Sparse Meets Dense: Unified Generative Recommendations with Cascaded Sparse-Dense Representations

We sincerely thank the reviewer for the constructive feedback and thoughtful questions. Below, we address the key concerns raised.

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For Weakness1 & Question 1: Large performance gap between GRU4Rec and SASRec

We appreciate the reviewer’s attention to this detail. Indeed, both GRU4Rec[1] and SASRec[2] are classical sequential recommendation models, but they differ significantly in their capacity to capture long-range dependencies and sequence context.

GRU4Rec leverages RNNs, which are known to struggle with modeling long user behavior sequences due to vanishing gradient issues. In contrast, SASRec employs self-attention mechanisms that allow the model to directly attend to any previous item in the sequence, thereby capturing richer patterns and long-range dependencies more effectively. This architectural advantage explains SASRec’s consistent outperformance on all datasets. This observation is also consistently reported in other research, such as TIGER[3] and S$^3$-Rec[4].

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For Weakness 1 & Question 2: Comparisons with the most recent methods

COBRA's core contribution lies in its novel cascaded sparse-dense representation for items, which integrates the strengths of both generative and dense retrieval paradigms through a coarse-to-fine generation process. Our primary focus is on this paradigm shift. We contend that most existing generative recommendation improvements focus on optimizing sparse ID generation, which is orthogonal to our paradigm-level innovation. We believe that such improvements could potentially be integrated into COBRA's sparse ID generation.

To further validate COBRA's effectiveness, we conducted additional experiments on the Amazon Beauty dataset, comparing COBRA with recent representative approaches: LC-Rec[5] , GenRec[6] , and LETTER[7]. The results are as follows:

As the results demonstrate, COBRA consistently achieves strong performance. Specifically, it shows a +4.3% improvement in Recall@5 compared to GenRec , a +13.1% improvement in Recall@10 over LC-Rec , and an +8.7% improvement in NDCG@10 compared to GenRec. While GenRec shows a slightly higher NDCG@5, COBRA generally achieves superior holistic performance, confirming the unique value of our cascaded sparse-dense paradigm.

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For Weakness 2 & Question 3: Equation format

We appreciate the reviewer’s suggestion regarding presentation. To improve clarity and align with academic writing standards, we will revise the methodology section by separating each key equation into its own line with proper numbering. This will be reflected in the final submission.

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For Weakness 3 & Question 4: Formal theoretical analysis on sparse-dense cascading

The reviewer raises an excellent point regarding the theoretical analysis of our cascaded design. Our approach addresses a key limitation of ID-based models like TIGER where discrete semantic IDs can limit expressiveness for fine-grained user intent. We augment each item with a dense representation to capture more comprehensive information, thus each item is represented by a (sparse, dense) pair. We theoretically demonstrate the superiority of our cascaded prediction modeling compared to an independent prediction approach.

Let $S_{1:t}$ be a user's behavior sequence. For an item, $C$ represents a discrete random variable for its sparse ID, and $X$ represents a continuous random variable for its dense vector. We denote the information entropy of a discrete random variable as $H$ and the differential entropy of a continuous random variable as $h$. Our objective is to model $P(Item\_{t+1} | S\_{1:t})$ for predicting the next interacted item. We consider two distinct approaches for modeling $Item_{t+1}$:

Approach 1: Independent Prediction Predict $C$ and $X$ separately based on the user's historical sequence $S\_{1:t}$. The probability distribution for this approach is formulated as: $P(Item_{t+1} | S_{1:t}) = P(C | S_{1:t}) \times P(X | S_{1:t}) \quad (1)$

Approach 2: Cascaded Prediction First predict the sparse information of the $Item_{t+1}$ using the user's historical sequence $S\_{1:t}$, and then utilize this sparse information along with the preceding sequence $S\_{1:t}$ to predict the dense vector of the next item. The probability distribution for this approach is formulated as: $P(Item_{t+1} | S_{1:t}) = P(C | S_{1:t}) \times P(X | C, S_{1:t}) = P(C, X | S_{1:t}) \quad (2)$

We demonstrate that the cascaded prediction modeling (Approach 2) consistently yields superior performance compared to independent prediction modeling.

