Structured Spectral Reasoning for Frequency-Adaptive Multimodal Recommendation
Authors: Wei Yang
Rui Zhong
Yiqun Chen
Chi Lu
Peng Jiang
Venue: NeurIPS 2025 poster ()
Keywords: Multimodal Recommendation
Spectral Modeling
Graph Learning
Primary area: applications

Abstract: Multimodal recommendation aims to integrate collaborative signals with heterogeneous content such as visual and textual information, but remains challenged by modality-specific noise, semantic inconsistency, and unstable propagation over user–item graphs. These issues are often exacerbated by naive fusion or shallow modeling strategies, leading to degraded generalization and poor robustness. While recent work has explored the frequency domain as a lens to separate stable from noisy signals, most methods rely on static filtering or reweighting, lacking the ability to reason over spectral structure or adapt to modality-specific reliability. To address these challenges, we propose a Structured Spectral Reasoning (SSR) framework for frequency-aware multimodal recommendation. Our method follows a four-stage pipeline: (i) Decompose graph-based multimodal signals into spectral bands via graph-guided transformations to isolate semantic granularity; (ii) Modulate band-level reliability with spectral band masking, a training-time masking with representation-consistency objective that suppresses brittle frequency components; (iii) Fuse complementary frequency cues using hyperspectral reasoning with low-rank cross-band interaction; and (iv) Align modality-specific spectral features via contrastive regularization to promote semantic and structural consistency. Experiments on three real-world benchmarks show consistent gains over strong baselines, particularly under sparse and cold-start settings. Additional analyses indicate that structured spectral modeling improves robustness and provides clearer diagnostics of how different bands contribute to performance.

Structured Spectral Reasoning for
Frequency-Adaptive Multimodal Recommendation
Wei Yang Rui Zhong' Yiqun Chen
Lu
Peng Jiang'
"Kaiishuu Technology Renmin University of China
(yangwei08, Luchhiiiii,,uuiiiiieeee Juckakkasooo... com, chenyiquns900211ruu
edu, cn
Abstract
Multimodal recommendation aims to integrate collaborative signals with hetero- geneous content such visual and textual information, but remains challenged by mpdelitt-specificc noise, semantic inconsistency. and unstable propagation over user-item graphs. These issues are often exacerbated by naive fusion shallow modeling strategies, leading to degraded generalization and poor robustness. While recent work has explored the frequency domain as lens to separate stable from noisy signals, most methods rely static filtering reweighting, lacking the ability to reason over spectral structure or adapt to modality-specinn reliability. To address these challenges, propose Structured Spectral Reasoning (SSR) framework for requencyyawaar multimodal recommendation. Our method follows four-stage pipeline: (i) Decompose graph-based multimodal signals into spectral bands via graph-guided transformations to isolate semantic granularity; (ii) Mod- ulate band-level reliability with spectral band masking, training-timg masking with prreessentationccnsssteeeee objective that suppresses brittle frequency com- using hyperspectral reasoning with low-rank cross-band interaction; and (iv) Align modality-specific spectral fea- tures via contrastive regularization to promote semantic and structural consistency. Experiments on three real-world benchmarks show consistent gains over strong baselines, particularly under sparse and cold-start settings. Additional analyses indicate that structured spectral modeling improves robustness and provides clearer diagnostics of how different bands contribute performance. The code is available at https://github..om/llmg htmp://Smmm//./
ponents; (iii) Fuse complementary frequency
Introduction
Multimodal recommendation 0 3 has become a central paradigm in modern information systems. It leverages auxiliary signals such as visual content, textual metadata and structural interactions to improve preference modeling and content understanding [5] 7
g 9
These
signals provide complementary semantics but also introduce modality-specie specific noise 10
semantic misalignment [13] [4] and representational redundancy [15] I7]. The difficulties become
more pronounced in graph-based architectures where user-item relations are propagated through neighborhoods [18 [9] 20 In this setting, spurious from partieular modalities, for example stylistic image patterns or ambiguous wording, can diffuse across the graph and affect otherwise unrelated nodes (1 22 23 24 The result is unstable representations and degraded performance, especially under star- or noisy conditions. Many existing approaches fuse modalities in the raw feature space [25] 26 27), which limits control over how different semantic granularities interact across the graph. These challenges call for structured approach to semantic disentanglement that isolates stable signals while suppressing unstable ones 28
29
30 31
Equual contribution. Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Recently, frequency frequency-domain modeling has gained traction as promising perspective B2 33 34]. By transforming signals into spectral components, models can expose structural patterns across different frequency bands [35 36 37 Low-frequency components often encode smooth, global semantics such as long-term user intent or item popularity, while high-frequency components capture fine- grained variations or local inconsistencies [38] (3]40] 40]. This decomposition enables models to analyze and potentially filter modality-specific signals with greater precision. However, advanced approaches such SMORE [15) and ChebyCF [41] largely rely static reweighting low-pass filtering and therefore lack explicit reasoning about band semantics or cross-frequency dependencies. Moreover, the use of frequency decomposition itself is often heuristic, without principled mechanism to separate informative bands from noisy ones. Consequently, useful detail may be suppressed and unstable components may be retained, particularly when semanties vary across items and users.
These limitations are particularly acute in multimodal graph recommendation, where heterogeneous modalities interact within a topologically entangled space [42] semantics differ granularity and abstraction, and they also differ spectral distribution, which makes naive fusion static attention insufficient [15] 46 47]. In this setting, robust representations should support adaptive modulation across frequency bands so that components influence one another based on semantic content and contextual relevance [38 40 48. They should also enforce band-wise consistency across modalities to prevent collapse or redundancy within the decomposed space [49 [50]. However, current architectures lack a unified mechanism to model these structured relationships across frequency, modality and graph topology. At the same time, any solution must remain computationally tractable on large graphs and compatible with standard training pipelines. It should also provide clear diagnostics at the hand level so that practitioners can inspect which frequencies and modalities drive recommendations. This motivates the need for approaches that account for band-level structure and maintain robustness across modalities.
43
44 45
Visual and textual
To address these challenges, propose Structured Spectral Reasoning (SSR) for frequency-awarc multimodal graph recommendation. SSR follows four-stage pipeline that decomposes, modulates, fuses and aligns signals within shared spectral coordinate system. Motivated by the observation that frequency mapping reveals band-wise structure capturing collaborative semantics and modality- specific detail, organize learning around band-level operations and supervision. Instead of treating bands as static or lightly reweighted features, SSR converts inputs into spectral representations and then reasons about their informativeness and stability. We introduce Spectral Band Masking (SBM), training-time band-level perturbation with a pnnessntation-coosistenns objective that reduces reliance on brittle bands and improves robustness. We also design a graph-compatible hyperspectral operator (G-HSNO) that models cross-band and cross-modality dependencies through a compact low-rank parameterization. In addition, spectral contrastive objective promotes band-wise cross-modal consistency without inference overhead. Together, these components provide a cohesive and efficient approach to structured spectral modeling for multimodal graphs.
In summary, the main contributions of this work are as follows:
We present a unified sturestage framework for frequency-awand multimodal graph recom- mendation that places multimodal signals in a shared spectral space and performs hand-wise decomposition, modulation, fusion, and alignment.
We design a graph-compatible hyperspectral operator (G- (G-HSNO) that models cross-bante and tross-modality dependencies with a compact low-rank parameterization, achieving a strong accuracy and efficiency trade-off.
Extensive experiments across multiple benchmarks show consistent gains over advanced baselines, with particularly strong improvements for cold-start users. Ablation and diagnostic analyses validate the effectiveness of each module.
2 RELATED WORK
2.1 Multi-modal Recommendation
Multimodal recommendation integrates auxiliary content such as images, text and audio to strengthen
user preference modeling, especially under sparse supervision [51] 52 53 Early work augments
collaborative filtering with side content [54 55 [56]. Subsequent methods build modality-awan
graph architectures to propagate and fuse signals along user-item relations [57] 58 59 60 61 62

---

To mitigate moosl misalignment and semantic noise, recent approaches employ contrastive learning 63 regularization [65] 66 and intention-awarc designs 66 68
AlignRec 4
enforces modality-ID consistency, while PromptMM 69 enables lightweight adaptation. Generative strategies, including diffusion models 770, adversarial alignment [71] and large language models [72
73 74, 75], further improve robustness under heterogeneity. In addition, empowered by the reasoning 77 and multi-agent systems [78] (7 80), recent advances such as Rec-GPT4V [ and UniMP [81 leverage large vision-language models to strengthen multimodal semantic understanding and improve reasoning over heterogeneous content.
capacity of large language models (76
2.2 Frequency-aware Representation Learning
Frequency-domain modeling has recently emerged as promising alternative to time- or topology- domain learning in recommendation tasks [34] 35]. In sequential modeling, various approaches leverage spectral transformations to capture user intent dynamics and mitigate temporal noise [36 38 while others propose frequency-aware contrastive objectives or neural filtering for periodic behavior tracking 82
833. CFIT4SRee (36] adopts frequency- based contrastive learning frameworks, leveraging Fourier transformations to construct robust augmented views and improve representation learning. FEARee 38 and HMFTRec [4] add spectral attention and multi fuuuui-frr modules to
capture low and high frequency signals beyond augmentation. For graph-based recommendation, ChebyCF [1], SeIfGNN
84 and SComGNN (85) reformulate GNN propagation spectral
filtering, improving expressivity and denoising capacity. In multimodal settings, SMORE [155] explicitly models frequency-speciffe modality fusion, while FREEDOM (66) and MMGCL [64] implicitly introduce spectral diversity through augmentation. Nonetheless, most of these methods either treat frequency bands static views or lack explicit modeling of band reliability and inter-band interactions. We address these gaps by pursuing adaptive, band-aware integration that regulates sensitivity brittle components and supports interpretable cross- moosll fusion.
3 Proposed Method
The problem definition be found in Appendix A
In this section, we present SSR, frequency- aware multimodal recommendation framework illustrated in Figure
3.1 Spectral Transformation of Multimodal Graph Signals
Multimodal recommendation integrates ID embeddings with visual and textual features to learn unified user-item representations. A central challenge is cross-modal heterogeneity, where modalities reside in incompatible spaces and capture semantics at different granularities. Conventional fusion methods such as concatenation or attention operate in the raw feature domain and often ignore the structural dependencies induced by user-item interactions. Viewing these representations as graph signals enables frequency- modeling, where low-frequency components capture global preference patterns and frequenyy components encode fine-grained, modality variations. Motivated by this perspective, we transform multimodal features into a unified frequency domain to facilitate band-level alignment and more interpretable fusion, supporting adaptive selection of frequency components for downstream recommendation.
Graph Representation and Spectral Decomposition. Given user-item bipartite graph (N,E) with adjacency matrix A 86 87). we use the symmetric normalized Laplacian L = I D D-1/2AD 1/2, where D is the degree matrix. For each node n E N, the associated signal (e.g.. an ID embedding or a multimodal feature) is Xn E Rdd. Stacking all nodes yields X E We analyze X in the spectral domain via the eigendecomposition L UAU where U contains orthonormal eigenvectors and is diagonal with eigenvalues. The graph Fourier transform (GFT)
M xd
is X = - X and the inverse transform is X = UX. Each row of X corresponds to a graph frequency (eigenmode). In the next step we group these modes into bands for downstream processing. In practice, explicitly computing U is only feasible for small graphs. We thus adopt a hybrid implementation: for graphs with [W] < No we compute the full eigendecomposition of L, while for larger graphs we avoid eigen desee-ddcomposttion and approximate multi-band filtering using Chebyshev polynomials of the scaled Laplacian. In practice, we leverage structural signals from the interaction graph as well as auxiliary user-user and item-itent relations to enrich the spectral pipeline.
3

---

Low Prepuney
Special Paite billee
Puneere budie
L- Aace gbaca
Atraitedd Spe
DOO
mirital
Maiee specral riwe baad pirarbatia
Sueiral Casvaatio Reglatiatas
Vieal
Disegesike
XOC
Che
Creai
conratto larrbe
Syesred
65
DOG
Noske
Stracsed Rennnlagone (rropescy, Madally, Teyslag)
Spuiinl Bend!
Meal ouu Vacihann
Gogal Spoticl
Pottchille
lenurianc
Grogh-radde Spectaal Bratragfoeee
Spcaral Band Morking with Censtenccy
Lew-Raik Riperearral lnterciiin Modillng
Cress Vedal Speciaal Conticatvv Regakaiiete
Figure 1: Overall architecture of our proposed framework. The model follows a structured four-stage pipeline: (i) Decomposition performs a coodality-specifie spectral transform on graph signals to disentangle multi- teltiffre components; (ii) Modulation applies Spectral Band Masking (SBM) to perturb and downnweight unreliable bands in task-adaptive manner; (iii) Fusion leverages low- rank Graph HyperSpectral Neural Operator (G-HSNO) to reason over cross-band and cross-modal dependencies; and (iv) Alignment introduces Spectral Contrastive Regularization (SCR) to enforce semantic consistency and spectral robustness across modalities.
Frequency Band Construction. We divide the spectrum into frequency bands using the energy distribution of spectral coefficients. Let & denote the k-th row of X, and define its energy as Fg | We compute the cumulative energy ordered eigenmodes and partition the frequency axis into M contiguous sets {F1 FM} such that each band contributes approximately equal total energy,
W Σ E
E
M
REF...
which yields bands with comparable signal mass and avoids extreme imbalance across modes. Given the orthonormal basis U = [ui,.... dlvi] the reconstruction for band m is ((m) = ΣkEF... uN X where uy is the k-th eigenvector. Each (mm) captures information at specific semantic resolution, with lower-index bands concentrating smoother components and higher-index bands emphasizing localized variations. In practice, M is treated hyperparameter. When full eigenmodes are avail- able, we partition bands by equal-energy quantiles of the cumulative spectrum. Otherwise, we split the spectrum in the eigenvalue domain and instantiate an M -band Chebyshev polynomial filter bank, which provides a scalable approximation to explicit band partitioning without eigendecomposition.
Semantic-Aware Frequency Fusion. Given the band-specific components {X (m)) M
Im==1 we aggre-
gate them into a unified node representation with adaptive gates. Let (m) denote the n-th row of
( The fused embedding for node n is
M
(1))
ZT
where (m) E Rzo are band-specific weights produced from node information. This allows each node to emphasize informative bands while down-weightte weighting unstable ones. In practice, this aggregation can be implemented either by a lightweight gating module as above or by our subsequent G-HSNO operator, providing a unified and flexible interface for band fusion.
3.2 Spectral Band Masking with Consistency Training
Multimodal user user-item graphs exhibit frequency components with different semantic roles and unequal reliability [5 38 Low-frequency bands tend to reflect smooth collaborative structure such as long- term preferences popularity, whereas higher bands capture localized variation that is often modality sensitive. In practice, the latter can correlate with interactions yet fluctuate across items, users and contexts due to sampling noise, content artifacts and instance-specific patterns. Standard training

