SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$$
L _ {t - 1} = \mathbb {E} _ {\mathbf {e} _ {n} ^ {0}, \boldsymbol {\epsilon}} \left[ \frac {\bar {\alpha} _ {t - 1}}{2 \tilde {\beta} _ {t}} | | \mathbf {e} _ {n} ^ {0} - f _ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} \mathbf {e} _ {n} ^ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon}, \mathbf {c} _ {n - 1}, t\right) | | ^ {2} \right] + C. \tag {14}
$$
Besides the conditional diffusion model, guided diffusion typically necessitates an additional unconditional one [25], which can be jointly trained using a classifier-free guidance scheme [36]. Specifically, during training, we randomly replace guidance signal  $\mathbf{c}_{n-1}$  by a dummy token  $\Phi$  with probability  $p_u$  to achieve the training of unconditional diffusion model.
It is important to note that in Equation (14),  $\mathbf{e}_n^0$  denotes the observed target item in interaction sequence, and  $\epsilon$  denotes the Gaussian noise. Therefore, DreamRec's training procedure does not require negative sampling. Instead, it concentrates on recovering the target item in the interaction sequence. Algorithm 1 shows the details of DreamRec's training phase.
4.2.2 Generation Phase of DreamRec
In the generation phase, we target to generate personalized oracle items for different users, given their historical interactions. To manipulate the influence of the guidance signal  $\mathbf{c}_{n - 1}$ , we would modify  $f_{\theta}(\mathbf{e}_n^t,\mathbf{c}_{n - 1},t)$  to conform to the following format:
$$
\tilde {f} _ {\theta} \left(\mathbf {e} _ {n} ^ {t}, \mathbf {c} _ {n - 1}, t\right) = (1 + w) f _ {\theta} \left(\mathbf {e} _ {n} ^ {t}, \mathbf {c} _ {n - 1}, t\right) - w f _ {\theta} \left(\mathbf {e} _ {n} ^ {t}, \Phi , t\right), \tag {15}
$$
3Please note that predicting  $\mathbf{e}_n^0$  and predicting  $\epsilon$  are equivalent due to  $\mathbf{e}_n^t = \sqrt{\bar{\alpha}_t}\mathbf{e}_n^0 +\sqrt{1 - \bar{\alpha}_t}\epsilon$ . Refer to Appendix A for more details.
where  $w$  is a hyperparameter controlling the strength of  $\mathbf{c}_{n-1}$ : A higher  $w$  value can enhance personalized guidance, but it could potentially undermine diffusion generalization, consequently deteriorating the quality of the generated oracle item.
Based on Equation (7), the one-step denoising process is straightforward as follows:
$$
\mathbf {e} _ {n} ^ {t - 1} = \frac {\sqrt {\bar {\alpha} _ {t - 1}} \beta_ {t}}{1 - \bar {\alpha} _ {t}} \tilde {f} _ {\theta} \left(\mathbf {e} _ {n} ^ {t}, \mathbf {c} _ {n - 1}, t\right) + \frac {\sqrt {\alpha_ {t}} \left(1 - \bar {\alpha} _ {t - 1}\right)}{1 - \bar {\alpha} _ {t}} \mathbf {e} _ {n} ^ {t} + \sqrt {\tilde {\beta} _ {t}} \mathbf {z}, \quad \mathbf {z} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}). \tag {16}
$$
During the inference stage, for a user characterized by historical interactions encoded as  $\mathbf{c}_{n-1}$ , the oracle item  $\mathbf{e}_n^0$  can be generated by denoising a Gaussian sample  $\mathbf{e}_n^T \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$  for  $T$  steps, in accordance with Equation (16). The generation phase of DreamRec is demonstrated in Algorithm 2.
4.2.3 Retrieval of Recommendation List
After generating the oracle item, the subsequent step involves obtaining the recommendation list tailored to the specific user. To achieve this, we retrieve the K-nearest items to the oracle item within the candidate set using an inner product measurement, forming the recommendaiton list. It's crucial to emphasize that the selection of K-nearest items is exclusive to the retrieval of the recommendation list and does not figure into the training phase. Conceptually, DreamRec transcends the confines of a limited candidate set, venturing into the entire item space in its pursuit of the oracle item.
