TV-Rec: Time-Variant Convolutional Filter for Sequential Recommendation

Thank you for your thoughtful and constructive feedback on our work. Below, we provide detailed responses to each of your concerns, including additional experiments and revisions that we will incorporate into the final version of the paper.

1. Concerns on Dataset Scale and Model Scalability

In sequential recommendation, scalability is often discussed with repect to sequence length. While our main experiments use a commonly adopted maximum sequence length of 50, we have included additional results with a much longer length of 200 (4 times longer) in Table 3 and Section 4.1.

Additionally, to further test scalability in extreme cases, we conducted experiments on the XLong dataset with a maximum sequence length of 1,000--20 times longer than in our main experiment. The dataset statistics are summarized below:

Table D. Statistics of the XLong Dataset

We followed the experimental settings of LRURec [1] and performed the experiments within the LRURec framework. The results are as follows:

Table E. Results on the XLong dataset

Although TVRec shows slightly lower performance compared to LRURec in Recall@20, it significantly outperforms in all other metrics. This demonstrates that TVRec handles extremely long sequences effectively, highlighting its strength in long-range modeling tasks.

2. Clarifying the purpose of Figure 5

Thank you for pointing this out. You're correct--FMLPRec achieves the fastest inference time, as reported in Appendix Table 7 and also depicted in Figure 5. However, the purpose of Figure 5 is not to emphasize inference speed alone, but rather to present a broader trade-off between inference time and recommendation accuracy (NDCG@20).

While FMLPRec is computationally efficient, its recommendation accuracy is significantly lower than that of other hybrid models such as TV-Rec, BSARec, and AdaMCT. Therefore, our key intent in Figure 5 is to highlight how TV-Rec achieves an excellent balance between speed and accuracy, especially among high-performing models.

We acknowledge that this intent might not have been sufficiently clear, and we will revise the caption and explanation in the main paper to emphasize that the figure aims to show the accuracy-efficiency trade-off, rather than showcasing the absolute fastest model.

3. What does inference time measure?

We would like to clarify that the inference time reported in Figure 5 and Table 7 refers to the computation time of the user sequence embedding, not the time taken for similarity-based retrieval or ranking over the item set.

Our focus in this work is on designing an efficient and expressive sequence encoder that captures temporal dynamics in user behavior. All compared models in our study share similar post-encoding steps (e.g., computing dot-product scores with item embeddings), so the variation in inference time mainly stems from the complexity of the sequence encoding architecture.

We will clarify this point in the main paper to ensure that the reported inference time is properly interpreted as the time for generating the sequence embedding.

Reference

[1] Linear Recurrent Units for Sequential Recommendation, WSDM 2024

Thank you for your careful and insightful review of our manuscript. Below, we respond to each point with further details and experimental results.

1. Regarding absence of strong recent models

We could not find any official publication or preprint corresponding to Time4Rec (ICLR 2024). If you could kindly provide a reference or link to the paper, we would be happy to verify it and include it in our comparison.

Additionally, we have incorporated results for several strong and recent graph-based models [1,2,3,4] in response to reviewer HzEw’s comments. We kindly invite you to refer to our response to reviewer HzEw (Answer 1) for the updated comparisons.

2. Expressive capacity or time-variant convolutional filter

Our proposed filter design can be viewed as a position-aware spectral filtering mechanism, where the filter matrix is constructed as: $\mathbf{G} = (\mathbf{U} \circ (\mathbf{H} \mathbf{\Lambda}^\top)) \mathbf{U}^\top,\quad \text{with } \mathbf{H} = \mathbf{C} \bar{\mathbf{B}}$. Here, $\mathbf{U}$ is the Graph Fourier Transform (GFT) matrix, $\bar{\mathbf{B}}$ is a truncated spectral basis, and $\mathbf{C}$ is a learnable coefficient matrix that modulates the frequency response in a position-dependent manner. This construction enables the model to express frequency-wise filters via linear combinations of the basis functions in $\bar{\mathbf{B}}$. The expressive capacity of the filter is thus determined by the span of $\bar{\mathbf{B}}$: any frequency response vector within this subspace can be exactly represented, and more general responses can be approximated in the $\ell_2$ sense as the number of basis vectors increases. Compared to fixed convolutional filters, our formulation allows more flexible spectral filtering. While we do not provide a formal approximation bound under a specific norm, the empirical results in Table 4 suggest that our construction is sufficiently expressive for modeling real-world sequential data. A theoretical characterization of the approximation capacity remains an interesting direction for future work.