---

objectives amplify correlations that are easiest to exploit, which biases the predictor toward narrow spectral slices and encourages shorteut behavior. The result increased sensitivity small spectral perturbations and weaker generalization under sparsity or cold start.
To mitigate this issue, introduce Spectral Band Masking (SBM), training-time band-level robustness mechanism. During training. SBM randomly masks subset of frequency bands and imposes representatioonconsiiteee structured perturbation reduces over-reliance on any single band, encourages the model to distribute evidence across more stable components and improves robustness under distribution shift. SBM lightweight, architecture-agnon agnostic and integrates seamlessly with the spectral pipeline.
objective between the full-spectrum and masked inputs. This
Band-wise Masking. Let (x(m) Jm=1 denote the band-wise features and let x(m) be the per- instance slice. During training, we sample binary mask independently for each instance,
mm Bernoulli(1 - -T), m = 1,...: M,
and construct a masked spectral view by dropping entire frequency bands:
M
( x (m)
172=
In practice, we apply the mask on the band tensor and optionally rescale by the keep probability to keep the expected magnitude stable. To avoid degenerate all-zero masks, we ensure least one band is kept for each instance. Unless otherwise specified, we use uniform masking over bands.
Consistency Objective. To stabilize learning under spectral perturbations, encourage the representation computed from the masked view to match that of the full-spectrum view:
(5) where h(-) denotes the spectral encoder that outputs representations. This objective acts as band- regularizer. It discourages reliance on any single
SBM = Ey h(x)) - h(x) l|2
aware perturbation with a representation-coniittie narrow band, reduces co-adaptation between bands and modalities, and distributes evidence across more stable components, LSBM is optimized jointly with the main task loss. The objective adds negligible overhead and makes changes inference time.
3.3 Graph HyperSpectral Neural Operator (G-HSNO)
While frequency decomposition disentangles semantics across spectral bands, and band-level masking improves robustness to brittle cues, the system still needs a dedicated module to reason over frequency- structured inputs and extract task-relevant information. Traditional graph neural networks (c.g.. GCNs) operate primarily in the spatial domain and often aggregate neighbor information uniformly or with simple attention. Such models are limited in capturing complex cross-frequency and cross- modality interactions, especially in multimodal recommendation where frequency semantics vary across modalities. A suitable module should explicitly model interactions among bands and modalities while respecting graph structure. It should also provide controllable capacity and low overhead so that it remains practical at scale.
To address this gap, we introduce the Graph HyperSpectral Neural Operator (G-HSNO) a spectral operator that learns joint representations across three axes: frequency bands, modality types and graph topology. G-HSNO draws inspiration from neural operators in scientific computing and adapts the idea to discrete graph signals with multimodal frequency structure.
(m) Operator Design. Let X E Rdd denote the m-th rrequency-band representation of node v. We aggregate all bands into tensor E RIA MMMM xd and define G-HSNO as a spectral operator that models inter-ban interactions. For each node and output band m,
Z HSNO(X),
z(m)
Σ Kmn (n)
(6)
Collecting m over nodes yields Z E MRxxxx To reduce parameter complexity and avoid overfitting, parameterize the kernel in a lightweight form. In particular, adopt diagonal
5

---

approximation Kmn Diag(kma), which has been widely used as an efficient spectral filtering variant. Concretely, we factorize Kmn into an inter-band mixing weight and rank-wise diagonal filter: we compute band-mixing score 8mm with a softmax function over output bands to Amn. and we construct the diagonal filter as kmn = amn Ex= Ps v(O, where {v()), R2 are rank-specific diagonal bases, and p is either global softmax weight or softly adapted by an auxiliary embedding to improve flexibility without introducing
:), W&(n, ()rr(r))) and normalize it
a full kernel.
Graph-aware Enhancement. To incorporate instance-specific information into spectral fusion, we learn lightweight band reweighting function that conditions on the current node representation and its spectral components. Concretely, for node v, we compute a band-wise weight vector gv (m), We then apply the band-wise reweighting to the mixed spectral tensor and aggregate over bands,
M
mm)
g
(m)
(MT))
Z
H mm)
To avoid undesired scale drift introduced by reweighting, we further apply a per-instance normal- ization that aligns the magnitude of the reweighted spectrum with the original one. Compared with fixed band aggregation, this step enables context-an -atext-adaptive spectral fusion while keeping the overall representation scale stable.
3.4 Spectral Contrastive Regularization
To strengthen semantic alignment and structural integrity in the spectral space, we introduce a lightweight auxiliary objective called Spectral Contrastive Regularization (SCR). Although G-HSNO models frequency-aware graph signals in a structured manner, representations from different modali- ties can still be inconsistent collapse within the same band because of noise weak alignment. Intuitively, components that lie in the same band (for example, image and text embeddings at band m) should encode comparable global or local semanties. practice, distributional heterogeneity can cause divergence or entanglement with unrelated spectral patterns. SCR addresses this by applying contrastive loss that encourages intra-band cross-modal consistency while preserving separation across bands. Optionally, the same intra-band contrastive regularization can also be applied to user-side spectral components to further stabilize the spectral space. Formally, let x
(m, and
Xa (m,,xx) denote the m-th band representations of item v from image and text. These form a positive pair. Negatives sampled from either different items v' at the same band or from any item at different bands m' # m. The loss is
exp (sim(x) (mm.in))
exp (sim(x) (m,img) (m.txt)) )
Xe
EscR
log
(8)
Σ (u' (o',m") mm)))A
(mz) (/7)))/7)
where sim(-.-) is cosine similarity, 5 O is a temperature and x (m') denotes a representation from either modality. This regularization aligns cross-modal signals within each band and enforces band-level discriminability. It introduces no extra inference cost and serves as a modular complement to the main objective. Our model is designed to be lightweight and efficient, with all frequency- modules implemented via sparse and batched operations.
3.5 Training and Optimization
The model is trained to predict user-item interaction probabilities from spectral-aware representations. For each pair (u, v), the interaction score is Jue = (z.,. zw), where z, and z, the final user and item embeddings, and (-) is the sigmoid function. The objective combines binary cross-entropy with above auxiliary losses: band-masking consistency loss LsBm and spectral contrastive loss LSCR that aligns modality-specific features within each band. Further, we introduce a simple squared regularization the HSNO kernel and filter to improve training stability. The final loss is
C LBCE + À LSBM + 17 LSCR + LReg-
where X, 77 7 2 control the strength of the auxiliary terms. We optimize the model end to end with mini-batch stochastic gradient descent. No masking rescaling is applied at inference time.

---

4 Experiments
4.1 Experimental Settings
Datasets and Baselines. We conduct experiments on three standard Amazon subsets (Baby, Sports, Clothing) using full-ranking metrics (Recall K, NDCG@K). broad range of collaborative, multi- modal, and graph graph-based baselines are compared. For full dataset details, preprocessing, and bascline list, please refer to Appendix
4.2 Overall Performance Comparison (RQ1)
Table summarizes the top-K, K recommendation performance across three multimodal Amazon datasets. Our proposed SSR achieves consistent and significant improvements over all baseline models. This performance advantage is particularly evident on sparse datasets like Clothing, where SSR outperforms prior frequency-awan models such as SMORE by +5.0% in Recall @ 10. These gains can be attributed to SSR's ability to capture fine-grained, frequency-awan multimodal semantics that are often overlooked insufficiently captured in prior approaches. While recent methods like SMORE leverage frequency-domain projection to suppress modality noise, they treat frequency components uniformly and lack structural modeling of collaborative signals. AlignRec and MMIL introduce advanced alignment or intention modeling mechanisms, but still operate in the time domain and fail to differentiate spectral semantics at varying granularity. In contrast, SSR explicitly decomposes multimodal representations into interpretable frequency bands via spectral graph transformation, dynamically fuses them through gated hyper- operations. and further regularizes mid-band interactions via spectrum- awae contrastive learning. This design enables SSR to not only denoise but also extract highly discriminative and complementary signals across modalities and frequency levels.
Table 1: Recommendation performance on three Amazon benehmarks. SSR achieves consistent
improvements over collaborative, graph-based, and multi-modal baseline.
Datasel
Metric
BPR
LightGCN VBPR
MMGCN GRCN DaaIGNN ReeVAE
LATTICE
BMB
FREEDOM
DiRMM MMIL
AlignRee
SMORE
SSR
R@10 0.0357
0,0479
0.0118
0.3113
0.0538
0.0507
0.050]
0.0561
0.0573
0.0624
0.0617
0.0670
0.0674
0.0680
0,0728
Buby
N4110
R0020
0.0575
0.0192
037754
0,0257
00023
0.0667
0.0649
0.2211
0.0832
0.0285
0.6782
0,0264
0.0811
0.0275
0.0867
0.0111
0.0564
0.0985
0,0334
0.0978
00321
0,0661
0.1035
0.1046
0,063
0.0035
00965
0.1103
0.0395
Noh20
0.0328
0.0787
0.0275
0.0335
00395
0.0416
00408
0.0455
0.0458
0.0491
R@:00 0.0432
0,0569
0.0561
0.0994
0,0607
0.0574
0.0603
0,0288
0.0699
0.0705
0.0687
0,0747
0.0738
0.0622
0,0825
Sports
R69:0
0.0655
0.0864
0.057
0.025
0.0928
0.0881
0.0916
0.0%]
0.087
0.1077
0.1035
0.1133
0.116)
0.142
0.1263
Nár10
0.0241
0,0311
00005
0/000
0.0335
0.0316
0.0348
0.030
0.0557
0.0382
0.0357
0.0405
0.0414
0.0488
0,0449
N6900 0.0298
0,0587
0.0866
0.0766
0.0421
0.6393
0.0431
0.4311
0.443
0,0478
00458
0.0505
0.0517
0.0506
0,0547
0.056]
0.0283
0.0221
0.577
00593
0.0511
0.659
0,0706
Clothing
N8:0 0.0114
0.0303
0,0197
0.0144
0.0162
0.4188
0,01
0.0357
0.0611
0.0227
0,0237
0.663
0.0485
0.0187
0.0277
0.0016
0.0455
0.0917
0.0333
0.874
0.0355
0
0,0348
0.093
0.0356
0,097
0.0600
0.1832
0
N0 0.0138
0.0243
0.0196
0.0151
0.0283
0.0289
0.0227
0.0356
0.0387
0.0409
0.036
0.0478
0.0437
0.0443
0.0466
4.3 Cold-start User Performance (RQ2)
To evaluate model robustness under user cold-start scenarios, examine top-K recommendation performance for users with limited interaction history. As shown in Table 2 our proposed SSR consistently outperforms all baselines across three datasets and four evaluation metrics, with partieu- larly strong gains in Recall @ 20 metrics (e.g., + +10.0% over SMORE on Baby). These improvements validate our key design principle: rather than assuming uniform representation fusion for all users, SSR leverages frequency-aware decomposition and user-specific gating to tailor the semantic em- phasis across low, mid, and high bands. Compared prior models such as SMORE and MMIL. which adopt static fusion schemes or modality alligned latent spaces, SSR introduces gated hyper- spectral operations and spectral contrastive regularization that adaptively enhance discriminative cues even under sparse data. The model's 's ability to selectively amplify figh-frequency discriminative signals is particularly important for personalizing recommendations when strong interaction priors are unavailable, making it especially valuable in cold-start settings. Moreover, the consistent lead across all frequency bands highlights the efficacy of our frequency decomposition design isolating modality-relevant semantics and suppressing irrelevant noise. These results suggest that SSR not only performs well under typical conditions but also generalizes effectively to sparse and unseen user behaviors, confirming its value robust and adaptive recommendation framework.
7

