{"id":"39ac2571-a6c4-4eec-bc07-2ad621f8cea5","arxiv_id":"2501.18783","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"RUN unrolls a proximal-gradient foreground-background model into a four-stage network that refines masks with state-space modules and images with reconstruction, achieving top results on multiple concealed object segmentation benchmarks.","lead":"A new architecture called RUN applies deep unfolding to concealed object segmentation, unrolling an optimization model into stages that refine masks and images together. It reports top results across camouflage, polyp, tubular, and transparent object benchmarks, and can be plugged into existing detectors.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed unfolding derivation is not a valid proximal-gradient step for the ℓ1 residual-sparsity term: ℓ1 has no Lipschitz gradient, so the Taylor surrogate in Eqs. (10)–(12) does not minimize the stated model, and the 'theoretically grounded' claim is unsupported.","rationale":"The reader's weakest assumption pointed to the hand-set certainty map fM/w in Eq. (5) and the gap between the theoretical scaffolding and the learned refinement modules. I agree that this is a real weakness, but I find an earlier, more fundamental problem: the derivation that produces the unrolled updates is itself not a valid proximal-gradient derivation for the stated ℓ1 term. This is an internal mathematical issue, not merely a disagreement with consensus or a request for more experiments. If the derivation in Eqs. (10)–(13) is invalid, then the paper's central claim to be 'theoretically grounded' is not supported, and the empirical results, while possibly strong, cannot be attributed to the unfolding of the proposed model. The compounding tautology in C=C·M+B reinforces this: because any mask can be made consistent with the data by choosing B=C−C·M, the model places even more weight on the arbitrarily chosen sparsity target and on the learned RSS/reconstruction modules. My proposed check is concrete and would settle the mathematical claim directly: compare the paper's closed-form update against a true proximal update and against direct minimization of the original objective. If the updates differ, the paper should either revise the theoretical claims or reframe the modules as heuristic. I therefore recommend keeping the reader's CONDITIONAL verdict: the paper's empirical contribution may still be valuable, but the theoretical framing needs to be corrected or substantially softened before acceptance.","tokens_in":19848,"tokens_out":8622,"duration_ms":93191,"concrete_test":"Implement a scalar/pixel-wise version of Eq. (4) and compare three updates from the same starting point: (i) the paper's Taylor/closed-form update Eq. (13), (ii) a true proximal-gradient step with soft thresholding on S, and (iii) a direct numerical minimization of Eq. (4). If Eq. (13) does not monotonically decrease the original objective or converges to a different point, the derivation is not a proximal-gradient solution. Additionally, in the full network, replace Eq. (18) with a soft-thresholding-based update (with a learnable threshold) and retrain on COD10K; if metrics are statistically indistinguishable, the claimed sparsity-based unfolding, not the heuristic refinement modules, is not the source of the gains.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The most load-bearing problem is in §3.2.1. The paper replaces the ℓ1 residual-sparsity term S(w·(M−fM)) with the quadratic Taylor surrogate in Eqs. (10)–(11), asserts that ∇S(R_{k−1}) is a Lipschitz continuous gradient, and then solves Eq. (12) by setting the derivative to zero, yielding the closed-form update Eq. (13) that is unrolled as Eq. (18). But for S(·)=ℓ1, the (sub)gradient is the sign function: it is not differentiable at 0 and is not Lipschitz continuous, so the Taylor expansion and the stationary-point step are not mathematically justified. A proximal-gradient iteration for ℓ1 would apply soft thresholding, not this quadratic surrogate. Consequently Eq. (18) is not the proximal-gradient solution of Eq. (4), and the claim that RUN's connections are 'derived strictly based on mathematical principles' does not hold as stated. This matters because the central novelty is a theoretically grounded unfolding: once ∇S and all constants are made learnable in Eq. (18), the model's relation to Eq. (4) is heuristic. A compounding issue is that C=C·M+B is trivially satisfiable for any M by B=C−C·M, so the data-fidelity term alone cannot identify the mask; the hand-set fM/w in Eq. (5) and the learned modules carry the segmentation signal, making the theoretical scaffolding less load-bearing than claimed.