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REVIEW 4 major objections 6 minor 2 cited by

$\text{S}^{3}$Mamba: Arbitrary-Scale Super-Resolution via Scaleable State Space Model

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read S3Mamba claims to bring state space models to arbitrary-scale super-resolution, achieving state-of-the-art results on DIV2K and COZ with linear computational complexity.

desk verdict A credible scale-modulated SSM module is buried under a self-inflicted novelty problem: the paper claims to be first SSM-based ASSR while citing MambaSR and never comparing against it. read the letter →

arxiv 2411.11906 v1 pith:PBYZBPDG submitted 2024-11-16 cs.CV

Peizhe Xia , Long Peng , Xin Di , Renjing Pei , Yang Wang , Yang Cao , Zheng-Jun Zha This is my paper · ORCID
classification cs.CV
keywords arbitrary-scalesuper-resolutionstatespacemodelimplicitneuralrepresentationscale-awareattentioncontinuouslinearcomputationalcomplexityMambaimagerestoration
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that state space models (SSMs), known for linear-complexity global modeling, can be adapted to arbitrary-scale super-resolution (ASSR) by making the discretization process scale-aware. It proposes S3Mamba, whose Scalable State Space Model (SSSM) modulates the state transition matrix and sampling step size using scale and coordinate information, plus a scale-aware self-attention mechanism. If correct, this would provide an efficient alternative to Transformer-based ASSR decoders, which incur quadratic complexity, while improving reconstruction quality and generalization to unseen magnifications.

What carries the argument

The central object is the Scalable State Space Model (SSSM), which modifies the standard SSM discretization by computing scale- and coordinate-aware modulation factors via MLPs, forming $\Delta'_{x_k} = \Delta_{x_k} \cdot \Delta^{\text{scale}}_{x_k}$ and $B'_{x_k} = B_{x_k} \cdot B^{\text{scale}}_{x_k}$ before applying zero-order hold. This carries the argument by making the recurrence adapt to the physical spacing between pixels at different scales, thereby unifying representations across magnifications; a scale-aware self-attention map, also generated by the SSSM from coordinates and scale, further refines the fused high-resolution features.

What would settle it

Run S3Mamba and MambaSR on the DIV2K validation set and the COZ test set under identical training protocols; if MambaSR attains comparable or higher PSNR/SSIM, or if its publication predates S3Mamba's submission as a valid SSM-based ASSR method, the paper's core claims of novelty and state-of-the-art performance would be falsified.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that injecting scale and continuous coordinate information into the SSM discretization process—specifically modulating the sampling interval $\Delta_{x_k}$ and the input matrix $B_{x_k}$ by multiplying them with scale- and coordinate-dependent factors (Eqs.\ 6–13)—creates a scale-adaptive continuous representation. This allows a single SSM-based decoder to handle arbitrary magnification factors while retaining the linear computational complexity of SSMs and outperforming existing INR-based methods on both synthetic and real-world benchmarks.

Load-bearing premise

The claim of being the first to introduce SSM into ASSR and of achieving state-of-the-art performance rests on the assumption that all relevant baselines, including MambaSR which the paper itself cites, are included in the comparisons.

Editorial extensions

If this is right

  • If SSSM works as claimed, SSM-based decoders can replace MLP and Transformer decoders in ASSR, providing linear complexity that scales to very large output resolutions.
  • The scale-modulated discretization could generalize beyond trained magnification factors, as the out-of-scale results on DIV2K suggest continuous representation across unseen scales.
  • The method is designed to be a plug-in module for existing SR backbones such as EDSR and RDN, so it could improve arbitrary-scale capability of many fixed-scale SR models.
  • The scale-aware self-attention mechanism may reduce artifacts in real-world degraded images, as indicated by the COZ experiments where SSIM improvements are noticeable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper cites MambaSR [66], an earlier SSM-based arbitrary-scale super-resolution method, but excludes it from all comparisons; if MambaSR is a valid baseline, the claim of being 'first' to introduce SSM to ASSR is questionable and the performance lead over SSM-based prior work is unverified.
  • The scale-conditional discretization idea could transfer to other continuous signal reconstruction tasks, such as arbitrary-scale inpainting or video frame interpolation, where coordinate- and scale-conditioned recurrence may help maintain temporal or spatial consistency.
  • The scale-aware self-attention map is generated from coordinates and scale alone, without image content; testing whether this content-agnostic conditioning generalizes across very different scene types would clarify its role versus learned content-based attention.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes S3Mamba, an arbitrary-scale super-resolution method built on a 'Scalable State Space Model' (SSSM) that modulates the discretization parameters Δ and B with scale and continuous coordinate information (Eqs. 6–13), together with a 'scale-aware self-attention' mechanism (Eq. 16). The method is evaluated on synthetic DIV2K and real-world COZ benchmarks using EDSR and RDN backbones, reporting state-of-the-art PSNR/SSIM at multiple in-scale and out-of-scale magnifications. The paper also claims to be the first to introduce SSMs into arbitrary-scale super-resolution and to maintain linear computational complexity.

