TV-Rec: Time-Variant Convolutional Filter for Sequential Recommendation
Authors: Yehjin Shin
Jeongwhan Choi
Seojin Kim
Noseong Park
Venue: NeurIPS 2025 poster ()
Keywords: Sequential Recommendation
Graph Signal Processing
Primary area: deep_learning
TL;DR: TV-Rec uses time-variant convolutional filters to model complex user behavior without self-attention, outperforming state-of-the-art baseline models across 6 datasets.

Abstract: Recently, convolutional filters have been increasingly adopted in sequential recommendation for their ability to capture local sequential patterns. However, most of these models complement convolutional filters with self-attention. This is because convolutional filters alone, generally fixed filters, struggle to capture global interactions necessary for accurate recommendation. We propose \textbf{T}ime-\textbf{V}ariant Convolutional Filters for Sequential \textbf{Rec}ommendation (TV-Rec), a model inspired by graph signal processing, where time-variant graph filters capture position-dependent temporal variations in user sequences. By replacing both fixed kernels and self-attention with time-variant filters, TV-Rec achieves higher expressive power and better captures complex interaction patterns in user behavior. This design not only eliminates the need for self-attention but also reduces computation while accelerating inference. Extensive experiments on six public benchmarks show that TV-Rec outperforms state-of-the-art baselines by an average of 7.49\%.

TV-Rec: Time- Variant Convolutional Filter for Sequential Recommendation
Yehjin Shin
Jeongwhan Choi Seojin Kim Noseong Park*
KAIST
(yehjin.shing shin, jeongwhan, choi, seojinkim, nossong)Okiist.ar
Abstract
Recently, convolutional filters have been increasingly adopted in sequential rec- ommendation for their ability to capture local sequential patterns. However, most of these models complement convolutional filters with self-attention. This is be- cause convolutional filters alone, generally fixed filters, struggle to capture global interactions necessary for accurate recommendation. We propose Convolutional Filters for Sequential Recommendation (TV-Rec), model inspired by graph signal processing, where time-variant graph filters capture position- dependent temporal variations in user sequences. By replacing both fixed kernels and eeff-atteniion with time-variant filters, TV-Rec achieves higher expressive power and better captures complex interaction patterns in user behavior. This de- sign not only eliminates the need for self-attention but also reduces computation while accelerating inference. Extensive experiments on six public benchmarks show that TV-Rec outperforms tfte-of-thee-rr baselines by an average of 7.49%.
Introduction
Recommender systems have become essential for guiding users through vast amounts of content
by providing personalized information based on users' historical interactions [41 B3 1 19 13]
3 8 16 21). Considering that preferences evolve time, sequential recommendation (SR)
has become widely used for capturing dynamic preferences using sequential patterns in users' interactions. Various approaches have been developed more accurately capture users' dynamic sequential patterns, including architectures such as Markov chains [25), RNNs [4]. and GNNs (36].
Transformers (32), a powerful architecture NLP, have been widely adopted encoders for many SR models, highlighting their ability to model long-term dependencies in data [8 30 24 6).
Despite their modeling power, self- attention mechanisms have funda- mental limitation: they lack induc- tive bias toward sequential structure. While position embeddings provide absolute position information, self- attention still treats all positions pair- wise without any inherent bias toward local proximity. As a result, makes it difficult to model fine-graine fine-grained, local- ized user behavior patterns 29) This limitation has led to the development of hybrid models that integrate con- volutional layers to introduce locality
Table 1: Comparison of existing methods based on three
points: i) convolutional filter type, ii) inference efficiency, and iii) recommendation performance. The double tick mark indicates better performance compared to a single tick mark.
Convolutional Filter
Self- Inference Attention
Rec. Performance
Model
Efficiency
SASRe:
BERT4Rec
30
Caser
Fixed
/
NextitNet
12
Fixed
/
FMLPRec
Fixed
AdaMCT
Fixed
X
/
BSARec
Fixed
//
TV-Rec (Ours)
Time-Variant
X
"Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

bias. For instance, AdaMCT [17 utilizes self-attention and ID convolution together to capture both long-term and short-term user preferences, while BSARec 29 addresses the limitations of self-attention by applying convolution using the Fourier Transform.
At the same time, convolution-only models have been explored for their effectiveness in capturing local sequential dependencies, which are particularly valuable in SR. As shown in Table I models such as Caser [3 NextItNet [42). and FMLPRec [47] use fixed convolutional filters to detect patterns in user sequences. These filters focus on users' recent behavior, which is advantageous recommending users' next items. However, their fixed nature limits their adaptability: the same filter is applied uniformly across positions, making it difficult to capture temporally evolving or position-speciffe semantics. While convolutional filters solve this issue by using multiple fixed filters to capture various patterns, these filters remain static and cannot adapt to the specific context or temporal variations at each position the sequence. This limits their expressiveness in modeling evolving user preferences, especially when user interests shift rapidly over time.
This reveals a fundamental trade-off:: convolution excels modeling local patterns but lacks flexibility, whereas self-attention is expressive but inefficient and insensitive to locality. To bridge this gap, we propose a new architecture called Kime-Varian Convolutional Filters for Sequential Recommendation (TV-Rec), which captures both local and global patterns while achieving greater efficiency than existing hybrid models such as AdaMCT and BSARec. We design time-varian convolutional filters to effectively capture temporal variations and emphasize the most relevant elements at each time step. Our key finding that existing complicated models based on self-attention and convolutional filters can be replaced with our time-variant convolutional filter.
Inspired by graph signal processing (GSP), reinterpret SR as line graph and, instead of using fixed convolution filters, apply time-variant graph filters, analogous to node-variant filters in the graph domain. These filters enable us effectively adapt weights across the sequence, eliminating the need for positional embeddings while directly encoding temporal signals. Moreover, the time-variant filters act as linear operators, resulting in faster inference with lower complexity.
To evaluate the effectiveness of TV-Rec we conduct extensive experiments on benchmark datasets. Our results indicate that TV-Rec consistently outperforms state-of-thee the-art baseline methods. Addi- tionally, we perform a series of experiments comparing the theoretical and practical complexity of TV-Rec with other recent hybrid baselines that combine convolution and self-attention. These experi- ments demonstrate improved recommendation accuracy and enhanced generalization capabilities. The contributions of this work are follows:
We propose Variant Convolutional Filters for Sequential Recommendation (TV-Rec), using varianariant convolutional filters to capture temporal dynamics and user behavior patterns more effectively (Sec.
We show that TV-Rec provides more expressive generalization (Sec. 3.4b and effectively captures both long-term preferences and recent interests via filters designed as functions of time (Sec.
We conduct extensive experiments on 6 benchmark datasets, and the results demonstrate that TV-Rec outperforms ofte-offtth-arr baseline methods by an average of 7. 7.49% (Sec. (.2). while achieving the optimal balance between accuracy and efficiency (Sec. (.6).
2
Preliminaries
In this section, we present the problem statement and the notations used in this paper. We then discuss GSP and the vori-variant graph filter, which are core components of TV-Rec.
2.1 Problem Statement
SR aims to model user behavior sequences based on implicit feedback predict and recommend the user's next interaction. Assume that we have a set of users 24 and set of items V. where [24] and [>] denote the total numbers of users and items, respectively. The interacted items of each user u e Z/ can (4)
(u) be chronologically ordered into sequence s(u) = [o[ 22 ...., "|stsy where of represents the
(u)
i-th item in the sequence of user u. For simplicity, the superscript (u), which indicates the user, will

---

be omitted henceforth. Therefore, the goal is to predict p(u s|+1 = 1/ S) and recommend a Top-r list of items as potential next interactions in the sequence.
2.2 Graph Signal Processing (GSP)
Our method, TV-Rec, incorporates key concepts from GSP. GSP analyzes signals on graphs, with graph filtering as a core operation that emphasizes or suppresses specific frequency components of the signal. Given a shift operator S RRNN,, which can be an adjacency matrix Laplacian matrix, graph filter G is defined as polynomial of S:
K
y=
Gx Gx
Σ S k=0
(I)
where x E R. a graph signal, hy are filter taps and K is the order of the filter.
This operation can be interpreted in the frequency domain using the graph Fourier transform (GFT), which enables the decomposition of graph signals into different frequency components. Given shift operator S, the GFT is defined using its cigen-decompositior
diag(A)U
where the matrix of cigenvectors, À is the vector of eigenvalues, and diag(-) indicates construct- ing diagonal matrix from vector. The GFT of a graph signal x is x U xr, and the inverse GFT is x = UX. In the frequency domain, the graph filter acts on the transformed signal x:
G
Σ ha diag diag(A)*)
where G forms diagonal matrix, allowing the calculation between the graph filter and the signal to be element-wise multiplication. The filtered signal in the time domain can be obtained by applying inverse GFT, y Uý.
In SR, GSP can be utilized to model user behavior sequences as graph signals by representing items as nodes in line graph. By applying graph filters, we can capture the complex dependencies between items and enhance the predictive performance of SR. Graph convolution in this setting aggregates information from neighboring items in the sequence, which are close in time, allowing the model to learn both local and global patterns in user interactions.
2.3 Variantriant Graph Filter
We focus on node-variant graph filters (28 7l. that apply distinct filter taps at each node position. As shown in Fig. [ conventional graph convolutional filters introduced above use a scalar as the filter tap (hx), whereas node-variant graph filters Gnv use vector (ha) for the filter tap, as follows:
K
= G
Σ l==
diag(h:)S*
where diag() indicates constructing diagonal matrix from vector, meaning that every node has different filter tap h2 [6( 11g ..... fig (N)) The set of filter taps can be represented in matrix form as E (K+() where the k-th column is h2-
While conventional graph convolutional filters are calculated by element-wise multiplication of the frequency responses of the graph signal and the filter, the frequency response of a node-variant graph filter is given as follows:
y = UT (HA ))x,
(5)
"In the general case, the GFT considers the Jordan decomposition S vJV-1 but we assume that S is diagonalizable matrix, the Jordan decomposition is equivalent the digendeecomposition.

---

hpp
h2
hz
(0)
(0)
(0))
ho
P2
lt
No
ngg
h₂
P2
h
Multiply
Multiply
X
X1
X2
O
0
Xp
X1
X
0
0
Sum
Sum
Yo Y1 3/2
Ya
Fixed Filter
(h) Care-Variant Convolutional Filter
Figure 1: Comparison of fixed filter in (a) and a variant convolutional filter in (b) under line graph expression of a sequence signals 24, with K = 2 and 3. The output yj, i... the filtered signal at index is produced by summing the filtered results. Arrow colors show each filter's contribution to the output y,, while different h; box colors represent different filters. In the fixed filter case in (a), the same filter h2 is applied to every node, while the time-variant convolutional filter in (b) allows each node to have its own filter.
where A [X++1 is Vandermonde matrix given by A₁ X wise product of matrices. The proof for the frequency response of the node-variant graph filter can be found in Appendix A
1 and denotes the element-
Node-variant graph filters provide a flexible, general approach to creating operators while preserving local implementation, effectively adapting to changing preferences. In line graph context, where each node represents a distinct time point, these filters function equivalently to time-variant convolutional filters. filters..
For consistency, will use this term in the following sections.
3 Proposed Method
Prediction Layer
Graph Fourier Transform (GFT)
In this section, present the design of TV-Rec. As shown in Fig. 2 TVV- Rec consists of modules: embedding layer, time-variant encoder, and pre- diction layer.
Add & Norm
$
dig(()
Feed Forward
GFT matri:
A
IGFT matrix:
Add & Norm
3.1 Embedding Layer
Element-wise
We first convert user's historical in- teraction sequence S to a fixed length N. If [S] 2 N, we truncate the se- quence keeping the most recent N items, and if |S] N, pad the sequence with zeros at the beginning. This process results in sequence of length N. denoted as (81, 82, ..). Using the item embedding matrix E E R VIxD where D the latent dimension size, we then apply a look-up operation to obtain the embedding representation of the sequence, followed by layer normalization and dropout. This process produces the final embedding of the user sequence X serving as the input for the time-variant encoder:
Filter Layer
multiplication
X
(U (HAT) ))TX
Embedding Layer
IGFT
Filter
GFT
Figure 2: Architecture of proposed TV-RRe.
x (Lopouu(LayerNorm/
E.ys E.N
(6)
where E, denotes the embedding of item from E. Note that positional embedding is not necessary due to the benefits of applying our time-variant convolutional filters.
'A Vandermonde matrix has rows formed by the powers of of values, with each element in the i-th row and j-th column given by z!

