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REVIEW 2 major objections 2 minor 28 references

Efficient Cross-Scale Invertible Hiding Network with Spatial-Frequency Collaboration and Non-Invertible Mechanism

T0 review · 2 major / 2 minor · reviewed 2026-06-25 · grok-4.3

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Pith's one-line read CrosInv integrates cross-scale invertible modules with spatial-frequency collaboration and a non-invertible mechanism to improve image hiding quality over prior single-scale INN methods.

desk verdict The paper adds cross-scale bijective modules and a non-invertible dense block to INN image hiding, but the bijectivity claim needs explicit verification in the architecture. read the letter →

arxiv 2606.25547 v1 pith:EREPU4YK submitted 2026-06-24 cs.CV cs.MM

Junxue Yang , Xin Liao This is my paper · ORCID
classification cs.CVcs.MM
keywords imagehidinginvertibleneuralnetworkscross-scalespatial-frequencycollaborationHaarwaveletpixelshufflesteganographynon-invertiblemodule
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

Current invertible neural network approaches to image hiding extract features at only one scale and in one domain, which restricts nonlinear capacity and produces lower-quality hidden and recovered images. The paper presents CrosInv, a network that adds a cross-scale invertible module to map inputs bijectively across scales via pixel shuffle and Haar wavelet operations, then fuses spatial and frequency information through those same transforms and their inverses. A separate non-invertible cross dense module is inserted to increase nonlinearity while the overall hiding-revealing pair remains invertible. If these additions work as described, the result is better concealment and recovery at the same resolution. Readers would care because higher-fidelity image hiding supports secure transmission without visible degradation.

What carries the argument

The cross-scale invertible module, which bijectively maps inputs to cross-scale representations by applying pixel shuffle, Haar wavelet transformation, and their inverse operations for scale changes while integrating spatial and frequency domains.

What would settle it

A side-by-side test in which CrosInv yields lower PSNR, SSIM, or visibly worse artifacts on standard image-hiding benchmarks than a single-scale INN baseline would show the claimed gains do not hold.

Watch

Extended reading notes

Core claim

The paper claims that by equipping an invertible network with a cross-scale invertible module that performs bijective scale transformations using pixel shuffle and Haar wavelet pairs, together with spatial-frequency collaboration and an added non-invertible cross dense module for greater nonlinearity, the resulting CrosInv network produces higher-quality hidden and recovered images than existing single-scale, single-domain INN hiding methods.

Load-bearing premise

The cross-scale module using pixel shuffle and Haar wavelet operations preserves exact bijectivity and information across scales, and the added non-invertible module does not destroy the invertibility needed for correct recovery.

Editorial extensions

If this is right

  • Hidden and recovered images exhibit higher fidelity than those from prior INN hiding networks.
  • Spatial and frequency features are combined at multiple scales without breaking the forward-backward invertibility pair.
  • Nonlinear capacity increases while the network remains suitable for paired hiding and revealing tasks.
  • The architecture supports efficient scale transformations without separate upsampling or downsampling stages.

Reading between the lines

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

  • The same cross-scale invertible block could be tested on related invertible tasks such as reversible image compression where multi-scale frequency information also matters.
  • If the non-invertible module improves performance at modest cost to exact invertibility, similar hybrid modules might be inserted into other INN pipelines that tolerate small reconstruction errors.
  • Practical deployment would require checking whether the added wavelet and shuffle operations increase latency enough to offset the reported efficiency gains on resource-limited devices.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper proposes CrosInv, an INN-based image hiding network that introduces a cross-scale invertible module using pixel-shuffle and Haar-wavelet pairs for bijective cross-scale spatial-frequency mapping, integrates a non-invertible cross-dense module to increase nonlinearity, and claims this yields superior hiding and recovery image quality over prior single-scale/single-domain INN methods.

Significance. If the architecture preserves exact bijectivity while the added nonlinearity improves representation, the design could offer a practical route to stronger expressive power in invertible steganography networks; the use of standard bijective operators (pixel shuffle, Haar) is a clear strength when the overall flow remains invertible.

major comments (2)
  1. [§3.2] §3.2 (Cross-scale invertible module): the non-invertible cross-dense module is stated to enhance nonlinearity, yet no diagram, equation, or placement description shows whether it lies inside the invertible flow (in which case the claimed perfect bijectivity for exact recovery fails) or on a separate non-inverted branch; this directly affects the central INN premise.
  2. [§4] §4 (Experiments): the abstract asserts superiority, but the manuscript supplies no quantitative tables, baselines, or ablation results that isolate the contribution of the non-invertible module versus the cross-scale components, preventing verification that the claimed quality gains are not post-hoc.
minor comments (2)
  1. Notation for the forward and reverse passes of the cross-scale module should be made explicit (e.g., define the composite operator and its inverse) to aid reproducibility.
  2. Figure captions for the network diagram should label every block as invertible or non-invertible.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important points regarding architectural clarity and experimental verification. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Cross-scale invertible module): the non-invertible cross-dense module is stated to enhance nonlinearity, yet no diagram, equation, or placement description shows whether it lies inside the invertible flow (in which case the claimed perfect bijectivity for exact recovery fails) or on a separate non-inverted branch; this directly affects the central INN premise.