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces RUN, a deep unfolding network for concealed object segmentation (COS). The task is formulated as a foreground-background decomposition C = C•M + B with an added ℓ1 residual-sparsity penalty on the mask M relative to a hand-crafted uncertainty-removal map fM and attention map w. The alternating optimization is unrolled into K stages; each stage contains a Segmentation-Oriented Foreground Separation (SOFS) module, consisting of a closed-form mask update plus a Reversible State Space (RSS) refinement, and a Reconstruction-Oriented Background Extraction (ROBE) module, consisting of a closed-form background update plus a lightweight U-shaped reconstruction network. The claimed contributions are the first deep unfolding for COS, reversible modeling in both mask and RGB domains, and state-of-the-art results on COD, polyp segmentation, tubular structure segmentation, transparent object detection, concealed defect detection, and salient object detection benchmarks.","tokens_in":20196,"tokens_out":8790,"duration_ms":87486,"significance":"If the mathematical grounding were correct, the paper would demonstrate a genuinely new route for applying deep unfolding to high-level vision, and the reported plug-and-play behavior (Tables 10-11) would be practically valuable. The experimental breadth is a real strength: results span six tasks, with ablations for each architectural choice and an analysis of stage number and small/multi-object subsets. The commitment to release code is also positive. However, the central theoretical claim is not currently supported: the Taylor surrogate for the ℓ1 term is invalid, and the fidelity term of the model is degenerate, so the hand-designed certainty maps carry the segmentation signal. These issues prevent the paper from substantiating the 'theoretically grounded framework' emphasized in the abstract and Figure 3, although the empirical results may still be salvageable through an honest reframing of the contribution as a heuristic unrolled architecture.","major_comments":[{"comment":"The Taylor expansion of the sparsity term S(wk•(M−fMk)) is mathematically unjustified for the stated ℓ1 norm. The function S(·)=ℓ1 is not differentiable at zero, and its (sub)gradient, the sign function, is not Lipschitz continuous; consequently Eq. (11) is not a valid global majorizing surrogate and Eq. (13) is not the proximal-gradient solution of Eq. (7). The claim that the connections in M̂(·) are 'derived strictly based on mathematical principles' (Fig. 3) is therefore unsupported. Because Eq. (18) later makes ∇S(·) learnable, the unrolled update is a heuristic whose relation to the original model is at best an analogy. To retain the theoretical claim, please replace the ℓ1 penalty with a smooth sparsity-inducing penalty (e.g., a Huber norm) for which a Lipschitz-gradient Taylor surrogate is valid, or use a proper proximal operator and derive the corresponding ISTA-style update.","section":"§3.2.1, Eqs. (10)-(13)"},{"comment":"The data-fidelity term ½∥C−C•M−B∥² is degenerate: for any mask M, the choice B = C − C•M gives zero fidelity, so this term imposes no constraint on M. All segmentation information in the model comes from the hand-crafted fM and w maps in Eq. (5) and from the learned regularizers and network modules. The 'residual sparsity constraint' is therefore an a priori certainty heuristic (forcing mask values toward 0.1 or 0.9 and excluding [0.4,0.6]) rather than a derived principle that 'minimizes segmentation uncertainties'. The paper should either provide a justification or sensitivity analysis for the specific thresholds in Eq. (5), or explicitly acknowledge that the model is a hand-designed prior and moderate the corresponding claims.","section":"§3.1, Eq. (4)"},{"comment":"Only the inner updates M̂k (Eq. 18) and B̂k (Eq. 20) are derived from the optimization; the RSS module (Eq. 19) and the reconstruction network B(•) (Eq. 21) are introduced as heuristic network components. Yet the abstract and Figure 3 imply that the entire stage is 'theoretically grounded'. Please clearly separate the derived and learned parts, and justify the non-derived components against generic alternatives (e.g., replace RSS with a standard residual block, or replace the closed-form update with a learned gated fusion) to establish that the derivation itself contributes to performance. The ablation in Table 5 removes RSS and VSS, but does not test whether the mathematically derived update is superior to a generic feature-fusion baseline.","section":"§3.2.2, Eqs. (18)-(21)"},{"comment":"Several reported gains over the best competing methods are very small (e.g., 0.001-0.005 in M and Sα on some datasets), and no error bars or statistical significance tests are provided. For the central COD results, please report multiple training runs with variance, or at least a significance test on the main metrics. In addition, the comparisons on polyp, tubular, and transparent object tasks would benefit from a clear statement of the backbone and training protocol used for each compared method, so that the gains cannot be attributed to architectural or preprocessing differences.","section":"Tables 1-4 and