In this section, we conduct experiments to demonstrate that: 1) DreamRec provides a powerful learning-to-generate framework for sequential recommendation; 2) DreamRec can better explore the item space without negative sampling; and 3) Guiding the diffusion process with historical interactions is important for personalized oracle item generation in DreamRec.
Datasets. We use three datasets from real-world sequential recommendation scenarios: YooChoose, KuaiRec, and Zhihu (the statistics of datasets are illustrated in Appendix B):
- YooChoose dataset comes from RecSys Challenge 2015  ${}^{4}$  . We preserve the purchase sequences for a moderate size of data. We only retain items with at least 5 interactions to avoid cold-start issue. Additionally, we exclude sequences that are shorter than 3 interactions in length.
- KuaiRec [42] dataset is collected from the recommendation logs of a video-sharing mobile app. We also remove items that are interacted with less than 5 times and sequences shorter than 3.
- Zhihu [43] dataset is collected from a socialized knowledge-sharing community. Users are presented with a recommended Q&A list and they can read their preferred ones. We remove items that are read less than 5 times and sequences that are shorter than 3 in length.
For all datasets, we first sort all sequences in chronological order, and then split the data into training, validation and testing data at the ratio of 8:1:1.
Baselines. We compare DreamRec against several competitive models, including GRU4Rec [4], Caser [10], SASRec [5], S-IPS [7], AdaRanker [12], CL4SRec [8] and DiffRec [40]. GRU4Rec, Caser, and SASRec adopt recurrent neural networks, convolutional neural networks, and Transformer encoders respectively to capture sequential patterns of user behaviors. S-IPS and AdaRanker leverage causal inference and neural process to address the issues of selection bias and temporal dynamics in sequential recommendation. CL4SRec designs three data augmentation methods and applies contrastive learning techniques to enhance the classification ability of sequential recommender. DiffRec proposes to incorporate the diffusion model in collaborative filtering, but it applies diffusion on user's interaction vectors — multi-hot vectors whose element of “1” indicates a positive interaction while “0” suggests a potential negative.
Training Protocol. We implement all models with Python 3.7 and PyTorch 1.12.1 in Nvidia GeForce RTX 3090. We preserve the last 10 interactions as historical sequence. For sequences with less than
4https://recsys.acm.org/recsys15/challenge/
Table 1: Overall performance comparison. The boldface denotes the best performance while the underline indicates the second best. The experiments are conducted 5 times and the average and standard deviation are reported.
YooChoose	KuaiRec	Zhihu
HR@20(%)	NDCG@20(%)	HR@20(%)	NDCG@20(%)	HR@20(%)	NDCG@20(%)
GRU4Rec	3.89±0.11	1.62±0.02	3.32±0.11	1.23±0.08	1.78±0.12	0.67±0.03
Caser	4.06±0.12	1.88±0.09	2.88±0.19	1.07±0.07	1.57±0.05	0.59±0.01
SASRec	3.68±0.08	1.63±002	3.92±0.18	1.53±0.11	1.62±0.01	0.60±0.03
IPS	3.81±0.05	1.73±0.03	3.73±0.03	1.40±0.05	1.66±0.04	0.64±0.02
AdaRanker	3.74±0.06	1.67±0.04	4.14±0.09	1.89±0.05	1.70±0.04	0.61±0.02
CL4SRec	4.45±0.04	1.86±0.02	4.25±0.10	2.01±0.09	2.03±0.06	0.74±0.03
DiffRec	4.33±0.02	1.84±0.01	3.74±0.08	1.77±0.05	1.82±0.03	0.65±0.09
DreamRec	4.78±0.06	2.23±0.02	5.16±0.05	4.11±0.02	2.26±0.07	0.79±0.01
(a) SASRec (no negative sampling).
(b) SASRec.
Figure 3: Visualization of the learned item embeddings on Zhihu dataset using T-SNE, where red points represent items. Figure 3a shows that without negative sampling, the item embeddings of SASRec are crowded in limited discrete zones. Figure 3b shows that With negative sampling, the item embeddings of SASRec concentrate on only part of the item space. Figure 3c shows that DreamRec explores most of the item space without requiring negative sampling.