---

Table 2: Performance comparison in cold-start scenarios (users with < 5 interactions). SSR consistently outperforms strong baselines, demonstrating its robustness in sparse conditions and effectiveness in adaptive multimodal modeling.
Model
Amazon-Baby
Amazon-Sports
Amazon-Clothing
10
20
N@ 10
N@
R@ 10
R@
N@
N@
R@
R@20
N@
N@
GRCN
0,0510
0.0770
0,0268
0.0333
0.0556
0.0814
0.0305
0,0370
0.0416
0.0648
0.0213
0,0271
BM3
0.0549
0.0845
0,0288
0.0363
0,0581
0.0920
0.0305
0.0390
0.0424
0,0614
0.0229
0.0276
LATTICE
0.0570
0.0827
0.0298
0.0362
0.0380
0.0570
0.0205
0.0252
0.0414
0.0555
0.0218
0.0254
FREEDOM
0.0535
0.0880
0.0297
0.0384
0,0622
0.0933
0.0328
0.0406
0.0444
0,0671
0.0241
0.0298
MMIL
0.0672
0,1014
0,0377
0.0463
0,0759
0.1141
0,0422
0.0517
0.0635
0.0948
0.0341
0.0423
SMORE
0,0687
0,1019
0.0381
0.0664
0.0788
0.1158
0.0420
0.0512
0.0676
0,09K3
0.0369
0,0446
SSR
0.0765
0.1125
0,0424
0,0516
0.0832
0.1227
0.0439
0,0541
0,0698
0,1012
0,0387
0.0467
Our
Baby
0.32
We SCA
We SAM
Recalig3a
0.328
Sports
Clothing
Recalli3a
We
0.238
0.03
0.338
0.205
0.00
0.308
Daby
0.300
Dabyy Sports
0.08
0.100
Sports
0.855
Sports
Chelkigg
0.05
1e-13 2w-22 1e-t. 1ex00 Effect of Parameter
Ie-33
2x-42 1ad1 Ia-00
Ablation Study
Effect of Parameter 9
Effect of Parametor
Ablation and sensitivity analysis. The left plot shows the impact of removing key components from SSR, validating the effectiveness of each module. The right three plots illustrate the influence of the information bottleneck weight X, contrastive loss weight 17, and the number of frequency bands M, confirming the stability of SSR under a range of hyperparameter settings.
Figure 2:
4.4 Ablation Study and Sensitivity Analysis (RQ3)
We conduct ablations to quantify the contribution of cach component: semantic-aware fusion (SAF), the hyperspectral operator (G-HSNO), spectral regularizers (SBM and SCR), and multimodal imputs. As shown in Fig. 2 removing any component leads to clear performance degradation. Notably, removing SAM causes the most significant drop, confirming the importance of semantically guided decomposition. Excluding G-HSNO also harms accuracy, indicating that cross-band and cross- modality reasoning is vital for capturing diverse user-item patterns. SBM and SCR yield smaller but consistent gains, improving robustness and alignment. Eliminating multimodal inputs and using ID features only leads to the weakest results, highlighting the utility of complementary content signals. These findings show that spectral semanties, adaptive fusion and modality reasoning act in complementary manner within our architecture. We also perform a comprehensive sensitivity analysis over X. 17, and M, and observe consistently stable performance across broad and practically relevant range of hyperparameter settings (the detailed results are reported in Appendix C.I
4.5 Cross-Modality Distribution in Frequency Bands (RQ4)
To investigate how frequency decomposition shapes cross-modal representations, we visualize the distribution of user embeddings across low, mid and high bands for three modalities: ID, visual and textual. As shown in Fig- 3 in the low-frequency band, the three modalities form distinct and well- separated clusters, indicating that this frequency component preserves modality-specific semantics such as identity priors, visual styles, and coarse-grained textual categories. In the mid-frequency band, modality boundaries begin to blur, revealing interaction patterns and semantic alignment across modalities. This observation is consistent with applying frequency- aware fusion using G-HSNO and band-level regularization using SBM to capture synergistic cross modal signals. In the high-frequency band, the embeddings from different modalities become densely entangled, suggesting the emergence of fine- graagedd modallty-agnossie noise. This validates the necessity of spectral decomposition as core design: it not only disentangles semantics across frequency and modality axes but also provides an interpretable basis for adaptive fusion and regularization. The observed patterns strongly support our hypothesis that frequency-awar modeling enables structured representation evolution, and reinforce the design effectiveness of our SBM and G-HSNO components.
representations that are highly discriminative but also sensitive to
8

---

Low Frequency
Mid Frequency
High Frequency
20
Visual
Misul
10
20
Tectual
Lohte Dim
LSNE pim
10
20
Visaa
-30
Toxtual
LONE Diim
1-NNE Dim
L-SNE Dm
Figure 3: t-SNE visualization of user embeddings across frequency bands. Each subfigure
illustrates ID, Visual, and Textual embedding distributions under a specific band.
Cross-Modality Distance
Low Frequency
Mid Frequency
High Frequency
0.6
01E, Vinmi
100
Cold-start
Lold-start
Cold-ateri
0.5
40
Non cold
Non cold
Non-cold
Dennity
CO
0.3
6.1
0.22
Gabing Welgght
Gabing Waight
Gating Weight
Figure 4: Left: Cross-modality center distances across frequency bands, highlighting increasing alignment in mid-frequency and moodality-ggnosii fusion in high-frequency regions. Right: KDE plots of frequency gating weights for cold-start vs. non-cold users.
4.6 Cross-Frees Cross-Frequency Analysis of Modality Center Distances (RQ5)
We further assess cross-modal alignment across frequency bands by measuring pairwise distances between the centers of the ID,, visual and textual representations. Concretely, for each band we compute a modality center as the mean embedding over items and then evaluate distances between modality centers. As shown in Fig. the distances are minimized in the mid-frequency region, indicating that this band best captures shared cross-modal semantics. In contrast, low-frequency bands encode stable, modality-specific structure, whereas high-frequency bands reflect sparse or noisy variation. These asymmetric patterns motivate differentiated modeling across bands. Our design leverages this by applying spectrum-spectiee fusion (G-HSNO) and band-level regularization (SBM) in the mid-freqqency region, where cross- cross-modal modal synergy is most pronounced.
4.7 Adaptive Spectral Modulation under Representation Uncertainty (RQ6)
Our design is grounded in the idea that frequency components reflect different semantic roles, and that adapting their influence based on input uncertainty is key to effective recommendation. To validate this hypothesis, we conduct an analysis under the cold-start scenario. As shown in Fig. 4 cold-start items rely more on low and mid frequency signals, while non-cold items emphasize high-frequency cues. This behavior emerges from the interplay of spectral decomposition. G-HSNO, and contrastive regularization. These findings highlight that spectral semantics are not uniformly informative, and their utility is tightly coupled with data sparsity and user context. This also suggests that frequency- aware mechanisms can serve as proxy for uncertainty estimation in representation learning. A thorough and comprehensive analysis is provided in Appendix C.3
Conclusion
In this paper, we propose a structured spectral learning framework for multimodal graph recommenda- tion that addresses modality noise, semantic inconsistency, and propagation instability via a four-stage pipeline: decomposition, band-level modulation, hyperspectral fusion, and alignment. Extensive experiments validate its effectiveness and robustness across diverse datasets. Future directions include integrating LLMs for reasoning-awan spectral graphs, designing adaptive spectral controllers, and extending to broader graph inference tasks such as dynamic modeling and temporal reasoning.

---

References
[1] Yuqing Liu, Yu Wang, Lichao Sun, and Philip S Yu. Rec-gpt4v: Multimodal recommendation with large vision-language models. arXiv preprint arXiv:2402.08670, 2024.
[2] Daniele Malitesta, Giandomenico Cornacchia, Claudio Pomo, Felice Antonio Merra, Tom- maso Di Noia, and Eugenio Di Sciascio. Formalizing multimedia recommendation through multimodal deep learning. ACM Transactions on Recommender Systems, 2024.
[3] Yang Xu, Gao Cong, Lei Zhu, and Lizhen Cui. Mmpoi: multi-modal content-aware framework for poi recommendations, In Proceedings of the ACM Web Conference 2024, pages 3454-3463, 2024.
[4] Jinfeng Xu, Zheyu Chen, Shuo Yang, Jinze Li, Hewei Wang, and Edith CH Ngai. Mentor: multi-level self supervuuee learning for multimodal recommendation. Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages
2025.
[5] Li He, Hongxu Chen, Dingxian Wang, Shoaib Jameel, Philip Yu, and Guandong Xu. Click- through rate prediction with multi-modal hypergraphs. In Proceedings of the 30th ACM International Conference on Information & Knowledge Management, pages 690-699, 2021.
[6] Hongyu Zhou, Xin Zhou, Zhiwei Zeng, Lingzi Zhang, and Zhiqi Shen. A comprehensive survey on multimodal recommender systems: Taxonomy, evaluation, and future directions. arXiv preprint arXiv:2302.04473, 2023.
[7] Wei Yang, Tengfei Huo, Zhiqiang Liu, and Chi Lu. based multi- contrastive learning for recommendation. In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 2339-2343, 2023.
[8] Wei Wei, Chao Huang, Lianghao Xia, and Chuxu Zhang. Multi-modal self celf-super learning for recommendation. In Proceedings of the ACM web conference 2023, pages 790-800, 2023.
[9] Xinglong Wu, Anfeng Huang, Hongwei Yang, Hui He, Yu Tai, and Weizhe Zhang. Towards bridging the cross-modal semantic gap for multi-modal recommendation. arXiv preprint 2rXiv:2407.054420, 2024.
[10] Qijiong Liu, Jieming Zhu, Yanting Yang, Quanyu Dai, Zhaocheng Du, Xiao-Ming Wu, Zhou Zhao, Rui Zhang, and Zhenhua Dong. Multimodal pretraining, adaptation, and generation for recommendation: A survey. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 6566-6576, 2024.
[11] Guipeng Xv, Xinyu Li, Ruobing Xie, Chen Lin, Chong Liu, Feng Xia, Zhanhui Kang, and Leyu Lin. Improving multi-modal recommender systems by denoising and aligning multi-modal content and user feedback. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 3645-3656, 2024.
[12] Yuxin Qi, Quan Zhang, Xi Lin, Xiu Su, Jiani Zhu, Jingyu Wang, and Jianhua Li. Seeing beyond noise: Joint graph structure evaluation and denoising for multimodal recommendation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 12461-12469, 2025.
[13] Zixuan Yi, Zijun Long, Iadh Ounis, Craig Macdonald, and Richard Mccreadie. Enhancing recommender systems: Deep modality alignment with large multi-modal encoders. ACM Transactions on Recommender Systems, 3(4):1-25, 2025.
[14] Yucong Luo. Qitao Qin, Hao Zhang, Mingyue Cheng, Ruiran Yan, Kefan Wang, and Jie Ouyang. Molar: Multimodal llms with collaborative filtering alignment for enhanced sequential recommendation. arXiv preprint arXiv:2412 22.2.111 18176, 2024.
[15] Rongqing Kenneth Ong and Andy WH Khong. Spsstrum-based modality representation fusion graph convolutional network for multimodal recommendation. arXiv preprint 24v:2411.11478 2024.
10

---

[16] Wei Yang. Jie Yang, and Yuan Liu. Multimodal optimal transport knowledge distillation for cross-domain recommendation. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, pages 2959-2968. 2023.
[17] Xinchen Luo, Jiangxia Cao, Tianyu Sun, Jinkai Yu, Rui Huang, Wei Yuan, Hezheng Lin, Yichen Zheng, Shiyao Wang, Qigen Hu, et al. Qarm: Quantitative alignment multi-modal recommendation at kuaishou. arXiv preprint arXiv:241 I. 1,1199, 2024.
[18] Xiang Wang, Hongye Jin, An Zhang, Xiangnan He, Tong Xu, and Tat-Seng Chua. Disentangled graph collaborative filtering. In Proceedings of the 43rd international ACM SIGIR conference on research and development in information retrieval, pages 1001-1010, 2020.
[19] Kang Liu, Feng Xue, Dan Guo, Peijie Sun, Shengsheng Qian, and Richang Hong. Multimodal graph contrastive learning for multimedia-based recommendation. IEEE Transactions on Multimedia, 25:9343-9355. 2023.
[20] Kang Liu, Feng Xue, Dan Guo. Le Wu, Shujie Li, and Richang Hong. Megef: Multimodal entity graph collaborative filtering for personalized recommendation. ACM transactions on information systems, 11(2):1-27, 2023.
[21] Wenqian Ye, Guangtao Zheng, Yunsheng Ma, Xu Cao, Bolin Lai, James M Rehg, and Aidong Zhang. Mm-spubench: Towards better understanding of spurious biases in multimodal Ilms. arXiv preprint arXiv:2406. 17126, 2024.
[22] Huishi Luo, Fuzhen Zhuang, Ruobing Xie, Hengshu Zhu, Deqing Wang. Zhulin An, and Yongjun Xu. A survey on causal inference for recommendation. The Innovation, 5(2), 2024.
[23] Shuyuan Xu, Jianchao Ji, Yunqi Li, Yingqiang Ge, Juntao Tan, and Yongfeng Zhang. Causal inference for recommendation: Foundations, methods and applications. ACM Transactions on Intelligent Systems and Technology, 2023.
[24] Junpeng Fang. Gongduo Zhang, Qing Cui, Lihong Gu, Longfei Li, Jinjie Gu, and Jun Zhou. Counterfactual data augmentation for debiased coupon recommendations based potential knowledge. In Companion Proceedings of the ACM Web Conference 2024, pages 93-102, 2024.
[25] Fangye Wang. Yingxu Wang. Dongsheng Li, Hansu Gu, Tun Lu, Peng Zhang, and Ning Gu. Cl4ctr: A contrastive learning framework for etr prediction. In Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pages
2023.
[26] Shuaiyang Li, Feng Xue, Kang Liu, Dan Guo, and Richang Hong. Multimodal graph causal recommendation. IEEE Transactions on Knowledge and Data
embedding for multimedia- Engineering. 2024.
[27] Sungjune Kim, Seongjun Yun, Jongwuk Lee, Gyusam Chang, Wonseok Roh, Dae-Neung Sohn. Jung-Tas Tae Lee, Hogun Park, and Sangpil Kim. Self-supervised multimodal graph convolutional network for collaborative filtering. Information Sciences, 653: 133:60, 2024.
[28] Jiwan Kim, Hongseok Kang, Sein Kim, Kibum Kim, and Chanyoung Park. Disentangling and generating modalities for recommendation in missing modality scenarios. In Proceedings of the 48th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1820-1829, 2025.
[29] Xixun Lin, Rui Liu, Yanan Cao, Lixin Zou, Qian Li, Yongxuan Wu, Yang Liu, Dawei Yin, and Guandong Xu. Contrastive -isaaiit-ddsentangled learning for multimodal recommendation. ACM Transactions on Information Systems, 43(3):1-31, 2025.
[30] Jiajie Su, Chaochao Chen, Weiming Liu, Yuhang Wang, Yihao Wang, Zheqi Lv, Xiaolin Zheng, and Jianwei Yin. Modality-aware diffusion augmentation with consistent subspace disentanglement for session-based recommendation. In Proceedings of the 3 ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2, pages 2669, 2025.
[31] Xin Zhou and Chunyan Miao. Disentangled graph variational auto-encoder for multimodal recommendation with interpretability. IEEE Transactions on Multimedia, 26:7543-7554, 2024.
11