---

3.2 Time- Variant Encoder
Time-Variant
We build our item encoder by stacking variant encoding blocks, each containing filter layer, a feed-forward network, and residual connection applied after both.
Filter Layer. In the E-th filter layer. with X as the input, we perform a filtering operation, then apply a residual connection and layer normalization, As shown Fig. we first transform X into the frequency domain as X U X where denotes the GFT matrix derived from a padded directed cyclic graph (DCG), which we adopt in place of a line graph ensure diagonalizability and enable spectral filtering (see Appendix [ for formal justification). Then, we calculate the time-variant convolutional filter using the filter tap H E CNx(K-1) and the Vandermonde matrix
RR (x(+)),));
G X (U (HA )) = (U (HA J
(7)
where indicates element- wise multiplication. Note that the inverse GFT matrix U is multiplied with the filter earlier than it is with the frequency response of the signal X To enhance expressive power, construct the filter matrix H follows:
H CB B
(8)
[B12
where C E NNm is the coefficient matrix that generates position- speciofc filters, and B E (m)(K+1) the normalized basis matrix. The parameter m determines the number of basis vectors. Since each node corresponds to position in the sequence, C can be considered as function of time. For numerical stability, we normalize B using the 1.2 norm along each row.
After Eq. ,, we use a residual connection with dropout and layer normalization to prevent overfitting:
F LayerNorm X Dropout x()).
Feed Forward Layer.
After the filter layer, we employ feed-forwart network for non-linearity:
F' FFN(F")) (GELU(F'W) + W bg.
(10)
where WT W DDD and by. by E DxD are learnable parameters. As in Eq. (9) apply
dropout layer, residual connections, and layer normalization to get the output of lts layer as follows:
x LayerNorm(F' + -Dropout(F*))
(11)
3.3 Prediction Layer and Training
Prediction Layer. After processing through L time-ariane encoding blocks, we compute the user's preference score for each item the entire item set follows:
p( = v|S) E. X
(12)
where E, is the embedding of item and X is the final sequence representation.
Model Training. Similar to other studies 29
we optimize our model using cross-entropy
loss Loe with an orthogonal regularization term Lurtho on the basis matrix B used in Eq. (
= - log
exp(ūn)
+a
(1 B real
I + B Bimag B
1
I
(13)
Σ EvEy exp(Ur)
imag
C.
Cotto
where g the ground-truth item, B and Bimay denote the real and imaginary components of B, a controls the regularization strength, I denotes the identity matrix, and F denotes the Frobenius norm.
5

---

3.4 Discussion
Relations to Other Methods. From a graph filtering perspective, several existing SR methods can be viewed as special cases within our tame-variant filter. In particular, 1D CNN in AdaMCT corresponds to a fixed graph convolutional filter, G in Eq. D. where K' is the kernel size. Similarly, FMLPRec and BSARec apply the discrete Fourier transform (DFT), mathematically equivalent to the GFT of DCG 127 26 29), representable G in Eq. 3 Our time-variant filter is a more general method that can be reduced to these approaches as special cases when the filters are fixed. By contrast, Transformer- based studies that interpret self-attention via graph filtering 4 34 differ from our approach, as TV-Rec reformulates SR as graph signal filtering without relying on self-attention.
Comparison to GNN-based Methods TV-Rec relates to GNN-based methods that model item dependencies through fiem-transition graphs [35 37 45), but differs in two key aspects. First, TV-Rec defines sequence positions rather than items as graph nodes. This enables the model to capture fine-grand tee-ggained temporal and positional dependencies that are often ignored when identical items are merged in graph. Second, while GNN-based models rely on iterative message passing, TV-Rec employs time-variant graph convolutional filters directly in the spectral domain without recursive propagation, yielding more efficient representation of temporal dynamics.
Why We Need Variant Graph Filters? In Fig. [ fixed filter applies the same weights in the sequence, emphasizing recent items. However, it also makes it difficult to capture specific patterns different stages. For instance, while the patterns at the end of the sequence may highlight recent items, the patterns at the beginning can provide crucial insights into the user's 's overall preferences. As result, the fixed filter may lose valuable information, particularly when attempting to understand carly-stage patterns. In contrast, our time-variant filter uses different filters for each position, allowing the model to capture both recent items and long-term preferences.
Why Pusitional Encoding is Unnecessary? Unlike Transformer- based models that require explicit positional encodings, TV-Ree naturally encodes positional information via the spectral properties of the graph. Since TV-Rec constructs DCG and applies the GFT, it shares the same frequency components as sinusoidal encodings (see Appendix C). Furthermore, the time-variant graph filter acts as a position-specffic operation, dynamically modulating frequency components without requiring additional embeddings. In Sec. 4.3 we confirm that adding positional embeddings does not offer a performance benefit.
Time Complexity. Assume that n is the length of the input sequence and d is the dimension of each input vector. The time complexity of self-attention is O(n + n²dd, where O(nd²) is for computing the key, query, and value matrices, and O(ndd) is for calculating the attention scores and applying them to the value matrix. The time complexity of our time-variant convolutional filter is O(n2m + ndd), where O(n2m) is for computing the filter tap H. and ((n2d) f) is for applying GFT to the input signal and multiplying it with the filter tap. Since m I n, this can be simplified to Onn" + n² d). The difference in complexity between self self-attention and the time-variant graph filter depends on the relative sizes of n and d, as it determines which term dominates. It is worth noting that the time-variant convolutional filter is a linear operator, G does not need to be computed for every inference, and can be precomputed after training, resulting in a time complexity of (n?
4 Experiments
4.1 Experimental Setup
We evaluate TV-Rec on benchmark datasets for SR, following the preprocessing procedures in 47 46]. For standard experiments, we set the maximum sequence length N to 50. Additionally, to examine performance on long-range dependencies, we conduct experiments on ML-1M and Foursquare with longer average interactions, setting N to 200. For evaluation, we use standard Top-r metrics (HR @r and NDCG@r for r E (5, 10, 20)) computed over the entire item set without negative sampling 200. Detailed experimental setups, including dataset statistics and optimal hyperparameter configurations, are provided in Appendix
D The source code is publicly available at h/t
github. www.un..coo/eeejjjjae in- shin/TV-Rec