3. Analysis on hyper-parameters

We would like to clarify that the basis matrix $B$ is not derived from a Vandermonde matrix, nor constructed using fixed frequency anchors. Instead, it is a fully learnable parameter matrix, jointly optimized during training. This allows the model to adaptively discover suitable spectral representations without relying on heuristic or hand-crafted frequency configurations. Regarding the number of basis vectors $m$, we have already included a sensitivity analysis in Appendix E.1, and we will update the main paper to explicitly refer to this study for clarity. As for the shift depth $K$, we initially set it equal to the sequence length $N$ following a full-coverage design. To address your concern, , we conducted an additional ablation varying $K$, and summarize the results in table below. As shown, except for Yelp, setting $K=50$ consistently yields the best performance across datasets. This supports our hypothesis that aligning the shift depth $K$ with the sequence length $N$ enables the model to capture more global context, thereby enhancing recommendation quality.

Table C. Ablation Study on $K$

4. Can personalization be incorporated into filters?

As discussed in Appendix I, TV-Rec is data-independent, meaning that it does not incorporate user- or item-specific information into filter generation. While this enables lower complexity and efficient inference, it also limits the model's ability to perform fine-grained personalization, such as user-specific self-attention in Transformer-based models. Incorporating user- or item-aware filters--while preserving the efficiency benefits of our graph-based framework--is an important direction for future work.

5. How does TV-Rec handle data sparsity or cold-start scenarios?

First, we note that our experiments are already conducted on datasets with sparse user-item interactions, which reflects realistic recommendation scenarios. Regarding the cold-start problem, TV-Rec, like most sequential recommendation models, relies on learned item embeddings from historical interactions. As a result, it cannot directly handle entirely new (unseen) items without interaction history. Nonetheless, if side information such as item attributes or metadata is available, the model could be naturally extended to support new items by generating embeddings from such auxiliary features. For new users, since sequential recommendation models inherently rely on sequences of interactions, it is difficult to make personalized predictions when no interaction history is available at all. However, if a user has even 1–2 interactions, TV-Rec can form a valid input sequence and generate meaningful recommendations.

Reference

[1] Session-Based Recommendation with Graph Neural Networks, AAAI 2019

[2] Graph Contextualized Self-Attention Network for Session-based Recommendation, IJCAI 2019

[3] Enhancing Sequential Recommendation with Graph Contrastive Learning, IJCAI 2022

[4] Self-supervised Graph Neural Sequential Recommendation with Disentangling Long and Short-Term Interest, ACM Transactions on Recommender Systems 2025

Thank you for your thoughtful and constructive feedback on our work. Below, we provide detailed responses to each of your concerns, including additional experiments and revisions that we will incorporate into the final version of the paper.

1. Justification for using GSP and the line graph structure in sequential recommendation

The core idea of TV-Rec is to model user sequences as graph signals and process them in the spectral domain using GFT. This spectral representation allows us to decompose sequential patterns into interpretable frequency components: high-frequency components reflect abrupt behavioral changes, while low-frequency components capture stable, smooth trends. Although the current manuscript does not explicitly associate specific frequency bands with behavioral categories (e.g., long-term vs. short-term preferences), TV-Rec employs position-specific spectral filters that modulate these components adaptively. This mechanism allows the model to dynamically emphasize or suppress different frequencies depending on the position in the sequence, enabling a fine-grained and temporally aware representation of user behavior. In contrast to attention-based or CNN-based SR models—which typically rely on fixed receptive fields or explicit positional encodings—TV-Rec directly operates in the spectral domain, offering a principled and flexible way to encode temporal inductive bias. A similar spectral perspective is adopted in BSARec [1], which applies GFT to model sequential signals in the frequency domain and modulates them using a learnable frequency rescaler.

Our choice of the line graph structure is motivated by both theoretical and practical considerations. First, designing GSP-based filters requires eigendecomposition of the graph Laplacian, which necessitates a normalized and consistent graph topology. The line graph satisfies this requirement and provides a uniform spectral basis that can be applied across all sequences regardless of content. Second, unlike models such as SR-GNN [2] that dynamically construct item-level graphs for each session—incurring significant computational overhead due to repeated graph building and message passing—TV-Rec operates on a fixed graph structure defined solely by sequence length. This enables highly efficient batched processing without any need for per-instance graph construction.

2. Comparison to graph-based methods

Our initial focus was on convolutional and hybrid baselines, as TV-Rec was designed to replace both self-attention and fixed convolution filters. However, we acknowledge that TV-Rec is grounded in graph signal processing principles, and thus comparisons with GNN-based sequential recommendation models are relevant. To address this, we have conducted additional experiments with four GNN-based baselines specifically designed for sequential recommendation (SR-GNN [2], GC-SAN [3], GCL4SR [4] and LS4SRec [5]) under the same settings as in Section 4.1. We note that most GCN-based recommendation models are designed for collaborative filtering with static user-item graphs, making them difficult to compare directly with sequential models like TV-Rec.