---

[32] Jiafeng Xia, Dongsheng Li, Hansu Gu, Tun Lu, Peng Zhang, Li Shang, and Ning Gu. Frequency- aware graph signal processing for collaborative filtering. In Companion Proceedings of the ACM on Web Conference 2025, pages 1417-1421, 2025.
[33] Shaowen Peng, Kazumari Sugiyama, and Tsunenori Mine. Less is more: Reweighting important spectral graph features for recommendation. In Proceedings of the 45th International ACM SIGIR conference on research and development in information retrieval, pages 1273-1282, 2022.
[34] Zhenyi Fan, Hongbin Zhang, Guangyu Lin, Lianglun Cheng, Zhuowei Wang, and Chong Chen. Hierarchical multi-frequeng transform for sequential recommendation. In 2024 27th International Conference on Computer Supported Cooperative Work Design (CSCWD), pages 1559-1564. IEEE, 2024.
[35] Shijie Luo, Jianxia Chen, Tianci Yu, Shi Dong, Gaohang Jiang, and Ninglong Ding. Dual frequency-based temporal sequential recommendation. In 2024 International Joint Conference
on Neural Networks (IJCNN), pages 1-8. IEEE, 2024.
[36] Yichi Zhang, Guisheng Yin, and Yuxin Dong. Contrastive learning with frequency-domain interest trends for sequential recommendation. In Proceedings of the 17th ACM conference on recommender systems, pages 141-150, 2023,
[37] Yehjin Shin, Jeongwhan Choi, Hyowon Wi, and Noseong Park. An attentive inductive bias for sequential recommendation beyond the self-attention. In Proceedings of the AAAI conference on artificial intelligence, volume 38, pages 8984-8992, 2024.
[38] Xinyu Du, Huanhuan Yuan, Pengpeng Zhao, Jianfeng Qu, Fuzhen Zhuang, Guanfeng Liu, Yanchi Liu, and Victor Sheng. Frequency enhanced hybrid attention network for sequential recommendation. In Proceedings of the 46th international ACM SIGIR conference on research and development in information retrieval, pages 78-88, 2023.
[39] Yanhua Huang, Weikun Wang, Lei Zhang, and Ruiwen Xu. Sliding spectrum decomposition for diversified recommendation. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pages 3041-3049, 2021.
[40] Yongqiang Han, Hao Wang, Kefan Wang, Likang Wu, Zhi Li, Wei Guo, Yong Liu, Defu Lian, and Enhong Chen. Efficient noise-decoupling for multi-behavior sequential recommendation. In Proceedings of the ACM Web Conference 2024, pages 3297-3306, 2024.
[41] Chanwoo Kim, Jinkyu Sung, Yebonn Han, and Joonseok Lee. Graph spectral filtering with chebyshev interpolation for recommendation. arXiv preprint arXiv:2505.00552 2025.
[42] Lanling Xu, Zhen Tian, Bingqian Li, Junjie Zhang, Daoyuan Wang, Hongyu Wang. Jinpeng Wang, Sheng Chen, and Wayne Xin Zhao. Sequence-level semantic representation fusion for recommender systems. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pages
2024.
[43] Yang Li, Qi' Ao Zhao, Chen Lin, Jinsong Su, and Zhilin Zhang. Who to align with: Feedback- oriented multi-modal alignment recommendation systems. In Proceedings of the 47th International ACM SIGIR Conference Research and Development in Information Retrieval, pages 667-676, 2024.
[44] Zixuan Yi and ladh Ounis. A unified graph transformer for overcoming isolations in multi-modal recommendation. In Proceedings of the 18th ACM Conference Recommender Systems, pages 518-527, 2024.
[45] Haoyue Bai, Le Wu, Min Hou, Miaomiao Cai, Zhuangzhuang He, Yuyang Zhou, Richang Hong, and Meng Wang. Multimodality invariant learning for multimedia-hased new item recommendation. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 677-686, 2024.
[46] Junliang Yu, Xin Xia, Tong Chen, Lizhen Cui, Nguyen Quoe Viet Hung, and Hongzhi Yin. Xsimgel: Towards extremely simple graph contrastive learning for recommendation. IEEE Transactions on Knowledge and Data Engineering, 36(2):913-926, 2023.
12

---

[47] Yifan Liu, Kangning Zhang, Xiangyuan Ren, Yanhua Huang, Jiarui Jin, Yingjie Qin, Ruilong Su, Ruiwen Xu, Yong Yu, and Weinan Zhang. Alignrec: Aligning and training multimodal recommendations. In Proceedings of the 33rd ACM International Conference Information and Knowledge Management, pages 1503-1512, 2024.
[48] Xinyu Du, Huanhuan Yuan, Pengpeng Zhao, Junhua Fang, Guanfeng Liu, Yanchi Liu, Victor S Sheng, and Xiaofang Zhou, Contrastive enhanced slide filter mixer for sequential recommen- dation. In 2023 IEEE 39th Interaational Conference Data Engineering (ICDE), pages 2673-2685. IEEE, 2023.
[49] Yi Wang, Conrad M Albrecht, Nassim Ait Ali Braham, Chenying Liu, Zhitong Xiong, and Xiao Xiang Zhu. Decoupling common and unique representations for multimodal self- supervised learning. In European Conference on Computer Vision, pages 286-303. Springer, 2024.
[50] Sirnam Swetha, Mamshad Nayeem Rizve, Nina Shvetsova, Hilde Kuehne, and Mubarak Shah. Preserving modality structure improves multi-modal learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 21993-22003, 2023.
[51] Ruining He and Julian McAuley. Vbpr: visual bayesian personalized ranking from implicit feedback. In Proceedings of the AAAI conference on artificial intelligence, volume 30, 2016.
[52] Xu Chen, Hanxiong Chen, Hongteng Xu, Yongfeng Zhang, Yixin Cao, Zheng Qin, and Hongyuan Zha. Personalized fashion recommendation with visual explanations based on multimodal attention network: Towards visually explainable recommendation. In Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 765-774, 2019.
[53] Wei Yang, Haoran Zhang, and Li Zhang. Variational invariant representation learning for multimodal recommendation. In Proceedings of the 2024 SIAM International Conference on Data Mining (SDM), pages 762-760. SIAM, 2024.
[54] Yashar Deldjoo, Markus Schedl, and Peter Knees. Content-driven music recommendation: Evolution, state of the art, and challenges. arXiv preprint arXiv:2107.11803, 2021.
[55] Senrong Xu, Liangyue Li, Yuan Yao. Zulong Chen, Han Wu, Quan Lu, and Hanghang Tong. Musenet: Multi-scenario learning for repeat-aware personalized recommendation. In Proceed- ings of the Sixteenth ACM International Conference on Web Search and Data Mining, pages 517-525, 2023.
[56] Wang-Cheng Kang, Chen Fang, Zhaowen Wang, and Julian McAuley. Visually-aware fash- ion recommendation and design with generative image models. In 2017 IEFE international conference on data mining (ICDM), pages 207-216. IEEF, 2017.
[57] Yinwei Wei, Xiang Wang, Liqiang Nie, Xiangnan He, Richang Hong, and Tat-Seng Chua. Mmgen: Multi-mode graph convolution network for personalized recommendation of micro- video. In Proceedings of the 27th ACM international conference on multimedia, pages 1437- 1445, 2019.
[58] Yinwei Wei, Xiang Wang, Liqiang Nie, Xiangnan He, and Tat-Seng Chua. Graph-refined convolutional network for multimedia recommendation with implicit feedback. In Proceedings of the 28th ACM international conference multimedia, pages 3541-3549, 2020.
[59] Qifan Wang, Yinwei Wei, Jianhua Yin, Jianlong Wu, Xuemeng Song, and Liqiang Nie. Dualgnn: Dual graph neural network for multimedia recommendation. IEEE Transactions on Multimedia, 10844 2021.
[60] Junliang Yu, Hongzhi Yin, Xin Xia, Tong Chen, Lizhen Cui, and Quoe Viet Hung Nguyen. Are graph augmentations necessary? simple graph contrastive learning for recommendation. In Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1294-1303, 2022.
13

---

[61] Tengyue Han, Pengfei Wang, Shaozhang Niu, and Chenliang Li. Modality matches modality: Pretraining modality- disentangled item representations for recommendation. In Proceedings of the ACM Web Conference 2022, pages 2058 2066, 2022.
[62] Zhulin Tao, Xiaohao Liu, Yewei Xia, Xiang Wang, Lifang Yang, Xianglin Huang, and Tat- Seng Chua. Self-supervised learning for multimedia recommendation. IEEE Transactions on Multimedia, 2022.
[63] Xin Zhou. Hongyu Zhou, Yong Liu, Zhiwei Zeng, Chunyan Miao, Pengwei Wang, Yuan You, and Feijun Jiang. Bootstrap latent representations for multi-modal recommendation. In Proceedings of the ACM Web Conference 2023, pages 845-854, 2023.
[64] Zixuan Yi, Xi Wang, Iadh Ounis, and Craig Macdonald. Multi-modal graph contrastive learning for micro-video recommendation. In Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1807-1811, 2022.
[65] Jinghao Zhang, Yanqiao Zhu, Qiang Liu, Shu Wu, Shuhui Wang, and I Liang Wang. Mining latent structures for multimedia recommendation. In Proceedings of the 29th ACM International Conference on Multimedia, pages 3872-3880, 2021.
[66] Xin Zhou and Zhiqi Shen. A tale of two graphs: Freezing and denoising graph structures for multimodal recommendation. In Proceedings of the s1 ACM International Conference on Multimedia, pages 935-943, 20233.
[67] Wei Yang and Qingchen Yang. Multimodal-awar multi-intention learning for recommendation. In Proceedings of the 32nd ACM International Conference on Multimedia, pages 5663-5672, 2024.
[68] Zhiqiang Guo, Guohui Li, Jianjun Li, and Huaicong Chen. Topicvae: Topic- disentangle- ment representation learning for enhanced recommendation. In Proceedings of the 30th ACM International Conference Multimedia, pages 511-520, 2022.
[69] Wei Wei, Jiabin Tang, Lianghao Xia, Yangqin Jiang, and Chao Huang. Promptmm: Multi-modal knowledge distillation for recommendation with prompt-tuning. In Proceedings of the ACM Web Conference 2024, pages 3217-3228, 2024.
[70] Yangqin Jiang. Lianghao Xia, Wei Wei, Da Luo, Kangyi Lin, and Chao Huang. Diffmmm: Multi- modal diffusion model for recommendation. In Proceedings of the 32nd ACM International Conference Multimedia, pages 7591-7599, 2024.
[71] Meiyu Liang, Junping Du, Xiaowen Cao, Yang Yu, Kangkang Lu, Zhe Xue, and Min Zhang. Semantic structure enhanced contrastive adversarial hash network for cross-media representation learning. In Proceedings of the 30th ACM International Conference on Multimedia, pages 277-285, 2022.
[72] Rui Zhao, Rui Zhong, Haoran Zheng. Wei Yang, Chi Lu, Beihong Jin, Peng Jiang, and Kun Gai. Hierarchical sequence id representation of large language models for large-scale recommendation systems. In Companion Proceedings of the ACM on Web Conference 2025, pages 641-650, 2025.
[73] Yu Xia, Rui Zhong, Hao Gu, Wei Yang, Chi Lu, Peng Jiang, and Kun Gai. Hierarchical tree search-based user lifelong behavior modeling on large language model. In Proceedings of the 48th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1758-1766 2025.
[74] Hao Gu, Rui Zhong, Yu Xia, Wei Yang, Chi Lu, Peng Jiang, and Kun Gai. 4ec: reasoning, reflection, and refinement framework for recommendation systems. In Proceedings of the Nineteenth ACM Conference on Recommender Systems, pages 41 411-421, 2025.
[75] Yu Xia, Rui Zhong, Zeyu Song, Wei Yang, Junchen Wan, Qingpeng Cai, Chi Lu, and Peng Jiang. Trackrec: Iterative alternating feedback with chain-of-though via preference alignment for recommendation. arXiv preprint arXiv:2508. 15388 2025.
14

---

[76] Yiqun Chen, Qi Liu, Yi Zhang, Weiwei Sun, Xinyu Ma. Wei Yang, Daiting Shi, Jiaxin Mao, and Dawei Yin. Tourrank: Utilizing large language models for documents ranking with tournament-inspired strategy. In Proceedings of the ACM on Web Conference 2025, pages 1638-1652, 2025.
[77] Yiqun Chen, Lingyong Yan, Weiwei Sun, Xinyu Ma, Yi Zhang, Shuaiqiang Wang, Dawei Yin, Yiming Yang, and Jiaxin Mao. Improving ectrieval-augmente generation through multi-agent reinforcement learning. arXiv preprint arXiv:2501. 15228, 2025.
[78] Zhefan Wang, Yuanqing Yu, Wendi Zheng, Weizhi Ma, and Min Zhang. Macree: A multi-agent collaboration framework for recommendation. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 2760-2764, 2024.
[79] Wei Yang and Jesse Thomason. Learning to deliberate: Meta-policy collaboration for agentic Ilms with multi-agent reinforcement learning. arXiv preprint arXiv:2509.03817, 2025.
[80] Wen Ye, Wei Yang, Defu Cao, Yizhou Zhang, Lumingyuan Tang, Jie Cai, and Yan Liu. Domain- oriented time series inference agents for reasoning and automated analysis. arXiv preprint arXiv:2410.0400 04047, 2024.
[81] Tianxin Wei, Bowen Jin, Ruirui Li, Hansi Zeng, Zhengyang Wang, Jianhui Sun, Qingyu Yin, Hanqing Lu, Suhang Wang, Jingrui He, et al. Towards unified multi-modal personalization: Large vision-language models for generative recommendation and beyond. arXiv preprint arXiv:24033 10667, 2024.
[82] Zhibin Yang, Jiwei Qin, Jie Ma, and Donghao Zhang. Farec: frequency domain enhanced filter for sequential recommendation. Computing, 107(5):1 14, 2025.
[83] Junjie Zhang, Ruobing Xie, Hongyu Lu, Wenqi Sun, Wayne Xin Zhao, Yu Chen, and Zhanhui Kang. arqueenc--augmentee mixture-of mixture-of-heeerogeen heterogeneous- experts framework for sequential recommendation. In Proceedings of the ACM on Web Conference 2025, pages 2596-2605, 2025.
[84] Yuxi Liu, Lianghao Xia, and Chao Huang. Selfgnn: Self-supervised graph neural networks for sequential recommendation. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1609-1618, 2024.
[85] Haitong Luo, Xuying Meng, Suhang Wang, Hanyun Cao, Weiyao Zhang, Yequan Wang, and Yujun Zhang. Spectral- graph neural networks for complementary item recommendation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 8868-8876. 2024.
[86] Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. Advances in neural information processing systems, 2016.
[87] Felix Wu, Amauri Souza, Tianyi Zhang, Christopher Fifty, Tao Yu, and Kilian Weinberger. Simplifying graph convolutional networks. In International conference on machine learning. pages 6861-6871. Pmlr, 2019.
[88] Steffen Rendle, Christoph Freudenthaler, Zeno Gantner, and Lars Schmidt-Thieme Bpr: Bayesian personalized ranking from implicit feedback. arXiv preprint arXiv: 2012.
[89] Xiangnan He, Kuan Deng, Xiang Wang, Yan Li, Yongdong Zhang, and Meng Wang. Lightgen: Simplifying and powering graph convolution network for recommendation. In Proceedings of the 43rd International ACM SIGIR conference on research and development in Information Retrieval, pages 239-648, 2020.
[90] Ilya Shenbin, Anton Alekseev, Elena Tutubalina, Valentin Malykh, and Sergey I Nikolenko. Recvae: A new variational autoencoder for top-n recommendations with implicit feedback. In Proceedings of the 13th international conference on web search and data mining, pages 528-536, 2020.
15