Theorem 1: Superiority of Cascaded Modeling Let $E_1$ be the information entropy of the independent prediction modeling probability distribution (Equation 1), and $E_2$ be the information entropy of the cascaded prediction modeling probability distribution (Equation 2). Then, it always holds that $E_2 \leq E_1$, where equality holds if and only if the random variables $C$ and $X$ are conditionally independent given $S\_{1:t}$.

Proof: We calculate the information entropy for both probability distributions given by equations (1) and (2).

For independent prediction modeling (Equation 1):

$$\begin{aligned} E\_1 &= -\sum\_{c} \int_{x} P(c|S_{1:t}) \times P(x | S_{1:t}) \log(P(c|S_{1:t}) \times P(x | S_{1:t})) dx \\\\ &= -\sum_{c} \int_{x} P(c|S_{1:t}) \times P(x | S_{1:t}) \log(P(c|S_{1:t})) dx \\\\ &\quad -\sum_{c} \int_{x} P(c|S_{1:t}) \times P(x | S_{1:t}) \log(P(x | S_{1:t})) dx \\\\ &= H(C | S_{1:t}) + h(X | S_{1:t}) \end{aligned}$$

Hence, under independent modeling, the total entropy decomposes additively over $C$ and $X$.

For cascaded prediction modeling (Equation 2):

$$\begin{aligned} E_2 &= -\sum_{c} \int_{x} P(c|S_{1:t}) \times P(x | c, S_{1:t}) \log(P(c|S_{1:t}) \times P(x | c, S_{1:t})) dx \\\\ &= -\sum_{c} \int_{x} P(c, x|S_{1:t}) \log(P(c, x|S_{1:t})) dx \\\\ &= H(C, X | S_{1:t}) \end{aligned}$$

Hence, cascaded modeling captures the full joint uncertainty of $C$ and $X$. By the subadditivity of information entropy[3]:$E_2 = H(C, X | S_{1:t}) \leq H(C | S_{1:t}) + h(X| S_{1:t}) = E_1$ Equality holds if and only if random variables $C$ and $X$ are conditionally independent.

Theorem 1 demonstrates that our cascaded modeling scheme always yields a probability distribution with lower information entropy. This implies that the resulting probability distribution is more concentrated, which is beneficial for model learning. Equality holds only when random variables $C$ and $X$ are conditionally independent, in which case $P(x|c, S_{1:t}) = P(x | S_{1:t})$. From equations (1) and (2), it is evident that both modeling approaches are equivalent under this condition. Consequently, cascaded modeling is generally superior to independent modeling.

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Conclusion

We thank the reviewer again for their detailed and insightful comments. We will incorporate all of the above improvements into the final version to enhance clarity, completeness, and academic rigor.

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Reference

1. Hidasi et al., "Session-based Recommendations with Recurrent Neural Networks"
2. Kang & McAuley, "Self-Attentive Sequential Recommendation", ICDM 2018
3. Rajput et al., "Recommender Systems with Generative Retrieval", NeurIPS 2023
4. Zhou et al., "S^3-Rec: Self-Supervised Learning for Sequential Recommendation with Mutual Information Maximization", CIKM 2020
5. Zheng et al., "Adapting Large Language Models by Integrating Collaborative Semantics for Recommendation", ICDE 2024
6. Cao & Lio, "GenRec: Generative Sequential Recommendation with Large Language Models", ECIR 2024
7. Wang et al., "Learnable Item Tokenization for Generative Recommendation", CIKM 2024

We sincerely appreciate the reviewer's thorough evaluation and constructive suggestions. Below we provide a comprehensive response addressing all concerns.

