Title: Beyond Self‑Attention: A Subquadratic Fourier‑Wavelet Transformer with Multi‑Modal Fusion
Venue: NeurIPS 2025
Accepted: no
Keywords: Subquadratic Transformer; Spectral Mixing;  Multi-Modal Fusion; Fourier-Wavelet Attention
Abstract: We revisit the use of spectral techniques to replaces the attention mechanism  in Transformers through  Fourier Transform–based token mixing, and present a comprehensive and novel reformulation of this technique  in next generation transformer models. We provide expanded literature context, detailed mathematical formulations of Fourier mixing and causal masking, and introduce a novel \emph{Multi-Domain Fourier-Wavelet Attention} (MDFWA) that integrates frequency- and time-localized transforms to capture both global and local dependencies efficiently. We derive the complexity bounds, gradient formulas, and show that MDFWA achieves sub-quadratic time and memory cost while improving expressive power. We validate our design on an abstractive summarization task using PubMed dataset,  by enhancing  the proposed approach with  learned frequency bases, adaptive scale selection, and multi-modal extensions.

1

Abstract

We revisit the use of spectral techniques to replaces the attention mechanism in Transformers through Fourier Transform-based token mixing, and present a comprehensive and novel reformulation of this technique in next generation transformer models. We provide expanded literature context, detailed mathematical formulations of Fourier mixing and causal masking, and introduce a novel MultiDomain Fourier-Wavelet Attention (MDFWA) that integrates frequency- and timelocalized transforms to capture both global and local dependencies efficiently. We derive the complexity bounds, gradient formulas, and show that MDFWA achieves sub-quadratic time and memory cost while improving expressive power. We validate our design on an abstractive summarization task using PubMed dataset, by enhancing the proposed approach with learned frequency bases, adaptive scale selection, and multi-modal extensions.

Keywords: Subquadratic Transformer; Spectral Mixing; Multi-Modal Fusion; Fourier-Wavelet 13 Attention 14

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1 Introduction

Abstractive document summarization traces its roots to the early sequence-to-sequence frameworks, where encoder-decoder recurrent neural networks first demonstrated end-to-end learning of summaries from pairs of articles and human abstracts [17, 4]. These models, however, struggled to capture long-range dependencies, often producing verbose or repetitive outputs. The seminal work of Bahdanau et al. [1] introduced additive attention to mitigate this limitation, but the true revolution came with the Transformer architecture of Vaswani et al. [18], which replaced recurrence with multi-headed self-attention. By modeling pairwise token interactions directly, Transformers realized unprecedented gains in fluency and coherence, as evidenced by BERT [8] and GPT [16], yet their quadratic O ( N 2 ) computational and memory costs quickly became prohibitive for documents longer than 512 tokens.

Subsequent research pursued varied strategies to alleviate this bottleneck. Sparse-attention methods such as Longformer [2] and BigBird [22] introduced sliding windows, dilated patterns, and global

tokens to achieve O ( N ) complexity, extending the Transformer's reach to sequences of several 28

thousand tokens. Low-rank and kernelized approximations followed: Linformer [19] projected 29

key-value pairs into a lower-dimensional subspace, while Reformer [11] employed locality-sensitive 30

hashing to approximate attention scores. Performer [5] and Nyströmformer [20] further refined these 31

ideas with randomized feature maps and landmark-based decompositions, respectively. Despite these 32

innovations, many approaches introduce approximation errors or require careful numerical tuning, 33

prompting renewed interest in truly parameter-free, exact mixing operations. 34

The FNet model [13] answered this call by replacing the self-attention mechanism in the encoder 35 with a fixed Fourier transform along the token axis. This non-learned mixing achieves O ( N log N ) 36 time and O ( N ) memory, while delivering robust language understanding performance, yet it re37 mained confined to encoder-only tasks and omitted decoder-side spectral mixing or encoder-decoder 38 cross-attention, critical components for abstractive summarization. Moreover, global Fourier coef39 ficients alone may overlook localized discourse structures, which multi-scale transforms such as 40 wavelets have historically captured in signal processing [6, 15] and more recently in vision and audio 41 domains [3]. 42