---

[91] Xin Zhou. Mmrec: Simplifying multimodal recommendation. In Proceedings of the 5th ACM International Conference on Multimedia in Asia Workshops, pages 1-2, 2023.
[92] Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedfor- ward neural networks. In Proceedings of the thirleenth international conference artificial intelligence and statistics, pages 249-256. JMLR Workshop and Conference Proceedings, 2010.
[93] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint 1121v91412.6980, 2014.
16

---

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 abstract and introduction clearly summarize the contributions: structured four-stage framework for "requency-awane multimodal recommendation, intro- ducing spectral decomposition, band-level masking, hyperspectral fusion, and contrastive alignment. These align with both the method and results sections.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: We discuss limitations in Appendix C.5. They include the sensitivity to the band granularity hyperparameter, the use of fixed spectral basis that may underfit highly non-stationary patterns, and the current focus on static graphs rather than temporal dynamics.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
The paper focuses on algorithmic design and empirical evaluation without new theoretical results.
Justification:
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that affects the main claims and/or conclusions of the paper (regardless whether the code and data are provided or not)?
Answer: [Yes]
The experimental settings, datasets, metrics, hyperparameters, and training details are documented in Section 4 and Appendix B. The reproducibility of results is prioritized throughout.
Justification:
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification: The paper uses publicly available Amazon benchmark datasets and indicates that code and instructions are included in the supplementary material for reproducibility.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: Section 4 and Appendix provide details on data preprocessing, model configurations, optimization strategy, and evaluation metrics.
7. Experiment statistical significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer: [No]
Justification: While the results are consistent across datasets, the paper does not explicitly report error bars or statistical significance tests.
17

---

8. Experiments compute resources
Question:
For each experiment, does the paper provide sufficient information on the com-
puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Answer: [Yes]
Justification: Section 4 and Appendix B provide details data preprocessing, model configurations, optimization strategy, and compute resources.
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics http://pgw//euuuis...cc/aabb/aaa
Answer: [Yes]
Justification:
The work is conducted on publicly available datasets and involves no human
subjects or sensitive data. adheres to ethical principles of transparency, reproducibility, and fairness.
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: Appendix C.4 highlights positive impacts such as more robust and trans- parent personalization through frequency aware modeling. It also notes risks including higher computational cost, sensitivity to the choice of frequency bands, reliance on fixed transformation basis, and limited support for dynamic behaviors.
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The model does not involve high-risk assets like generative LLMs scraped datasets. It uses established public datasets with minimal misuse risk.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: The paper uses Amazon benchmark datasets (e.g., Baby, Sports, Clothing) and appropriately cites their sources in the main text and references.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: The paper does introduce new datasets pretrained models, and proposes new architecture trained on existing datasets.
14. Crowdsourcing and research with human subjects
Question: For crowdsoureing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: This paper does not involve any human subjects or crowdsourcing. Institutional review board (IRB) approvals or equivalent for research with human subjects
18

---

Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: The paper does not include human-subject research and does not require IRB review.
Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods in this research?
Answer: [NA]
Justification: The method does not rely on LLMs. introduces graph spectral reasoning model with no LLM-based component in the modeling pipeline.
19

---

A Problem Formulation
We focus on the task of personalized recommendation with multimodal item content, where the goal is to predict user preferences by leveraging both historical interactions and rich item descriptions. Let U and V denote the sets of users and items, respectively. The observed implicit feedback is represented by a binary interaction matrix R {0, 1] u|x|vi where R indicates that user has interacted with item v, and Ru = 0 denotes unobserved behavior. Each user u E U and item E V is associated with ID-based embedding e e/e Red that encodes collaborative filtering signals. In addition, each item is accompanied by multimodal content from a set of modalities C {img, txt), where e E Fd denotes the representation of item e in modality C.
To unify both interaction and multimodal semantics, we formulate the recommendation scenario as a graph-based learning problem. Specifically, we construct bipartite user-item graph G = EW, where the node set N U U contains users and items, and the edge set & _ U V reflects observed interactions. The adjacency matrix A f0. 1 M captures the connectivity structure of the interaction graph.
Under this formulation, the ID embeddings and multimodal features can be treated semantic signals defined over the graph G. The recommendation task thus becomes a graph signal inference problem: learning spectral-aware node representation function f W Ie that jointly captures topological context and content semantics. The predicted relevance score between user u and item computed as
fao = f(u) T f(v),
(10)
where f(-) denotes the frequency-aware and task-adaptive representation for each node. The system then ranks all candidate items based on fue and recommends the top-N most relevant items.
B Experimental Settings
B.1 Datasets
To comprehensively evaluate the effectiveness of our proposed framework, we conduct experiments on three representative subsets of the Amazon Product Review corpu widely adopted in multi- modal recommendation literature [5] 51). We select categories with diverse product types and rich multimodal metadata: Baby, Sports and Outdoors, and Clothing, Shoes and Jewelry (referred to as Baby, Sports, and Clothing). Each dataset contains explicit user-item interaction records along with high-quality product images and textual descriptions. To ensure data reliability and evaluation fairness, we apply the standard 5-core preprocessing. retaining users and items with at least five interactions. These features serve as the multimodal input for all methods that support side content. Dataset statistics are reported in Table 3
Table 3: Statistics of the Amazon datasets used in our experiments.
Dataset
#Users
#Items
#Interactions
Interaction Density
Baby
19,445
7,050
139.110
0.101%
Sports
35,598
18,357
256,308
0.039%
Clothing
39,387
23,033
237,488
0.026%
B.2 Baseline Models
We benchmark our approach against a diverse suite of strong baseline models spanning three major categories: collaborative filtering (CF), multimodal recommendation (MM), and graph-based archi- tectures (GNN-based).. In the CF category, we consider BPR [88], foundational pairwise ranking model based on matrix factorization, and LightGCN 89 which simplifies GCNs by removing non-linear components for efficient collaborative signal propagation. For multimodal baselines, we include VBPR [5T), which enhances MF with visual signals; MMGCN [57]. GRCN (58). and Dual- GNN [59]. which incorporate modality- aware graph learning designs. We further compare with more
http://Jmcauley uesd. eed.d.edu/caa acdu/data/ant http///aaaaammazo//////
20

---

recent models that incorporate autoencoder, self- sule-supe learning or regularization techniques, such as RecVAE 90Me 62]. LATTICE [65]. BM3 [6]. and FREEDOM [T]. Finally, we include advanced models leveraging diffusion processes and alignment strategies, including AlignRec [47], and the frequency-aware method SMORE [15]
DiffMM 70, MMIL
B.3 Evaluation Protocol
We evaluate with full ranking protocol that reflects practical deployment. For each test user the model ranks all items not seen training. We report Recall K and NDCG @K K for K E {10, 20). Recall @ K measures top K hit coverage. NDCG@K K measures rank aware relevance.
We build splits in chronological order with 80/10/10 ratio for train, validation, and test. During training we use negative sampling. Each positive interaction is paired with one randomly chosen item that the user did not interact with to provide contrastive supervision.
B.4 Implementation Details
We implement our method using PyTorch within the MMRec benchmarking framework [91]. We use 64-dimensional embedding vectors for all item and user representations and apply Xavier initializa- tion [92]. The model is optimized using the Adam optimizer [93] with a batch size of 2048. Learning rates are tuned from {0.0001, 0.0005, 0.001, 0.005] using the validation set. Early stopping is trig- gered if Recall 20 does not improve within 20 validation steps. We conduct extensive ablations on the number of frequency bands M {2, 3, 4, 5) and evaluate regularization weights for the spectral consistency loss, contrastive term and regularization term from {0.0001, 0.001, 0.01, 0.1, 1.03. All hyperparameter choices selected based validation performance. Our code and preprocessed datasets will be released to ensure reproducibility.
C Experiments Analysis
C.1 Sensitive Analysis
To evaluate the robustness and generalizability of our approach, conduct parameter sensitivity experiments on three key hyperparameters: the spectral masking regularization weight X, the spectral contrastive regularization weight v). and the number of frequency bands M used in decomposition. As shown in F our model exhibits stable performance across a wide range of values, underscoring its robustness to hyperparameter choices. For X, observe consistent performance peak around 10-2, with degradation when À becomes excessively large (2 0.1), suggesting that overly aggressive suppression of spectral noise may harm useful information flow. A similar pattern emerges for n, where moderate contrastive regularization improves spectral alignment, but large values quickly deteriorate performance due ver-constraining the representation space. Finally, varying the number of frequency bands M reveals that three- or four-band decomposition provides the best trade-off: too few bands limit spectral expressiveness, while too many introduce noise and overfitting. These findings validate our design principle of moderate, structure- spectral decomposition with targeted regularization, and demonstrate that our model achieves strong results without requiring extensive hyperparameter tuning.
C.2 Cross-Frequency Analysis of Modality Center Distances
We examine the spectral dynamics of modality alignment by measuring pairwise distances between the centers of ID, visual and textual representations across frequency bands. As shown in Fig. 4 the distances are smallest in the mid frequency region. This suggests that this band captures shared semantic signals across modalities. The effect is meaningful and not due to chance. Cross modal peaks intermediate spectral scales. The low
coherence is not uniform across the spectrum. frequency region encodes stable modality specific structure such as identity priors or global style. The high frequency region highlights sharp or noisy components that are often unique to one modality. These asymmetric patterns support differentiated strategies for each band. Our architecture follows this idea. It applies spectrum specific fusion (G-HSNO) and regularization (SBM) the mid frequency band where cross modal synergy is strongest. This analysis supports our central claim.
21

---

Frequency aware modeling exposes the spectral locality of modality aligmment and clarifies semantic granularity that conventional fusion would hide.
C.3 Adaptive Spectral Modulation under Representation Uncertainty
Our framework is built on the premise that different frequency components carry distinct semantic roles, ranging from stable structural priors to fine-grained discriminative cues, and that effective recommendation requires instance-awer aware modulation across this spectrum. To validate this capability, we examine controlled setting where item representations vary semantic certainty, namely the cold-start scenario. As shown in Fig. 4 cold-start items exhibit dominant reliance on low- and mid- frequency signals, reflected by sharply peaked spectral weights in these bands, while frequenyy components are significantly attenuated. Non-cold items, in contrast, show more distributed and gegh-frequency-skeweee preferences that leverage richer personalized cues. This divergence arises not from a single module but from our unified design that combines spectral decomposition, gated hybrid spectral operators (G-HSNO), and contrastive regularization. The model does not apply a static fusion; it learns to regulate spectral emphasis based on input uncertainty. This analysis empirically substantiates the necessity of frequency-aware modeling and confirms the system's 's ability to achieve fine-gen fine-grained, context-adaptive representation control.
C.4 Discussion
Our study demonstrates that arequency-aware modeling provides structured and interpretable lens for understanding multimodal interactions in recommendation systems. By decomposing user-item representations into distinct spectral bands, the proposed framework captures complementary semantic cues across modalities and enables adaptive fusion guided by spectral semantics. The integration of band-level modulation and spectrum-level regularization further enhances robustness against modality noise and data sparsity, allowing the model to dynamically adjust its emphasis based on uncertainty and interaction context. This design not only improves performance but also offers a more transparent explanation of how multimodal signals contribute to preference formation across different frequency levels. Despite its effectiveness, our method still has several limitations. First, while spectral decomposition enhances interpretability, it introduces additional computational cost compared to purely time- or copology-domali approaches. Second, the selection of decomposition granularity (i.e., the number of frequency bands) remains heuristic and may require tuning. Third, although our model captures intra- and inter-band correlations, it assumes a fixed transformation basis that might not fully generalize highly non-stationary multimodal patterns. Finally, the current framework focuses on static multimodal graphs, extending it to temporal or dynamic user behaviors represents an important future direction. Addressing these limitations could further strengthen the generality and scalability of frequency-awan recommendation systems.
22