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For Weakness 1: Baseline Comparison with LETTER

We appreciate the reviewer's suggestion to include Learnable Item Tokenization for Generative Recommendation (LETTER[1] ) as a baseline. We recognize LETTER's valuable contribution in proposing a learnable item tokenizer that incorporates regularization to capture hierarchical semantics, collaborative signals, and code assignment diversity within item identifiers. Our initial exclusion of LETTER as a direct baseline was primarily due to the distinct focus of our work. While LETTER optimizes the item tokenization process, enhancing the quality of discrete representations, COBRA introduces a cascaded sparse-dense paradigm. Our method's primary advancement lies in jointly modeling sparse ID generation and dense vector refinement, enabling end-to-end optimization and conditional generation where sparse IDs explicitly guide dense prediction.

To comprehensively address this point, we conducted comparisons between COBRA and LETTER's implementations (LETTER-TIGER and LETTER-LC-Rec) on the Amazon Beauty dataset:

Our approach achieves performance improvements of 7.9-38.1% over LETTER-TIGER and 3.1-11.3% over LETTER-LC-Rec across all metrics. This demonstrates the effectiveness of COBRA's cascaded sparse-dense generative approach.

Furthermore, we consider LETTER's optimization of the item tokenization process to be an effective plug-and-play enhancement for semantic IDs, which does not conflict with our core contribution. In future work, COBRA could incorporate designs from LETTER to improve the generation process of sparse IDs, potentially yielding even better results.

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For Weakness 2: Model Scalability

For public datasets, we primarily utilized a lightweight architecture (1-layer encoder, 2-layer decoder) to demonstrate efficiency. To address scalability concerns, we modified model parameters (2-layer encoder, 4-layer decoder) and conducted additional experiments on the Amazon Beauty dataset:

Given the smaller scale of public datasets, further deepening the network does not yield significant benefits. This aligns with scaling law research[2-3] and our industrial experience, indicating that model size increases must correspond with data volume for gains. As supporting evidence, in larger-scale industrial scenarios, we have deployed a COBRA model with a more substantial architecture (6-layer encoder + 8-layer decoder), achieving significant benefits in industrial applications. These findings demonstrate that COBRA's cascaded paradigm can flexibly scale according to data volume, exhibiting architectural flexibility and real-world scalability.

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For Weakness 3: Theoretical Analysis and Cold-Start Robustness

Theoretical Justification for Cascaded Design

The reviewer raises an excellent point regarding the theoretical analysis of our cascaded design. Our approach addresses a key limitation of ID-based models like TIGER[4] where discrete semantic IDs can limit expressiveness for fine-grained user intent. We augment each item with a dense representation to capture more comprehensive information, thus each item is represented by a (sparse, dense) pair. We theoretically demonstrate the superiority of our cascaded prediction modeling compared to an independent prediction approach.

Let $S_{1:t}$ be a user's behavior sequence. For an item, $C$ represents a discrete random variable for its sparse ID, and $X$ represents a continuous random variable for its dense vector. We denote the information entropy of a discrete random variable as $H$ and the differential entropy of a continuous random variable as $h$. Our objective is to model $P(Item\_{t+1} | S\_{1:t})$ for predicting the next interacted item. We consider two distinct approaches for modeling $Item_{t+1}$:

Approach 1: Independent Prediction Predict $C$ and $X$ separately based on the user's historical sequence $S\_{1:t}$. The probability distribution for this approach is formulated as: $P(Item_{t+1} | S_{1:t}) = P(C | S_{1:t}) \times P(X | S_{1:t}) \quad (1)$

Approach 2: Cascaded Prediction First predict the sparse information of the $Item_{t+1}$ using the user's historical sequence $S\_{1:t}$, and then utilize this sparse information along with the preceding sequence $S\_{1:t}$ to predict the dense vector of the next item. The probability distribution for this approach is formulated as: $P(Item_{t+1} | S_{1:t}) = P(C | S_{1:t}) \times P(X | C, S_{1:t}) = P(C, X | S_{1:t}) \quad (2)$

We demonstrate that the cascaded prediction modeling (Approach 2) consistently yields superior performance compared to independent prediction modeling.