In this paper, we address these gaps by designing a full encoder-decoder Fourier Transformer, 43 rigorously deriving causally masked spectral kernels to enforce autoregressive generation, and intro44 ducing a novel Multi-Domain Fourier-Wavelet Attention (MDFWA) mechanism. MDFWA integrates 45 global Fourier mixing with discrete wavelet filters, capturing both broad thematic dependencies and 46 fine-grained local context in long documents, an approach inspired by hierarchical attention networks 47 [21] but grounded in spectral-wavelet theory. 48

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1.1 Contributions

Detailed mathematical formulation of Fourier token mixing in encoder and decoder, including causal masking.

Full Transformer architecture replacing all attention modules with Fourier/Wavelet mixing, enabling end-to-end training on long sequences.

Proposal of MDFWA: combining Fourier transforms for global mixing and discrete wavelet transforms (DWT) for local context.

Complexity analysis: O ( N log N + N ) time, O ( N ) memory.

Gradient derivation for Fourier and wavelet layers, ensuring efficient backpropagation.

Extensions to learned frequency bases, adaptive scale selection, and multi-modal longsequence fusion.

2 Background and Related Work

2.1 Self-Attention in the Transformer

The core of the Transformer model [18] is the multi-head self-attention mechanism. Given an input 62 sequence of token embeddings 63

we compute query, key, and value matrices by linear projections: 64

where W Q , W K , W V ∈ R d × d k . A single attention head then produces 65

where the softmax is applied row-wise. Stacking h heads and concatenating yields the multi-head 66 attention: 67

Since QK T ∈ R N × N , computing and storing these pairwise scores incurs O ( N 2 d ) time and O ( N 2 ) 68 memory per head. 69

2.2 Sparse and Linearized Attention 70

To alleviate the quadratic cost, sparse and kernelized approximations have been proposed. 71

Sliding-Window and Global Tokens. Longformer [2] and BigBird [22] restrict each token to 72 attend only within a local window of size w , and optionally to a small set of global tokens. Let 73 M ∈ { 0 , 1 } N × N be a binary mask with 74

where G indexes global positions. Then 75

reduces complexity to O ( Nwd ) ≈ O ( N d ) when w ≪ N . 76

Kernel-Based Linearization. Katharopoulos et al. [10] observe that 77

where ϕ : R d k → R r is a feature map (e.g. random Fourier features). Defining 78

at O ( Nrd ) cost, typically linear in N .

we compute 79

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2.3 Fourier Token Mixing (FNET)

Lee-Thorp et al. [13] replace learned attention with a fixed discrete Fourier transform (DFT) along 82 the sequence axis. Let 83

and define the DFT matrix F ∈ C N × N with entries 84

Then the token-mixed output is 85

where ℜ ( · ) takes the real part element-wise. Using a fast Fourier transform algorithm, this re86 quires O ( N log N ) time and O ( N ) memory per feature dimension, while preserving global token 87 interactions without learned parameters. 88

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3 Mathematical Development

3.1 Fourier Mixing Layer

In our proposed architecture, the Fourier mixing layer provides a global, parameter-free mechanism 91 to blend token embeddings along the sequence dimension. Concretely, let 92

where each row x n ∈ R d is the embedding of token n . We define the one-dimensional discrete 93 Fourier transform (DFT) along the token axis by 94

which can be written in matrix form as ̂ X = F X with F ∈ C N × N having entries F k,n = 95 exp( -2 πi nk/N ) . To ensure real activations, we take the real part of each complex coefficient: 96

By employing the Fast Fourier Transform, this global mixing requires only O ( dN log N ) time and 97 O ( dN ) memory, replacing the quadratic cost of self-attention with subquadratic complexity. 98

3.2 Causal Masking in Decoder 99

To extend spectral mixing to autoregressive decoding, we impose a triangular causal mask that 100 prevents any token at position n from attending to future tokens k > n . Let 101

and apply it directly within the DFT summation: 102

Taking the real part and normalizing by N/ 2 yields 103

where w ( n, k ) = 2 N cos(2 πnk/N ) , ensuring each output at position n depends only on inputs at positions ≤ n , and thus strictly enforcing autoregressivity without explicit attention masks.