2-1. Performance Comparison

As shown in Table A, TV-Rec consistently outperforms these models across three datasets, confirming that its time-variant design captures temporal dependencies more effectively than message-passing GNN architectures. To ensure a comprehensive evaluation, we will report the results on the remaining three benchmark datasets during the discussion phase once the experiments are complete.

Table A. Comparison to GNN-based methods

2-2. Architectural Comparison

SR-GNN and GC-SAN adopt local item transition graphs, where each session or user sequence is transformed into a directed graph based on item co-occurrence. On the other hand, GCL4SR and LS4SRec construct global item transition graphs (e.g., WITG) derived from the aggregated behavior of all users. While TV-Rec also leverages a graph-based view of sequential data, it differs from these baselines in several fundamental aspects.

First, although the graph structure in TV-Rec is superficially similar to local item transition graphs, the key distinction lies in how the nodes are defined. Existing methods treat items as nodes, meaning that repeated occurrences of the same item in different positions map to the same node. In contrast, TV-Rec considers positions in the sequence as nodes, allowing even the same item to be treated as distinct nodes depending on its temporal position. This design choice enables the model to capture fine-grained temporal and positional dependencies, which are often overlooked when items are treated identically across time.

Second, all four baselines explicitly employ GNNs to propagate and learn node representations. In contrast, TV-Rec does not use GNNs at all, and instead utilizes time-variant convolutional filters inspired by graph signal processing. These filters operate over a structured graph without relying on iterative message passing. As a result, TV-Rec achieves significantly faster training and inference times, while maintaining superior or comparable accuracy.

3. Statistical Significance Testing

To validate the robustness of TV-Rec, we conducted the Mann-Whitney U test [6], comparing its performance against the best baseline for each dataset using HR@20 and NDCG@20 metrics. The results show statistically significant improvements on all datasets, with p-values below 0.05 for each comparison:

Table B. Mann-Whitney U Test Result

These results provide strong evidence that our TV-Rec consistently outperforms state-of-the-art (SOTA) baselines on all datasets, demonstrating its robustness across different metrics and datasets.

4. Regarding orthogonal regularization

Eq. (13), $B_{real}$ and $B_{imag}$ refer to the real and imaginary parts of the basis matrix $B$ used in constructing the filter tap matrix $H$ (see Eq. (8)). Since $B$ is complex-valued due to the use of GFT, we explicitly separate and regularize its real and imaginary components. Orthogonal regularization is applied to encourage the rows of $B$ to be orthonormal, which improves the numerical stability and expressiveness of the filter. This allows $B$ to span a well-conditioned subspace, reducing redundancy and improving generalization [7,8].

5. Regarding the experimental setting of basic graph filter in ablation study

We apologize for the lack of clarity in the ablation study. The basic graph filter in Section 4.3 refers to a version of TV-Rec where the time-variant filter is replaced with a standard (non-time-variant) graph filter—i.e., the latter case. This ablation shares the same overall architecture as TV-Rec, allowing for a direct comparison of filter designs. The formulation of this standard filter corresponds to Eq. (3). We will revise the caption to clarify this and avoid confusion.

Reference

[1] An Attentive Inductive Bias for Sequential Recommendation beyond Self-Attention, AAAI 2024

[2] Session-Based Recommendation with Graph Neural Networks, AAAI 2019

[3] Graph Contextualized Self-Attention Network for Session-based Recommendation, IJCAI 2019

[4] Enhancing Sequential Recommendation with Graph Contrastive Learning, IJCAI 2022

[5] Self-supervised Graph Neural Sequential Recommendation with Disentangling Long and Short-Term Interest, ACM Transactions on Recommender Systems 2025

[6] "Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules." Statistics surveys 4 (2010).

[7] Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?, NeurIPS 2018

[8] Orthogonal Graph Neural Networks, AAAI 2022

Thank you for your insightful and constructive feedback. In this response, we address each of your comments in detail and provide additional experimental results and clarifications.

1. Comparison with graph-based methods

Our initial focus was on convolutional and hybrid baselines, as TV-Rec was designed to replace both self-attention and fixed convolution filters. However, we acknowledge that TV-Rec is grounded in graph signal processing principles, and thus comparisons with GNN-based sequential recommendation models are relevant. To address this, we have conducted additional experiments with four GNN-based baselines specifically designed for sequential recommendation (SR-GNN [1], GC-SAN [2], GCL4SR [3] and LS4SRec [4]) under the same settings as in Section 4.1. We note that most GCN-based recommendation models are designed for collaborative filtering with static user-item graphs, making them difficult to compare directly with sequential models like TV-Rec.

1-1. Performance Comparison

As shown in Table A, TV-Rec consistently outperforms these models across three datasets, confirming that its time-variant design captures temporal dependencies more effectively than message-passing GNN architectures. To ensure a comprehensive evaluation, we will report the results on the remaining three benchmark datasets during the discussion phase once the experiments are complete.