Theorem 1: Superiority of Cascaded Modeling Let $E_1$ be the information entropy of the independent prediction modeling probability distribution (Equation 1), and $E_2$ be the information entropy of the cascaded prediction modeling probability distribution (Equation 2). Then, it always holds that $E_2 \leq E_1$, where equality holds if and only if the random variables $C$ and $X$ are conditionally independent given $S\_{1:t}$.

Proof: We calculate the information entropy for both probability distributions given by equations (1) and (2).

For independent prediction modeling (Equation 1):

$$\begin{aligned} E\_1 &= -\sum\_{c} \int_{x} P(c|S_{1:t}) \times P(x | S_{1:t}) \log(P(c|S_{1:t}) \times P(x | S_{1:t})) dx \\\\ &= -\sum_{c} \int_{x} P(c|S_{1:t}) \times P(x | S_{1:t}) \log(P(c|S_{1:t})) dx \\\\ &\quad -\sum_{c} \int_{x} P(c|S_{1:t}) \times P(x | S_{1:t}) \log(P(x | S_{1:t})) dx \\\\ &= H(C | S_{1:t}) + h(X | S_{1:t}) \end{aligned}$$

Hence, under independent modeling, the total entropy decomposes additively over $C$ and $X$.

For cascaded prediction modeling (Equation 2):

$$\begin{aligned} E_2 &= -\sum_{c} \int_{x} P(c|S_{1:t}) \times P(x | c, S_{1:t}) \log(P(c|S_{1:t}) \times P(x | c, S_{1:t})) dx \\\\ &= -\sum_{c} \int_{x} P(c, x|S_{1:t}) \log(P(c, x|S_{1:t})) dx \\\\ &= H(C, X | S_{1:t}) \end{aligned}$$

Hence, cascaded modeling captures the full joint uncertainty of $C$ and $X$. By the subadditivity of information entropy[5]: $E_2 = H(C, X | S_{1:t}) \leq H(C | S_{1:t}) + h(X| S_{1:t}) = E_1$ Equality holds if and only if random variables $C$ and $X$ are conditionally independent.

Theorem 1 demonstrates that our cascaded modeling scheme always yields a probability distribution with lower information entropy. This implies that the resulting probability distribution is more concentrated, which is beneficial for model learning. Equality holds only when random variables $C$ and $X$ are conditionally independent, in which case $P(x|c, S_{1:t}) = P(x | S_{1:t})$. From equations (1) and (2), it is evident that both modeling approaches are equivalent under this condition. Consequently, cascaded modeling is generally superior to independent modeling.

Cold-Start Robustness Mechanisms

As noted, cold-start presents a challenging problem in recommendation systems. However, COBRA can effectively handle cold-start scenarios to a considerable extent.

1) Content-Based Dense Representations for Cold-Start Items: COBRA processes raw item attributes (e.g., title, description) to generate dense vectors. Crucially, this process operates independently of auto-incrementing system ID. This ensures that even for cold-start items with no interaction history, meaningful dense representations are generated based purely on their content.

2) Leveraging Semantic IDs for Cold-Start Items: For cold-start items, we generate sparse IDs using the same method as TIGER. As discussed in Section 4 of the TIGER[2] paper, compared to "Random IDs" used in traditional recommendation methods and KNN in semantic space, semantic IDs can effectively leverage content-based semantic information, ensuring that items still possess meaningful semantic ID even in cold-start scenarios.

3) Empirical Validation in Cold-Start Scenarios: Moreover, according to our online A/B test results, cold-start advertisements achieved a 2.43% increase in conversion, demonstrating the robustness of the COBRA method in cold-start scenarios.