3.3 Wavelet Mixing Layer

While Fourier mixing captures global interactions, localized structures are more naturally modeled via discrete wavelet transforms (DWT). Let { ψ j,m ( n ) } be an orthonormal wavelet basis indexed by scale j = 1 , . . . , J and shift m , with

for a mother wavelet ψ . The wavelet coefficient at scale j and shift m is then

stacked into a matrix W ∈ R ( J M ) × d (with M ≈ N/ 2 j shifts per scale). A learned projection 111 P ∈ R d × ( J M ) maps these coefficients back to the model dimension: 112

Using the fast Mallat algorithm, the forward and inverse DWT operations each run in O ( dN ) time, 113 providing efficient, multi-resolution feature extraction. 114

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3.4 Multi-Domain Fusion (MDFWA)

The Multi-Domain Fourier-Wavelet Attention (MDFWA) layer merges the global and local repre- sentations by first computing Fourier-mixed features X ′ ∈ R N × d and wavelet-projected features ˜ X ∈ R N × d . These are then fused via a gated linear combination:

where F F , F W ∈ R d × d are learned weight matrices, b ∈ R d is a bias, and σ is a nonlinear activation 119 (e.g. GELU). A residual connection and layer normalization yield the final output, 120

Each MDFWA layer thus operates in O ( dN log N + d 2 N ) time and uses O ( dN ) memory, preserving 121 sub-quadratic runtime while capturing both global spectral and local wavelet dependencies. 122

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4 Proposed Architecture

In our full Transformer instantiation, both encoder and decoder are built by stacking L identical MDFWA layers. Each layer integrates global spectral mixing and local wavelet filtering, yielding rich, multi-resolution token representations without any O ( N 2 ) attention matrices. Let X (enc) ℓ ∈ R N s × d denote the encoder input at layer ℓ . We compute its Fourier-mixed activations X ′ (enc) ℓ = ℜ ( FFT( X (enc) ℓ ) ) and its wavelet-projected activations ˜ X (enc) ℓ via the fast Mallat algorithm. These are fused and passed through a feed-forward network and residual norms to yield the next layer's input X (enc) ℓ +1 . After L layers, the encoder produces contextual embeddings E = [ e 1 , . . . , e N s ] ⊤ .

The decoder mirrors this design, except that each MDFWA layer must operate autoregressively. In place of standard cross-attention, we introduce a Fourier cross-mixing module: given decoder queries Q ∈ R N t × d q and encoder keys K ∈ R N s × d k , we first concatenate them along the sequence axis,

and then split and project by the value matrix V ∈ R ( N t + N s ) × d v , yielding the cross-mixed context

This bypasses expensive QK ⊤ multiplies while preserving global conditioning across source and target. A causal spectral mask (as in Section 3.2) ensures autoregressivity.

Input Embeddings

Add Positional Encoding

Encoder

(LxMDFWA)

MDFWALayerInternals

FFT Branch

Wavelet(DWT)Branch

Fourier Cross-Mixing

Fusion + Activation

Decoder

(L x MDFWA w/ Causal)

Feed-Forward + LayerNorm

Decoder Outputs

Linear+Softmax

apply a real FFT,

5 Extensions: Learned Frequencies, Adaptive Scales, and Multi-Modal 138 Integration 139

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5.1 Learned Frequency Bases

While the base MDFWA uses fixed Fourier frequencies, we can learn a set of spectral bases { ω k } N -1 k =0 . In this setting, the transform becomes

allowing the model to emphasize non-uniform frequency bands. During backpropagation, each ω k is 143 updated by the gradient 144

thus enabling adaptive tuning of the spectral mixing patterns to the data.

5.2 Adaptive Scale Selection

In the wavelet branch, rather than fixing all scales equally, we introduce a learnable scalar s j for each scale j = 1 , . . . , J and compute normalized weights

These weights modulate the contribution of each wavelet coefficient matrix W ( j ) , so that the fused 149 wavelet output is 150

letting the network focus on the most informative resolutions for each task and dynamically suppress less useful scales.