---

Table 2: Performance comparison of different methods. Best results are in bold and second-best results are underlined. 'Improv.' indicates the relative improvement against the best baseline.
Datasets
Metric
Caser
GRU[Rec SASRec BERT4Rec NexifiNet FMI FMI.PRec DuoRec LRURRec AdaMCT BSARec TV-Rec Improv.
HR@5
0.0149
0.0170
0.0368
0.0491
0.0549
0.0423
0.0680
0.0648
0.0675
0.0714
0.0721
0.98%
HR
0,0253
0.0307
0.0574
0,0742
0.0779
0.0639
0.0944
0,0889
0.0925
0.0990
0.1017
2.73%
HR
0,0416
0.0499
0.0860
0.1079
0.1100
0.0949
0.1279
0.1197
0.1299
0.1393
0.1403
0.72%
Beauty
NDCG@5
0.0089
00105
0.0241
0,0318
0,0392
0.0272
0.0485
0.0472
0.0489
0.0501
0.0513
2.40%
NDCG@ 10
0.0122
0.0149
0.0307
0.0399
0.0467
0.0341
0.0570
0.0549
0.0569
0.0590
0.0608
3.05%
NDCG@20
0.0164
0.0198
0.0484
0.0547
0.0419
0.0654
0,0627
0.0664
0.0691
0.0705
2.03%
HR@5
0.0091
0.0131
0.0215
0.0279
0.0311
0.0222
0.0390
0.0351
0.0386
0.0422
0.0431
2.13%
HR@10
0.01477
0,0211
0.0319
0,0434
0,0458
0.0358
0.0549
0.0502
0.0544
0.0623
0.0635
1.93%
Sports
HR
0.0253
0,0347
0.0485
0.0658
0.0682
0.0549
0.0779
0.0698
0.0769
0.0865
0,0880
1.73%
NDCG@5
0.0064
0.0084
0.0142
0.0122
0.0212
0.0148
0.0242
0.0272
0.0296
0.0298
0.68%
NDCG@ 10
0.0082
0.0110
0.0178
0.0232
0,0260
0.0191
0.0328
0.0291
0.0322
0.0361
0.0363
0.55%
NDCG@20
0.0109
0.0144
0.0217
0.0288
0,0316
0,0239
0.0385
0.0340
0.0379
0.0422
0.0425
0.71%
HR@5
0.0131
0.0137
0.0165
0.0243
0.0247
0.0195
0.0277
0.0240
0.0239
0.0260
0.0290
4.69%
HR
0,0230
0.0267
0,0411
0,0425
0,331
0.0450
0.0396
0.0404
0,0446
0.0474
5.33%
Yelp
NDCG@5
20
0.0080
0,0388
0.0086
0,0412
0.0445
0,0103
45100
0,0681
0,0894
111151
0.0518
0,112
0.0179
0.0730
0.0151
0.0656
0.0670
0.0153
0.0162
0.0718
0.0186
0.0777
6.44%
3.91%
NDCG@ 10
0,0112
0.0119
0.0135
0,0208
0.0208
0,0100
0.0234
0.0201
0.0206
0.0222
0.0245
4.70%
NDCG@20
0.0151
0,0162
0.0180
0.0275
0.0276
0.0211
0.0304
0.0266
0.0272
0.0290
0.0321
5.59%
HR5
0.0303
0.0339
0.0422
0.0388
0,0431
0.0450
0.0404
0.0358
0.0468
0.0505
0.0596
18.02%
IR 10
0,0459
0,0600
0,0624
0.0670
0.0587
0.0532
0.0716
0.0679
0.0853
19.13%
LasiFM
HR
0.0606
0.0550
0.0972
0.0908
0,0916
0,1000
0.0872
0.0807
0.1018
0.1119
0.1202
7.42%
NDCG@5
0.0222
0.0231
0.0301
0,0213
0,0264
0,0321
0.0276
0.0257
0.0330
0.0348
0.0402
15.52%
NDCG@10 0.0269
0.0249
0.0382
0,0291
0.0325
0.0392
0.0336
0.0312
0,0409
0.0405
0.0484
18.34%
NDCG@20
0,0306
0,0288
0.0458
0,0366
0,0402
0.0475
0.0407
0.0380
0.0485
0.0514
0.0572
11.28%
HR
0,1033
0.1225
0. 1406
0,1651
0,1858
0.1329
0.1821
0.1916
0.1773
0. 1909
0,2013
5 5.06%
HR@10
0.1671
0,1925
0,2199
0,2442
0,2724
0,2089
0.2690
0.2848
0,2560
0.2798
0.2904
1.97%
ML-IM
2R
0,259
0.2906
0.3250
0,3459
0.3853
0.3212
0.3757
0.3886
0.3647
0.3844
0.4079
4.97%
NDCG@5
0.0663
0.0779
0.0920
0.1077
0.1264
0,0861
0.1226
0.1339
0.1185
0. 0.1286
0.1371
2.39%
NDCG@ 10
0.0868
0.1006
0.1174
0.1332
0.1543
1,1
0.1507
0,1640
0.1438
0.1573
0.1658
1.10%
NDCG@20
0.1
0.1253
0,1438
0.1588
0.1829
0. 0.1388
0.1776
0.1901
0.1711
0.1836
0.1955
2.84%
HR@5
0,0139
0.0148
0.0139
0.0139
0.0129
0.0120
0.0139
0.0148
0.0157
0.0148
0.0175
11.46%
HR
0.0175
0,0157
0.0185
0.0157
0,0175
0.0175
0.0185
0.0166
0,0185
0.0212
0.0259
22.17%
Fourquuae
NDCG@5
0,0268
0.0099
0.0231
0.0110
0,0102
0.0268
0.0108
0.0231
0.0093
0,0203
0.0076
0.0240
0.01 10
0.0240
0.0110
0.0212
0.0259
0.0105
0.0111
0.0277
0.0134
0.0314
13.36%
20.72%
NDCG@ 10
0.0110
000113
0.0117
0.0113
0.0108
0.0094
0.0124
0.0116
0.0113
0.0130
0.0161
23.85%
NDCU@20 0.0133
0.0132
0.0137
0.0132
0,0115
0.0110
0.0139
0.0127
0.0131
0.0147
0.0176
19.73%
Table 3: Results of long-range modeling performance.
Datasets
Metric
Caser
GRU4Ree SASRee
BERT+Roe NextliNet FMLPPec DuoRee LRURce AdaMCT BSARee
TV-Ree Improv.
HR@5
0,1
0.1518
0.1558
0.1730
0.1978
0.1397
0.1930
0.2233
0.1760
0.1949
0.2255
0.99%
HR@10
0.1869
0.2374
0,2399
0.2573
0,2882
0.2296
0.2795
0.3175
0,2619
0.2917
0.3232
1.80%
ML-IM
HR
0.2942
0.3455
0.3551
0.3695
0.3970
0,3462
0.3854
0.4205
0.3695
0.4005
0.4306
2.40%
NDCG@5
0.0696
0.0981
0.1014
0.1147
0.1334
0.0885
0.1292
0,1316
0.1167
0.1327
0.1572
3.69%
NDCU@10
0,0939
0.1256
0.1285
0,1418
0.1175
0.1571
0.1820
0.1441
0.1639
0.1886
3.63%
NDCG@20
0,1209
0.1528
0.1576
0.1701
0,1901
0.1468
0.1838
0.2079
0.1715
0.1913
0.2157
3.75%
HR
0.01.9
0.0120
0.0111
0.0102
0,0083
0.0120
0.0120
0.0129
0.0120
0.0129
0.0148
6.47%
HR 10
0.0194
0.0157
0.0175
0,0157
0.0166
0.0148
0.0194
0.0139
0.0157
0.0175
0.0212
9.28%
HR@
0.0231
0.0194
0.0295
0.0240
0.0259
0.0194
0.0286
0.0185
0.0305
0.0305
0.0323
5.90%
Foursquare
NDCG@5
0.0105
0,0099
0.0085
0.0078
0.0068
0.0087
0.0078
0.0099
0.0094
0.0089
0.0108
2.86%
NDCG@ 10
0.0125
0.0111
0.0105
0.0096
0.0095
0.0096
0.0102
0.0102
0.0106
0.0103
0.0129
4.88%
NDCG@ 20 0.0133
0.0120
0.0136
0.0117
0.0118
0.0108
0.0126
0.0114
0.0142
0.0135
0.0158
11.27%
4.2 Overall Performance
Sequential Recommendation Results. As shown in Table 2. TV-Rec outperforms all baseline methods, with an average accuracy improvement of 7.49% over the strongest baselines. The im- provements are particularly significant on LastFM (19.13% on HR @ 10 and 18.34% on NDCG@ 10) and Foursquare (22.17% on HR @ 10 and 23.85% on NDCG@ @ 10). On larger datasets like ML- TV-Rec still shows gains with improvements of 5.06% on HR @ 5 and 2.39% on NDCG@5. However, for E-commerce datasets like Beauty and Sports, the improvements are more subtle but still consistent (0.98% and 2.13% on HR @5, respectively). Among the baselines, recent hybrid methods that combine convolution and self-attention, such as AdaMCT and BSARec, show strong performance. BS achieves the second-best results in many cases. For ML-1M, LRURec shows competitive results with its specialized architecture for long sequences, while DuoRec achieves second- best performance for Yelp. Despite these strong baselines, TV-Rec consistently outperforms them by significant margins.
7

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Table 4: Results of performance comparison with GNN- methods.
Beauty
Sports
Yelp
LastFM
MI.IM
Foursquare
Methods
H@
N@
H@:00
N@
H@
N0
H@20
N@20
H@
N@
H@
N@20
TV-Ree
0.1403
0.0705
0,0880
0.0425
0.0777
0.0321
0.1202
0.0572
0.4079
0.1955
0.0314
0.0176
SR-GNN
0.0847
0.0374
0.0517
0.0224
0.0609
0.0252
0.0872
0.0379
0.2940
0.1390
0.0222
0.0137
GC-SAN
0,1059
0.0546
0.0608
0.0289
0.0635
0.0260
0.0807
0.0394
0.3255
0.1611
0,0212
0.0131
GCLASR
0.1206
0.0601
0.0744
0.0356
0.0684
0.0276
0.0908
0.0398
0.3381
0.1607
0.0185
0.0123
Table 5: Ablation studies.
Beauty
Sports
Yclp
LastFM
ML-IM
Foursquare
Methods
H@20 N@
20
N@20
H@20 N@20
H@20
N@20
H@-20
N@ 20
H@:2 N@
TV-Rec
0.1403 0,0705
0,0880
0.0425
0.0777
0.0321
0.1202
0.0572
0.4079
0.1955
0,0314 0.0176
(1) Positional Emhedding
0.1408 0.0702
0.0842
0.0396
0.0763
0.0320
0.1018
0,0496
0.4017
0.1936
0.0313
0.0160
(2) Basic Gruph Filter
0.1402 0.0692
0.0857
0.0408
0.0747
0.0307
0.1165
0.0543
0,3974
0.1933
0.0212
0.0113
(3) Identity Basis
0.1400 0.0698
0.0851
0.0410
0.0765
0.0317
0,1138
0.0539
0.4015
0.1930
0.0277
0.0141
(4) Basis Normalization
0.1336 0.0689
0,0841
0,0412
0.0634
0,0264
0.0963
0,0418
0.3985
0.1912
0.0305
0.0144
Long-Range Sequential Recommendation Results. To examine the performance of TV-Rec on long-range dependencies, we additionally conduct experiments on ML-1M and Foursquare, which have long average interaction length, by setting the maximum length N to 200. As shown in Table 3 TV-Rec outperforms all baseline models in long-range SR tasks. Our model achieves an average improvement of 4. 74% on all metrics compared to the top baseline performances. The improvement is particularly significant in NDCG metrics, with TV-Rec showing up to 1 11.27% gain in NDCG@ 20 for Foursquare. For ML- 1M, we observe that LRURec performs strongest among baselines due to its linear recurrent unit designed for long sequences. For Foursquare, Caser and AdaMCT show the highest baseline performance. The superior results of TV-Rec on these settings show the effectiveness of our time-variant filters on extended user interaction histories. This shows the ability of our approach to maintain recommendation accuracy even when processing sequences with hundreds of interactions.
Comparison to GNN-based Methods. To further examine its effectiveness. we also compare TV-Rec with three representative GNN-based sequential recommendation models: SR-GNN GC-SAN (37, and GCLASR (45, under the same experimental settings described in Section 4.1
35
While most GNN-based recommendation methods are tailored for collaborative filtering on static user-item graphs, these GNN-based sequential models utilize item-transinn crn--rraniiion graphs to model local or global item dependencies. As shown in Table TV-Rec consistently outperforms all GNN-based sequential models, confirming the advantage of its time-variant filtering design. By operating directly on sequence positions instead of propagating messages over item-transition graphs, TV-Rec achieves more efficient representation of temporal dependencies.
4.3 Ablation Studies
We conduct ablation studies validate the design choices of TV-Rec. The results are shown in Table 5 (1) First, we test an ablation model with added learnable positional embeddings. Unlike recent SR models (29 177. TV-Rec performs effectively without positional embeddings because our time-variant filter inherently captures position-specific information. The first ablation model yields inconsistent results on all datasets. (2) Second, we define the second ablation model by replacing our viriintriant filter with basic graph filter. This ablation model degrades the performance, which confirms the effectiveness of our method as discussed in Sec. 4.5 (3) Third, validate our filter construction method (Eq. 8), we define the third ablation model by setting B as an identity matrix, which makes H equal to C. This ablation model degrades results compared to our filter construction method. (4) Fourth, we compare against the fourth ablation model that uses the basis matrix B directly without normalization, demonstrating the effectiveness of our normalization approach. These results prove that each component of our design contributes to the superiority of TV-Rec.
8

---

4.4 Parameter Sensitivity
We analyze the sensitivity of the parameters m and dropout rate p, as shown in Figs. other hyperparameters are fixed at their optimal values. Additional results, including sensitivity to filter order and weight decay a, are provided in Appendix
3 3
All
Sensitivity to m. We employ basis matrix B in the time-variant graph filter (Eq. (8), where controls the number of basis vectors, influencing both expressiveness and computa- tional cost. As shown in Fig. B performance on Beauty peaks at m 32 but drops sharply for smaller values, indicating the need for richer representations. Conversely, LastFM achieves its best results at m = 8, with performance degrading as m increases, suggesting that compact representation suffices for this dataset.
0.006 0.08 0.000
1 0:40
0,66
NDCG@20
HRB20
NDCG@20
HR
NDC6820
NIDC G02 HR
(a) Beauty
(h) LastEM
Figure Sensitivity to the number of basis vectors
m.
NDCG@20 810570.0099 80047
0.008
0.13
Sensitivity to p. The effect of dropout rate p on Sports and Foursquare is shown in Fig. For Sports, larger p values improve perfor- mance, while for Foursquare, smaller p values work better. Datasets with fewer interactions tend to benefit from higher dropout rates, which help prevent overfitting by encouraging more general representations.
NDCG@20
HR@20
0.0% Luus
NIDC 20
6
HRg000
HRgg20
0.1
0.2
0.3
0.4
0.5
0.1
02
0.3
0.4
(a) Sports
(b) Foursquare
Figure 4: Sensitivity to dropout rate p.
4.5 Analyzing Filter Behavior and Case Study
To understand why our time-variant filter works better than fixed basic graph filter (3). we analyze their learned repre- sentations via visualizations and a case study. Fig. rreeelss the key difference be- tween approaches: the basic graph filter applies the same filter to all nodes, while our variant filter applies different filters to each node.
0.10
0.15
20
0.08
30
0.05
40
0.02
0.00
50
10
20
30
40
20
30
40
50
Shift
Shift
Both filters assign higher weights to lower shifts, meaning they give stronger weights recent items. However, unlike the basic graph filter, the time-variant convolutional filter starts with similar weights for the etrly-stage nodes, reflect- ing the model's s focus on understanding overall patterns. As the sequence pro- gresses, the filter's weights shift to em- phasize recent items, allowing the filter to capture temporal shifts more accurately. This shows the to adapt to both early and recent changes, boosting performance.
(a) Basic Graph Filter
(b) Time- Time-Variant Filter
Figure 5: Visualization of learned graph filters on LastFM. The x-axis denotes the number of shifts in graph convo- lution, while the y-axis represents individual nodes, with higher numbers indicating more recent time points.
O-ana
Comedy
Action
Westom
Fixed Filtar
Time-Variant Filter
Earty-stage
Mid-stage
Recent
filter's ss ability
Comedt
Comcay
Figure 6: Case Study ML-IM.
Our case study on ML- (see Fig. 6 shows this advantage in practice. The ba-
sic graph filter focuses solely on Western films from recent interactions, while our time-variant filter captures both user's s recent Western interest and their broader Comedy preference. These findings confirm our statement that applying different filtering operations at different temporal positions important for effective sequential recommendation.

