{"id":"30c2dc33-2aaa-4946-a5fa-2420025ecc61","arxiv_id":"2508.11961","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"PEdger++ improves fast edge detection by combining predictions from two network architectures, a momentum average over training epochs, and multiple parameter samples into soft targets and a final weighted model.","lead":"This paper presents PEdger++, a lightweight edge detection model that combines a fast network and a recurrent network during training, then runs only the fast network at inference. The work targets real-time edge detection on resource-constrained devices, reporting accuracy and speed improvements over prior efficient detectors.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Closed-form ensemble weights in Eqs. (8)-(9) do not solve the stated constrained minimization, undermining the Bayesian-posterior optimality claim; empirical SOTA may stand, but the theory needs reframing.","rationale":"The reader's weakest assumption identifies the same load-bearing issue: the closed-form weights in Eqs. (8)-(9) are not a correct solution to the constrained optimization in Eq. (6). I have checked the Lagrange conditions and the normalization constant; they confirm that the formula is at best a heuristic and at worst inconsistent. The mutual-information theorem is also a definitional restatement that does not rescue the derivation. The empirical results, while plausible, do not depend on the theoretical optimality for their measured values; the concern affects the paper's framing and the claimed novelty of the weighting scheme, not necessarily the reported ODS-F numbers. Therefore the appropriate verdict remains CONDITIONAL: the authors should either supply a valid derivation (e.g., using a proper KKT analysis that yields a different form, or a numerical solver) or explicitly demote the weighting to a heuristic. I see no grounds for REJECT, since the core empirical claim is supported by extensive tables and ablations. No other concern—such as the use of a validation split or the mutual-information wording—is more load-bearing than this one.","tokens_in":29209,"tokens_out":6032,"duration_ms":73071,"concrete_test":"On a small validation split (e.g., BSDS val), compute G(X; Θ_s) for S=3 sampled parameter sets from a trained momentum network. Solve the constrained problem Eq. (6) using projected gradient descent or SLSQP, enforcing Σ_s W_s = 1 and W_s ≥ 0, and compare the resulting optimal weights to Eqs. (8)-(9) (after any normalization). If the closed-form weights do not achieve the same or lower validation loss and do not satisfy the constraints, the derivation is invalid. Additionally, re-run the full training pipeline replacing Eqs. (8)-(9) with the true numerical optima; if ODS-F changes significantly, the heuristic is load-bearing; if not, the theory is cosmetic.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central theoretical support for the parameter-ensemble weighting is invalid. Eq. (6) minimizes the pixel-wise BCE loss L(M, Y) over W_s subject to Σ_s W_s = 1 and W_s ≥ 0, where M = Σ_s W_s G_s. For an interior optimum, the Lagrange condition requires (M - Y)/(M(1-M)) * G_s = -λ for every s. Unless all sampled predictions G_s are pixel-wise identical (or M = Y), no interior solution exists; the optimum lies on the boundary of the simplex. The closed-form Eq. (8) instead sets W_s proportional to Σ_nv G_s * (Y/M - (1-Y)/(1-M)), which is essentially the negative gradient of the loss with respect to W_s, but it ignores the dependence of M on every W_s. The constant C = Nv/(2ΣY_nv) does not enforce Σ_s W_s = 1 and, as written, can yield negative weights. Thus the derivation is not a valid Lagrange-multiplier solution. The subsequent claims that these weights are 'optimal' and that the ensemble maximizes mutual information (Theorem 1) are therefore unsupported. Algorithm 1 uses these weights to build the soft targets in Eq. (11) and the final weighted parameter average in Eq. (10); if the formula is not a true optimum, the theoretical framing of the Bayesian-posterior approximation collapses to a heuristic. The measured ODS-F numbers are empirical and likely reproducible, so the central accuracy claim is not necessarily false—but the paper's theoretical contribution is overstated unless the formula is corrected or explicitly presented as a heuristic.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents PEdger++, an edge detection framework that combines three forms of cross-information: a recurrent and a non-recurrent network trained collaboratively, momentum networks that fuse parameters across epochs, and multiple Monte-Carlo-style parameter samples whose predictions are merged with weights derived from a validation split. The final inference uses only the non-recurrent network, whose parameters are a weighted average of the sampled parameters. On BSDS500 with PASCAL VOC augmentation, the authors report ODS-F 0.835 (716K params, 92 FPS) without pre-training and 0.857 (12.7M params, 37.6 FPS) with a ResNet50 backbone, claiming state-of-the-art accuracy for efficient edge detection. The paper includes extensive comparisons on BSDS/NYUD/Multicue, ablations of each ensemble component, and an efficient training variant.","tokens_in":29637,"tokens_out":7702,"duration_ms":90394,"significance":"Assuming the empirical measurements