(c) DreamRec.
10 interactions, we would pad them to 10 with a padding token. We leverage AdamW as the optimizer. The embedding dimension of items is fixed as 64 across all models. The learning rate is tuned in the range of [0.01, 0.005, 0.001, 0.0005, 0.0001, 0.00005]. Despite that DreamRec does not require L2 regularization, we tune the weight of L2 regularization for all baselines in the range of [1e-3, 1e-4, 1e-5, 1e-6, 1e-7]. For all baselines, we conduct negative sampling from the uniform distribution at the ratio of 1: 1, which is not conducted in DreamRec. For our DreamRec, we fix the unconditional training probability  $p_u$  as 0.1 suggested by [36]. We search the total diffusion step  $T$  in the range of [50, 100, 200, 500, 1000, 2000], and the personalized guidance strength  $w$  in the range of [0, 2, 4, 6, 8, 10].
Evaluation Protocol. We follow the widely used top-K protocol to evaluate the performance of sequential recommendation and adopt two widely used metrics: hit ratio (HR) and normalized discounted cumulative gain (NDCG) [4, 5]. Sequential recommenders within the learning-to-classify paradigm usually leverage the classification logits on candidate items to select top-K items. For DreamRec, we first generate the oracle item with Algorithm 2, and then we find the K-nearest items in the candidate set for top-K recommendation with the measurement of inner product. Note that the selection of K-nearest items is only conducted at the evaluation phase, and is not involved in the training phase.
In this section, we compare DreamRec against baseline models in terms of top-K recommendation performance. Table 1 shows the experimental results. Overall, DreamRec substantially and consistently outperforms compared models, which demonstrates the superiority of our proposed learn-to-generate paradigm in sequential recommendation.
Note that all baselines are within the learning-to-classify paradigm: GRU4Rec, Caser and SASRec are backbone models; IPS and AdaRanker enhance classification ability by solving data biasing issues; and CL4SRec further equips classification objectives with contrastive learning techniques. We do witness in Table 1 that these auxiliary tasks improve the performance of backbone models.
(a) YooChoose.
(b) KuaiRec.
Figure 4: Ablation study of classifier-free guidance by adjusting the guidance strength  $w$  on Yoo-Choose (subfigure 4a), KuaiRec (subfigure 4b), and Zhihu (subfigure 4c) datasets.
(c) Zhihu.
In terms of DreamRec, it reshapes sequential recommendation purely as an oracle item generation task without those auxiliary tasks, and it has already achieved better performance in our experiments. We believe designing auxiliary tasks can also boost the generation of oracle items in sequential recommendation, yet we leave this as future work since it is beyond the scope of this paper.
5.3 Visualization
In this section, we visualize the learned item embeddings using T-SNE [44] to demonstrate that DreamRec can well explore the underlying distribution of item space without negative sampling.
Specifically, we first train three recommenders on Zhihu dataset (results on other datasets included in Appendix C): 1) SASRec without negative sampling; 2) SASRec with negative sampling; and 3) DreamRec that does not require negative sampling. Then we use T-SNE to visualize the learned item embeddings under the default setting of scikit-learn  $^{5}$ . Figure 3 demonstrates the visualization results, where each item is represented as a red point. From Figure 3 we can observe that: 1) Negative sampling is necessary for classification-based sequential recommenders: if no negative sampling is conducted, plenty of items may be crowded pathologically in limited discrete zones of the item space, making them indistinguishable; 2) Negative sampling makes classification easier since items are better shattered, but they are biased to concentrate more on part of the zone of item space; and 3) By reshaping sequential recommendation as a learning-to-generate framework, DreamRec explores most of the zones of item space without requiring negative sampling. These observations provide strong empirical support for our claims made in Section 1.