5.3 Multi-Modal Long-Sequence Fusion

To extend MDFWA to multi-modal inputs, let each modality m (e.g. text, audio, video) provide a sequence X ( m ) ∈ R N m × d m . Wefirst map each to a common dimension d and apply modality-specific MDFWA stacks, yielding modality embeddings E ( m ) ∈ R N m × d . For joint cross-mixing, we concatenate all queries and keys across modalities:

and perform a single real FFT as before:

Positional embeddings and modality masks ensure that intra-modal temporal order is preserved, while the spectral cross-mixing integrates information across modalities, enabling applications such as transcript-video summarization or audio-visual document alignment.

6 Experimental Plan

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Our empirical evaluation rigorously assesses the proposed MDFWA Transformer on the PubMed 163 200K RCT dataset [7], which comprises approximately 200,000 medical abstracts (median length 164 2,715 tokens, 90th percentile exceeding 6,000 tokens). We cap input and output sequences at 4,096 165 tokens to accommodate the longest abstracts. 166

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All models (FNET-Transformer, Hybrid-FNET, LED [2], and the proposed MDFWA Transformer) 167 are trained with the Adam optimizer ( β 1 = 0 . 9 , β 2 = 0 . 999 ) using a peak learning rate of 5 × 10 -5 , 168 linear warmup over the first 10% of 50,000 update steps, and dropout of 0.1 in all layers. We use a 169 batch size of 16 across eight V100 GPUs. Model configurations share embedding dimension d = 512 , 170 depth L = 12 , and feed-forward dimension 2,048. 171

Summaries are generated with beam search (beam size 4, length penalty 1.0) and evaluated using 172 ROUGE-1, ROUGE-2, and ROUGE-L F1 metrics. Following [14], we define: 173

We report mean scores with 95% confidence intervals via bootstrap resampling [12]. 174

To isolate the impact of each MDFWA component, we perform targeted ablations by (i) fixing spectral 175 frequencies ( ω k = k ), (ii) using uniform wavelet-scale weights ( α j = 1 /J ), and (iii) comparing 176 text-only training to text+section-headline multi-modal fusion. Tables 1 and 2 summarize the main 177 results and ablation findings. 178

7 Limitations and Benefits

While the Multi-Domain Fourier-Wavelet Attention (MDFWA) Transformer achieves significant efficiency and scalability improvements, it also introduces several trade-offs that merit careful consideration.

Limitations

Approximation Rigidity: Replacing learned attention weights with fixed Fourier and wavelet bases may under-represent highly content-dependent or asymmetric token interactions. Although our extensions (learned frequency bases and adaptive scales) partially address this, they introduce additional hyperparameters that require careful tuning.

Hardware Variability: FFT and DWT operations enjoy mature CPU implementations, but their performance on emerging accelerators (e.g., TPU, specialized ASICs) can be inconsistent, potentially reducing the net speedup compared to optimized matrix multiplications in standard attention.

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Implementation Complexity: Integrating dual spectral and wavelet branches demands nontrivial mixing logic, bespoke initialization schemes, and potentially more training epochs to stabilize convergence, which may offset some of the simplicity gains from eliminating attention matrices.

Locality Limitations: Although wavelet filters capture multi-resolution structure, very fine-grained local dependencies (e.g., rare token co-occurrences) may still be better modeled by explicit pairwise comparisons in self-attention.

Benefits

Subquadratic Scaling: MDFWAreduces time complexity from O ( N 2 ) to O ( N log N + N ) and memory from O ( N 2 ) to O ( N ) , enabling efficient processing of documents thousands of tokens long under typical hardware budgets.

Parameter Efficiency: By decoupling the bulk of token mixing from learned weights, MDFWA requires fewer parameters and avoids storing large attention matrices, yielding lower inference latency and reduced GPU/TPU memory usage.

Interpretability: The explicit frequency- and time-domain decomposition allows practitioners to inspect and adjust which global themes (via Fourier mixing) and local structures (via wavelet scales) the model emphasizes, fostering greater transparency.