Significance. If the claims were established, the SSSM would be a useful architectural contribution: it adapts the selective-scan mechanism of Mamba to continuous coordinate and scale conditioning, potentially giving an efficient, context-aware decoder for arbitrary-scale SR. The ablation studies (Tables 3–4) show small but consistent gains when the SSSM, global feature extraction, and the proposed gating module are added, suggesting the core design is not empty. However, the headline contributions—novelty, state-of-the-art performance, and linear-complexity advantage—are currently under-supported by the evidence in the manuscript. The paper is empirical, and the main results are quantitative comparisons, so the missing baseline, missing error bars, and absent complexity analysis are load-bearing.

major comments (4)
  1. [Section 2.2, Section 4.1, Tables 1-2] The paper cites MambaSR [66], titled 'Arbitrary-scale super-resolution integrating mamba with fast fourier convolution blocks', in Section 2.2, yet omits it from all quantitative comparisons in Tables 1 and 2. Section 4.1 then claims 'we introduce the State Space Model into arbitrary-scale super-resolution for the first time.' This is internally inconsistent: if MambaSR is a functional SSM-based ASSR method, the novelty claim is false, and the claimed performance lead over SSM-based competitors is untested. The authors should add MambaSR to the comparison (or justify its exclusion) and revise the 'first' claim accordingly.
  2. [Table 2, Section 5.2] The claimed state-of-the-art performance on DIV2K is not supported by the reported numbers. Against the strongest baseline CiaoSR, the differences are at most 0.02–0.03 dB, and the direction is not consistent: at ×3 the proposed method is worse on both backbones (31.13 vs 31.15 for EDSR; 31.40 vs 31.42 for RDN), and similar reversals appear at ×24 and ×30. No error bars, standard deviations, or statistical significance tests are reported, so these differences are within typical run-to-run noise for SR training. The statement in Section 5.2 that 'our method achieves the best performance in most scenarios' needs quantitative support, such as multiple seeds with variances or paired tests.
  3. [Section 4.2, Eq. (16)] The module named 'scale-aware self-attention' is not an attention mechanism. Equation (16) computes a coordinate- and scale-dependent modulation αweight from SSSM, multiplies it elementwise with features, and then applies SSSM twice more. There are no attention scores, no queries/keys/values, no normalization over feature positions, and no learned dependence on the feature content. This is a multiplicative gating operation, and describing it as 'self-attention' misrepresents the contribution. The authors should either rename the module or provide a formal definition that justifies the 'attention' terminology.
  4. [Abstract, Section 4.1, Section 5.2] The paper repeatedly claims linear computational complexity and states in Section 5.2 that 'our computational complexity is only half of its, as shown in the supplementary materials,' but the supplementary material and appendix are not included in the submitted manuscript. No complexity analysis, FLOPs table, inference-time measurement, or formal scaling argument appears in the main text. Since the efficiency claim is one of the stated headline contributions, it needs to be substantiated in the manuscript itself, or explicitly deferred to a version that contains the appendix.
minor comments (6)
  1. [Section 1 heading] The heading 'Introdution' is a typo and should be 'Introduction'.
  2. [Table 2] The table note 'Bold and Bold indicate the best performance and second-best performance, respectively' appears corrupted; it likely should describe bold and underline formatting.
  3. [Tables 1 and 2] The notation for reference [7] is inconsistent: Table 1 uses 'LIT', while Table 2 uses 'CLIT'. Use one consistent abbreviation.
  4. [Figure 1 caption] The caption contains 'discredited low-resolution images', which should be 'discretized low-resolution images'.
  5. [Eq. (16)] The notation 'αweight = SSSM(coordHR, scale)' is unclear because SSSM was previously defined as a sequence model on features; clarify how coordinates and scale are prepared as inputs to the state space model.
  6. [Section 4.2 and Conclusion] The paper refers repeatedly to an appendix and supplementary material for additional comparisons and analyses, but this version contains no such sections; either include them or adjust the references.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular dependency found; the paper's SSSM is an empirical architectural component, and the only notable issue (omitting the cited SSM-based ASSR competitor MambaSR from comparisons) is a factual/comparison concern, not circular reasoning.