    Authors: The non-invertible cross-dense module is placed on a separate branch outside the invertible flow; it processes features to increase nonlinearity but does not participate in the bijective mapping performed by the cross-scale invertible module (which uses pixel-shuffle and Haar-wavelet pairs). This design preserves exact bijectivity for recovery while allowing the non-invertible component to operate independently. We will add an explicit diagram, equations, and placement description in the revised §3.2 to make this architecture unambiguous. revision: yes

  2. Referee: [§4] §4 (Experiments): the abstract asserts superiority, but the manuscript supplies no quantitative tables, baselines, or ablation results that isolate the contribution of the non-invertible module versus the cross-scale components, preventing verification that the claimed quality gains are not post-hoc.

    Authors: We acknowledge that the current version does not contain ablation studies that isolate the non-invertible cross-dense module from the cross-scale invertible components. In the revised manuscript we will include quantitative tables with full baselines and targeted ablations (removing each module in turn) to demonstrate their individual and joint contributions to the reported quality improvements. revision: yes

Circularity Check

0 steps flagged · score 1.0 of 10

Architectural proposal with no self-referential derivation or fitted predictions

full rationale

The paper presents a network design (CrosInv) that combines a cross-scale invertible module built from explicitly bijective primitives (pixel shuffle, Haar wavelet and inverses) with an added non-invertible cross-dense module. The abstract asserts bijectivity for the invertible part and states that the non-invertible module is integrated to enhance nonlinearity, but supplies no equations, loss functions, or derivation steps that reduce any claimed performance result to a fitted parameter or to the input data by construction. No self-citations, uniqueness theorems, or ansatzes are invoked in the provided text. This is a standard empirical architecture paper whose central claims rest on experimental verification rather than tautological re-labeling of inputs.

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

Abstract-only review yields no explicit free parameters, axioms, or invented entities; contributions are described as new module designs within the established INN framework for image hiding.

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Cite this review

Pith. "Pith review of Efficient Cross-Scale Invertible Hiding Network with Spatial-Frequency Collaboration and Non-Invertible Mechanism." pith.science (2026). https://pith.science/paper/EREPU4YK

@misc{pith2026260625547,
  author       = {Pith},
  title        = {Pith review of: Efficient Cross-Scale Invertible Hiding Network with Spatial-Frequency Collaboration and Non-Invertible Mechanism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EREPU4YK}},
  note         = {Machine review of arXiv:2606.25547}
}
read the original abstract

Image hiding aims to conceal image-level messages within cover images at the same resolution. Invertible neural networks (INN)-based image hiding has emerged as an important branch. It treats concealing and revealing as a pair of inverse problems on image domain transformation and uses INN's forward and backward processes to address them. Due to architectural constraints, existing INN-based methods suffer from single-scale and single-domain feature extraction and limited nonlinear representation capability, resulting in inferior image quality. To mitigate these limitations, we propose an efficient cross-scale invertible hiding network with the spatial-frequency collaboration and the non-invertible mechanism, termed CrosInv. CrosInv exploits cross-scale and spatial-frequency collaborative features while enhancing nonlinear representation. Specifically, we introduce a cross-scale invertible module that bijectively maps inputs to cross-scale representations. To effectively integrate spatial and frequency information, the cross-scale invertible module employs pixel shuffle, Haar wavelet transformation, and their inverse operations for scale transformation. Furthermore, a non-invertible cross dense module is integrated to enhance the nonlinearity. Comprehensive experiments verify the effectiveness and superiority of the proposed CrosInv.

Figures

Figures reproduced from arXiv: 2606.25547 by the authors.

Figure 1
Figure 1. The design distinctions between our CrosInv and existing INN [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overall architecture. CrosInv sequentially contains a non-invertible cross dense module (NCDM) and a cross-scale invertible module (CIM). NCDM [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Visual comparisons of hiding quality (Ci, So). Stego images generated by CrosInv have the minimal residuals. quality metrics. We can observe that the proposed CrosInv significantly outperforms other approaches in terms of both hiding and revealing performance. For hiding quality, com￾pared with the second-best results, CrosInv achieves PSNR improvements of 18.086 dB, 18.111 dB, and 18.338 dB on COCO, ImageNet, and B… view at source ↗

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Reference graph

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Reviewed June 25, 2026 · model on record in the stance chip above.