---

4.6 Model Complexity and Runtime Analyses
To evaluate the efficiency of TV-Rec, we analyze the number of parameters and inference time. The results
TV Roc BSARec
RGaMCT
across the full dataset are provided in the Appendix G As shown in Fig. 7 TV-Rec achieves the best balance be- tween performance and computational efficiency. Among lop-performing methods, TV-Rec has the fastest inference time with the smallest number of parameters, compared to hybrid models that combine convolution and self-attention, such as AdaMCT and BSARec. Compared to SASRec and BERT4Rec, which only self-attention, TV-Rec pro- vides faster inference time and superior recommendation accuracy. While FMLPRec runs slightly faster with its sim- ple architecture, it achieves this through a basic graph filter that degrades recommendation quality. Considering the improved performance of TV-Rec, the marginally higher inference time than FMLPRec is acceptable.
NDCG@20
NextiiNet
BERTAReC
FMLPPRec
0.04
SASRec
0.03
Caser:
PRoC
SASRcc
AdaMCT
0.02
NextitNict
BERT4Rec
TV-Rec
RSARec
Caser
0.6
0.7
0.9
1.
Inference Time (seconds)
Figure 7: Comparison of model infer- ence time and NDCG@t @ 20 on Beauty, The size of each circle corresponds to the number of parameters.
Related Work
5.1
Sequential Recommendation
SR has evolved from early approaches that used Markov chains 225 and RNNs 14] to model sequential dependencies. Transformer-based models such as SASRec 18 and BERT4Rec use self-attention to capture global dependencies and establish new performance benchmarks. Recent advanced methods have emerged to address specific challenges and
trade-offs in SR. FMLPRec [7] proposes a filter- enhanced MLP to eliminate frequency domain noise, while FEARec 6 and DuoRec 24 use contrastive learning approaches for better sequence representa- models. LRURee 43 explores linear recurrent units to halance efficiency and performance. In addition, SR 10 have been explored for potential in
tion. AC-TSR 48 calibrates unreliable attention weights generated by Transformer-basee
models 22
40
33 based on state space models
SR.
5.2 Hybrid Approaches and Convolution SR
competitive alternatives 5] The first to use convolution in SR was Caser [31, which treats user-item interactions as images for 2D convolutions, followed by NextItNet (4). which uses dilated ID convolutions. FMLPRec 477 incorporated Fourier transforms within an all-MLP architecture to enhance sequence representations. AdaMCT [17 incorporates ID convolution into Transformer-basse recommendation model to capture both long-term and short-term user preferences.
Recent research has shown that convolution- based methods
existing SR methods 31 38 39
47
17
29
BSARec 29 has recently achieved state-of-the-arr results by addressing the limitations of self- attention through the application of convolution using the Fourier transform. However, these models typically require self-attention to achieve optimal performance. Our work differs by introducing time-variant convolutional filters that achieve high performance without relying on self-attention.
6
Conclusion
We focus on the inherent limitations of conventional convolutional filters. Since these filters are fixed, they may struggle to capture the complex patterns required for SR. To address this issue, we introduce TV-Rec, which uses time-variant convolutional filters that apply different filters to each data point. TV-Rec achieves high performance without relying on self-an self-attention, even in long-range modeling. Our method also benefits from fast inference times due to its linear operator nature. We validated effectiveness and efficiency of T'-Ree through extensive experiments on datasets. future work, we plan to explore both the theoretical and practical relationships between our time-variant filter and recent advances state space models, which have demonstrated strong connections with convolutional filters. We leave limitations in Appendix
10

---

Acknowledgments
This work partly supported by the Institute for Information & Communications Technology Planning & Evaluation (IITP) grants funded by the Korean government (MSIT) (No. RS-2022- 13220113, Developing Sustainable Collaborative Multi-modal Lifelong Learning Framework), Samsung Electronics Co., Ltd. (No. G01240136, KAIST Semiconductor Research Fund (2nd)), and Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-IT2402-08.
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The main claims clearly stated in abstract and introduction: we address the limitation of existing convolution-based sequential recommendation models and introduce
TV-Rec.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No
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is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
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Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification:
We discuss the limitation of our work Appendix J
Guidelines:
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The authors are encouraged to create a separate "Limitations" section in their paper.
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Supplementary Materials for 'TV-Rec: Time-Variand Convolutional Filter for Sequential Recommendation"
A Proof of Frequency Response of Variant Graph Filters
In this section, we provide detailed proof of the frequency response of the node-variant graph filter Goy stated in Eq. (5), following the derivation in 7
Proof. We begin by considering the definition of the node-variant graph filter. Let E RN represent the input graph signal, S IR XxN represent the shift operator, and let h& be vector of filter taps. By using the node-variant graph filter Gnes the output graph signal y calculated follows:
K
G
diag(h;)S*
(14)
k==
where diag(-) indicates constructing a diagonal matrix from a vector, and K is the order the filter. Recall that the frequency response the input signal & is U x, and similarly ý = U y, where the shift operator S is eigen-decomposed by S = U diagg()) (A)U" which results in:
K
y y U= y= U
diag hy ) x
(15)
U
diag(h; (h:) diag(>*)
(16)
where A CN is the k-th column of Vandermonde matrix A (x+(k))) given by A
[X*], X The set of filter taps hg can be represented in matrix form as H (Nx(K+1) Each
element of the summation in Eq. (16) as follows:
diag(h; U diag(A*)
Σ
n
Xf
(17)
if
k=0
Uij
(18)
where (/ is the i-th row and k-th column of H. Using the matrices H and A, holds that HA T CNNN
E
K
HA
(19)
k==0
Substituting Eq.
19
into Eq.
18 results in:
K
diag(h; U diag(A
- HA J6s
(20)
where denotes element-wise multiplication between matrices.
Therefore, Eq. (16) becomes:
ÿ y= == (HA ()A)))
(21)
This completes the proof.
21

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B Theoretical Justification for DCG-Based Filtering
This section theoretically shows that spectral filtering on the zero-padded DCG is equivalent to filtering on the line graph, ensuring no backward information flow.
To perform spectral filtering, the model must apply GFT, which requires eigen decomposition of the graph shift operator (i.e., the adjacency or Laplacian matrix). However, when the sequence is modeled line graph, the resulting adjacency matrix has rank exactly N because the first node (i.e., the most past item) has no incoming edges. This results in one row of the matrix being entirely zero, making it defective and thus non-diagonalizable.
To resolve this, we model the sequence as a DCG, which differs from the line graph by a single edge connecting the last node to the first. This addition makes the adjacency matrix circulant, ensuring diagonalizability and enabling spectral filtering in the Fourier domain. However, the added edge introduces a backward connection from the future to the past, which could lead to information leakage in the reverse temporal direction.
To prevent reverse information flow while maintaining spectral tractability, we adopt a padding strategy. Specifically, we pad the sequence x E IR- with zeros by forming the extended vector:
ERN
(22)
where E RRK the zero vector. Using the circulant shift operator S E R(N+R)x(N+K)) that represents the DCG, we define spectral filter of order K as follows:
(
S*
(23)
where hy denotes the filter coefficients. The filtered output ý is then computed by applying the filter to the padded input:
y = (S))
(24)
We obtain a result identical to applying the same filter on the original sequence x modeled as a line graph by extracting the first N elements of y as follows:
(25)
where 1 : N denotes taking the first N elements of the vector. This equivalence holds because the last K entries of X zeros. Although the circulant matrix S performs circular shifts, the filter involves powers of up to order K, so these zero entries do not influence the first N output values. Consequently, this effectively blocks any eyclic information flow that would lead to backward leakage.
As result, spectral filtering on the zero-padded DCG provides the correct filtering output equivalent to causal convolution on a line graph, while benefiting from the computational efficiency and diagonalizability of circulant matrices.
C Equivalence of Positional Encoding and Graph Fourier Basis
Unlike Transformers, which require explicit positional encoding (e.g., sinusoidal or learnable). TV- Rec captures positional information inherently through spectral decomposition on DCG. This section provides formal connection between positional encodings in Transformer and the graph Fourier basis used in TV-Rec.
Sinusoidal Positional Encoding in Transformer. The original Transformer model uses sinusoidal functions to encode absolute position pos as follows:
pos
pos
(E(pos.20) = sin (10000//a)
(poee cos
10000
where d denotes the embedding dimension. This produces set of periodic signals with varying frequencies that form basis for encoding positional variation.
22

---

Graph Fourier Basis in TV-Rec. In TV-Rec, we define the shift operator S as the adjacency matrix of directed cyclic graph. Its dggendeccopoosition yields the graph Fourier basis C where:
2
2
U km
22rk//N
cOs
sin
This corresponds to the DFT basis, which is an orthonormal set of complex exponential spanning R* (or C.))
Equivalence in Representational Capacity. While the frequency components used in Transformer positional encodings are sampled on a logarithmic scale and those in GFT are linearly spaced, both sets of basis functions composed of trigonometric functions. As such, they span the same space of length-N periodic signals. Formally, the real-valued DFT basis used in TV-Rec corresponds to sin 2m and cos (2rkn) for various k, which can represent any finite-length sinusoidal signal, including those used in Transformer encodings. Therefore, although the sampling strategies differ, the span of both bases covers the same function space, which indicates that the spectral basis used in TV-Rec is functionally equivalent to the sinusoidal encodings in Transformer models, in the sense that both span the same space of position-dependent trigonometric functions.
Implication for Positional Encoding. TV-Rec projects the input sequence ar the GFT domain as 8 -U* x, and reconstructs it via x: = Uä, thereby implicitly encoding frequency- posi- tional variations. The time-variant filter then modulates these frequency components per position, which makes explicit positional embeddings unnecessary, as position-sensitivy modulation is already embedded in the spectral filtering process. TV-Rec's s design leverages the spectral basis achieve the same functional role as positional encoding in Transformers. It achieves this without requiring explicit embeddings, while retaining full expressiveness modeling temporal variation.
D Detailed Experimental Settings
D.1 Datasets
We evaluate our model using 6 SR datasets that vary in sparsity and domain. We follow the data pre- processing procedures outlined in [46] 47). considering all reviews and ratings implicit feedback.
Detailed statistics can be found in Table 6
Amazon Beauty and Sports are Amazon datasets of product reviews from 233 widely used for SR. For this study, we use the "Beauty" and "Sports and Outdoors" categories.
Yelp" is popular business recommendation dataset. We records from after 2019/01/01 due to its large size.
LLasF includes artist listening records and is used to recommend musicians to users.
ML-1M [12 is a movie recommendation dataset from MovicLens It is commonly used to evaluate recommendation algorithms due to its detailed user interaction data.
Foursquare provides user check-ins across New York city over 10 months (April 2012 to February 2013).
D.2 Baselines
To evaluate the performance of our method, we compare it with the following ten SR baseline methods:
Caser 31 is CNN-based model that captures complex user patterns through horizontal
and vertical convolutions.
httpss/wwww.yepp.com/atttc
"naup://groupleas.or////tt httppp/ppw.....ooaaaaceeeeoonnna
23