4) Addressing Poorly Learned IDs: The reviewer's concern regarding "poorly learned IDs" representing an extreme edge case is valid. While our end-to-end training framework fosters mutual learning between sparse and dense representations, inherently reducing the likelihood of such scenarios, the performance under poorly learned sparse IDs could be further analyzed. We plan to explore the effects of such extreme edge cases and potential mitigation strategies (e.g., adaptive weighting of sparse/dense contributions based on ID quality confidence) as part of our future work.

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References

[1] Wang et al., "Learnable Item Tokenization for Generative Recommendation", CIKM 2024
[2] Hoffmann et al., "Training Compute-Optimal Large Language Models", 2022
[3] Hou et al., "Scaling Law of Large Sequential Recommendation Models", 2023
[4] Rajput et al., "Recommender Systems with Generative Retrieval", NeurIPS 2023
[5] Cover & Thomas. Elements of Information Theory. Wiley-Interscience, USA, 2006

We thank the reviewer for their thorough feedback and constructive suggestions, which have significantly helped us improve the manuscript. We address each point below.

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For Weakness 1: Computational Overhead

We appreciate this important concern. For our complexity analysis, we define $L$ as the sequence length, $T$ as the number of tokens per item, and $D$ as the embedding dimension.

Training Complexity

Inference Complexity

To ensure practical efficiency, we employ several key techniques during implementation. These include sequence Packing and FlashAttention to minimize computational waste. Furthermore, caching is utilized to decouple the encoder computation, significantly speeding up the inference process. Thanks to these optimizations, COBRA achieves over 30% Model FLOPs Utilization, surpassing typical recommendation benchmarks[3]. This efficiency has enabled successful deployment, serving over 200 million daily users.

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For Weakness 2: Missing Implementation Details

We apologize for the omission of critical implementation details. We will add a "Implementation Details" table in the Appendix. Below is a comprehensive list of all key hyperparameters:

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For Weakness 3: Missing Baselines (ColaRec, LC-Rec, RPG)

We thank the reviewer for highlighting these recent and important generative recommendation baselines. We agree that a comprehensive comparison is valuable for positioning our work within the evolving landscape of the field.

Regarding RPG[4] , we note its publication on arXiv in June 2025, which falls after our submission deadline. For ColaRec[5] and LC-Rec[6], their core contributions lie in aligning semantic IDs with collaborative information, often leveraging pre-trained graph-based representations. While conceptually related to generative recommendations, their distinct methodological focus on explicit semantic-collaborative alignment differs from COBRA's emphasis on unified cascaded sparse-dense representations through end-to-end training.

However, to ensure a more comprehensive comparison, we have now conducted experiments on public datasets with LC-Rec. The results on the "Beauty" dataset are as follows:

COBRA consistently outperforms LC-Rec across all metrics, with improvements ranging from 6.4% to 20.8%. This further validates the effectiveness of COBRA's cascaded sparse-dense representation approach for generative recommendation.

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For Weakness 4: Ablation Studies on Public Datasets

We initially conducted ablation studies primarily on industrial datasets due to their direct relevance to our business objectives. To address the reviewer's concern about generalizability, we have now performed additional ablation analyses on the "Beauty," "Sports & Outdoors," and "Toys & Games" public datasets. The Recall@10 results are summarized below:

The results on public datasets align with those from the industrial setting, demonstrating that the absence of any key component (Dense, ID, or BeamFusion) leads to a performance drop. This confirms the robustness and generalizability of COBRA's proposed components across different scales and data characteristics.