Table A. Comparison to GNN-based methods

1-2. Architectural Comparison

SR-GNN and GC-SAN adopt local item transition graphs, where each session or user sequence is transformed into a directed graph. On the other hand, GCL4SR and LS4SRec construct global item transition graphs (e.g., WITG) derived from the aggregated behavior of all users. While TV-Rec also leverages a graph-based view of sequential data, it differs from these baselines in several fundamental aspects.

First, although the graph structure in TV-Rec is superficially similar to local item transition graphs, the key distinction lies in how the nodes are defined. Existing methods treat items as nodes, meaning that repeated occurrences of the same item in different positions map to the same node. In contrast, TV-Rec considers positions in the sequence as nodes, allowing even the same item to be treated as distinct nodes depending on its temporal position. This design choice enables the model to capture fine-grained temporal and positional dependencies, which are often overlooked when items are treated identically across time.

Second, all four baselines explicitly employ GNNs to propagate and learn node representations. In contrast, TV-Rec does not use GNNs at all, and instead utilizes time-variant convolutional filters inspired by graph signal processing. These filters operate over a structured graph without relying on iterative message passing. As a result, TV-Rec achieves significantly faster training and inference times, while maintaining superior or comparable accuracy.

2. Time-variant graph filter vs. standard graph convolution

We would like to clarify that we already include an ablation study comparing our time-variant graph filter with a standard graph convolution (denoted as “Basic Graph Filter”) under identical conditions (Table 4, Section 4.3). As shown, replacing the time-variant filter with a standard graph filter leads to performance degradation across all datasets, clearly demonstrating the benefit of our design. To improve clarity, we agree that the caption or description in this section could better highlight this intent. We will revise it accordingly so that readers can more easily recognize the purpose and significance of this comparison.

3. Clarification on model behavior and filter design

We appreciate detailed feedback regarding the lack of practical implementation details for the time-variant filter. Below, we address the three key concerns raised: (1) the dynamic behavior during inference, (2) the interaction between the graph Fourier transform and filter taps, and (3) the parameter learning process. We agree that clearer explanations would improve readability and reproducibility, and we will incorporate these clarifications into the final version of the paper.

3-1. Dynamic behavior during inference

As noted in Appendix I, the term “time-variant” refers to the use of different filters across sequence positions—not to input-dependent adaptation. TV-Rec applies the same learned filters to all inputs during inference. These filters are position-specific but fixed once trained, making the model data-independent at test time and contributing to its computational efficiency. We will revise the text to avoid this confusion.

3-2. Interaction between GFT and filter taps

To clarify how the graph Fourier transform interacts with the learned filter taps, we provide the following pseudocode summarizing the spectral filtering process:

# X       : [batch_size, N, d]        # Input sequence
# U       : [N, N]                    # GFT matrix
# C       : [N, m]                    # Coefficient matrix
# B       : [m, K+1]                  # Pre-normalized basis 
# Λ       : [N, K+1]                  # Vandermonde matrix (Λ)

# Step 1: Transform input to spectral domain
X_freq = U.T @ X                     # Graph Fourier Transform

# Step 2: Construct spectral filter
H = C @ B                            # [N, K+1], B is pre-normalized
H_proj = H @ Λ.T                     # [N, N]

# Step 3: Apply element-wise scaled inverse GFT
F = U * H_proj                       # Element-wise product

# Step 4: Apply filter and return to time domain
X_out = F @ X_freq                   # Final output

This filtering mechanism allows the learned filter taps to modulate graph frequency responses in a position-aware yet data-independent manner.

3-3. Parameter learning

All filter parameters—including the coefficient matrix $C$ and the basis matrix $B$—are learned jointly through standard backpropagation. To encourage diversity and improve numerical stability, we apply an orthogonality regularization to B (Eq. 13), promoting a well-conditioned and expressive spectral basis.

4. Clarifications on captions, terminology, and citations

We apologize for the lack of clarity in certain parts of the paper. We will revise the table and figure captions to provide clear and sufficient context. Additionally, we will include proper references for the baseline models used in the experiments. Regarding the terminology, we would like to point out that abbreviations such as "SR" are defined at the beginning of the Introduction. Nevertheless, we acknowledge the importance of clarity for a broader readers and will ensure that key terms are clearly introduced when they first appear in the main text.

Reference

[1] Session-Based Recommendation with Graph Neural Networks, AAAI 2019

[2] Graph Contextualized Self-Attention Network for Session-based Recommendation, IJCAI 2019

[3] Enhancing Sequential Recommendation with Graph Contrastive Learning, IJCAI 2022

[4] Self-supervised Graph Neural Sequential Recommendation with Disentangling Long and Short-Term Interest, ACM Transactions on Recommender Systems 2025