5.4 Controlling the Personalized Guidance of DreamRec
As introduced in Section 4.2.2, achieving personalized oracle item generation requires guidance from the corresponding interaction sequence. To achieve controllable guidance in DreamRec, we adopt the classifier-free guidance technique. However, we should carefully adjust the value of guidance strength  $w$  in Equation (15), as a higher value may hurt the generalization of diffusion and lead to generating lower-quality oracle items. To shed light on this issue, we conduct experiments on the three datasets by adjusting the value of  $w$ . As shown in Figure 4, we observed that increasing the value of  $w$  initially leads to better recommendation accuracy. This supports our intuition that stronger guidance leads to better personalization. However, as we continue to increase the value of  $w$ , we observe a decline in performance. This is in line with our analysis that concentrating too much on the guidance signal may hurt the generation quality of oracle items.
We propose DreamRec, reshaping sequential recommendation as a learning-to-generate task, instead of a learning-to-classify task as almost all previous methods do. DreamRec is based on the analysis of user behaviors that, after several interactions with the recommendation system, users tend to fantasize about an oracle item they would "ideally" consume. The oracle item does not have to be the next item in the dataset, and even should not be limited to the pre-defined candidate set. By
<sup>5</sup>https://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html
modeling the underlying data-generation distribution with diffusion model, DreamRec promises to generate unobserved oracle items. Moreover, targeting to model the data-generation process directly, DreamRec makes it possible to discard negative samples in sequential recommendation, which can hardly be achieved by previous classification-based models. Experiments show that DreamRec brings consistent improvements to sequential recommendation, implying its superiority in modeling user behaviors.
Meanwhile, DreamRec also has a few limitations: 1) the sampling process is quite slow with the iteration of total diffusion steps; and 2) the training process is more time-consuming. We believe these can be resolved in further research with more advanced generation models such as consistency model [45]. Moreover, as an initial attempt of reshaping sequential recommendation as an oracle item generation task, DreamRec provides many research opportunities such as designing auxiliary tasks (e.g., contrastive learning or data augmentation) to enhance oracle item generation. Another research line could be designing other encoders for guidance representation, or other model architectures for the denoising process of DreamRec.
The proposed DreamRec can significantly improve the performance of sequential recommendation. Therefore, it can be applied to real-world platforms to provide more satisfying recommendation results. One concern of generating oracle items is the potential for privacy disclosure. Despite that we encode the oracle item with vector representations, one may decode the representation and snoop on users' preference explicitly. Therefore, we kindly advise researchers to be cautious about the usage of generated oracle items.
This research is supported by the National Natural Science Foundation of China (9227010114, U21B2026, 62302321), the University Synergy Innovation Program of Anhui Province (GXXT-2022-040), and the Hong Kong Polytechnic University under grant (P0045485).
[39] Yu Wang, Zhiwei Liu, Liangwei Yang, and Philip S. Yu. Conditional denoising diffusion for sequential recommendation. CoRR, abs/2304.11433, 2023.
[40] Wenjie Wang, Yiyan Xu, Fuli Feng, Xinyu Lin, Xiangnan He, and Tat-Seng Chua. Diffusion recommender model. In SIGIR, 2023.
[41] Jiancan Wu, Xiang Wang, Xingyu Gao, Jiawei Chen, Hongcheng Fu, Tianyu Qiu, and Xi-angnan He. On the effectiveness of sampled softmax loss for item recommendation. CoRR, abs/2201.02327, 2022.
[42] Chongming Gao, Shijun Li, Wenqiang Lei, Jiawei Chen, Biao Li, Peng Jiang, Xiangnan He, Jiaxin Mao, and Tat-Seng Chua. Kuairec: A fully-observed dataset and insights for evaluating recommender systems. In CIKM, 2022.
[43] Bin Hao, Min Zhang, Weizhi Ma, Shaoyun Shi, Xinxing Yu, Houzhi Shan, Yiqun Liu, and Shaoping Ma. A large-scale rich context query and recommendation dataset in online knowledge-sharing. CoRR, abs/2106.06467, 2021.
[44] Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(11), 2008.
[45] Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. Consistency models. CoRR, abs/2303.01469, 2023.