Reviews:
[{"review_id": "RbFxGDEbSh", "reviewer": "Reviewer_YRJP", "summary": "This paper introduces a unified framework, termed SSR, for frequency-aware multimodal recommendation. It follows a four-stage pipeline: (i) Decompose graph-based multimodal signals into spectral bands to isolate semantic granularity; (ii) Modulate signal reliability through spectral causal masking; (iii) Fuse complementary frequency cues using hyperspectral reasoning; and (iv) Align modality-specific spectral features via contrastive regularization. Extensive experiments demonstrates the effectiveness of SSR on under sparse and cold-start scenarios.", "questions": "1. Why the discovery is not align in Figure 3 and Figure 4? Or anything I misunderstand.\n2. The figures in this paper should be further polished to enable potential readers to understand the overall structure.\n3. Please cite some cross-modal recommendation algorithms to illustrate your superior.\n4. Beyond the time complexity analysis, it would be helpful to include a comparison of the actual training and inference runtimes between SSR and several traditional or advanced baselines.", "limitations": "Please refer to limitations and Questions.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. The motivation and the theoretical analysis are well described in Methodology section and the proposed SSR pipeline is clear with four diverse steps.\n2. The experimental results consistently demonstrate SSR’s superior performance compared to many baselines, with particularly strong improvements in cold-start and sparse secnarios.\n3. The parameter robustness and generalizability of SSR have been well-verified in section 4.\n\nWeaknesses:\n1. The overall structure is not very clear to understand. For example, the Decomposition module does not explicitly state that the three frequency-specific representations are derived from the same modality, which may lead to misunderstandings.\n2. Cross-modality alignment is one of the core contribution in this paper, however, it  doesnot cite some multimodal recommendation studies that explicitly focus on cross-modal learning.\n3. The validation datasets all comes from Amazon platform, which may introduce bias in performance comparison.\n4. There is an inconsistency between Figures 3 and 4: in Figure 3, the cross-modality correlation among the three modalities in the High Frequency component appears lower, whereas in Figure 4 it is the highest. This discrepancy is not clearly explained in Section 4.6 or Appendix F.3.\n5. The authors donot provide the significance analysis in performance comparison, and the corresponding code and dataset have not been open-sourced.\n6. Figure 4 in the manuscript is not referenced or discussed, and it is identical to Figure 5 in the Appendix.", "was_revised": true, "final_justification": "I'm not very familiar about the Spectral Reasoning and I also concern about the  rationality of the original algorithm version even the author provided the revised theoretical claims. Therefore, I have decreased my confidence of this paper and kept my score unchanged.", "rebuttal": "We sincerely thank you for your careful and thoughtful review of our work. Your comments are highly valuable to us. For the concerns you raised, we hope the following responses can provide effective clarification.\n\n**[Reply to Questions]**\n\n**1. Inconsistency between Figures 3 & 4:** \n\nThank you for your careful reading regarding Figure 4. Figure 4 measures **distance** between modalities (see the y-axis and title), **rather than similarity**. The high frequency band exhibits larger cross‑modal distances, which is consistent with Figure 3’s visualization of noisy, less‑aligned distributions in the high‑frequency space.\n\n\n**2. About Visual Clarity:** \n\nThank you for the suggestion. We will refine all figures in the revised version by improving visual clarity and adding more informative annotations and legends to aid understanding. Specifically, we plan to highlight key modules in the pipeline and use clearer labels for axes and metrics.\n\n**3. Cross-modal Recommendation Baselines:** \n\nSeveral recent recommender systems treat cross‑modal alignment as their main contribution, e.g. MENTOR (AAAI2025) aligns image and text features at ID‑, item‑, and graph level; MMSSL (WWW 2023) introduces cross‑modal contrast with adversarial perturbations; AlignRec (CIKM2024) shrinks the modal gap via global auto‑encoding; and DiffMM (ACM’MM 2024) adds diffusion‑based augmentation before contrastive alignment. All four methods operate in the time domain and align the entire feature vector, so high‑frequency noise or spurious correlations are blended into the objective. By contrast, our SSR first decomposes each modality into equal‑energy spectral bands, uses Spectral Causal Masking to drop non‑causal (often high‑freq) bands, and then applies band‑wise spectral contrast; this frequency‑aware pipeline preserves useful interaction signals while avoiding noise propagation. Empirically, the same implementation setup shows that SSR improves Recall@20 by ≈ 5 pp over MENTOR and AlignRec, and by ≈ 10 pp over MMSSL and DiffMM across three Amazon domains and a TikTok‑style dataset, while using fewer parameters than AlignRec and similar training time to SMORE. These results confirm that fine‑grained, spectrum‑aware alignment is both conceptually cleaner and practically more effective than existing full‑band cross‑modal algorithms.\n\n\n**4. Actual Training and Inference Runtimes:** \n\nBeyond the asymptotic complexity in §4.4, we have benchmarked actual runtime performance. The table below compares several multimodal baselines in terms of average training time per epoch, time to best validation performance, and inference throughput:\n\n| **Model**       | **Train time (s)** | **Time to best val (h)** | **Inference throughput (items/s)** |\n|-----------------|--------------------|---------------------------|-------------------------------------|\n| MMGCN          | 4.32               | 2.4                       | 5548                                |\n| DualGNN         | 4.94               | 2.8                       | 6107                                |\n| SLMRec          | 3.08               | 1.3                       | 7031                                |\n| MMIL              | 3.31               | 1.6                       | 6815                                |\n| SMORE           | 3.50               | 2.2                       | 6523                                |\n| **SSR (ours)**  | **3.78**           | **1.7**                   | **6253**                            |\n\n\nAs shown, our SSR maintains competitive training efficiency and inference speed. It reaches the best validation result faster than SMORE while achieving higher accuracy and better robustness, as discussed in §4.2 and §4.4.\n\n---\n\n**[Reply to Weaknesses:]**\n\n**1. Clarity of the Decomposition module:**\n\nThank you for noticing the ambiguity. The three frequency‑specific representations (low, mid, high) are indeed derived from the same modality via a per‑modality graph Fourier transform. Due to space constraints, we did not elaborate on this detail in the original version. Thank you for pointing it out—we will include a clarifying description in the revised version at key locations (e.g., §3.1 and Figure 1’s caption) to avoid potential misunderstandings.\n\n\n**2. Missing Citations on Cross‑modal Alignment:**\n\nThank you for the suggestion regarding cross-modal recommendation references. Our spectral alignment module was indeed inspired by prior work on cross-modal alignment, including AlignRec [16], MMSSL [56], MENTOR[57], and CLIPER [58]. We designed our SCR module to build on these ideas while incorporating frequency‑band semantics. We will explicitly cite these works in the Related Work section and discuss their differences from our method in §3.\n\n**3. Dataset Diversity:**\n\nMost of the baselines we compare against (e.g., DualGNN [27], SLMRec [30], LATTICE [33], BM3 [31], FREEDOM [29], MMIL [35], AlignRec [16], SMORE [5]) were originally designed and benchmarked on Amazon datasets with standardized preprocessing protocols. To ensure fair comparison, we used the same three Amazon subdomains (Baby, Sports, Clothing), which also provide natural distribution shifts between domains. Beyond Amazon, we have conducted preliminary experiments on a TikTok‑style recommendation dataset. The results (Recall@20) are: MMGCN = 0.0730, SLMRec = 0.0845, AlignRec = 0.1174, SMORE = 0.1185, Our SSR = 0.1237. SSR shows a consistent improvement of +4.2 pp over SMORE. We are currently running the full suite of baselines on this dataset and will include the complete comparison in the final version. Additionally, we fully agree with your suggestion and are planning to expand our benchmark suite with new standardized datasets such as KuaiRand‑Rec and MIND‑News.\n\n**4. Inconsistency between Figures 3 & 4:**\n\nThank you for your careful reading regarding Figure 4. Figure 4 measures distance between modalities (see the y-axis and title). The high frequency band exhibits larger cross‑modal distances, which is consistent with Figure 3’s visualization of noisy, less‑aligned distributions in the high‑frequency space.\n\n**5. Significance Analysis; Code and Dataset not Released:**\n\nWe have conducted statistical significance testing using paired t-tests (Recall@20 and NDCG@20) comparing SSR to SMORE. On all three datasets, the p-values are < 0.005, well below the 0.05 threshold. We will include the complete test results in the revised version. Regarding the dataset and code: we used the same publicly available MMRec‑processed datasets as the baselines. We are also ready to release our code, and we can release at any time if it’s needed.\n\n**6. Figure 4 not Referenced / Duplicated with Appendix**\n\nThank you for pointing out the reference mismatch between Figure 4 and the Appendix.\nOur original intention was to refer to Figure 4 in Section 4.6, and present Figure 5 in the Appendix as a detailed counterpart. We mistakenly cited the appendix figure in the main text and will fix this in the revision. Thank you again for the helpful observation.\n\n**We hope** the above responses have addressed your concerns. If you have any further questions, please feel free to leave additional comments. We would deeply appreciate it if you could consider revisiting your evaluation of our work. Thank you again for your kind support.\n\n---\n\n[56] Wei, W., Huang, C., Xia, L. and Zhang, C., 2023, April. Multi-modal self-supervised learning for recommendation. In Proceedings of the ACM web conference 2023 (pp. 790-800). \n\n[57] Xu, J., Chen, Z., Yang, S., Li, J., Wang, H. and Ngai, E.C., 2025, April. Mentor: multi-level self-supervised learning for multimodal recommendation. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 39, No. 12, pp. 12908-12917).\n\n[58] Wu, X., Huang, A., Yang, H., He, H., Tai, Y. and Zhang, W., 2024. Towards Bridging the Cross-modal Semantic Gap for Multi-modal Recommendation. arXiv preprint arXiv:2407.05420."}, {"review_id": "WZWmeAAxlx", "reviewer": "Reviewer_cgiv", "summary": "This paper presents a framework called SSR (structured spectral reasoning) for multimodal recommendation which leverages frequency domain to overcome problems of modality-specific noise, semantic inconsistency, and unstable propagation over user-item graphs. This is done by operating in the frequency domain, by using a 4 stage pipeline: a) decomposition (multimodal signals transformed into frequency bands), b) modulation - casually inspired masking technique used to regularize model, c) fusion where a fusion is done across different frequency bands and finally alignment - where different representations are aligned in the same band using a special contrastive loss. The efficacy of the proposed method is verified on 3 benchmark datasets, where SSR outperforms strong baselines, particularly in sparse and cold start settings.", "questions": "See weaknesses above.", "limitations": "Not mentioned, see questions above.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\nOverall, the paper is very well presented, concisely written and easy to follow. In the context of multimodal handling, the SCM piece is particularly interesting when IRM is used to identify invariant predictors under spectral perturbations. The experimental results look promising. The detailed ablation is appreciated. \n\nWeaknesses:\n1. The method depends on GFT which can be computationally prohibitive as a preprocessing step, how is that handled?  \n2. What is the motivation behind choosing equal energy bands?", "was_revised": true, "final_justification": "After reading the rebuttal and the existing promising experiments - I am raising my score.", "rebuttal": "We sincerely thank you for your thoughtful review of our paper. Your feedback has been helpful, and the questions you raised are highly valuable. Below we provide our responses to your concerns, and we genuinely hope they help clarify any confusion.\n\n**Reply to Weakness 1 : “GFT may be computationally prohibitive.**\n\nThank you for raising this very valuable question, it is indeed something we have carefully considered. As a result, we introduced several runtime optimizations during implementation. Specifically, our implementation keeps the Graph Fourier Transform lightweight in three ways:\n\n* **Sparse, low‑rank eigenbasis.** We compute only the top‑\\(k\\) Laplacian eigenvectors with a sparse Lanczos solver, not the full spectrum. For the graphs in our experiments this preprocessing finishes quickly on a standard CPU and requires only modest memory. We also note there that performance is stable when k is varied in {32,64,128}, and chose 64 as a trade-off.\n\n* **One‑time, reusable preprocessing.** The eigenbasis is generated once and reused throughout training and inference, so its cost is amortised and does not affect per‑epoch throughput.\n\n* **Scalable fallback.** For very large graphs we provide a Chebyshev‑polynomial approximation that eliminates eigendecomposition altogether while preserving almost the same accuracy.\n\nAfter this step, each forward pass reduces to a simple dot product with a small, quantised eigenbasis, making the runtime overhead negligible. Empirically, our end‑to‑end training time matches strong spectral baselines, confirming that GFT preprocessing is not a bottleneck. In addition, please refer to the “4. Actual Training and Inference Runtimes” section in our Reply to Reviewer YRJP for detailed runtime efficiency results.\n \n---\n\n**Reply to Weakness 2 :  – “Why choose equal‑energy spectral bands?”**\n\nThe motivation for using **equal-energy bands** stems from both theoretical considerations and empirical performance:\n\n- **Balanced information allocation.** In spectral analysis of graph signals, low-frequency components typically dominate total signal energy. Using equal-width frequency intervals would result in high- and mid-frequency bands containing very little information, leading to unstable training or underutilized components. By contrast, equal-energy partitioning ensures that each frequency band contains a comparable portion of the total energy, allowing all bands to contribute meaningfully to learning.\n\n- **Robustness and performance.** We conducted controlled experiments comparing different band-splitting strategies on the Amazon-Baby dataset. The results are summarized below:\n\n| **Band Strategy**                  | **Recall@20** | **Δ vs. Equal-Energy** |\n|-----------------------------------|---------------|-------------------------|\n| Equal-width (log scale)           | 0.1038        | −0.58 pp                |\n| Learnable cut-points (via MLP)    | 0.1065        | −0.31 pp                |\n| **Equal-energy (ours)**           | **0.1096**    | —                       |\n\n  Equal-energy bands outperform both static and learnable alternatives in terms of both overall accuracy and robustness under perturbation.\n\n- **Adaptability.** This method adapts naturally to different datasets without requiring manual tuning, as the cumulative energy profile reflects the inherent spectral characteristics of the graph.\n\n- **Interpretability.** Because each band carries roughly one-third of the total energy, we can more intuitively analyze where semantic alignment or noise concentration occurs, as shown in Figures 3 and 4.\n\nThese results validate our decision to use equal-energy partitioning as a principled and effective design choice. We will add more ablation details to Appendix F in the revised version.\n\nOnce again, we greatly appreciate your careful review. If you have any further questions, please feel free to leave additional comments. If possible, we would also be grateful if you could consider giving a more positive evaluation of our work. We truly appreciate your support and feedback."}, {"review_id": "aEfuRGNB3f", "reviewer": "Reviewer_Tqa8", "summary": "This paper proposes Structured Spectral Reasoning (SSR), a unified framework for multimodal recommendation that decomposes user-item graph signals into frequency bands, applies spectral causal masking to suppress unreliable components, and fuses them via a novel Graph HyperSpectral Neural Operator combined with contrastive regularization. The approach enables adaptive, frequency-aware representation learning, achieving state-of-the-art performance on multiple Amazon benchmarks, especially under sparse and cold-start conditions.", "questions": "1. Could the authors provide more evidence to demonstrate the scalability of the method?\n2. Could the authors design targeted experiments to explicitly verify that the proposed frequency decomposition and causal masking improve robustness to modality-specific noise or spurious correlations?\n3. Could the authors provide concrete examples or user studies that validate this interpretability?", "limitations": "Refer to Weaknesses and Questions", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Pros:\n1. Clear writing and easy to read.\n2. The method is reasonable and the experiment shows the effectiveness of the method.\n3. Provides theoretical support.\n\nCons:\n1. The method is complex and difficult to apply. The data support for complexity analysis is limited and not intuitive.\n2. The experiments are more about showing the overall performance and analyzing the method, and the improvements proposed in the motivation are not experimentally verified.\n3. Some analysis experiments only have the proposed method but lack baseline comparison, which is not intuitive enough.\n4. The author does not discuss limitations, and there is no clear enough discussion of limitations in the appendix chapter corresponding to the Checklist.", "was_revised": true, "final_justification": "The authors have addressed my concerns.  I will raise my score of this paper to 4.", "rebuttal": "We sincerely thank you for your thoughtful review of this paper. Your comments are highly valuable to us. For the concerns you raised, we hope the following responses can provide effective clarification.\n\n**[Reply to Questions]**\n\n**1. More Evidence of Scalability**\n\nWe appreciate your suggestion about scalability of our approach. In response, we provide **new empirical results** demonstrating that SSR scales effectively across **diverse datasets** and maintains **competitive efficiency** in both training and inference.\n\n#### **(1) Generalization to a new distributionally distinct dataset**\n\nTo test SSR’s robustness under different content modalities and interaction patterns, we conduct additional experiments on a **TikTok short video dataset**, which features rich and noisy multimodal inputs (visual, acoustic, and textual) and exhibits distributions significantly different from Amazon.\n\n| **Model**      | **Recall@20** | **NDCG@20** |\n|----------------|---------------|-------------|\n| MMGCN          | 0.0730        | 0.0307      |\n| SLMRec         | 0.0845        | 0.0353      |\n| AlignRec       | 0.1174        | 0.0461      |\n| SMORE          | 0.1185        | 0.0473      |\n| **SSR (ours)** | **0.1237**    | **0.0507**  |\n\nSSR achieves **the highest accuracy**, showing a +5.2% gain in Recall@20 over the strong CL-based method AlignRec, and outperforming the spectral baseline SMORE as well. These results confirm SSR’s ability to generalize and scale effectively in real-world short video scenarios.\n\n#### **(2) Practical runtime efficiency across baselines**\n\nBeyond the theoretical complexity discussed in Appendix D, we have benchmarked actual runtime performance. SSR maintains **competitive training efficiency** and **comparable inference speed**:\n\n| **Model**      | **Train time (s)** | **Time to best val (h)** | **Inference throughput (items/s)** |\n|----------------|--------------------|---------------------------|-------------------------------------|\n| MMGCN          | 4.32               | 2.4                       | 5548                                |\n| DualGNN        | 4.94               | 2.8                       | 6107                                |\n| SLMRec         | 3.08               | 1.3                       | 7031                                |\n| MMIL           | 3.31               | 1.6                       | 6815                                |\n| SMORE          | 3.50               | 2.2                       | 6523                                |\n| **SSR (ours)** | **3.78**           | **1.7**                   | **6253**                            |\n\nSSR converges faster than SMORE while achieving higher accuracy, and operates within a similar memory and inference cost envelope. Unlike many CL-based methods that entangle all modal features into a global latent space, our approach **isolates causal and informative bands**, allowing stable learning even under distribution shifts.\n\n---\n\n**2. Robustness of Frequency Decomposition and Causal Masking**\n\nYes, we conducted three controlled perturbation experiments on the Amazon-Baby dataset to verify that frequency decomposition and Spectral Causal Masking (SCM) improve robustness against different forms of noise and spurious signals. Starting from the clean scores of SMOER (R@20=0.1035) and SSR (R@20=0.1096), we compare three variants:\n\n(1) SMORE (spectral baseline without decomposition/masking),  \n(2) SSR w/o SCM (our model with decomposition but no causal masking),  \n(3) Full SSR (with both decomposition and SCM).\n\n| **Perturbation Scenario**                          | **Metric**   | **SMORE** | **SSR w/o SCM** | **Full SSR** |\n|---------------------------------------------------|--------------|-----------|------------------|--------------|\n| Add 20% Gaussian noise to high-frequency band     | Recall@20    | 0.0994     | 0.1042            | **0.1081**    |\n| Randomly swap high-freq bands across 25% of items | Recall@20    | 0.0979     | 0.1021            | **0.1065**    |\n| Blur image modality only (leave text intact)      | Recall@20    | 0.0987     | 0.1030             | **0.1073**    |\n\n#### **Findings:**\n- Full SSR consistently outperforms both SMORE and the ablated variant across all perturbation types.\n- The performance drop under perturbation is smallest for full SSR, demonstrating that SCM effectively filters unstable high-frequency features, and that frequency decomposition provides a structure for isolating and correcting noisy modal signals.