---

Table 6: Statistics of the processed datasets.
Users
# Items
# Interactions
Avg. Length
Sparsity
Beauty
22,363
12,101
198,502
8.9
99.93%
Sports
25,598
18,357
296,337
8.3
99.95%
Yelp
30,431
20,033
316,354
10.4
99.95%
LastEM
1,090
3,646
52,551
48.2
98.68%
MI-IM
6,041
3,417
999,611
165.5
95.16%
Foursquare
1,083
9,989
179,468
165.7
98.34%
GRU4Rec 14] a GRU-based model that captures temporal dynamics and patterns in user
interactions.
SASRec
18
is Transformer-base model that uses multi-head self-attention mechanism.
BERT4Rec 30
a bidirectional Transformer-based model, using masked item training
scheme.
NextItNet 42 is CNN-based model that uses dilated convolutions and residual connec- tions capture both short- and long-range dependencies in user behavior sequences.
FMLPRec 47 uses Fourier Transform and learnable filters in an all-MLP architecture to reduce noise and enhance sequence representations.
DuoRec 24 employs model-level augmentation and sementic positive samples for con- trastive learning using SASRec as its base model.
LRURec uSes linear recurrent units for rapid inference and recursive parallelization.
AdaMCT 17 is a hybrid model combining Transformer attention with local convolutional
filters capture long- and short-term preferences.
BSARec 29
hybrid model that combines Transformer self-attention with the Fourier Transform to address the oversmoothing problem.
SR-GNN 35 is session-based recommendation model which converts user sessions into graphs and applies GNNs to capture item transition relationships.
GC-SAN is GNN-based model that dynamically builds graph for each sequence and combines GNN with self-attention to model both local and long-range item dependencies.
GCL4SR 45 is GNN-based model that constructs global item transition graph across users and uses graph contrastive learning to integrate global and local context.
D.3
Metrics
To evaluate the recommendation performance, we use widely adopted Top-r metries, HR @r (Hit Rate) and NDCG@r (Normalized Discounted Cumulative Gain), with r set to 5, 10, and 20. For fair comparison, examine the ranking results across the entire item without negative sampling 20
D.4 Implementation Details
All experiments, including the baselines, were conducted using the following software and hard- ware configurations: UBUNTU 20.04.6 LTS, PYTHON 3.9.7, PYTORCU 2.2.2, CUDA 11.1.74, and NVIDIA Driver 550.54. The hardware setup included dual INTEL XEON CPUs and an NVIDIA RTX A6000 GPU.
Hyperparameters for Standard Sequential Recommendation. We determine the optimal hyper- parameters for the baselines according to their suggested settings. The experiments are performed with the following hyperparameters: learning rates of (5 10-4 x 10-3), 33, orthogonal regularization coefficient of (0, x 10 3 1 x 10 10-5), dropout rates of [0.1, 0.2, 0.3, 0.4, 0.5), and m values of (8. 16, 32). The order of the time-variant convolutional filter K equal to the maximum sequence length N, which is set to 50. The batch size is set to 256, the dimension D to 64, and the number of time-variant blocks I. to 2. We use the Adam optimizer for training. For reproducibility, the best hyperparameter settings are detailed in Table

---

Table 7: Best hyperparameters of TV-Rec.
Dataset
Learning Rate
p
L = 50
Beauty
5 10
0
0.5
32
Sports
5 10
0.5
16
Yelp
5 10
1 1 10
0.1
16
LastFM
1 10
10
0.4
ML-IM
1x 10-3
1x 10
0.3
8
Foursquare
5 10
1 10
0.2
8
L= 200
ML-IM
x 10-3
0
0.1
16
Foursquare
x 10
1 1x
10
0.1
8
0.078
0.070
0.140
0.083
NDCG@20 0.066 0.068
NDCG@20
NDCG@20
0.136 0 138
HR@20
HR@20
HR@20
31 086
0.073 0.075
0.008
NDCG@20
NDCG@20
NDCG@20
HR@20
HR@220
HR@220
16
32
50
8
16
32
50
16
32
50
(a) Beauty
(b) Sports
(c) Yclp
0.058
0.120
0.196
0.408
0.018 0.024 0.031
NDCG@20
0. 0.1
HR@20
NDCG@20
0.193
0.420
HR@20
NDCG@20
HR@20
0.046
NDCG@20
0.10
NDCG@20
20
NDCG@ 20
HR@20
HR@20
16
32
50
16
32
50
32
50
77
m
(d) LastEM
(c) ML-IM
Foursquare
Figure 8: Sensitivity to the number basis vectors m.
E Sensitivity Studies
In this section, we investigate the sensitivity of four hyperparameters: the number of basis vector m. dropout rate p. orthogonal regularization coefficient a and filter order K. The results are shown in Figs. 8 and Table respectively. We keep optimal settings for all other hyperparameters except the one being examined.
Sensitivity to m. In our time-variant graph filter, we use a hasis matrix B E [mx((+11) as shown Eq. (8). The parameter m determines the number of basis vectors, which affects the expressive power and computational complexity. To explore its effect, we extend the initial parameter search range of m {8, 16, 32} to include
{4, 50). Fig. shows NDCG@20 and HR @ 20 by varying m. For Beauty, the best accuracy is achieved with m 32, and both NDCG@20 and HR @20 drop significantly as m decreases. This suggests that for Beauty, a larger number of basis vectors is beneficial, possibly due to the complexity of user-item interactions in this dataset. In contrast, LastFM, the best accuracy is achieved with m 8. and as m increases, both NDCG@ 20 and HR @0 decline dramatically. This behavior may be attributed to the particular characteristics of music recommendation on LastEM, where a more condensed representation is sufficient to capture user preferences.
25

---

0.071
0.140
01.088
0.078
NDCG@20
NDCG@20
NDCG@20
0.069
0.133 136
HR@20
0.083
HR@20
0.073 0.0730.075 0.075
HR@20
01075
0.067
NDCG@20 HR@20
NDCG@20
NDCG@20
HR@20
HR@20
0.4
0.5
(a) Beauty
(b) Sports
(c) Yelp
0.057
0.120
0.408
0.0260.028 0.031 HR@20
NDCG
NDCG@20
NDCG@20
0.042 0.049
0.094 0. 106
HR@20
0.390
HR@20
0.373
NDCG@20
NDCG@20
NDCG@2 20
HR@2
HR.320
HR,220
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
P
P
(d) LastFM
(e) ML-IM
(l) Foursquare
Figure 9: Sensitivity to dropout rate p.
0.078
0.140
0.088
0.032
NDCG@20
NDCG@20
0 0404
NDCG@20
0.138 0. 1399
HR@20
HR@220
HR@20
0.070
0.077
0404
0.085
0.031
NDCG@20
NDCG@20
NDCG@22 20
HR@20
HR@20
HR@20
1o-7
le-5
1e-3
le-1
1e-5
10-3
1e-1
1e-7
le-5
1e-3
1e-1
(a) Beauty
(b) Sports
(c) Yelp
0.057
0,120
0.195
0.403
0.017
NDCG@20
0.055
0:114
HR@20
NDCG@20
401
HR@20
NDCG@20
0.015
HR@20
0108
3335
0.053
NDCG@20
NDCG@20
0.013
NDCG@20
HR
1e-7 1e:5
LastFM
(e) ML-IM
Foursquare
Figure 10: Sensitivity to orthogonal regularization coefficient a.
Sensitivity to p. The effect of the dropout rate is analyzed in Fig. For Sports, larger value of p leads to better performance. Conversely, for Foursquare, lower value of p results in improved performance. Datasets with many interactions tend achieve better accuracy with small p. whereas those with fewer interactions typically perform better with a large p. This is because lower data diversity of datasets with fewer interactions leads model easily overfit. A higher dropout rate helps prevent overfitting by encouraging the model learn more general patterns.
Sensitivity to The parameter search range for a is extended from (0, 1 x 10-3 1 x 10-5) to (0, 10 10-1.1 x 10-3 10-5 10-"), and experiments are conducted with these values. Fig.
10 shows NDCG@20 and HR @20 by varying For LastEM, the best accuracy is achieved
26

---

Table 8: Sensitivity filter order K.
Beauty
Sports
Yelp
LasIFM
ML-IM IM
Foursquare
K
N@20
I1@:20
N@
11@20
N@
II@20
N@20
11@20
N@20
11@20
N@
3
0.1380
0.0690
0.0839
0.0405
0.0731
0.0295
0.1046
0.0443
0.3901
0.1843
0.0240
0.0116
5
0.1364
0.0680
0.0849
0.0407
0,0752
0.0308
0.1147
0.0490
0.3823
0.1814
0.0268
0.0116
10
0.1378
0.0688
0.0853
0.0410
0.0741
0.0303
0.1165
0.0532
0.3922
0.1898
0.0268
0.0139
25
0.1371
0.0684
0.0854
0.0409
0.0774
0.0323
0.1248
0.0546
0.3957
0.1891
0.0295
0.0163
50
0.1403
0.0705
0.0880
0.0425
0.0777
0.0321
0.1202
0.0572
0.4079
0.1955
0.0314
0.0176
Table 9: Results on XLong.
Metrie
SASRee
LRURee
TV-Rec
Improv.
HR@3
0,3612
0.4266
0.4844
13.55%
HR @ 10
0.4680
0.5137
0,5353
4.20%
HR@20
0.5612
0,5874
0.5774
-1.70%
NDCG@5
0.2656
0.3227
0.3905
21.00%
NDCG@11 10
0.2979
0.3510
0.4071
15.98%
NDCG@20
0,3232
0.3697
0.4178
13.01 %
with a = 10 10-3 adequate level of orthogonal regularization is crucial maintain effective filter diversity and prevent overfitting in this dataset. In contrast, for Sports and Yelp datasets, the highest accuracy occurs at relatively lower values, and performance deteriorates noticeably indicate that too strong orthogonal regularization overly constrains the filter parameters, limiting the model's s ability to adapt the data distribution in these domains. These results emphasize the importance of adjusting a based on the characteristics of the dataset, balancing the regularization strength to achieve optimal performance.
3. Both NDCG@20 20 and HR @:20 drop significantly as a decreases, suggesting that an
increases. This behavior may
Sensitivity to filter order K. We analyze the sensitivity of the filter order K, which is equivalent to the kernel size in CNN-based models. As shown Table & except for Yelp and LastFM, 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.
F
Additional Results on XLong
To further test scalability extreme cases, we conducted experiments on the XLong dataset, which contains 69,069 users, 2.12 million items, and approximately 66.8 million interactions. The sequences are exceptionally long, with an average length 958.8 8 and a density of about x 10-4, roughly 20 times longer than in our main experiments. We followed the experimental settings of LRURec 43 and performed the experiments within the LRURee framework. As shown in Table 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-rangs modeling tasks.
G Model Complexity and Runtime Analyses
In this section, we provide a comprehensive analysis of model complexity and runtime efficiency for the entire datasets. Table 10 shows a detailed comparison of our proposed TV-Rec model with 7 baseline models in different datasets. Our TV-Rec consistently shows competitive parameter efficiency in all datasets, maintaining a comparable or slightly lower number of parameters than most advanced baselines. terms of training efficiency, our TV-Rec shows competitive training cost in most datasets, often comparable to or slightly higher than SASRec and FMLPRec. TV-Rec shows strong inference efficiency, often having the lowest or near-lowest inference costs among all models, especially in datasets such Beauty, Sports, and Yelp.
27