S1-S2"}],"minor_comments":[{"comment":"The text states 'I is an all-ones matrix', but the equations use I in an inverse, which requires the identity matrix; an all-ones matrix would be singular. Please correct this typo and define whether operations such as C² and wk² are element-wise.","section":"Eqs. (13) and (17)"},{"comment":"The notation M_i in Eq. (5) is not defined; it appears to refer to the pixel value of the previous mask M_{k-1}, but this should be stated explicitly, and the subscripts for the updated maps fMk and wk should be clarified.","section":"Eq. (5) and Section 3.1"},{"comment":"The captions and panel labels in Figure 2 are difficult to follow (e.g., panels (c)-(k) with mixed use of C, B, M, and hat symbols), and Figure 3 contains many unlabeled arrows and matrix-inverse notations. Please revise the figures for readability.","section":"Figure 2 and Figure 3"},{"comment":"The citation to Goldstein (1977) for the Taylor expansion is questionable, as that paper works with Lipschitz continuous functions rather than differentiable surrogates for ℓ1; a standard proximal-gradient textbook reference would be more appropriate.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has strong empirical breadth, and the idea of extending reversible strategies to the RGB domain via a reconstruction network is interesting. The main barrier is that the 'theoretically grounded' narrative is not supported by the mathematics as written: the ℓ1 Taylor surrogate is invalid, and the model's fidelity term is degenerate. I believe this is fixable by switching to a smooth sparsity penalty or by reframing the contribution as a heuristic unrolled architecture with the optimization model serving only as inspiration. Given the authors' track record and the thorough experiments, this is worth a major revision rather than rejection. I would also suggest the editor ask the authors to clarify the comparison settings for the non-COD tasks and to provide variance estimates."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"RUN is the first deep unfolding network for concealed object segmentation, and the empirical work is solid: consistent state-of-the-art results across COD, polyp, tubular, transparent, and SOD benchmarks, with careful ablations and a useful plug-and-play refiner. The mask-level plus RGB-level reversible design is a genuine extension of FEDER, and the idea of tying segmentation to reconstruction via unrolled proximal steps is worth taking seriously.\n\nThe soft spots are mostly in the framing, not the experiments. The stress-test note is right: Eqs. (10)-(11) replace the ℓ1 residual-sparsity term with a quadratic Taylor surrogate, but ℓ1 has no Lipschitz gradient, so the closed-form update in Eq. (13) is not the proximal-gradient solution of Eq. (4). A proximal-gradient treatment of ℓ1 would use soft thresholding. The paper's own claim that 'unlike ℓ1-norm methods, Eq. (12) can be solved directly' is an admission that they switched to a smooth surrogate. That is a legitimate modeling choice, but the 'theoretically grounded' language overstates it. Once all constants and ∇S are learnable, the connection to Eq. (4) is heuristic. This weakens the central novelty claim, but it does not invalidate the architecture.\n\nA second issue: the decomposition C = C·M + B is always satisfiable for any M by setting B = C − C·M, so the data-fidelity term alone cannot identify the mask. The hand-crafted fM and w maps in Eq. (5) carry the segmentation signal. The model is therefore not as 'novel' as presented; it is an optimization-inspired way to encode a certainty prior. That is fine, but it should be said plainly.\n\nThe empirical comparison also lacks error bars and the code is not released. The reported gains are often small (0.001–0.01 in Sα or Fβ), so some differences may be noise. Asking for code and error bars is reasonable.\n\nWho is this for? Researchers working on COS or on applying unfolding techniques to high-level vision. They will get a clear architectural template and a benchmark set that shows where it works. The paper deserves serious peer review, but the theory section needs an honest rewrite and the empirical claims need reproducibility support before I would trust the numbers.","headline":"A solid first deep-unfolding paper for concealed object segmentation whose empirical breadth is real, but the claimed theoretical grounding is overstated because the ℓ1 surrogate step is not a proximal-gradient update.","tokens_in":20732,"tokens_out":2831,"would_cite":true,"duration_ms":29895,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Deep unfolding with reversible RGB-mask modeling achieves state-of-the-art concealed object segmentation.","keywords":["concealed object segmentation","deep unfolding network","reversible modeling","foreground-background separation","residual sparsity constraint","visual state space","image reconstruction","camouflaged object detection"],"falsifier":"A direct test: retrain RUN with the residual sparsity term removed ($\\alpha = 0$) and with $f_M$ set to the identity, keeping all other components identical, then compare on COD10K and on the transparent-object datasets GDD and GSD; if the metrics do not degrade, the uncertainty-removal model is not the source of the reported gains.","tokens_in":19638,"feed_emoji":"👁️","tokens_out":7451,"duration_ms":73168,"temperature":0.7,"pith_summary":"The paper sets out to prove that concealed object segmentation, finding objects that blend into their background, improves when the reversible reasoning between foreground and background is carried out not only on prediction masks but also on the RGB image itself. To do this it introduces RUN, a network built by unrolling the proximal-gradient iterations of an explicit image-decomposition model into four stages, each containing a mask-domain module (SOFS) and an image-domain module (ROBE). The paper's central claim is that jointly optimizing segmentation and image reconstruction directs the network to uncertain regions and reduces both false positives and false negatives. If the claim holds, a low-level-vision technique, deep unfolding, transfers to high-level vision, and reconstruction becomes a principled component of segmentation rather than a separate auxiliary output.","feed_headline":"One unfolding framework tops five concealed-object segmentation tasks","feed_subtitle":"By coupling mask- and RGB-domain reversible reasoning, RUN's reconstruction step sharpens uncertain regions and lifts every benchmark.","key_machinery":"The load-bearing mechanism is the alternating proximal-gradient pair derived from Eq. (4): the mask update $\\hat{M}_k = (Q_a)^{-1}(Q_b M_{k-1} + C^2 - C B_{k-1} + Q_c)$ and the background update $\\hat{B}_k = ((1+\\lambda)I)^{-1}(\\lambda B_{k-1} + C - C \\cdot M_k)$, whose connections dictate how priors and image combine at every stage and give RUN its interpretability. The residual sparsity certainty map $(f_M, w)$ of Eq. (5) injects the concealed-object inductive bias, pushing masks to high certainty and ignoring the ambiguous band, and it is the component RUN ablates in variants CM1 through CM5. The two learned refiners are the Reversible State Space module, two Visual State Space blocks with small and large receptive fields plus an auxiliary edge output, for the mask domain, and the lightweight U-shaped reconstruction network $\\mathcal{B}(\\cdot)$ that outputs both the refined background and the reconstructed image for the RGB domain.","core_discovery":"RUN models a concealed image $C$ as a foreground term plus background, $C = C \\cdot M + B$, where $M$ is the segmentation mask. To the usual data-fidelity and regularization terms it adds a residual sparsity constraint $S(w \\cdot (M - f_M))$ whose target map $f_M$ forces confident pixels toward 0.1 or 0.9 and whose weight $w$ zeroes out ambiguous pixels in [0.4, 0.6]. The alternating proximal-gradient update for $M$ and $B$ is then unfolded into $K$ network stages: SOFS applies the closed-form mask update and refines it with a Reversible State Space module built from two Visual State Space blocks, while ROBE applies the closed-form background update and refines it with a lightweight U-shaped reconstruction network that also outputs the reconstructed image $\\hat{C}_k$. Because the foreground and background are estimated by independent modules, their conflicting judgments appear as distortion-prone regions in reconstruction, and resolving those distortions focuses the network on uncertain areas. The paper reports state-of-the-art results across camouflaged object detection, polyp, tubular, transparent, and defect segmentation, plus salient object detection, and shows the framework can refine or integrate with existing methods.","pith_inferences":["A natural extension the paper leaves open is learning the certainty thresholds, 0.1, 0.9, and the [0.4, 0.6] ambiguity band, per dataset instead of hand-setting them; transparent and tubular targets might benefit most from data-driven thresholds.","If the unification of segmentation and reconstruction is the real source of gain, the same alternating unfolding with a reconstruction consistency term could be applied to other high-level tasks with natural decomposition models, such as shadow removal or reflection separation, where foreground-background conflicts also produce distortions.","The haze experiments are reported only as curves; a numerical study varying degradation type, low light, blur, and noise, would clarify whether the ROBE/RGB-domain reversible module is broadly degradation-robust or specifically effective against haze.","Because the reconstruction loss is plain MSE, the attention-directing effect may depend on the reconstruction network's capacity and loss; testing perceptual or adversarial reconstruction losses could reveal whether the mechanism is loss-agnostic."],"forward_implications":["If RUN's claim is right, input reconstruction