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For Weaknesses 5-6: Formatting and Typos

We appreciate you pointing out these errors. We have thoroughly reviewed the manuscript and made the following corrections:

• The notation of $\text{Encoder}$ in line 108 have been changed to $\mathbf{Encoder}$ for consistency throughout the paper.
• In Figure 1, both sides now explicitly show the encoder to prevent any misunderstanding regarding COBRA's architecture.
• In Line 170, the formula have been revised to $v_{{item}_j}$. We have also explicitly clarified in the text that "the sparse ID is mapped into a dense vector space through an embedding layer" in Section 3.1 to ensure clarity in the methodology.

All these modifications will be incorporated into the final version of the paper.

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For Question 1: Advantages of using the same codebook sizes across all levels

Using a uniform codebook size (32) across all three levels for public datasets offers design simplicity and streamlines quantization implementation. Based on current empirical observations, this configuration yields satisfactory results. However, a detailed investigation into the impact of varying codebook sizes remains an avenue for future research.

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For Question 2: Number of levels being dataset-dependent and COBRA's adaptability

The optimal number of semantic ID levels is primarily driven by Performance Requirements and Computational Cost. In industrial scenarios, there's a critical demand for retrieving a large number of diverse items from vast candidate sets within strict latency constraints. Based on our practical experience, employing finer-grained ID hierarchies significantly increases the computational overhead of beam search, which can severely impact real-time performance. Conversely, for smaller datasets or scenarios with less stringent latency requirements, more hierarchical levels might be permissible to capture finer semantic distinctions if needed.

COBRA demonstrates its adaptability by successfully operating with different semantic ID structures while achieving strong performance. This flexibility indicates that COBRA's core architecture effectively integrates these representations, allowing for configurations that balance semantic granularity with the practical demands of the deployment environment.

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For Question 3: Rationale for COBRA w/o Dense using 3-level semantic IDs vs. COBRA's 2-level IDs on industrial dataset

COBRA's full model uses $32 \times 32$ IDs because dense representations provide significant fault tolerance, allowing for a coarser ID design.

In contrast, "COBRA w/o Dense" completely removes dense vectors, necessitating much finer-grained sparse IDs to compensate for lost information. A $32 \times 32$ ID set would be insufficient for the 2 million industrial advertisements, leading to substantial information loss and consequently poor recall. Therefore, a $256 \times 256 \times 256$ configuration is used for "COBRA w/o Dense" to maximize its representational capacity and enable a fair baseline comparison against the full model. This highlights the synergistic benefit of COBRA's cascaded sparse-dense approach, achieving superior performance with a less complex sparse ID structure.

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References

[1] Rajput et al., "Recommender Systems with Generative Retrieval", NeurIPS 2023
[2] Kang & McAuley, "Self-Attentive Sequential Recommendation", ICDM 2018
[3] Zhou et al., "OneRec: Optimizing Recommendation Training Efficiency", Technical Report 2023
[4] Hou et al., "Generating Long Semantic IDs in Parallel for Recommendation", KDD 2025
[5] Wang et al., "Content-Based Collaborative Generation for Recommender Systems", CIKM 2024
[6] Zheng et al., "Adapting Large Language Models by Integrating Collaborative Semantics for Recommendation", ICDE 2024

We sincerely appreciate your constructive feedback and insightful comments on our paper. Thank you for acknowledging the clarity of our presentation and the strength of our experimental results. We have thoroughly addressed your concerns regarding contribution evaluation, baseline comparisons, time complexity, and implementation settings. Below is our response incorporating additional analyses and experiments.

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For Weakness 1 & Question 1: Enhanced Evaluation of Core Contributions

To rigorously validate the necessity of our cascaded bi-represented formulation—which extends beyond a simple combination of generative retrieval (GR) and dense retrieval (DR)—we conducted comprehensive experiments on public datasets. Our experimental design compares two variants:

Recall@10 performance across public datasets:

COBRA outperforms ensembling approaches in Recall@10 metrics. For example:

• On Beauty: Ensembling-BeamFusion (0.0664) vs. COBRA (0.0725, +$9.2\\%$)
• On Sports & Outdoors: Performance gap of $10.6\\%$ between Ensembling-Linear and COBRA

This demonstrates that cascaded generation—where sparse IDs explicitly condition dense vector refinement—is fundamentally more effective than ensembling separate GR and DR methods. The joint training ensures dense vectors are semantically anchored to sparse IDs, avoiding ambiguous retrievals.