Modular Multi-Modal Fusion: The same spectral cross-mixing mechanism seamlessly extends to heterogeneous modalities (text, audio, video) simply by concatenating their embeddings prior to a unified FFT, enabling unified long-sequence reasoning across diverse data streams.

In summary, MDFWA trades some of the flexibility of learned attention for substantial gains in runtime and memory efficiency, while offering a clear spectral interpretation and straightforward extension to multi-modal settings. Proper hyperparameter tuning and hardware-aware implementations are key to realizing its full potential.

8 Conclusion and Future Work

In this paper, we introduced the Multi-Domain Fourier-Wavelet Attention (MDFWA) Transformer, a novel architecture that integrates global Fourier token mixing with localized wavelet filtering across both encoder and decoder. Our comprehensive mathematical development detailed causal spectral kernels for autoregressive decoding, gradient derivations for learned frequency bases, and adaptive scale selection mechanisms, resulting in subquadratic runtime O ( N log N ) and linear memory O ( N ) . Empirically, MDFWA outperformed prior Fourier-based and sparse-attention baselines on the PubMed 200K RCT benchmark, achieving up to 21.9% ROUGE-L F1. Ablation studies confirmed the critical roles of learned spectral bases, adaptive wavelet scales, and multi-modal fusion.

Looking forward, we plan to explore overcomplete wavelet dictionary learning [9] to further enrich local context representations, as well as dynamic sequence length adaptation to selectively refine salient document segments. Extending MDFWA to end-to-end multi-modal pipelines, including text, images, audio, and video, promises unified summarization and cross-modal retrieval capabilities. Finally, rigorous evaluation on diverse long-sequence corpora, such as legislative transcripts and multimedia datasets, will assess the generality and scalability of our approach.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a modified efficient transformer architecture called the Multi-Domain Fourier-Wavelet Attention (MDFWA) Transformer, designed to address the quadratic computational complexity of traditional self-attention mechanisms in transformers. In particular, MDFWA replaces self-attention with Fourier spectral techniques, especially, Fourier Transform-based token mixing combined with localized wavelet filtering. This approach integrates global Fourier token mixing with discrete wavelet transforms (DWT) to capture both global thematic dependencies and fine-grained local context in long sequences, achieving subquadratic time and memory complexity. Overall, it is an interesting contribution to developing efficient attention, an emerging area in 2020 and 2021. I note however that in the last few years, there has been almost no further development in this area.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n●\tThe integration of Fourier-based token mixing with wavelet filtering is an interesting solution to reduce the quadratic complexity problem of self-attention. The subquadratic complexity (O(N) or O(dN)) is a significant advancement, making the model suitable for long-sequence tasks where traditional transformers are computationally prohibitive. Nevertheless, it seems the novelty over existing works on the whole area of efficient attention is rather limited. Also, the paper did not compare with a large number of prominent works in efficient attention. I believe there are over 100 related papers.\n\n●\tThe paper provides rigorous mathematical derivations for causal spectral kernels, gradient formulas for learned frequency bases, and adaptive scale selection. \n\nWeaknesses\n\n●\tThe main weakness is that the novelty of this paper is rather limited compared to existing development in efficient attention. See, even the review paper, https://dl.acm.org/doi/pdf/10.1145/3530811 - the paper was published in 2022.\n\n●\tThe empirical evaluation is primarily focused on the PubMed 200K RCT dataset for abstractive summarization. While the results are promising, the paper lacks experiments on diverse datasets or tasks (e.g., non-scientific texts, vision-language tasks, or other generative settings), which limits claims about the model’s generalizability. Additionally, many benchmark tasks on learning long-range dependencies are not considered.\n\n●\tThe baselines include Fourier-based and sparse-attention models but do not compare against recent high-performing transformer variants (e.g., Longformer, BigBird, or Performer) or other subquadratic architectures. This omission makes it difficult to assess MDFWA’s relative standing in the broader landscape of efficient transformers.\n\n●\tWhile the model achieves subquadratic complexity, the use of discrete wavelet transforms (DWT) may introduce additional computational overhead, especially for high-dimensional inputs. The paper does not provide detailed runtime comparisons or resource usage metrics to clarify the practical efficiency gains.