is not a side effect of segmentation but an active mechanism: resolving RGB distortions where foreground and background estimates disagree is what sharpens the mask.","The same unfolding recipe transfers across at least five concealed-object tasks and salient object detection, suggesting that hand-designed decomposition models plus proximal-gradient unrolling can compete with task-specific architectures in high-level vision.","RUN works as a plug-and-play component: initializing its first mask with another method's output refines that method without retraining, and inserting existing modules into RUN's stages gives larger gains after retraining.","In simulated haze, RUN degrades more gracefully than comparable methods, and replacing its reconstruction network with a dehazing-aware one further resists degradation, pointing toward degradation-resistant high-level vision.","Four stages are enough: K=2 already beats most compared methods, K=4 is the chosen trade-off, and K=6 through K=8 add only marginal gains."],"supporting_citations":[{"why":"Supplies the reversible mask-level modeling with foreground and background masks and edge assistance that RUN extends to the RGB domain, plus the training strategy RUN adopts for the segmentation loss.","marker":"(He et al., 2023b)"},{"why":"Defines the COD task protocol and the CHAMELEON, CAMO, COD10K, and NC4K datasets used for training and evaluation.","marker":"(Fan et al., 2020a)"},{"why":"Provides the proximal gradient optimization scheme and cooperative unfolding structure that RUN adapts for its multi-stage network.","marker":"(Fang et al., 2025)"},{"why":"Supplies the Taylor-expansion approximation of Lipschitz continuous functions used to convert the sparsity term into a solvable closed-form update.","marker":"(Goldstein, 1977)"},{"why":"Supplies the Visual State Space modules that RUN combines into its Reversible State Space module for non-local information extraction.","marker":"(Liu et al., 2024b)"},{"why":"Provides the practice of excluding ambiguous pixels in [0.4, 0.6] and setting extreme mask values to 0.1 and 0.9, which becomes the certainty model in Eq. (5).","marker":"(He et al., 2024a)"},{"why":"Supplies the lightweight U-shaped reconstruction network structure used in ROBE and the joint-optimization rationale linking segmentation with reconstruction.","marker":"(Xu et al., 2023)"},{"why":"Provides the degradation-resistant unfolding approach and the haze simulation protocol used in the degraded-scenario experiments, and the soft-thresholding baseline tested as CM2.","marker":"(He et al., 2023a)"}],"fun_headline_variants":["Reversible unfolding with RGB and mask beats COS benchmarks","RUN: dual-domain reversible net tops concealed object benchmarks","Residual sparsity sharpens reversible unfolding for hidden objects","Reversible state space and reconstruction refine COS","Unfolding reversible reasoning in mask and RGB wins COS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the hand-set certainty rule of Eq. (5): pixels with mask values in [0.4, 0.6] are treated as uninformative and all other pixels are pushed toward 0.1 or 0.9, and if that rule misdescribes how transparent or tubular objects actually appear, the unrolled updates bias the network toward the wrong regions.","fun_headline_variants_meta":{"raw":{"variants":["Reversible unfolding with RGB and mask beats COS benchmarks","RUN: dual-domain reversible net tops concealed object benchmarks","Residual sparsity sharpens reversible unfolding for hidden objects","Reversible state space and reconstruction refine COS","Unfolding reversible reasoning in mask and RGB wins COS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000505,"raw_usage":{"total_tokens":2523,"prompt_tokens":1064,"completion_tokens":1459,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":680,"completion_tokens_details":{"reasoning_tokens":1380}},"tokens_in":680,"tokens_out":1459,"duration_ms":11729,"temperature":1.0,"reasoning_tokens":1380,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T22:28:07.662826+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct test: retrain RUN with the residual sparsity term removed ($\\alpha = 0$) and with $f_M$ set to the identity, keeping all other components identical, then compare on COD10K and on the transparent-object datasets GDD and GSD; if the metrics do not degrade, the uncertainty-removal model is not the source of the reported gains.","supporting_citations":[{"cited_title":"Real-world image dehazing with coherence-based label generator and cooperative unfolding network","cited_arxiv_id":null,"evidence_quote":"Provides the proximal gradient optimization scheme and cooperative unfolding structure that RUN adapts for its multi-stage network."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Taylor-expansion approximation of Lipschitz continuous functions used to convert the sparsity term into a solvable closed-form update."}],"review_version":1}