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For Weakness 2: Time Complexity Analysis

We appreciate this important concern. For our complexity analysis, we define $L$ as the sequence length, $T$ as the number of tokens per item, and $D$ as the embedding dimension.

Training Complexity

Inference Complexity

To ensure practical efficiency, we employ several key techniques during implementation. These include sequence Packing and FlashAttention to minimize computational waste. Furthermore, caching is utilized to decouple the encoder computation, significantly speeding up the inference process. Thanks to these optimizations, COBRA achieves over 30% Model FLOPs Utilization, surpassing typical recommendation benchmarks[3]. This efficiency has enabled successful deployment, serving over 200 million daily users.

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For Question 2: Comparison with Multi-Interest Retrieval Methods

We appreciate your suggestion to include multi-interest retrieval baselines. To provide a more comprehensive evaluation beyond sequential paradigms (TIGER for GR, SASRec for DR), we conducted experiments comparing COBRA against state-of-the-art multi-interest methods. Following literature findings that ComiRec[2] generally outperforms MIND[1], we focus our comparison on ComiRec:

Key Observations

1. Consistent Superiority:
   COBRA demonstrates significant performance advantages over ComiRec across all metrics, with particularly notable gains in early-position ranking (Recall@5 and NDCG@5).

2. Architectural Distinction:
   While ComiRec generates multiple interest embeddings per user, COBRA's cascaded paradigm fundamentally differs by:

   • Explicitly conditioning dense vector generation on sparse IDs
   • Enabling mutual refinement of both representations through end-to-end training

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For Question 3: Ablation Studies on Public Datasets

We initially conducted ablation studies primarily on industrial datasets due to their direct relevance to our business objectives. To address the reviewer's concern about generalizability, we have now performed additional ablation analyses on the "Beauty," "Sports & Outdoors," and "Toys & Games" public datasets. The Recall@10 results are summarized below:

The results on public datasets align with those from the industrial setting, demonstrating that the absence of any key component (Dense, ID, or BeamFusion) leads to a performance drop. This confirms the robustness and generalizability of COBRA's proposed components across different scales and data characteristics.

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For Question 4: Experimental Settings Clarifications

Beam Size ($M$) Configuration:

• Public Datasets (Table 1): $M=20$
  Optimal for smaller item pools ($11K$-$18K$ items), balancing diversity and efficiency.
• Industrial Dataset (Table 2): $M=50$
  Necessary for large-scale scenarios to ensure broad interest coverage.

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Conclusion

We have demonstrated COBRA's performance gains stem from its cascaded sparse-dense generative paradigm, not simply GR/DR ensembling. The consistent performance gap across datasets validates each component's necessity. Our comparison with multi-interest methods highlights the architectural uniqueness of our approach, while complexity analyses confirm its practical scalability.

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Revision Plan:

We will incorporate all modifications below in the final version:

1. Complete ablation tables (public + industrial datasets)
2. Expanded complexity analysis section
3. Multi-embedding Retrieval baseline comparisons
4. Engineering optimization details

Thank you for your valuable feedback, which has significantly strengthened our work.

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References

[1] Li et al., "Multi-Interest Network with Dynamic Routing", CIKM 2019
[2] Cen et al., "Controllable Multi-Interest Framework for Recommendation", KDD 2020
[3] Rajput et al., "Recommender Systems with Generative Retrieval", NeurIPS 2023
[4] Kang & McAuley, "Self-Attentive Sequential Recommendation", ICDM 2018
[5] Zhou et al., "OneRec: Optimizing Recommendation Training Efficiency", Technical Report 2023