{"id":"d161e04e-1365-4557-933d-2e644e24ac68","arxiv_id":"2501.11784","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Implicit neural networks can generate attribution masks that are smoother under area constraints and iteratively yield multiple non-overlapping explanations for a deep model's prediction.","lead":"This paper shows that small coordinate-based neural networks can produce visual explanations for image classifiers, generating smooth masks of controlled size and, one by one, several non-overlapping explanations of why an image was classified. The approach offers a way to inspect not only what a model sees in an object, but also the background cues it relies on.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The key claimed advantage—area-continuous, monotonic masks from a single conditioned INR—rests on smooth generalization in the area parameter, which is only shown qualitatively and could fail for interpolated areas.","rationale":"The reader's weakest assumption identifies exactly this spot: the conditioning on a must generalize smoothly for the central advantage to hold. I agree. The paper's claim is not primarily that INRs achieve the highest precision (Table 1 is competitive but not uniformly best), but that INRs provide area-continuous, monotonic masks and a route to multiple explanations. The continuity part is demonstrated only qualitatively in Figure 1. The mathematics in Equations (2)-(3) does not enforce continuity across a; it supervises each sampled a independently, so the smoothness is an empirical property of the MLP and Fourier encoding, not a guaranteed consequence of the loss. This is load-bearing because if the INR is only locally valid, the main advertised advantage over extremal perturbations disappears, and the method reduces to a slower, per-image training procedure with no clear benefit. The paper is otherwise internally consistent, the code is public, and the quantitative precision results are plausible, so this concern warrants tightening the evaluation rather than rejection. The Algorithm 1 off-by-one is a fixable presentation issue and is secondary to the main concern.","tokens_in":11087,"tokens_out":7318,"duration_ms":78242,"concrete_test":"Using the released code, pick one PASCAL VOC and one ImageNet image, train an INR as in Section 3.4, then feed a dense grid a = 0.00, 0.01, ..., 1.00 through the trained network without retraining. For each a, threshold the output mask at 0.5, compute the actual area fraction and the post-softmax probability Phi(M_a). Report (i) Spearman rank correlation between requested and actual area; (ii) maximum absolute jump in actual area between adjacent grid values; (iii) number of inversions. If rho < 0.95 or max jump > 0.05, the 'well-behaved/monotonic' claim in Section 4.1 is unsupported. Also re-run training with a held-out subset of area values; if Phi at held-out values drops significantly below the training-value envelope, conditioning does not generalize as claimed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing concern is that the claimed area-continuity and monotonicity of masks (Sections 1 and 4.1) is not guaranteed by the training objective and is never measured. In Section 3.4, the area parameter a is scaled to [0,1], uniformly sampled each epoch, and fed through Fourier features alongside pixel coordinates. Equations (2)-(3) supervise each sampled a independently: Ra(Ma) forces the sorted mask values to match the step function ra, but nothing ties adjacent a values together. A ReLU MLP with a six-frequency Fourier encoding can interpolate smoothly, but it can also produce non-monotonic or discontinuous responses in a, especially at area values not seen near the inference set {0.025, 0.05, 0.1, 0.2}. Figure 1 shows only a few selected masks; no quantitative continuity or monotonicity metric is reported. Since the abstract and Section 1 advertise 'well-behaved with respect to area constraints' and 'better monotonic correspondence' as a principal advantage over extremal perturbations, this missing evidence directly threatens the central claim. A secondary, smaller inconsistency: Algorithm 1 line 2 sums M_i for i=0..n at iteration n, including the not-yet-generated M_n; the text says 'previously computed masks,' so the pseudocode appears off-by-one and should sum M_0 through M_{n-1}.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes using implicit neural representations (INRs) to generate attribution masks for deep image classifiers. The first contribution reformulates extremal perturbations: a coordinate-based MLP, conditioned on an area parameter a uniformly sampled from [0,1], is trained against the post-softmax probability with an area-sorting regularizer (Eqs. 2–4), yielding masks that the authors claim are smooth and continuous in a. The second contribution is an iterative procedure that adds a Dice-based penalty to the loss (Eq. 6) to generate multiple non-overlapping attribution masks for the same image (Algorithm 1). Experiments use pretrained ResNet50 models on 752 ImageNet-S validation images and 2230 PASCAL VOC 2007 test images; the method is compared with extremal perturbations, RISE, and GradCAM using precision and hit rate. The reported numbers are a mean precision of 0.68 on ImageNet (vs. 0.63 for extremal perturbations) and 0.44 on VOC (vs. 0.46, asserted not statistically significant), with successive explanations on ImageNet degrading in precision from 0.68 to 0.30.","tokens_in":11377,"tokens_out":5884,"duration_ms":60264,"significance":"If the empirical claims are substantiated, the paper would make a useful contribution to explainable AI: a single INR conditioned on an area parameter is a practical way to query attribution masks at arbitrary areas without retraining, and the iterative non-overlap procedure can reveal that a classifier uses contextual regions (e.g., water and sky for 'boat') rather than only the object itself. The authors release code and evaluate on two datasets with a standard pretrained architecture, which is commendable. The main weaknesses are that the paper's headline advantage—area-continuity and monotonicity—is not measured quantitatively, and the statistical reporting is incomplete (no variances despite five training runs per image, and an unspecified t-test). These gaps are load-bearing for the central claims, but they are addressable with additional analysis rather than being fundamental flaws.","major_comments":[{"comment":"The abstract and Section 1 advertise 'well-behaved' attribution masks with respect to the area constraint, and Section 4.1 claims 'better monotonic correspondence between the area constraint and the actual calculated mask area.' This is a principal claimed advantage over extremal perturbations, yet the training procedure in Section 3.4 supervises each sampled area independently through Eq. (2) and Eq. (3); nothing in the loss explicitly enforces continuity or monotonicity across neighboring area values. Figure 1 