are reproducible, the paper makes a practically important contribution: it demonstrates that a compact detector can reach accuracy comparable to much larger transformer/diffusion models while running one to two orders of magnitude faster. The ablation studies (Tabs. 9-11) support the claim that each of the three integration mechanisms contributes. The parameter study (Tab. 12) and scalability table (Tab. 7) are useful. The release of code is a strength. However, the theoretical apparatus in §3.3 — the claimed optimal weights and the mutual-information theorem — is not valid as written, and this is the main novelty over the authors' previous PEdger. The empirical results may stand, but the paper currently overstates its theoretical grounding.","major_comments":[{"comment":"The closed-form weights in Eqs. (8)-(9) do not solve the stated constrained optimization. The objective in (6) depends on W_1,...,W_S through M = Σ_s W_s ∘ G_s. The Lagrange condition for an interior optimum of the BCE loss subject to Σ_s W_s = 1 is G_s(X;Θ_s) ∘ (M - Y)/(M(1-M)) = const for all s, which is not what Eq. (8) expresses. Eq. (8) is essentially a one-step negative-gradient update that treats M as fixed when differentiating; it omits the dependence of M on every W_s. It also does not enforce the constraints: at a non-edge pixel (Y=0) the bracketed term equals -G_s/(1-M) < 0, so every W_s is negative, and the normalization constant C cannot repair this. Because Algorithm 1 uses these weights to construct the soft targets (11)-(13) and the final parameter average (10), the \"optimal\" and \"Bayesian posterior\" claims are unsupported. The method should either be derived correctly (e","section":"§3.3, Eqs. (6)-(9)"},{"comment":"The proof of Theorem 1 is a definitional restatement rather than a substantive equivalence. Once p(Y|W,X) is defined by the product of Bernoulli probabilities with mean M=Σ_s W_s G_s, the conditional entropy is exactly the expected BCE, so minimizing the empirical loss is minimizing NLL by construction. The theorem does not show that the particular W_s from Eqs. (8)-(9) maximize mutual information, and the mutual-information objective I(Y;W_s|X) is not even well-defined without a distribution on W_s. The claim following Eqs. (8)-(9) that the calculated weights \"can also maximize mutual information\" is therefore unsupported. I recommend removing the theorem or replacing it with a precise statement about NLL minimization under the ensemble model.","section":"§3.3, Theorem 1"},{"comment":"Algorithm 1 (line 20) says \"Sample parameters Θ_s\" but the paper never specifies the distribution for the main (recurrent/non-recurrent) algorithm. The text invokes Monte Carlo Dropout, yet the architecture description in Sec. 3.1 does not mention dropout layers; the efficient variant (Algorithm 2) uses random weight pruning instead. This ambiguity makes the \"multiple parameter samplings\" component and the Bayesian interpretation non-reproducible. Please specify exactly how Θ_s^R and Θ_s^NR are generated, or revise the text to describe the actual stochastic weight perturbation.","section":"§3.3 and Algorithm 1, sampling mechanism"}],"minor_comments":[{"comment":"The last norm has an unbalanced parenthesis: \\|(1 - \\tilde{Y}_{nt}) \\circ \\log(1 - G(X_{nt})\\|_1 should be \\|(1-\\tilde{Y}_{nt}) \\circ \\log(1 - G(X_{nt}))\\|_1.","section":"Eq. (15)"},{"comment":"References [3] and [4] are identical (Balabanov et al.), as are [51] and [52] (Lakshminarayanan et al.); please merge the duplicates.","section":"References"},{"comment":"The pre-trained configurations are described in the text as using two non-recurrent networks, but Algorithm 1 formulates recurrent/non-recurrent training. Please clarify which algorithm and network pair corresponds to each row.","section":"Tabs. 1-2"},{"comment":"The denominator can be zero when both predictions are exactly 0.5; add a small epsilon for numerical stability.","section":"Eq. (12)"},{"comment":"The dataset column repeats 'BSDS' in a way that is confusing; a single multi-row header would be clearer.","section":"Table 3"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The empirical workload is solid and the paper is likely to be a useful contribution to efficient edge detection. My main concern is the invalid derivation of the ensemble weights and the tautological Theorem 1; these support the paper's main claimed novelty over the authors' prior PEdger. If the authors reframe the weighting as a heuristic and either remove or correct the theory, I would be willing to accept. I also note that the paper's 'state-of-the-art' claim is benchmark-specific: on BSDS without VOC the largest pre-trained variant does not beat MuGE (Tab. 1)."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The empirical half of this paper is in good shape; the theoretical half is not. PEdger++ assembles known pieces — a recurrent and a non-recurrent stream, momentum-averaged weights, MC-dropout-style parameter sampling, and soft targets — into a detector that hits 0.835 ODS-F on BSDS w/ VOC at 92 FPS with 716K parameters and 0.857 with a ResNet-50 backbone at 37.6 FPS. Those numbers are genuinely useful for the efficiency/speed/accuracy trade-off, and the ablation study is thorough: they test each ensemble component, the validation-set weighting, the two-stage alternative, and several hyperparameters. The Multicue and NYUD results look consistent. I have no reason to doubt the measured numbers, and the GitHub link means the code is at least promised.