---

Table 10: Parameters number and execution efficiency analysis of models.
Dalaset
Metrics
TV-Rec
AdaMCT
BSARec
FMLPRec
NextliNet
BERT4Ree
SASRec
Caser
6 Parameters
854,208
878,208
880,318
851,200
981,696
877.888
877,824
2,909,532
Training Cost (slopoch)
13.20
12.30
11.35
11.85
18.9184
21.98
11.21
65,54
Beauty
Inference Cost (slopoch)
0.5697
0.6647
0,7299
0.5427
1.0267
0.5821
0.6316
1.044
NDCG@20
0.0704
0.0691
0.0664
0.0419
0.0547
0.0484
0.0379
0.0164
# Parameters
1,248, 160
1,278,592
1,264,318
1,251,584
1, 1,644,224
1,278,272
1,278,208
4,835,756
Training Cost (slepoch)
19.46
17.63
18.44
31.60
14.26
98.21
Sports
Inferenze Cost (slepoch)
0,7411
0,9049
0.9679
0.7049
1.2724
0.8016
0,8460
1,5715
2D
0,0428
0,0422
0.0379
0.0239
0,0316
0,0288
0,0217
0.0109
Parameters
1,355,424
1,385
1,365,522
1,358,848
1,751,488
1,385,536
1,385,472
3,925,238
Yelp
Training Cost (slepoch)
21.89
20.87
21.83
20.20
32.88
37.57
16.74
111.62
Inference Cost (s/opoch)
0.6388
0.8527
0.8890
0.6223
1.2348
0.7225
0.7322
1.3220
NDCG@ 20
0.0338
0.0290
0.0272
0.0211
0.0276
0.0275
0.0180
0.0151
# Paramelers
303,440
337,088
322,814
310,080
981,696
336,768
336,704
998,646
Last'M
Training Cost (slopoch)
2.41
2.51
2,66
2.51
19.1253
4.29
2.30
13.22
Inference Cost (slepoch)
0,2649
0,2807
0.3228
0.2678
1,068
0.3018
0,3061
0.3445
NDCG@20
0,0582
0.0514
0.0485
0.0475
0.0402
0.0366
0,0458
0.0306
# Parameters Training Cost (slepoch)
298,368
322,368
308,094
295,360
556,928
322,048
321,984
961,326
26.60
27.68
31.40
24.67
40,7731
46.51
22.50
102.99
MI.IM
Inference Cost (slepoch)
0,4129
0,4180
0.4474
0.3594
0.7269
0.4202
0,4181
0.5817
NDCG@ 20
0.1951
0,1836
0.1711
0.1388
0.1829
0.1588
0,1438
0.1101
# Parameters
719,040
743,040
728.766
716.032
1,108.672
742,720
742,656
1,073,044
Training Cost (slepoch)
6.01
5.79
5.81
5.11
8.9109
9.06
5.27
21.01
Foursquare
Inference (slepocls)
0,2900
0,2913
0.3562
0,2521
0.2871
0.3178
0.3703
2DCG@20
0.0170
0.0147
0.0131
0.0110
0.0115
0.0132
0.0137
0.0133
Table 11: Performance comparison between TV-Rec and the second-bes bascline methods across 6 datasets. Results show the mean and standard deviation for 10 runs with different random seeds using the best hyperparameter settings.
Datascts
Methods
HR@5
HR@ 10
HR #0
NDCG@5
NDCG@ 10
NDCG@20
BSARec
0,069420.001
0.097820.002
0.1352a0.002
0,049620.001
0.058720001
10.081
Beauty
TV-Ree
0.0706e0.001
0.0997a0.001
0.1375#0.002
0.0500e0.001
0.059420001
0.0689#00001
BSARec
0,041720.001
0.0600a0.001
0.084420.001
0,028840.001
0.0349.0001
0.0411
Sports
TV-Ree
0.0420g0.001
0.06 1.00.002002
0.0863+0.002
0.0290a0.001
0.0351
0.0415#0001
DucRec
0.0268=0.001
0.0453+0.001
0.0733+0.011
0.0170
0.0230=0000
0.0300=0.000
Yelp
TV-Rec
0.0284-0.001
0.0472+0.001
0.0759+0.001
0.0179+0.000
0.0240=000t
0.0312+0.00
BSARee
0.0501
0.0707
0.034240.02 0.1051
0.0412=0002
0.0498=0.002
LastFM
TV-Rec
0.0508+0.005
0.0750+0.006
0.1090+0.007
0.0343+0.00
0.0420=a00
0.0506=0.00
LRURee
0.195520.002
0.28 820.002
0.387 L20.002
0. 0.1366a0.02
0.160400002
0.186920.002
ML-IM
TV-Rec
0.2024+0.005
0.2901 +0.005
0.3972+0.005
0. 0.1365=0.004
0. 0.144700008
0. 0.0
BSARec
0.0133+0.003
0.0.7500.003
0.025500.003
0.0098+0.002
0.011 10111+a000 1-0000
0.01 00130+0.00
Foursquare
TV-Rec
0.0151:0.002
0.0214.0.00
0.0289a0.002
0.0105a0.002
0.0126=0002
0.0145:0.002
Overall, TV-Rec presents a balance between model complexity, computational efficiency, and rec- ommendation performance. Our TV-Rec achieves the best performance metrics while maintaining competitive or better efficiency in both training and inference compared to state-of-the ft-thh--rt art models.
H Statistical Significance of Experimental Results
To ensure the reliability of our evaluation, we conducted each experiment using 10 different random seeds under the best hyperparameter settings for both our proposed model and the second-bes baseline model. The second-best models for each dataset are as follows: BSARec for Beauty, Sports, LastFM, and Foursquare; DuoRec for Yelp: and LRURee for ML-IM. We then report the mean and standard deviation of the performance metrics calculated across these runs to reflect variability caused by random initialization. The detailed results, including these statistics, are provided in Table I1
28

---

I
Broader Impact
This work proposes TV-Rec. time-varian convolutional filter for sequential recommendation. Its improved efficiency and performance can positively impact real-world recommender systems by reducing computational cost and energy consumption. However, potential negative societal impacts include reinforcing user biases, limiting content diversity, and risking privacy violations if sensitive user behavior data is mishandled. TV-Rec's reliance on user interaction logs raises concerns about data privacy and fairness in recommendations. To mitigate these issues, we recommend careful data governance, fairness auditing, and the development of
training pipelines.
Limitation
While TV-Rec achieves strong performance and inference-ting time efficiency, it has several limitations. First, the training process of TV-Rec involves some additional computational complexity due to repeated GFT and inverse GFT operations, well the generation of position-specific filters. Moreover, to enable spectral filtering, TV-Rec replaces the original line graph with DCG, which adds extra nodes through padding and increases the dimensionality of the spectral domain. These factors can lead to moderate increases in training time and memory usage. However, as shown in Table IO] this overhead remains manageable and does significantly impact training scalability in practice. Second, the filter generation in TV-Rec is data-independent, relying solely on temporal position rather than sequence content. While this design improves generalization and structural simplicity, may limit the model's s adaptability to instance-specing behavior or irregular patterns. Nonetheless, the inference-time efficiency and architectural simplicity make these trade-offs acceptable for many practical applications. Overall, these trade-offs are justified by TV-Rec's s strong empirical results and practical efficiency.
29