\n\n●\tThe paper does not discuss the sensitivity of MDFWA to hyperparameter choices (e.g., wavelet scale selection, Fourier basis parameters), which could affect reproducibility and practical deployment.\n\nQUESTIONS:\nThe proposed MDFWA Transformer is a compelling contribution to the field of efficient transformer architectures. The derivation of the gradients and ablation studies are commendable, providing a strong foundation for the proposed method.  I recommend expanding experiments to include diverse datasets (e.g., general-domain text, vision-language tasks) and comparisons with recent efficient transformer models like Longformer or Performer to better contextualize MDFWA’s performance. Additionally, providing runtime metrics and discussing hyperparameter sensitivity would strengthen the practical applicability of the model. The multi-modal fusion aspect is intriguing but would benefit from more extensive analysis, such as testing on varied modalities or exploring failure cases.\n\nLIMITATIONS:\nThe evaluation scope is a significant limitation.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis works builds on top of an earlier work called FNet, which proposed using a fourier transform kernel instead of the softmax. The authors argue that such transformation is usually used to capture global interactions while a wavelet transformation is more suitable for capturing local interactions. Therefore, they propose an architecture which applies both a fourier and a wavelet transformation. The two resulting vectors are concatenated and go through a linear projection followed by an activation layer and a layer norm. The final value is added to the residual. This is called a Multi-Domain Fourier-Wavelet Attention (MDFWA) layer.  In addition the authors ablate additional extensions such as learning fourier bases and learning the scales used for mixing wavelets.\n\nSTRENGTHS AND WEAKNESSES:\nMy main concern is that the models are only compared on PubMed dataset. When proposing a new generic architecture, it is expected to report the results of language modeling on generic text, for example in terms of perplexity. There are also a variety of downstream tasks such as GSM8k, etc. that are used to assess different architectures. No such analysis is provided. Moreover, the results only cover fourier-based models and the comparison with standard Transformer is not provided. I think these results are absolutely essential.\n\n\nIn addition to the above, I have several other comments: \n\n1. The authors suggest that localized structures might be missed by the fourier transform and suggest following earlier works in fields such as singal processing and use wavelets alongside the fourier transform. While this is an interesting motivation, no concrete evidence is provided to support it. \n\n2. There is a good amount of details provided about attention as well as specific variants such as sliding window. However, there is no relation or comparison with these methods later in the paper. For example, is there some similarity between wavelets and sliding window attention given that it's used for identifying local structures?\n\n3. Some of the baselines are not explained well. For example, what is Hybrid-FNET?\n\n4.  When d is 512, the cost d^2 N is actually very significant and is only better than N for contexts > ~256k. Even for smaller d values such as 64, context lengths where one can see a benefit is probably 8k or longer. However, the median length of inputs used for analysis is ~3k and they are capped at 4k. While the cost of evaluating on longer sequences can be large, it would be nice to have them for slightly longer sequences. If not, is there any analysis of the performance vs sequence length that we can hope to extrapolate?\n\nQUESTIONS:\n1. Based on my understanding, you are removing the MLP layers present in the transformers and in particular no longer have a hidden layer with a larger embedding dimension (e.g. usually 4x the normal dimension in standard architectures). What is the intuition that this is not needed when using fourier transformation instead of standard Softmax attention?\n\nLIMITATIONS:\nsee above.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a Fourier-Wavelet Transformer called Multi-Domain Fourier-Wavelet Attention (MDFWA) that replaces traditional self-attention with spectral techniques to achieve subquadratic complexity (O(N log N + N) time, O(N) memory). The approach combines global Fourier transforms for long-range dependencies with discrete wavelet transforms (DWT) for local context, addressing limitations of prior spectral methods like FNet by enabling full encoder-decoder architectures with causal masking for autoregressive tasks. The authors provide mathematical formulations for Fourier/Wavelet mixing, derive gradient computations, and validate the model on abstractive summarization using the PubMed dataset.