\n\nThe soft spot is the derivation of the ensemble weights in Eqs. (8)-(9). It is presented as the Lagrange-multiplier solution to the constrained validation-loss minimization in Eq. (6), but it is not a solution. The fused prediction M depends on every W_s, and the formula treats each weight as if it could be optimized independently while M stays fixed. It also doesn't enforce the sum-to-one constraint, and it can produce negative weights. The optimum of that BCE loss over the simplex is generally on the boundary, not at the interior point the formula implies. Theorem 1 is essentially the standard fact that minimizing negative log-likelihood maximizes mutual information between predictions and targets; it doesn't validate the closed form. The authors lean hard on 'optimal weights' and 'Bayesian posterior approximation' later in the paper, and those claims don't survive.\n\nThat said, the empirical method doesn't depend on the derivation for its measured results. The validation-based weighting can be reframed as a reasonable heuristic, and the ablations show it beats simple averaging and confidence selection. If the authors drop the optimality language, or actually solve the constrained problem and find a different formula, the paper is in decent shape. As it stands, the theory section needs major rework before publication.\n\nThis is a paper worth sending to a serious referee — the empirical contribution deserves scrutiny, and the flaws are fixable rather than fatal. I'd be more comfortable citing the benchmark numbers than the Bayesian claim. For a reading group, it's a reasonable example of how far ensemble tricks can push a small edge detector, but it's not a must-read.","headline":"Solid empirical engineering with a shaky theoretical wrapper: the accuracy/speed numbers are worth attention, but the claimed optimality of the ensemble weights does not hold up.","tokens_in":30062,"tokens_out":2900,"would_cite":true,"duration_ms":34116,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper proposes PEdger++, a collaborative learning framework that assembles cross-information from heterogeneous network architectures, different training moments, and multiple parameter samplings to make lightweight edge detection both","keywords":["edge detection","collaborative learning","Bayesian neural networks","model ensemble","soft targets","momentum networks","lightweight architecture","epistemic uncertainty"],"falsifier":"Compute the weights W_s from Eqs. (8)–(9) on a held-out validation split and check whether they sum to one and whether they yield a lower validation binary cross-entropy than equal weights or a directly optimized constrained solution; if equal weights or a numerical optimization beats the closed-form on ODS-F, the claimed optimality of the weight formulas is falsified.","tokens_in":29122,"feed_emoji":"⚡","tokens_out":6086,"duration_ms":67231,"temperature":0.7,"pith_summary":"PEdger++ claims that ensemble diversity can substitute for heavy architectures in edge detection. It trains a recurrent and a non-recurrent network together, fuses parameters across epochs with a momentum network, and approximates a Bayesian posterior over network parameters by sampling several parameter sets per epoch and weighting each by its validation-set generalization. The result, the paper reports, is a 716K-parameter detector trained from scratch that reaches ODS-F 0.835 at 92 FPS on BSDS with VOC data, and a 12.7M ResNet50-backed version that reaches ODS-F 0.857 at 37.6 FPS. If true, this would make high-accuracy edge detection practical on resource-constrained devices.","feed_headline":"Compact edge detector reaches 0.835 ODS-F at 92 FPS","feed_subtitle":"Three-way ensemble of architectures, training moments, and parameter samples matches far larger models at a fraction of the compute.","key_machinery":"The load-bearing object is the weighted parameter ensemble that stands in for a Bayesian posterior. At each epoch, S parameter samples are drawn from the momentum networks, each is assigned a pixel-wise weight by the closed-form formulas in Eqs. (8)–(9), and the fused prediction is a confidence-weighted combination of the recurrent and non-recurrent momentum-network outputs (Eq. 12). That fused map is blended with ground truth into soft targets that supervise training (Eq. 13), while the final inference parameters are a norm-weighted average of the samples (Eq. 10). The mechanism converts ensemble diversity into both a better training signal and a better test-time model without extra inferen","core_discovery":"The central claim is that cross-information from three sources—heterogeneous architectures, training moments, and parameter samplings—can be assembled so that a compact, fast network matches or exceeds the accuracy of much larger detectors. The paper treats network parameters as random variables drawn from an approximate Bayesian posterior, samples S parameter sets per epoch via Monte Carlo dropout, and assigns each sample a pixel-wise ensemble weight derived from a claimed closed-form solution to a validation-loss minimization (Eqs. 8–9). The weighted predictions of the