, optimizing user preferences using the BPR loss. In line with  (Zhou et al., 2023b, a), we concatenate an item’s image feature and text feature for learning user preferences.

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  GRCN (Wei et al., 2020): enhances the user-item bipartite graph by eliminating false-positive edges to facilitate multimodal recommendations. Utilizing the refined graph, it subsequently learns the representations of users and items through information propagation and aggregation using GCNs.

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  SLMRec (Tao et al., 2022): employs self-supervised learning methods within a Graph Neural Network framework to capture underlying relationships. The self-supervised learning (SSL) tasks enhance the supervised learning tasks by extracting latent signals directly from the data. This approach involves performing self-supervised data augmentation operations, namely FD, FM, and FAC, followed by the application of contrastive loss for optimization.

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  BM3 (Zhou et al., 2023a): presents a novel self-supervised learning approach aimed at mitigating computational resource expenses and errors caused by incorrect supervision signals. It leverages a straightforward dropout technique to produce contrastive views and employs three distinct contrastive loss functions to refine the resultant representations.

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  FREEDOM (Zhou and Shen, 2023): employs an item-item graph for each modality, structured similarly to LATTICE (Zhang et al., 2021), but these graphs are frozen prior to training. It also introduces degree-sensitive edge pruning techniques to eliminate noise from the user-item interaction graph.

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  MGCN (Yu et al., 2023): purifies modality features using item behavior information to avoid noise contamination and enriches these features in separate views, enhancing feature distinguishability. Additionally, a behavior-aware fuser adaptively learns the relative importance of different modality features.

We illustrate the distribution of token ids obtained from tokenization for the original modality features across three datasets (e.g., Music, Baby, Office) in Figure 6. From Figure 6, we observe the following: (i) Through tokenization of the raw modality features in the textual and visual domains, we obtain Token IDs that approach a approximately uniform distribution. In other words, for a given Token ID, there are approximately $\frac{N}{DK}$ items sharing the same token, where $N$ represents the total number of items, and $DK$ denotes the total number of tokens; (ii) Compared to the visual modality, the distribution of tokens in the textual modality is more uniform. This partly explains why tokens in the text modality outperform those in the vision modality for recommendation in Section 4.7.

The original multimodal features of items preserve effective semantic information, such as similarity characteristics between items. In this section, we investigate whether Token IDs retain such semantic information, specifically whether items with similar Token IDs also share similar content. We randomly select items as queries and retrieve the first two items with the most similar Token IDs; the results are presented in Figure 5. By utilizing appropriate queries, semantic similarity between items can be discovered solely through token similarity. This demonstrates that the discretized tokens still retain the similarity information from the original multimodal features.