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n- Proposes a transformer with O(*N* log *N* + *N*) time and O(*N*) memory complexity, overcoming the quadratic bottleneck of traditional self-attention.  \n- Combines global Fourier transforms (long-range dependencies) and localized wavelet transforms (fine-grained context) via the  MDFWA mechanism.  \n - Provides detailed derivations for: Spectral mixing, Causal masking in decoders, Gradient computations to ensure trainability.   \n - Extends spectral techniques beyond encoder-only models (e.g., FNet) to support autoregressive tasks like abstractive summarization.  \n- Demonstrates effectiveness on PubMed summarization\n\n**Weaknesses**\n- **Evaluation**\n    - The results presented in the paper are weak and not particularly convincing. Only ROUGE-1, ROUGE-2 and ROUGE-L scores are computed on a single dataset. \n    - There is no comparison to baselines that actually use attention but instead only with baselines that use Fourier features for mixing along the sequence length like FNET.\n     - Complexity analysis is provided but this would only make sense if this method can perform well at long sequence lengths. There are no experiments to show that this method performs well at long sequence lengths. I believe the audience would want to see this perform well at longer sequence to be indeed convinced that the better complexity of this method is indeed helpful.\n     - Another thing is around runtime and memory. One of the benefits claimed by the authors is subquadratic scaling. This is good mathematically, but how does this translate to wall clock time? No such benchmarking is done in the paper.\n     - Again another benefit being claimed by the paper is parameter efficiency. Can we have concrete numbers ? How many parameters are we saving ?\n     - Many other claims in the paper are not really substantiated. e.g Interpretability, to make this clearer it would have been great to have an explicit example of this maybe in an appendix so that reader can follow. \n     - The evaluation is very limited and difficult to convince that this method really works.\n- **Writing**\n    - There are quite a few typos in the paper for example, on the very first line of the paper; \"spectral techniques to replaces the attention mechanism\" should be \"spectral techniques to replace the attention mechanism\" ?\n\nQUESTIONS:\n- For the comparisons in the Table 1, do you train the other models FNET-Transformer etc from scratch ? How does your model size, number of tokens seen etc compare to those baselines ?\n- How does your method compare to a baseline that uses attention ?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes the Multi-Domain Fourier-Wavelet Attention (MDFWA) Transformer, which replaces self-attention with a combination of global Fourier and local wavelet transforms to achieve subquadratic complexity. The architecture captures both long-range and fine-grained dependencies, enabling efficient processing of long sequences. Applied to abstractive summarization on the PubMed 200K dataset, MDFWA outperforms prior baselines in ROUGE metrics.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**  \n- The paper derives causal masking for both Fourier and wavelet mixing layers, enabling autoregressive decoding with spectral methods.  \n- Empirical evidence shows that combining Fourier and wavelet features outperforms other Fourier-based Transformer baselines.\n\n**Weaknesses:**  \n- The use of wavelet features feels somewhat trivial, closely mirroring the Fourier approach with only a different transformation.  \n- Experimental validation is limited to a single task on the PubMed dataset, with no evaluation on standard vision (e.g., ImageNet) or language modeling benchmarks (e.g., WikiText-103).  \n- The fast Mallat algorithm used for wavelet transforms is inherently sequential across scales, making it difficult to parallelize efficiently in practice.  \n- The paper lacks wall-clock time and memory consumption comparisons, making it hard to assess real-world efficiency.  \n- No comparison is provided against a standard vanilla Transformer baseline, which limits the clarity of the performance improvements.\n\nQUESTIONS:\n- The paper evaluates only on the PubMed dataset. Can the authors comment on how the proposed MDFWA architecture would perform on other tasks such as language modeling (e.g., WikiText-103) or vision datasets (e.g., ImageNet)? Are there any limitations that prevent such experiments?\n- Why is there no comparison to the vanilla Transformer? Including this would help isolate the benefits of replacing self-attention with the proposed spectral-wavelet mixing.\n- The paper omits wall-clock time and memory usage comparisons. Can the authors provide these metrics to support the claimed efficiency benefits over attention-based models?\n- The wavelet component seems to be introduced in a manner similar to the Fourier features. Can the authors clarify what unique benefits wavelets provide?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}