two momentum networks are fused by a confidence-aware rule (Eq. 12) and blended into soft targets (Eq. 13) that supervise","pith_inferences":["The paper's gains may come more from ensemble diversity and soft-target smoothing than from the specific Bayesian-posterior interpretation; an ablation that replaces Eqs. (8)–(9) with equal weights would separate those effects.","The validation-weighted sampling scheme could transfer to other pixel-labeling tasks, such as semantic segmentation or depth estimation, where epistemic uncertainty is also a bottleneck, though the paper only tests edge detection.","Algorithm 2's use of stochastic weight pruning on a single network hints that the recurrent architecture's contribution may be mostly a source of diversity, not a necessary component; testing Algorithm 2 with the same compute budget could confirm this.","The reported sweet spot of S=3 parameter samples and Nv=30% validation split is empirical; the optimal values likely shift with dataset size and backbone capacity, so the method may need re-tuning for new domains."],"forward_implications":["A 716K-parameter edge detector trained from scratch can reach ODS-F 0.835 at 92 FPS, making state-of-the-art edge detection feasible on mobile and embedded hardware.","With a ResNet50 backbone the same framework reaches ODS-F 0.857 at 37.6 FPS with 12.7M parameters, beating recent Transformer- and diffusion-based detectors at a small fraction of their compute.","The validation-set-weighted parameter ensemble improves accuracy over other Bayesian-approximation strategies within the same framework, as shown in the paper's comparisons.","The efficient training variant (Algorithm 2) cuts training time by about 40% with only a 0.3–0.6 percentage-point drop in ODS-F, so the approach scales to larger data regimes.","The same architecture transfers to NYUD and Multicue with state-of-the-art-level results, suggesting the collaborative-learning principle is not dataset-specific."],"supporting_citations":[{"why":"The preliminary PEdger version this work extends and the direct baseline it improves upon in speed and accuracy.","marker":"[27]"},{"why":"Provides the error-ambiguity decomposition that motivates assembling diverse predictors to reduce generalization error.","marker":"[49,94,9]"},{"why":"PiDiNet, the efficient lightweight detector whose accuracy the paper aims to surpass at comparable cost.","marker":"[91]"},{"why":"Monte Carlo Dropout, the mechanism used to sample multiple parameter sets from the momentum networks.","marker":"[89,28]"},{"why":"Adaptive gradient clipping replaces batch normalization and underpins the reported fast inference speeds.","marker":"[10]"},{"why":"Progressive soft-target refinement, the source of the schedule in Eq. (14) that blends fused predictions with ground truth.","marker":"[45]"},{"why":"BSDS500, the primary benchmark dataset and evaluation protocol on which the main quantitative claims rest.","marker":"[2]"},{"why":"Multi-scale side-output and bidirectional aggregation designs that motivate the recurrent and non-recurrent architectures.","marker":"[106,57,36]"}],"fun_headline_variants":["PEdger++: compact edge detector matches big models, 92 FPS","Fast edge detection via cross-information ensemble, PEdger++","Tiny edge detector, big accuracy: PEdger++ at 92 FPS","PEdger++: three-source ensemble shrinks compute, boosts edges","Edge detection without the bulk: PEdger++ prunes, fuses, wins"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing premise is that the closed-form ensemble weights in Eqs. (8)–(9) actually solve the constrained validation-loss minimization in Eq. (6); the derivation treats each weight as if the fused prediction M did not depend on all the other weights and never enforces the stated sum-to-one constraint, so if those weights are not truly optimal, the Bayesian-posterior approximation and the soft-target refinement built on them lack their stated justification.","fun_headline_variants_meta":{"raw":{"variants":["PEdger++: compact edge detector matches big models, 92 FPS","Fast edge detection via cross-information ensemble, PEdger++","Tiny edge detector, big accuracy: PEdger++ at 92 FPS","PEdger++: three-source ensemble shrinks compute, boosts edges","Edge detection without the bulk: PEdger++ prunes, fuses, wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000109,"raw_usage":{"total_tokens":897,"prompt_tokens":763,"completion_tokens":134,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":31}},"tokens_in":507,"tokens_out":134,"duration_ms":2340,"temperature":1.0,"reasoning_tokens":31,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T19:41:44.142178+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the weights W_s from Eqs. (8)–(9) on a held-out validation split and check whether they sum to one and whether they yield a lower validation binary cross-entropy than equal weights or a directly optimized constrained solution; if equal weights or a numerical optimization beats the closed-form on ODS-F, the claimed optimality of the weight formulas is falsified.","supporting_citations":[{"cited_title":"TPAMI 45(12), 14956–14974 (2023) 22 Yuanbin Fu et al","cited_arxiv_id":null,"evidence_quote":"PiDiNet, the efficient lightweight detector whose accuracy the paper aims to surpass at comparable cost."}],"review_version":1}