A Proving the Equivalent of Equation (9) and (14)
Recall that in Equation (3) - (5), we have formulated the generation task in DDPM as optimizing the variational bound of negative log-likelihood, where the  $t$ -th term is as follows:
$$
L _ {t - 1} = D _ {K L} \left(q \left(\mathbf {x} ^ {t - 1} \mid \mathbf {x} ^ {t}, \mathbf {x} ^ {0}\right) \| p _ {\theta} \left(\mathbf {x} ^ {t - 1} \mid \mathbf {x} ^ {t}\right)\right). \tag {17}
$$
Since  $q(\mathbf{x}^{t - 1}|\mathbf{x}^t,\mathbf{x}^0)$  and  $p_{\theta}(\mathbf{x}^{t - 1}|\mathbf{x}^t)$  are both Gaussian distributions, we can apply the Rao-Blackwellized Theorem [32] to compute Equation (17), resulting in:
$$
L _ {t - 1} = \mathbb {E} _ {q} \left[ \frac {1}{2 \tilde {\beta} _ {t}} \left\| \tilde {\boldsymbol {\mu}} _ {t} \left(\mathbf {x} ^ {t}, \mathbf {x} ^ {0}\right) - \boldsymbol {\mu} _ {\theta} \left(\mathbf {x} ^ {t}, t\right) \right\| ^ {2} \right] + C, \tag {18}
$$
$$
\tilde {\boldsymbol {\mu}} _ {t} \left(\mathbf {x} ^ {t}, \mathbf {x} ^ {0}\right) = \frac {\sqrt {\bar {\alpha} _ {t - 1}} \beta_ {t}}{1 - \bar {\alpha} _ {t}} \mathbf {x} ^ {0} + \frac {\sqrt {\alpha_ {t}} \left(1 - \bar {\alpha} _ {t - 1}\right)}{1 - \bar {\alpha} _ {t}} \mathbf {x} ^ {t}. \tag {19}
$$
Note that  $\mathbf{x}^t = \sqrt{\bar{\alpha}_t}\mathbf{x}^0 +\sqrt{1 - \bar{\alpha}_t}\epsilon$  we have:
$$
\begin{array}{l} \tilde {\boldsymbol {\mu}} _ {t} (\mathbf {x} ^ {t}, \mathbf {x} ^ {0}) = \frac {\sqrt {\bar {\alpha} _ {t - 1}} \beta_ {t}}{1 - \bar {\alpha} _ {t}} \mathbf {x} ^ {0} + \frac {\sqrt {\alpha_ {t}} (1 - \bar {\alpha} _ {t - 1})}{1 - \bar {\alpha} _ {t}} \mathbf {x} ^ {t} \\ = \frac {\sqrt {\bar {\alpha} _ {t - 1}} \beta_ {t}}{1 - \bar {\alpha} _ {t}} \frac {\mathbf {x} ^ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon}}{\sqrt {\bar {\alpha} _ {t}}} + \frac {\sqrt {\alpha_ {t}} (1 - \bar {\alpha} _ {t - 1})}{1 - \bar {\alpha} _ {t}} \mathbf {x} ^ {t} \tag {20} \\ = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon}\right). \\ \end{array}
$$
In DDPM,  $\mu_{\theta}$  is reparametrized as:
$$
\boldsymbol {\mu} _ {\theta} \left(\mathbf {x} ^ {t}, t\right) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} ^ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} _ {\theta} \left(\mathbf {x} ^ {t}, t\right)\right). \tag {21}
$$
Substituting Equation (20) and (21) back to Equation (18), we can obtain the simplified version of  $L_{t-1}$  as expressed in Equation (9):
$$
L _ {t - 1} = \mathbb {E} _ {\mathbf {x} ^ {0}, \epsilon} \left[ \frac {\beta_ {t} ^ {2}}{2 \tilde {\beta} _ {t} \alpha_ {t} (1 - \bar {\alpha} _ {t})} | | \epsilon - \epsilon_ {\theta} (\sqrt {\bar {\alpha} _ {t}} \mathbf {x} ^ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t) | | ^ {2} \right] + C. \tag {22}
$$
We can adopt an alternative reparametrization of  $\pmb{\mu}_{\theta}$  similar to Equation (13):
$$
\boldsymbol {\mu} _ {\theta} \left(\mathbf {x} ^ {t}, t\right) = \sqrt {\bar {\alpha} _ {t - 1}} f _ {\theta} \left(\mathbf {x} ^ {t}, t\right) + \frac {\sqrt {\alpha_ {t}} \left(1 - \bar {\alpha} _ {t - 1}\right)}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon}. \tag {23}
$$
Then we can derive:
$$