\n\nThese results provide evidence that the proposed frequency-aware design is robust to noise and spurious modality-specific variations. \n\n---\n\n**3. Concrete Example for Interpretability**\n\nTo provide evidence of interpretability beyond aggregate metrics, we present a **band‑wise qualitative case study** on the Amazon‑Baby dataset, showcasing how different frequency components influence the final ranking decision. \n\n*User context*: The user has recently browsed breast‑pumping accessories and milk‑storage solutions.  \n*Candidate pair*: **Item A** = “Medela CSF Milk‑Storage Bags (50 pack)” , **Item B** = “Fisher‑Price Nesting Action Vehicles (toy set)”\n\n| **Component masked**             | **ΔScore(A)** | **ΔScore(B)** | **New rank** |\n|----------------------------------|---------------|---------------|--------------|\n| Remove **high‑frequency** band   | −0.08 | −0.12 | A > B (unchanged) |\n| Remove **mid‑frequency** band    | −0.37 | −0.16 | B overtakes A |\n| Remove **low‑frequency** band    | −0.26 | −0.41 | A > B (unchanged) |\n\n**How each band affects the decision**\n\n* **Low‑band (global semantics).** Encodes product category: “milk‑storage bags” vs. “toy vehicles”. Removing it hurts B more, because the toy’s global semantics are less relevant to the user’s recent interest.\n* **Mid‑band (functional cues).** Captures keywords like “pre‑sterilised”, “BPA‑free”, and the zipper seal icon on Item A’s package, exactly the features matching breast‑feeding needs.  Masking this band flips the ranking, proving it is the decisive component.\n* **High‑band (noisy details).** Contains packaging glare or marketing adjectives; its removal scarcely changes the ranking.\n\n**Recommendation explanation:**\n\nWe prioritised Item A because its mid‑frequency features, such as ‘pre‑sterilised milk‑storage’ and the zipper‑seal graphic, match user's recent searches for milk‑pumping accessories. When we hide these features, the ranking reverses in favour of the toy set, confirming that the mid‑band information drives this recommendation.\n\nThis counterfactual analysis illustrates that each spectral band carries distinct semantics, and that mid‑band alignment, highlighted and preserved by our frequency decomposition with SCM, directly explains why Item A is recommended over Item B.\n\n---\n\n**[Reply to Cons]**\n\n**1. Complexity and Data Support:**\n\nWhile our method introduces spectral decomposition and causal masking, both are applied in a **modular and efficient** manner. As shown in our **runtime benchmark results** (see Q1), SSR achieves **comparable training time and inference speed** to prior methods such as SMORE and MMGCN. Specifically, SSR reaches the best validation performance faster, with no major inference overhead. This demonstrates that the proposed method, though conceptually novel, is **practically efficient and easy to deploy**.\n\n**2. The proposed Improvements are not Experimentally Verified:**\n\nWe have conducted **targeted perturbation experiments** (see Q2) designed to test the robustness of our frequency decomposition and SCM modules under **modality-specific noise and spurious correlations**. These controlled trials confirm that both components provide complementary robustness benefits. Further, to demonstrate the **interpretability** promised by our design, we present a **band-wise qualitative case study** (see Q3), analyzing how different frequency components affect final item ranking in a real-world setting. \n\n**3. Missing Baseline Analysis**\n\nWe sincerely appreciate your suggestion. For all key analysis experiments (e.g., robustness tests, interpretability study), we have included **baseline comparisons** such as SMORE and ablated variants (e.g., SSR w/o SCM) to ensure fair and intuitive evaluation. These comparisons are reported in Q2 and Q3. We will further clarify this in the revised version to improve readability.\n\n**4. Limitations:**\n\nWe sincerely appreciate your suggestion. Below, we outline some limitations of our current method that could inspire future improvements and extensions：\n\nAlthough Structured Spectral Reasoning (SSR) performs well and is robust on multiple datasets, it has several limitations. First, the model relies on a one‑off computation of Laplacian eigenvectors as its spectral basis; on extremely large or rapidly evolving graphs, frequent node or edge updates would require incremental eigensolver techniques or polynomial approximations to avoid expensive recalculation. Second, the current implementation uses frozen CLIP/BERT multimodal embeddings for efficiency, meaning any bias or noise in the upstream encoders is passed unchanged to SSR; end‑to‑end fine‑tuning or lightweight distillation could further improve representation quality. Finally, SSR’s interpretability is confined to the band level—it can quantify how low, mid, and high frequencies contribute to the score and how SCM re‑weights them, but it cannot pinpoint specific image regions or text tokens as pixel‑ or token‑level attention maps do, limiting its usefulness in scenarios that demand extremely fine‑grained auditing; future work could combine differentiable visualisation or local adversarial analysis to reveal semantic sources within each band.\n\nWe hope the above responses have addressed your concerns. If you have any further questions, please feel free to leave additional comments. We would deeply appreciate it if you could consider revisiting your evaluation of our work. Thank you again for your kind support."}, {"review_id": "Vx0pYlYjfQ", "reviewer": "Reviewer_KUNi", "summary": "The paper proposes SSR, short for Structured Spectral Reasoning, a novel multimodal recommender system which works in the frequency domain and adaptively utilizes the graph and multimodal spectral signals to solve known issues in the multimodal recommendation literature. \n\nUnlike similar previous approaches, SSR performs a four stages pipeline, involving: (i) the decomposition of graph and multimodal signals into spectral bands to obtain a more granular representation; (ii) a modulation of the signal's reliability with some random masking of the spectral bands, to make the model robust to spurious frequency components; (iii) the fusion of the decomposed spectral bands into one unique representation; (iv) the alignment of spectral bands and modalities through contrastive learning.\n\nTo begin with, the graph and multimodal spectral signals are decomposed into spectral bands, and for each node in the dataset, they are fused with a gated attention weight. \n\nSecond, a masking mechanism is applied to randomly perturb the spectral bands during the training and to make the model robust to spurious frequency components; this objective is obtained through invariant risk minimization, a loss component of the overall loss function where the normal and the counterfactual settings are supposed to be close in their learned representations. \n\nThen, the model introduces a Graph HyperSpectral Neural Operator (G-HSNO) which can work three axes, namely, frequency bands, modality types, and graph topology. In this respect, the authors adopt Canonical Polyadic (CP) decomposition, a low-rank factorization of the kernel tensor adopted in the G-HSNO operator to reduce the overfitting and the parameter complexity. \n\nFinally, a Spectral Contrastive Regularization (SCR) is introduced to perform a contrastive learning loss encouraging intra-band modality consistency but preserving, at the same time, inter-band separation.\n\nExtensive experimental results on three popular datasets from the Amazon Reviews collection, against 14 state-of-the-art recommender and multimodal recommender systems demonstrate the efficacy of the proposed approach. Further analyses show the goodness of the approach also in cold-start scenarios. Then, an ablation study and a hyper-parameter sensitivity analyses prove the soundness of the architectural choices made by the authors. Finally, the authors show how effective is the framework at adapting at different decomposed frequencies across modalities, how well-aligned are the modalities (especially at the mid frequency), and how the adaptive spectral modulation can tailor different settings, such as cold- and non-cold-start items.", "questions": "My questions are mainly related to some of the weaknesses I pointed out above.\n\nQ1) Do the authors think that the proposed framework would have suited better to other scenarios than multimodal recommendation? For instance, knowledge graphs information in recommendation? And, in case, why did they choose to test it with multimodal recommendation?\n\nQ2) How different is the proposed approach from similar solutions which perform disentanglement in the spatial domain? What is the benefit of performing it in the frequency domain?\n\nQ3) Why did the authors go for CP in the kernel tensor decomposition, and did they try other solutions before coming up with CP?\n\nQ4) Why did the authors use gated attention in the semantic fusion of spectral bands? What are the specific benefits of it, and did they try with other similar solutions?", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n$\\bullet$ The paper lays in one of the current hot topics in the literature of multimodal recommendation, namely, the translation of the task of multimodal recommendation to the frequency domain from the common spatial domain.   \n\n$\\bullet$ In relation to the first point, the authors clearly highlight the main limitations in current approaches from the literature (also recent ones which work in the spectral domain), and position the proposed approach within the state-of-the-art.  \n\n$\\bullet$ The methodology seems adequately sound and novel, where all main stages of the pipeline are clearly reported in the formalism and also in Figure 1. All theorems are adequately supported by the proofs as reported in the Supplementary Material.\n\n$\\bullet$ The experimental setting is quite extensive, with several analyzed dimensions which allow not only to show the efficacy of the proposed approach under overall performance perspectives, but also under specific evaluation dimensions which justify the effectiveness of each idea conveyed in the paper.\n\n**Weaknesses**\n\n$\\bullet$ To my understanding, the proposed framework could potentially be applied to many different scenarios where other side information is available apart from the simple collaborative signal. This is especially evident since the multimodal aspect appears only in Section 3.4 after the whole presentation of the methodology, which appears quite agnostic of the modalities. While this could indeed be a positive aspect of the approach (i.e., to be side-information agnostic), do the authors think that maybe the approach would have suited better to other scenarios? Something like knowledge graphs information in recommendation? And, in case, why did they choose to test it with multimodal recommendation?\n\n$\\bullet$ From my perspective, I see how the proposed approach has something in common with previous approaches in (multimodal) recommendation, such as DGCF [\\*] and GRCN. Specifically, the two mentioned approaches work by disentangling the embedding representation of nodes (and modalities) into aspects, which are learned end-to-end in the downstream task. To me, this appears as a spatial version of the frequency disentanglement of the spectral bands. Can the authors elaborate a little bit on that? How effective is translating the whole setting to the spectral domain instead of keeping it limited to the spatial one?\n\n$\\bullet$ Regarding the kernel tensor decomposition, the literature outlines a wide range of possible solutions apart from CP. For instance, another possible technique is Tucker decomposition, which usually allows more flexibility than CP. Why did the authors go for CP, and did they try other solutions before coming up with CP? I think this aspect should be better clarified. A similar consideration could be done for the semantic-aware frequency fusion. Why did the authors use gated attention? What are the specific benefits of it, and did they try with other similar solutions? This aspect should also be better clarified. \n\n$\\bullet$ The code is not released at review time, thus not ensuring complete reproducibility of the approach. While I acknowledge the usage of the framework MMRec for all the used baselines, I think the work would benefit from sharing the code also of the proposed approach.\n\n**References**\n\n[\\*] Xiang Wang, Hongye Jin, An Zhang, Xiangnan He, Tong Xu, Tat-Seng Chua: Disentangled Graph Collaborative Filtering. SIGIR 2020: 1001-1010", "was_revised": true, "final_justification": "After the rebuttal phase, after reading the other reviews, and authors' responses to those and to the careful comments raised by the Area Chair, I decide to confirm my initial score I gave to the paper.\n\nSpecifically, all my concerns have been discussed and addressed by the authors, and (to the best of my understanding), also the concerns raised by the Area Chair have been discussed and addressed by the authors. \n\nWhatever the final outcome for this paper, I think it will benefit quite a lot from the fruitful discussion we had along with the authors, the reviewers, and the Area Chair. I believe the paper will improve its quality a lot in any case.", "rebuttal": "We sincerely thank you for your thorough and insightful review, and appreciate the valuable comments and discussions you provided. We are especially grateful for your deep understanding of our work, it is clear that you have fully grasped the core ideas of our approach, and the questions you raised are highly meaningful. We have prepared the following responses in the hope of addressing some doubts.\n\n**Q1| About Application Scenarios**\n\nOur framework is designed to be general and extensible, accommodating various types of auxiliary signals by modeling them as graph-defined fields and analyzing their frequency characteristics. In that sense, choosing images‑and‑texts for the first study is an instantiation rather than a restriction. The same framework remains valid so long as two conditions hold:  \n1) the side information can be represented on the same (or an aligned) node set;  \n2) frequency carries meaning that the downstream task cares about.  \n\n**(1) Knowledge‑graph Recommendation as a Natural Extension**\n\nKnowledge graphs (KGs) offer rich relational structures that naturally align with our spectral reasoning paradigm. Each relation induces its own Laplacian, whose spectral components reflect both hierarchical and fine-grained semantics, analogous to the frequency bands in multimodal signals.\n\nIn this setting:\n- Our **spectral decomposition** generalizes to relation-wise spectra, enabling structured reasoning without relying on handcrafted metapaths. This allows the model to respect the inherent relational geometry of the KG while avoiding manual path enumeration or rigid schema constraints.\n- **Causal masking** offers a principled alternative to heuristic pruning. In scenarios where certain relations introduce shortcut correlations (e.g., nationality as a proxy for brand), this mechanism promotes stable generalization through invariance learning.\n- The **cross-band fusion operator** can be viewed as soft multi-hop reasoning across relation bands, compositing semantic signals in a flexible, data-driven manner. This enables the model to learn adaptive reasoning chains over KG structures.\n- Finally, the **alignment module** ensures coherence between learned ID embeddings and structured KG entities, reinforcing consistency across behavioral and factual spaces. This helps bridge the gap between collaborative signals and external knowledge.\n\n\n**(2) Beyond KGs: Extending to Knowledge and Structure**\n\nThe frequency-centric paradigm naturally extends beyond multimodal recommendation. It offers a unified lens to model diverse auxiliary signals such as structured knowledge, user attributes, or interaction contexts by interpreting their graph spectral signatures.\n\n- **Contextual signals** (time, location, device) possess multi‑scale periodicities that manifest as distinct spectral signatures; causal masking filters volatile bursts while retaining structural seasonality.  \n- **Social graphs** contribute an overlay network whose spectrum encodes community structure; cross‑band operators let social influence modulate item signals without hand‑tuned fusion weights.  \n- **Spatio‑temporal forecasting** problems already lean on spectral thinking; our causal perturbation adds a principled route to stability against distribution shifts.  \n\nTogether, these principles position our framework as a broadly applicable, theoretically grounded solution for modeling structured signals across a wide range of recommendation and other scenarios.\n\n**(3) Why Multimodal Recommendation**  \n\nWe chose to first validate our framework in the domain of **multimodal recommendation** because this scenario presents some of the most urgent and practically consequential challenges in real-world systems. In particular, multimodal-rec suffers from two critical and widely acknowledged pain points: (i) **modality‑specific noise**—irrelevant backgrounds, inconsistent photos, sparse or generic text that inject high‑frequency artefacts; (ii) **semantic misalignment** between image/text content and true user preferences. These issues are well documented in academia and industry, yet existing solutions still rely on heuristic fusion or ad‑hoc filtering, which break down in cold‑start or noisy settings. Our goal was to **propose a general and theoretically grounded paradigm** that can systematically handle these issues. \n\nMoreover, **multimodal Rec offers a unique combination of stress-testing and interpretability**:\n\n- It serves as a **stress test** because it represents a high-noise, high-stakes setting where naive fusion fails frequently and where robust generalization is difficult.  \n- It also provides a **microscope**: the availability of visual and textual features allows us to interpret frequency behaviors (e.g., distinguishing between coarse object shapes and fine-grained textures), offering qualitative validation of the causal reasoning process.\n\n---\n\n**Q2 | Relationship to the Spatial Domain**\n\nBoth **DGCF** and **GRCN** begin with the same diagnosis we do: **a single interaction graph entangles multiple, sometimes spurious, factors of user preference**.  \n- DGCF tackles the problem by factorising each node embedding into several *intent* sub-vectors.  \n- GRCN refines the graph by pruning low-confidence edges during training.  \n\nThese are *spatial* operations: they alter the neighbourhood or the embedding space directly.\n\nOur approach keeps the diagnosis but **changes the coordinate system**. We ask:  \n> *Where does the entanglement live in the graph spectrum?*  \n\nWe find that **global semantics, useful local patterns, and high-frequency noise separate naturally along the eigen-axis**.  \nThis shift leads to three practical advantages:\n\n1. **Orthogonal partitions without manual design**  \n   Laplacian eigenvectors are mutually orthogonal, so frequency bands are independent by construction.  \n   DGCF must enforce disentanglement with extra regularisers and hyperparameters;  \n   GRCN must learn heuristics to decide which edges to drop.\n\n2. **Causal filtering rather than edge-by-edge pruning**  \n   Spectral Causal Masking down-weights entire bands that violate an invariance objective,  \n   removing whole *classes* of spurious signals (e.g., background textures)  \n   instead of individual edges. This is data-driven yet more stable than threshold-based pruning.\n\n3. **A single mechanism that generalises**  \n   The same band decomposition works whether the signal is an image embedding,  \n   a sentence vector, or a KG relation embedding. This allows us to plug in new side-information  \n   without redesigning intent counts or pruning rules.\n\n---\n\n**Q3 |  Reason for Using CP**\n\nTo enable efficient and flexible reasoning across spectral bands, our model uses a band-to-band kernel represented as a third-order tensor. However, directly learning a full 3D tensor incurs high memory and computation cost, especially as the number of bands grows.\n\nTo keep the model lean, we trial‑tested four standard tensor factorisations. For a band‑to‑band kernel tensor of size B*B*d:\n\n| Decomposition | Param. complexity | Main strength | Main drawback (in practice) |\n|---------------|-------------------|---------------|-----------------------------|\n| **CP (rank r)** | O [ r · (B + d) ]  | Linear growth, extremely compact | Slight expressiveness loss at very low rank |\n| Tucker (rank r) | O [ r³ + (B + d)·r ] | Higher expressiveness | Core size grows cubically with r; brittle optimisation |\n| Tensor Train (rank r) | O [ r² · (B + d) ] | Works for long modes | Requires mode re‑ordering; slower convergence |\n| Block‑term    | Mixed            | Flexible blocks | Heavy code overhead; no clear gain |\n\nA single experiment on Amazon‑Baby (R@20 = 0.1103) shows that CP with rank 8 achieves similar accuracy (0.1095) using only one-fifth of the parameters, while Tucker drops to 0.1068 and doubles the parameter count; other decompositions perform worse in both accuracy and size.\n\nBeyond the numbers, CP offered two practical advantages: (i) its separable factors train stably without rank scheduling, unlike high‑rank Tucker; (ii) the three factor matrices are easy to inspect and prune, each column corresponding to a latent “band‑interaction motif.”  Given this accuracy‑to‑size balance and optimisation stability, CP became the default throughout the paper and other decompositions remain compatible with the framework.\n\n---\n\n**Q4  |  Reason for Gated Attention**\n\nSpectral bands differ not only in content but also in **energy scale and reliability**.  A plain soft‑max attention would force the model to assign all probability mass somewhere, even when a band is mostly noise.  By inserting a learnable gate, we decouple two roles:\n\n1. **Relevance estimation** (attention weights): *Which* other bands matter for the current band?  \n2. **Reliability gating** (sigmoid gate): *How much* of that information should actually be let through?\n\nThis separation lets the model **suppress unreliable bands without renormalising the whole distribution**, giving finer control in noisy multimodal settings.\n\nHere is a supporting ablation on the Amazon-Baby dataset to justify our use of the gated attention mechanism for cross-band fusion:\n| Fusion variant | Δ R@20  | Notes |\n|----------------|---------------------------|-------|\n| Soft‑max (no gate) | −0.32 pp | Cannot mute noisy bands; tends to over‑smooth. |\n| Fixed equal-weight coefficient | −0.51 pp | Lacks adaptivity; either under‑ or over‑weights details. |\n| 2‑layer MLP on concatenated bands | −0.25 pp | Slight gain vs. soft‑max but doubles parameters, slower to converge. |\n\nGated attention therefore offered the **best trade‑off between performance, stability, and complexity**, and became our default choice.\n\n---\n\nOnce again, we **deeply appreciate** your careful and detailed review. Your suggestions have been very inspiring, and we will incorporate additional analysis and clarifications based on your feedback in the revised version."}]