Reviews:
[{"review_id": "kHE1wx9ECC", "reviewer": "Reviewer_HzEw", "summary": "This article highlights the limitations of traditional convolutional filters in sequential recommendation tasks due to their fixed nature. To tackle this, the authors propose TV-Rec, a novel method that employs time-variant convolutional filters. These filters adaptively apply different filters to each data point, allowing for the capture of complex patterns. A key advantage of TV-Rec is its ability to achieve high performance in long-range modeling without the need for self-attention. Additionally, it boasts fast inference times due to its linear operator nature. The effectiveness and efficiency of TV-Rec have been rigorously validated through extensive experiments on six datasets.", "questions": "1. Given that TV-Rec is built on graph signal processing principles, why does the paper not include mainstream graph-based sequential recommendation models (e.g., those leveraging graph neural networks or graph convolutional networks) as baselines in its experimental evaluations? \n \n2. Without comparisons to such graph-based models, how can readers assess whether TV-Rec offers significant advantages or uniqueness in capturing sequential dependencies compared to existing graph convolutional approaches?  \n\n3. The paper claims the time-variant graph filter is a core innovation, but does it include dedicated ablation studies that directly compare this filter with standard graph convolution operations under the same experimental settings to explicitly demonstrate the former’s superiority?  In the absence of such comparative ablation experiments, how can the claim that the time-variant graph filter is a more effective design choice than traditional graph convolution for modeling the dynamics and complexity of user sequences be validated?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "TV-Rec addresses the inherent limitations of conventional fixed convolutional filters in super-resolution by introducing time-variant filters that dynamically adapt to each data point, enabling the capture of complex patterns without relying on self-attention mechanisms. This approach not only achieves high performance in long-range modeling but also maintains fast inference speeds due to its linear operator nature, as validated through extensive experiments across six datasets, demonstrating both superior effectiveness and practical efficiency.\n\n\nA major drawback of the paper is its insufficient explanation of the practical implementation of the time-variant filter: while it cites graph signal processing concepts and provides mathematical formulations (e.g., filter matrix \\(H\\) and frequency-domain operations), the main text lacks a clear, step-by-step description of how the filter dynamically adapts per data point during inference, how the graph Fourier transforms interact with filter taps, or how parameters are learned during training. This omission hinders readability and reproducibility, particularly for readers unfamiliar with graph signal processing.\n\nA critical omission in the paper is its failure to benchmark TV-Rec against existing graph-based sequential recommendation models (e.g., GNNs or graph convolutional approaches), despite its reliance on graph signal processing principles. This absence of comparison prevents readers from evaluating TV-Rec's relative performance and novelty within the broader graph-driven sequential recommendation literature, thereby undermining its contextual significance.\n\nThe paper suffers from overly terse table and figure captions (e.g., \"Ablation studies\" for Table 4 and \"Visualization of learned graph filters on LastFM\" for Figure 3), which omit critical context about experimental objectives, variables, and key insights. This lack of detail forces readers to deduce significance from the main text, diminishing the work's clarity and professional presentation.\n\nThe paper’s casual use of ambiguous abbreviations (e.g., \"SR\" for sequential recommendation without explicit definition) risks confusion, particularly for readers unfamiliar with the field. Moreover, Section 4.4 fails to provide proper citations for compared methods (AdaMCT, BSARec, SASRec, BERT4Rec, FMLPRec), hindering source verification and weakening the academic rigor of the complexity and runtime analysis.", "was_revised": true, "final_justification": "The author's rebuttal has addressed most of my concerns. Thus, I will increase the score.", "rebuttal": "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.\n\n## **1. Comparison with graph-based methods**\nOur 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. \n\n### **1-1. Performance Comparison**\n\n\nAs 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.\n\n**Table A. Comparison to GNN-based methods**\n\n| Datasets    | Metric    | SR-GNN  | GC-SAN  | GCL4SR | LS4SRec | TV-Rec |\n|-------------|-----------|---------|---------|--------|----------|---------|\n| **Beauty**  | Recall@5  | 0.0365  | 0.0570  | 0.0631 | 0.0626   | 0.0721  |\n|             | Recall@10 | 0.0567  | 0.0784  | 0.0880 | 0.0876   | 0.1017  |\n|             | Recall@20 | 0.0847  | 0.1059  | 0.1206 | 0.1200   | 0.1403  |\n|             | NDCG@5    | 0.0238  | 0.0408  | 0.0438 | 0.0442   | 0.0513  |\n|             | NDCG@10   | 0.0303  | 0.0477  | 0.0519 | 0.0522   | 0.0608  |\n|             | NDCG@20   | 0.0374  | 0.0546  | 0.0601 | 0.0604   | 0.0705  |\n| **LastFM**  | Recall@5  | 0.0385  | 0.0376  | 0.0385 | 0.0505   | 0.0596  |\n|             | Recall@10 | 0.0532  | 0.0569  | 0.0633 | 0.0752   | 0.0853  |\n|             | Recall@20 | 0.0872  | 0.0807  | 0.0908 | 0.1147   | 0.1202  |\n|             | NDCG@5    | 0.0248  | 0.0273  | 0.0249 | 0.0352   | 0.0402  |\n|             | NDCG@10   | 0.0295  | 0.0334  | 0.0328 | 0.0431   | 0.0484  |\n|             | NDCG@20   | 0.0379  | 0.0394  | 0.0398 | 0.0531   | 0.0572  |\n| **Foursquare** | Recall@5  | 0.0157  | 0.0148  | 0.0148 | 0.0148   | 0.0175  |\n|             | Recall@10 | 0.0203  | 0.0175  | 0.0166 | 0.0157   | 0.0259  |\n|             | Recall@20 | 0.0222  | 0.0212  | 0.0185 | 0.0194   | 0.0314  |\n|             | NDCG@5    | 0.0117  | 0.0114  | 0.0113 | 0.0124   | 0.0134  |\n|             | NDCG@10   | 0.0132  | 0.0122  | 0.0119 | 0.0127   | 0.0161  |\n|             | NDCG@20   | 0.0137  | 0.0131  | 0.0123 | 0.0136   | 0.0176  |\n\n### **1-2. Architectural Comparison**\n\nSR-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.\n\nFirst, 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.\n\nSecond, 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.\n\n## **2. Time-variant graph filter vs. standard graph convolution**\nWe 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.\n\n## **3. Clarification on model behavior and filter design**\n\nWe 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.\nWe agree that clearer explanations would improve readability and reproducibility, and we will incorporate these clarifications into the final version of the paper.\n\n### **3-1. Dynamic behavior during inference**\nAs 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.\n\n### **3-2. Interaction between GFT and filter taps**\nTo clarify how the graph Fourier transform interacts with the learned filter taps, we provide the following pseudocode summarizing the spectral filtering process:\n\n```python\n# X       : [batch_size, N, d]        # Input sequence\n# U       : [N, N]                    # GFT matrix\n# C       : [N, m]                    # Coefficient matrix\n# B       : [m, K+1]                  # Pre-normalized basis \n# Λ       : [N, K+1]                  # Vandermonde matrix (Λ)\n\n# Step 1: Transform input to spectral domain\nX_freq = U.T @ X                     # Graph Fourier Transform\n\n# Step 2: Construct spectral filter\nH = C @ B                            # [N, K+1], B is pre-normalized\nH_proj = H @ Λ.T                     # [N, N]\n\n# Step 3: Apply element-wise scaled inverse GFT\nF = U * H_proj                       # Element-wise product\n\n# Step 4: Apply filter and return to time domain\nX_out = F @ X_freq                   # Final output\n```\nThis filtering mechanism allows the learned filter taps to modulate graph frequency responses in a position-aware yet data-independent manner.\n\n### **3-3. Parameter learning**\nAll 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.\n\n\n## **4. Clarifications on captions, terminology, and citations**\nWe 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. \nRegarding 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.\n\n## **Reference**\n[1] Session-Based Recommendation with Graph Neural Networks, AAAI 2019\n\n[2] Graph Contextualized Self-Attention Network for Session-based Recommendation, IJCAI 2019\n\n[3] Enhancing Sequential Recommendation with Graph Contrastive Learning, IJCAI 2022\n\n[4] Self-supervised Graph Neural Sequential Recommendation with Disentangling Long and Short-Term Interest, ACM Transactions on Recommender Systems 2025"}, {"review_id": "E6NNRmT8Rs", "reviewer": "Reviewer_Y8Cz", "summary": "The paper introduces TV-Rec, a novel architecture for sequential recommendation that leverages time-variant convolutional filters inspired by graph signal processing. These filters adapt dynamically to different temporal positions in a user’s interaction sequence, in contrast to traditional fixed convolutional filters or self-attention mechanisms. TV-Rec eliminates the need for self-attention and positional embeddings while providing better performance and computational efficiency. The model is evaluated on six benchmark datasets and consistently outperforms ten state-of-the-art methods.", "questions": "- In Eq. (13), what do $B_{\\text{real}}$ and $B_{\\text{imag}}$ represent, and why is orthogonal regularization applied to these components?\n- In Fig. 3a, how is the basic graph filter learned? Is it derived from a baseline method or from TV-Rec with static (non-time-variant) filters?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### **Strengths**\n\n- The paper is well-written and clearly structured. The motivation is well-articulated, and Table 1 effectively contextualizes the proposed method among existing approaches.\n- The concept of a time-aware (time-variant) convolutional filter is novel and intuitively meaningful.\n- The method is grounded in solid theoretical foundations, with a well-developed formulation based on graph signal processing.\n- The interpretability of TV-Rec is enhanced by filter behavior analysis and an illustrative case study.\n- The experimental evaluation is thorough, covering both qualitative and quantitative aspects. The authors also include comprehensive hyperparameter analysis in the appendix.\n\n### **Weaknesses**\n\n- While the paper focuses on leveraging GSP for sequential recommendation, the benefits of this framework are not thoroughly connected to the SR context. For instance, in Lines 106–109, the statement that GSP helps \"capture complex dependencies\" is too vague. The paper would benefit from a more precise explanation of how GSP-derived filters concretely improve sequential modeling.\n- The decision to model user sequences as a line graph is not well-justified. Why choose a line graph over other graph structures? How sensitive is the performance to the graph construction method? This should be discussed more explicitly.\n- Given that TV-Rec uses graph-based modeling, it would be helpful to relate and compare this work to existing GNN-based recommendation methods. Even a brief discussion or experimental comparison would strengthen the paper.\n- Although the authors provide mean and standard deviation of experimental results in the appendix, it would improve transparency to report p-values or statistical significance directly in the main text.", "was_revised": true, "final_justification": "After considering the authors' rebuttal and the discussion, I am satisfied that my main concern—lack of comparison with graph-based methods—has been adequately addressed through additional experiments. The new results strengthen the empirical validation, and I encourage the authors to include them in the final version. I did not identify any significant unresolved issues, and the discussion with other reviewers further reinforced the paper's strengths in methodology, novelty, and empirical results. Based on this, I have increased my score and recommend acceptance.", "rebuttal": "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.\n\n## **1. Justification for using GSP and the line graph structure in sequential recommendation**\n\nThe 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.\n\nOur 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.\n\n## **2. Comparison to graph-based methods**\nOur 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. \n\n### **2-1. Performance Comparison**\n\n\nAs 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.\n\n**Table A. Comparison to GNN-based methods**\n\n| Datasets    | Metric    | SR-GNN  | GC-SAN  | GCL4SR | LS4SRec | TV-Rec |\n|-------------|-----------|---------|---------|--------|----------|---------|\n| **Beauty**  | Recall@5  | 0.0365  | 0.0570  | 0.0631 | 0.0626   | 0.0721  |\n|             | Recall@10 | 0.0567  | 0.0784  | 0.0880 | 0.0876   | 0.1017  |\n|             | Recall@20 | 0.0847  | 0.1059  | 0.1206 | 0.1200   | 0.1403  |\n|             | NDCG@5    | 0.0238  | 0.0408  | 0.0438 | 0.0442   | 0.0513  |\n|             | NDCG@10   | 0.0303  | 0.0477  | 0.0519 | 0.0522   | 0.0608  |\n|             | NDCG@20   | 0.0374  | 0.0546  | 0.0601 | 0.0604   | 0.0705  |\n| **LastFM**  | Recall@5  | 0.0385  | 0.0376  | 0.0385 | 0.0505   | 0.0596  |\n|             | Recall@10 | 0.0532  | 0.0569  | 0.0633 | 0.0752   | 0.0853  |\n|             | Recall@20 | 0.0872  | 0.0807  | 0.0908 | 0.1147   | 0.1202  |\n|             | NDCG@5    | 0.0248  | 0.0273  | 0.0249 | 0.0352   | 0.0402  |\n|             | NDCG@10   | 0.0295  | 0.0334  | 0.0328 | 0.0431   | 0.0484  |\n|             | NDCG@20   | 0.0379  | 0.0394  | 0.0398 | 0.0531   | 0.0572  |\n| **Foursquare** | Recall@5  | 0.0157  | 0.0148  | 0.0148 | 0.0148   | 0.0175  |\n|             | Recall@10 | 0.0203  | 0.0175  | 0.0166 | 0.0157   | 0.0259  |\n|             | Recall@20 | 0.0222  | 0.0212  | 0.0185 | 0.0194   | 0.0314  |\n|             | NDCG@5    | 0.0117  | 0.0114  | 0.0113 | 0.0124   | 0.0134  |\n|             | NDCG@10   | 0.0132  | 0.0122  | 0.0119 | 0.0127   | 0.0161  |\n|             | NDCG@20   | 0.0137  | 0.0131  | 0.0123 | 0.0136   | 0.0176  |\n\n### **2-2. Architectural Comparison**\n\nSR-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.