full rationale

The paper does not present a derivation that reduces to its inputs. Section 4.1 proposes an architectural mechanism (Eqs. 6-13): a learnable MLP conditions the discretization step Delta and input matrix B on scale and coordinates, then standard zero-order-hold discretization is applied. This is an empirical design choice, not a theorem; no target quantity is defined in terms of the proposed SSSM and then "predicted" from it. Eq. (16) reuses the SSSM to produce a scale-aware attention weighting and again to refine HR features; this is functional module reuse in a network, not self-definitional circularity, because the paper makes no claim that the module's behavior is derived from itself, it simply stacks the same differentiable block. The ablations in Tables 3 and 4 compare configurations without fitted constants being relabeled as predictions. The only potentially self-referential load-bearing claim is the novelty assertion in Sections 1 and 4.1 ("we introduce the State Space Model into arbitrary-scale super-resolution for the first time"), which is undermined by the paper's own citation of MambaSR [66], an SSM-based ASSR method published in Mathematics 12(15):2370, 2024. That is a factual/comparison flaw (an omitted baseline that would affect the SOTA claim), but it is not circular reasoning: the empirical pipeline is externally benchmarked against DIV2K and COZ with standard metrics and standard backbones. The cited prior work [76] used to construct the SSSM block is an external Vision Mamba reference, not a self-citation chain, and the one same-author citation [14] is not load-bearing. Therefore no circular step is identifiable, and the circularity score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim is empirical; no fitted physical constants. The training scale range is a hand-chosen hyperparameter. The main assumptions are the validity of zero-order-hold discretization, bicubic degradation for synthetic data, and the scale/coordinate modulation hypothesis.

free parameters (1)
  • training scale range = U(1,4)
    Section 5.1: scale s sampled from uniform distribution U(1,4) to generate training pairs; the choice bounds the in-scale range and affects out-of-scale performance (e.g., x6 to x30).
assumptions (4)
  • standard math Zero-order hold discretization of SSM (Eq. 4) is a valid approximation of the continuous ODE.
    Used as the starting point for SSSM in Section 4.1.
  • domain assumption Bicubic downsampling provides the paired LR/HR examples for training on DIV2K.
    Section 5.1: GT patches are downsampled bicubically to generate LR images; this is the standard synthetic degradation model and may not generalize to real-world blur/noise.
  • ad hoc to paper Scale and coordinate modulation of Delta and B is sufficient to unify continuous representations across scales.
    This is the core design hypothesis of SSSM in Section 4.1; no independent theoretical justification is given.
  • domain assumption COZ benchmark is representative of real-world ASSR.
    Used as the real-world test set in Section 5.1.

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Cite this review

Pith. "Pith review of $\text{S}^{3}$Mamba: Arbitrary-Scale Super-Resolution via Scaleable State Space Model." pith.science (2026). https://pith.science/paper/PBYZBPDG

@misc{pith2026241111906,
  author       = {Pith},
  title        = {Pith review of: $\textS^3$Mamba: Arbitrary-Scale Super-Resolution via Scaleable State Space Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PBYZBPDG}},
  note         = {Machine review of arXiv:2411.11906}
}
abstract

Arbitrary scale super-resolution (ASSR) aims to super-resolve low-resolution images to high-resolution images at any scale using a single model, addressing the limitations of traditional super-resolution methods that are restricted to fixed-scale factors (e.g., $\times2$, $\times4$). The advent of Implicit Neural Representations (INR) has brought forth a plethora of novel methodologies for ASSR, which facilitate the reconstruction of original continuous signals by modeling a continuous representation space for coordinates and pixel values, thereby enabling arbitrary-scale super-resolution. Consequently, the primary objective of ASSR is to construct a continuous representation space derived from low-resolution inputs. However, existing methods, primarily based on CNNs and Transformers, face significant challenges such as high computational complexity and inadequate modeling of long-range dependencies, which hinder their effectiveness in real-world applications. To overcome these limitations, we propose a novel arbitrary-scale super-resolution method, called $\text{S}^{3}$Mamba, to construct a scalable continuous representation space. Specifically, we propose a Scalable State Space Model (SSSM) to modulate the state transition matrix and the sampling matrix of step size during the discretization process, achieving scalable and continuous representation modeling with linear computational complexity. Additionally, we propose a novel scale-aware self-attention mechanism to further enhance the network's ability to perceive global important features at different scales, thereby building the $\text{S}^{3}$Mamba to achieve superior arbitrary-scale super-resolution. Extensive experiments on both synthetic and real-world benchmarks demonstrate that our method achieves state-of-the-art performance and superior generalization capabilities at arbitrary super-resolution scales.

Figures

Figures reproduced from arXiv: 2411.11906 by the authors.

Figure 1
Figure 1. (a) During real-world imaging, the continuous 3D physical world is discretized into an image through cameras and ISPs, resulting [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (a) Illustration of the proposed S 3Mamba framework. (b) The SSSM Block consists of the SSSM, along with multiple instance normalization layers, depthwise convolution (DWConv), and projection layers. (c) The Scalable State Space Model (SSSM) is proposed to modulate the state transition matrix and the sampling matrix of step size during the discretization process, achieving scalable and continuous representation mode… view at source ↗
Figure 3
Figure 3. Visual comparison with existing methods on the real COZ dataset [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Visual comparison with existing methods on the DIV2K dataset [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Forward citations

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Pith tools

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