{"id":"9715ecb9-ce8b-4aba-a1fc-850be1aa02af","arxiv_id":"2606.25547","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"CrosInv is an INN-based architecture for image hiding that adds cross-scale bijective mapping and non-invertible modules to overcome single-scale and single-domain limitations of prior methods.","lead":"The paper proposes CrosInv, a cross-scale invertible network for hiding images that combines spatial-frequency features via pixel shuffle and Haar wavelets with a non-invertible dense module to boost quality. Smart generalists might read it to understand advances in secure multimedia embedding techniques.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Whether the non-invertible cross-dense module can be integrated without violating the bijectivity required for exact recovery","rationale":"The reader’s weakest_assumption directly names the same bijectivity risk. Because the full manuscript is now accessible, the same assumption remains the single load-bearing point; no other internal inconsistency appears in the abstract-level description of the architecture.","tokens_in":1688,"tokens_out":319,"duration_ms":9011,"concrete_test":"Extract the exact forward and reverse equations (or pseudocode) for one cross-scale invertible block that contains the non-invertible module; verify algebraically that applying the reverse operations recovers the input tensor to machine precision on a random 64×64 patch.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the overall mapping remain invertible so that the reveal process exactly inverts the hide process. The cross-scale module is constructed from pixel-shuffle and Haar-wavelet pairs (both bijective), but the paper inserts a non-invertible cross-dense module “to enhance nonlinearity.” No derivation or architectural diagram shows how this module is placed inside the invertible flow (e.g., as a residual branch whose inverse is never needed, or as a separate non-invertible path whose output is discarded on the reverse pass). If the non-invertible block participates in the forward mapping that must later be inverted, the claimed perfect bijectivity fails; if it does not, the claimed “enhancement of nonlinear representation” is weaker than stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1827,"tokens_out":417,"duration_ms":14560,"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":[{"comment":"§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.","section":"§3.2"},{"comment":"§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.","section":"§4"}],"minor_comments":[{"comment":"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.","section":null},{"comment":"Figure captions for the network diagram should label every block as invertible or non-invertible.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[{"response":"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_made":"yes","referee_comment":"[§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."},{"response":"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_made":"yes","referee_comment":"[§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."}],"tokens_in":1308,"tokens_out":404,"duration_ms":21837,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing here is an incremental architecture for INN-based image hiding that tries to fix single-scale and limited-nonlinearity problems by using cross-scale mappings plus a non-invertible dense block. The cross-scale module relies on pixel shuffle and Haar wavelet pairs, which are bijective, to move between scales while mixing spatial and frequency information. That part is a straightforward response to the limitations the authors list in prior work.\n\nThe non-invertible cross-dense module is added to increase nonlinearity. This is the soft spot. The stress-test note is right to flag it: the overall hide-reveal process must remain exactly invertible for perfect recovery. The abstract does not show where the non-invertible block sits in the flow or whether it is isolated so the inverse never touches it. If the block participates in the forward mapping that later gets inverted, the bijectivity guarantee breaks. The paper needs a clear diagram or equation that settles this; without it the central claim is weaker than stated.\n\nExperiments are described as showing superiority, but the abstract supplies no numbers, baselines, or implementation details, so the practical gain is hard to judge from what is given. The citation pattern is normal for the subfield and does not look circular.\n\nThis is for people already working on neural steganography or invertible networks in multimedia security. A reader building similar models could pick up the module designs, but the work is too specialized and narrow to interest a broader audience.\n\nIt deserves peer review. The targeted fix is honest and the bijectivity question is concrete enough that referees can check it directly against the full architecture and results.","headline":"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.","tokens_in":2288,"tokens_out":411,"would_cite":false,"duration_ms":32997,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"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.","keywords":["image hiding","invertible neural networks","cross-scale","spatial-frequency collaboration","Haar wavelet","pixel shuffle","steganography","non-invertible module"],"falsifier":"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.","tokens_in":2580,"feed_emoji":"🖼️","tokens_out":718,"duration_ms":14500,"temperature":0.7,"pith_summary":"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.","feed_headline":"Cross-scale invertible network raises image hiding quality","feed_subtitle":"Pixel-shuffle and Haar-wavelet modules let spatial-frequency features collaborate across scales while a non-invertible block adds nonlineari","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Cross-scale invertible hiding network with spatial-frequency collab","CrosInv with cross-scale module and non-invertible block","Spatial-frequency collaboration via pixel shuffle and wavelets","Non-invertible cross dense module in invertible hiding network"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Cross-scale invertible hiding network with spatial-frequency collab","CrosInv with cross-scale module and non-invertible block","Spatial-frequency collaboration via pixel shuffle and wavelets","Non-invertible cross dense module in invertible hiding network"]},"model":"grok-4.3","cost_usd":0.007265,"raw_usage":{"total_tokens":3336,"prompt_tokens":645,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":72649500,"prompt_tokens_details":{"text_tokens":645,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2628,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":645,"tokens_out":63,"duration_ms":18613,"temperature":1.0,"reasoning_tokens":2628,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T21:19:24.980742+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"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.","supporting_citations":[],"review_version":1}