\begin{array}{l} \tilde {\boldsymbol {\mu}} _ {t} \left(\mathbf {x} ^ {t}, \mathbf {x} ^ {0}\right) - \boldsymbol {\mu} _ {\theta} \left(\mathbf {x} ^ {t}, t\right) \\ = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} ^ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon}\right) - \sqrt {\bar {\alpha} _ {t - 1}} f _ {\theta} (\mathbf {x} ^ {t}, t) - \frac {\sqrt {\alpha_ {t}} (1 - \bar {\alpha} _ {t - 1})}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} \\ = \frac {1}{\sqrt {\alpha_ {t}}} \left(\sqrt {\bar {\alpha} _ {t}} \mathbf {x} ^ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon}\right) - \sqrt {\bar {\alpha} _ {t - 1}} f _ {\theta} \left(\mathbf {x} ^ {t}, t\right) - \frac {\sqrt {\alpha_ {t}} \left(1 - \bar {\alpha} _ {t - 1}\right)}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} \tag {24} \\ = \sqrt {\bar {\alpha} _ {t - 1}} \mathbf {x} ^ {0} + \frac {\sqrt {\alpha_ {t}} (1 - \bar {\alpha} _ {t - 1})}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} - \sqrt {\bar {\alpha} _ {t - 1}} f _ {\theta} (\mathbf {x} ^ {t}, t) - \frac {\sqrt {\alpha_ {t}} (1 - \bar {\alpha} _ {t - 1})}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} \\ = \sqrt {\bar {\alpha} _ {t - 1}} \left(\mathbf {x} ^ {0} - f _ {\theta} \left(\mathbf {x} ^ {t}, t\right)\right). \\ \end{array}
$$
Therefore Equation (18) can be simplified to another version:
$$
L _ {t - 1} = \mathbb {E} _ {\mathbf {x} ^ {0}, \epsilon} \left[ \frac {\bar {\alpha} _ {t - 1}}{2 \tilde {\beta} _ {t}} | | \mathbf {x} ^ {0} - f _ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} \mathbf {x} ^ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , t\right) | | ^ {2} \right] + C \tag {25}
$$
So far we have proven that Equation (22) (predicting noise) and (25) (predicting target) are two equivalent versions of training objective for diffusion in theory. In practice, DDPM shows that Equation (22) performs well in image generation, while study [22] shows Equation (25) in more suitable in text generation. In sequential recommendation, we adopt Equation (25) (or equivalently, Equation (14)) to acquire our objective in DreamRec for oracle item generation.
B Detailed Experimental Settings
B.1 Statistics of Datasets
The statistics of the adopted datasets are summarized in Table 2.
Table 2: Statistics of datasets.
Dataset	YooChoose	KuaiRec	Zhihu
#sequences	128,468	92,090	11,714
#items	9,514	7,261	4,838
#interactions	539,436	737,163	77,712
(b) SASRec.
Figure 5: Visualization of the learned item embeddings on YooChoose dataset using T-SNE. DreamRec explores most of the item space without requiring negative sampling.
(a) SASRec (no negative sampling).
Figure 6: Visualization of the learned item embeddings on KuaiRec dataset using T-SNE. DreamRec explores more of the item space without requiring negative sampling.
C More Ablation Studies
C.1 Visualization on YooChoose and KuaiRec Datasets.
We further visualize the learned item embedding visualization on YooChoose and KuaiRec datasets in Figure 5 and Figure 6. Similar to Zhihu dataset (Figure 3), SASRec without negative sampling may fail to distinguish different items, since plenty of items gather in limited zones of the item space. Consequently, negative sampling is necessary for classification-based sequential recommenders. In contrast, DreamRec directly models the data-generation distribution and can better explore item space without the requirement of negative sampling.