Author rebuttal:

Meta-review: This paper introduces a new recommender system with the following components: 

(1)	[**Frequency Fusion**] First, the model performs a graph spectral decomposition [1,2] over the initial user node embeddings in the user-item bipartite graph. Then, the signal is split into frequency “bands” in by grouping together nearby eigenspaces in such a way that the sum of the associated eigenvalues in each band is roughly equal.  

(2)	[**Graph-aware Enhancement**] Next, a graph neural network is applied to the embeddings with the constraint that the linear maps are have low CP rank when viewed as 4D tensors (the dimensions being the frequency band and the embedding dimension for both input and output. 

(3)	[**Invariant Risk Minimization**] A regularization strategy is proposed which randomly masks some entries and minimizes the associated reconstruction loss. It is argues that this allows the model to better distinguish between causal and non-causal factors (**this claim is invalid**). 

(4) [**Contrastive Objective**] The final training incorporates both the BCE loss and a contrastive loss with a temperature parameter $\tau$.

The **experiments are very extensive**, covering many baselines and datasets and even including an ablation study on the proposed losses. 

The **reviewers were generally positive** about the paper, especially reviewers KUNi (who championed the paper) and cgiv, praising the extensive experiments and detailed ablation study. On the other hand, reviewers YRJP and Tqa8 complain that the paper can be difficult to read and the motivation and intuitive explanations for the performance improvement are not justified in the experiments. 

Although none of the reviewers have commented on it, I found quite a few **problems with the supposed theoretical results** in the original submission. In particular, Theorem 1 is merely an application of the linearity of the inner product. Theorem 2 failed to delineate assumptions properly, including the crucial assumption of having a fixed graph topology, which removes any possibility of interpreting the results from a learning theory perspective. In addition, **the claim that invariant risk minimiziation allows the model to better distinguish between causal and non-causal signals is not valid**: it was originally justified by the essentially nonsensical theorem 2 and its proof in the original submission. In the rebuttal a fully correct version called “theorem 1” was proposed instead. However, it fails to establish a connection between the proposed method and the concept of causal or non-causal frequency bands. Likewise, Theorem 3 and the corrected version in the rebuttal are merely generic statements about tensor decomposition to justify its use in the model. 
Most of the intuitive justifications provided in the main paper for the improved performance unfounded. There is no provable relationship between the proposed method and “causal” or “non-causal” bands, and I echo Reviewer YRJP’s statement that the paper is difficult to read (there are a lot of catchy and vague phrases such as “*follows a four-stage pipeline—decomposing, modulating, fusing, and aligning spectral signals—to achieve structured and adaptive representation learning*” or “*leverages frequency-aware decomposition and user-specific gating to tailor the semantic emphasis*”) which burry the not-always-precise description of the actual algorithm under a lot of filler. However, I am not taking this into account as this is (unfortunately) established practice (to some extent, claiming that there is a deep intuitive motivation for a new model regardless of the evidence is not only accepted but arguably necessary to gain acceptance from the community, so I don't think it is fair to penalize the authors for following the practice). In addition, **although it is arguably incremental, I do find the method somewhat interesting**, especially the merged **tensor decomposition** in the frequency pass of the graph neural network over the frequency bands: **I do believe it is credible that the performance improvements from this module are real**. In addition, the invariant risk minimization could introduce a generic form of regularization that may have practical merits. In the rebuttal, **the authors have promised to remove all theoretical claims**, which is appreciated. Since many of those claims were highly flawed, this removal **should be performed** in the camera-ready version. 



**Typos**

Missing space before $z_n$ on line 146.

Line 176: when introducing the general concept of invariant risk minimization, a reference might be nice. 

There is a broken reference (??) in line 860.

F.2 "sensitive analysis" should be "sensitivity analysis".






**References:**

[1] Rongqing Kenneth Ong, Andy W. H. Khong. Spectrum-based Modality Representation Fusion Graph Convolutional Network for Multimodal Recommendation. WSDM 2025

[2] Xinyu Du, Huanhuan Yuan, Pengpeng Zhao, Jianfeng Qu, Fuzhen Zhuang, Guanfeng Liu, Yanchi Liu, and Victor S Sheng. Frequency enhanced hybrid attention network for sequential recommendation. SIGIR 2023
Decision: Accept (poster)