\n\nFirst, 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.\n\nSecond, 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.\n\n\n## **3. Statistical Significance Testing**\nTo 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:\n\n**Table B. Mann-Whitney U Test Result**\n| Dataset        | HR@20 p-value    | NDCG@20 p-value |\n|----------------|------------------|-----------------|\n| Beauty         | 5.31e-05         | 0.0329          |\n| Sports         | 1.38e-05         | 0.0200          |\n| Yelp           | 4.85e-05         | 0.0001          |\n| LastFM         | 5.53e-10         | 4.85e-06        |\n| Foursquare  | 7.74e-10         | 0.0388          |\n| ML-1M          | 0.0024           | 0.0205          |\n\nThese 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.\n\n## **4. Regarding orthogonal regularization**\nEq. (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]. \n\n## **5. Regarding the experimental setting of basic graph filter in ablation study**\nWe 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.\n\n\n## **Reference**\n[1] An Attentive Inductive Bias for Sequential Recommendation beyond Self-Attention, AAAI 2024\n\n[2] Session-Based Recommendation with Graph Neural Networks, AAAI 2019\n\n[3] Graph Contextualized Self-Attention Network for Session-based Recommendation, IJCAI 2019\n\n[4] Enhancing Sequential Recommendation with Graph Contrastive Learning, IJCAI 2022\n\n[5] Self-supervised Graph Neural Sequential Recommendation with Disentangling Long and Short-Term Interest, ACM Transactions on Recommender Systems 2025\n\n[6] \"Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules.\" Statistics surveys 4 (2010).\n\n[7] Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?, NeurIPS 2018\n\n[8] Orthogonal Graph Neural Networks, AAAI 2022"}, {"review_id": "zjCzfdjHek", "reviewer": "Reviewer_xQNR", "summary": "This paper proposes TV-Rec, a sequential recommendation model that leverages graph signal processing to perform spectral filtering on user behavior sequences. By constructing time-variant filters for each position via a low-rank formulation, the model avoids using position embeddings or attention. Experimental results on six datasets show strong performance and efficiency compared to prior methods.", "questions": "1.\tWhat is the theoretical expressive capacity of the filter design?\n\nCan the authors formalize whether the C \\cdot \\bar{B} construction is capable of approximating arbitrary frequency responses under certain norms or graph structures?\n\n2.\tCan personalization be incorporated into filters?\n\nCurrently, all filters are position-specific but shared across users. Could user- or item-aware adaptation (e.g., via embeddings or gating) enhance personalization, especially in cold-start scenarios?\n\n3.\tHow does TV-Rec handle data sparsity or cold-start scenarios? \n\nGiven its dependence on spectral structures, how robust is the model when faced with sparse user interactions or new users/items with limited historical data, which are common challenges in real-world recommendation systems?", "limitations": "No", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper introduces a novel sequential recommendation approach using spectral graph signal processing (GSP). Its key innovation is time-variant convolutional filters assigning unique spectral filters per position, replacing position embeddings and self-attention with an efficient low-rank factorization.\n2. Experiments on six benchmarks show consistent gains over 10 state-of-the-art models, supported by ablation studies and efficiency analysis.\n3. The approach offers a compelling alternative to the dominant Transformer-based models, which often require heavy computation and explicit position encoding.\n\nWeaknesses:\n1. Key design choices such as the number of basis vectors m, shift depth K, or basis configuration ω are not systematically analyzed. It remains unclear whether the method is robust under different settings.\n2. The basis matrix \\bar{B} is constructed heuristically via Vandermonde form, but the selection of frequency anchors and the number of basis vectors lack theoretical or empirical justification. Please explain the rationale behind their choice in the main paper.\n3. Strong recent models like Tim4Rec are not included in the comparison. Their absence weakens the empirical competitiveness of the claims.", "was_revised": true, "final_justification": "The author's rebuttal has addressed some of my concerns. Thus, I will increase the score.", "rebuttal": "Thank you for your careful and insightful review of our manuscript. Below, we respond to each point with further details and experimental results.\n\n## **1. Regarding absence of strong recent models**\nWe 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.\n\nAdditionally, 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.\n\n\n## **2. Expressive capacity or time-variant convolutional filter**\nOur 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.\n\n## **3. Analysis on hyper-parameters**\nWe 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.\nRegarding 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.\nAs 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.\n\n**Table C. Ablation Study on $K$**\n| dataset    | K  | HR@05  | HR@10  | HR@20  | NDCG@05 | NDCG@10 | NDCG@20 |\n|------------|----|--------|--------|--------|---------|---------|---------|\n| Beauty     | 3  | 0.0704 | 0.0992 | 0.1380 | 0.0499  | 0.0592  | 0.0690  |\n|      | 5  | 0.0701 | 0.0996 | 0.1364 | 0.0492  | 0.0587  | 0.0680  |\n|      | 10 | 0.0703 | 0.0986 | 0.1378 | 0.0498  | 0.0589  | 0.0688  |\n|      | 25 | 0.0700 | 0.0982 | 0.1371 | 0.0495  | 0.0586  | 0.0684  |\n|      | 50 | 0.0721 | 0.1017 | 0.1403 | 0.0513  | 0.0608  | 0.0705  |\n| Sports     | 3  | 0.0408 | 0.0596 | 0.0839 | 0.0283  | 0.0344  | 0.0405  |\n|      | 5  | 0.0414 | 0.0601 | 0.0849 | 0.0285  | 0.0344  | 0.0407  |\n|      | 10 | 0.0415 | 0.0595 | 0.0853 | 0.0287  | 0.0345  | 0.0410  |\n|      | 25 | 0.0403 | 0.0592 | 0.0854 | 0.0283  | 0.0343  | 0.0409  |\n|      | 50 | 0.0431 | 0.0635 | 0.0880 | 0.0298  | 0.0363  | 0.0425  |\n| Yelp       | 3  | 0.0270 | 0.0458 | 0.0731 | 0.0166  | 0.0226  | 0.0295  |\n|        | 5  | 0.0272 | 0.0455 | 0.0752 | 0.0174  | 0.0233  | 0.0308  |\n|        | 10 | 0.0280 | 0.0465 | 0.0741 | 0.0174  | 0.0233  | 0.0303  |\n|        | 25 | 0.0290 | 0.0494 | 0.0774 | 0.0188  | 0.0253  | 0.0323  |\n|        | 50 | 0.0290 | 0.0474 | 0.0777 | 0.0186  | 0.0245  | 0.0321  |\n| LastFM     | 3  | 0.0413 | 0.0642 | 0.1046 | 0.0266  | 0.0340  | 0.0443  |\n|      | 5  | 0.0514 | 0.0780 | 0.1147 | 0.0315  | 0.0400  | 0.0490  |\n|      | 10 | 0.0523 | 0.0771 | 0.1165 | 0.0355  | 0.0434  | 0.0532  |\n|      | 25 | 0.0560 | 0.0862 | 0.1248 | 0.0352  | 0.0448  | 0.0546  |\n|      | 50 | 0.0596 | 0.0853 | 0.1202 | 0.0402  | 0.0484  | 0.0572  |\n| ML-1M      | 3  | 0.1907 | 0.2778 | 0.3901 | 0.1281  | 0.1562  | 0.1843  |\n|       | 5  | 0.1874 | 0.2768 | 0.3823 | 0.1260  | 0.1547  | 0.1814  |\n|       | 10 | 0.2000 | 0.2879 | 0.3922 | 0.1354  | 0.1636  | 0.1898  |\n|       | 25 | 0.1960 | 0.2844 | 0.3957 | 0.1325  | 0.1611  | 0.1891  |\n|       | 50 | 0.2013 | 0.2904 | 0.4079 | 0.1371  | 0.1658  | 0.1955  |\n| Foursquare | 3  | 0.0120 | 0.0194 | 0.0240 | 0.0081  | 0.0105  | 0.0116  |\n|  | 5  | 0.0129 | 0.0203 | 0.0268 | 0.0075  | 0.0099  | 0.0116  |\n|  | 10 | 0.0148 | 0.0166 | 0.0268 | 0.0109  | 0.0115  | 0.0139  |\n|  | 25 | 0.0222 | 0.0249 | 0.0295 | 0.0142  | 0.0151  | 0.0163  |\n|  | 50 | 0.0175 | 0.0259 | 0.0314 | 0.0134  | 0.0161  | 0.0176  |\n\n\n\n## **4. Can personalization be incorporated into filters?**\nAs 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.\n\n## **5. How does TV-Rec handle data sparsity or cold-start scenarios?**\nFirst, we note that our experiments are already conducted on datasets with sparse user-item interactions, which reflects realistic recommendation scenarios. \nRegarding 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.\nFor 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.\n\n## Reference\n[1] Session-Based Recommendation with Graph Neural Networks, AAAI 2019\n\n[2] Graph Contextualized Self-Attention Network for Session-based Recommendation, IJCAI 2019\n\n[3] Enhancing Sequential Recommendation with Graph Contrastive Learning, IJCAI 2022\n\n[4] Self-supervised Graph Neural Sequential Recommendation with Disentangling Long and Short-Term Interest, ACM Transactions on Recommender Systems 2025"}, {"review_id": "fnvBdbGJ1J", "reviewer": "Reviewer_ANZm", "summary": "The paper proposes a new technique to allow sequential recommendation models to more flexibly adapt to different temporal patterns. Existing sequential models are fairly \"rigid\" (just an ordered sequence of events), whereas the proposed approach can potentially be more adaptive to context and different dynamics at different positions in the sequence. The specific contribution is based on a time-varying convolutional filter.", "questions": "-- Can you comment on model scalibility? I see there is some scalability analysis, though the method seems not to have been evaluated on large datasets.\n\n-- The results in the scalability table don't seem to match the numbers in the table (FMLPRec seems to be the winner in the figure?)\n\n-- I don't totally follow what's shown in the inference time analysis. Many of these methods reduce inference to nearest-neighbor search in some latent space such that I don't really see why inference time should vary so much (though maybe that's sort of what the table shows). Though might have misunderstood something here.", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "-- Reasonable idea which seems to offer a unique perspective on a problem that's studied in a large number of papers.\n\n-- Fairly promising results.\n\n-- A decent enough set of baselines and datasets, to the point that the experiments are reasonably thorough.\n\n-- Datasets maybe on the small side, not sure about scalability.", "was_revised": true, "final_justification": "The clarifications made by the authors seem reasonable. They do add new experiments which go beyond normal \"clarifications\" though I don't mind that too much. Otherwise my scores and opinions seem not too different from other reviewers (and also borderline) so am keeping the score.", "rebuttal": "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.\n\n## **1. Concerns on Dataset Scale and Model Scalability**\nIn 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.\n\nAdditionally, 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:\n\n**Table D. Statistics of the XLong Dataset**\n|Dataset|XLong|\n|-|-|\n|\\# of Users|69,069|\n|\\# of Items|2,122,932|\n|\\# of Interactions|66.8M|\n|Average Length|958.8|\n|Density|5e-4|\n\nWe followed the experimental settings of LRURec [1] and performed the experiments within the LRURec framework. The results are as follows:\n\n**Table E. Results on the XLong dataset**\n\n| Metric    | SASRec  | LRURec  | TV-Rec   | Improvement |\n|-|-|-|-|-|\n| Recall@5  | 0.3612  | 0.4266  | 0.4844  | 13.55% |\n| Recall@10 | 0.4608  | 0.5137  | 0.5353  | 4.20%  |\n| Recall@20 | 0.5612  | 0.5874  | 0.5774  | -1.70% |\n| NDCG@5    | 0.2656  | 0.3227  | 0.3905  | 21.00% |\n| NDCG@10   | 0.2979  | 0.3510  | 0.4071  | 15.98% |\n| NDCG@20   | 0.3232  | 0.3697  | 0.4178  | 13.01% |\n\nAlthough 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.\n\n## **2. Clarifying the purpose of Figure 5**\n\nThank 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).\n\nWhile 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.\n\nWe 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.\n\n## **3. What does inference time measure?**\n\nWe 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.\n\nOur 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.\n\nWe 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.\n\n\n## **Reference**\n[1] Linear Recurrent Units for Sequential Recommendation, WSDM 2024"}]

Author rebuttal:

Meta-review: This paper introduces TV-Rec, a novel sequential recommendation model leveraging time-variant convolutional filters inspired by graph signal processing. By dynamically adapting filters to each temporal position, TV-Rec captures complex sequential dependencies without relying on self-attention or positional embeddings, enabling both high performance and efficient inference. The approach is well-motivated, with a clear low-rank formulation and spectral filter design, offering interpretability and a compelling alternative to Transformer-based methods. Extensive experiments demonstrate consistent improvements over ten state-of-the-art models, supported by ablation studies, efficiency analyses, and qualitative visualizations. Some parts, such as sensitivity to hyperparameters, heuristic choices in the basis construction, and comparisons to GNN-based sequential recommenders, could be further improved.
Decision: Accept (poster)