is qualitative, and Section 4.1 reports no quantitative metric for continuity or monotonicity. Since the evaluation only uses a in {0.025, 0.05, 0.1, 0.2}, the behavior at interpolated areas is not demonstrated. Please define and report a quantitative measure, for example the mean absolute deviation of the computed mask area from the target a, or the average per-pixel overlap between masks at adjacent area values, including areas not used in the evaluation; alternatively, temper the continuity claims to what the experiments actually support.","section":"Abstract, Section 4.1, Section 3.4"},{"comment":"The text states that the implicit network was trained five times per input image to evaluate variability with respect to weight initialization, but Table 1 reports only mean precision and hit rate values, with no standard deviations, confidence intervals, or per-image distributions. The claim that the VOC difference between the proposed method (0.44) and extremal perturbations (0.46) is 'not statistically significant' cannot be checked without these details, and the t-test setup (paired or unpaired, per-image or per-mask, correction for multiple comparisons) is not described. Please report variance statistics and a precise statistical protocol, or move the significance statement to results that include them.","section":"Section 3.3.1, Table 1"},{"comment":"In Algorithm 1, the baseline mask is computed as M^b = sum_{i=0}^n M_i before M_n has been generated; for n=1 this includes the undefined mask M_1. This contradicts the accompanying text, which says previously computed masks are combined, and an implementation following the pseudocode literally would not impose the intended non-overlap penalty. The sum should run over i=0,...,n-1 (or, equivalently, over the masks output before iteration n). This is a small but load-bearing correction for the reproducibility of the multiple-explanation method.","section":"Algorithm 1, line 2"}],"minor_comments":[{"comment":"The notation 'x ∈ R2 → [0,1]^2' is garbled; it should state that pixel coordinates are x ∈ [0,1]^2 (after normalization).","section":"Section 3.1"},{"comment":"The network is defined as f_l(x,c) with a conditioning variable c, but the surrounding text only introduces the coordinates x and the area parameter a; please define c or replace it with a consistently.","section":"Equation (4)"},{"comment":"The binarization procedure is specified only for GradCAM and RISE saliency maps. Since the precision metric in Eq. (7) applies to binary masks, the authors should state explicitly how the soft masks produced by the proposed method and by extremal perturbations are converted to binary masks (e.g., threshold at 0.5 or another value).","section":"Section 3.4"},{"comment":"The 'Combination, max' row is ambiguous: it should state that the maximum precision is taken over the three iterations for each image and then averaged across images, rather than being a single global maximum.","section":"Table 2"},{"comment":"The phrase 'actual calculated mask area' is not defined. It should be clarified whether this is the sum of soft mask values, the area after binarization at a fixed threshold, or another quantity.","section":"Section 4.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of a computer vision / XAI venue and the core idea is worth pursuing. The main risk is that the advertised advantage over extremal perturbations—area continuity and monotonicity—is currently supported only by qualitative examples; a quantitative continuity or monotonicity experiment would either solidify or substantially weaken the central claim. I would encourage the editor to ask for that analysis, together with proper variance reporting, before considering acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does something genuinely new: it reformulates extremal perturbations using a coordinate-based implicit network, conditions the mask on an area parameter so you can query any area without retraining, and extends this to an iterative Dice-loss procedure that produces multiple non-overlapping explanations. The multi-mask idea is the most interesting part — the boat/sky/water example in Figure 6 is a nice illustration of a model leaning on context. The writing is clear, the code is public, the limitations section is honest, and the experiments cover two datasets with a pretrained ResNet50. Credit where due: this is a sensible, well-scoped contribution.\n\nThe soft spots are real but fixable. The headline claim of \"well-behaved\" masks with respect to area, and \"better monotonic correspondence,\" rests almost entirely on qualitative Figure 1. Nothing in the training objective couples adjacent area values — each sampled a is supervised independently — so smoothness and monotonicity are empirical hopes, not guarantees. The paper should report a quantitative continuity or monotonicity metric, e.g., the actual mask area at the four test constraints versus the requested areas and the variation between nearby queries. That would either support or soften the claim. Table 1 reports only means, with no variance, even though five runs per image were averaged; error bars or a significance test for the ImageNet result are needed. The manually selected binarization thresholds for GradCAM and RISE are a common but slightly uncomfortable choice. There is also a small off-by-one in Algorithm 1: line 2 sums M_i for i=0..n before M_n has been generated; it should sum 0..n-1. The intention is clear, but it should be fixed.\n\nThe central idea holds up. The precision gains are modest (0.68 vs 0.63 on ImageNet), and the VOC difference is not significant, but the method’s value is not only the scores — it’s the ability to generate area-conditioned masks and multiple disjoint explanations from one framework. The evaluation weaknesses do not sink the paper, but they do make the current version conditional.\n\nWho is this for? Researchers in explainable AI, specifically those working on perturbation-based attribution and multi-explanation methods. It deserves a serious referee. I would recommend acceptance after minor revisions: add error bars, quantify the monotonicity/continuity claim, fix the pseudocode, and clarify the statistics. I’d bring it to a reading group if the topic were on the table, but it is not a must-cite for me personally.","headline":"A solid, clearly written method paper that makes a real contribution by adapting INRs to attribution masks, but the advertised area-continuity advantage is asserted more than demonstrated.","tokens_in":11883,"tokens_out":2839,"would_cite":false,"duration_ms":30578,"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 argues that implicit neural representations — coordinate-based networks that map pixel positions and an area condition to a mask value — make attribution masks smoothly queryable by area and allow several non-overlapping…","keywords":["implicit neural representations","attribution masks","extremal perturbations","explainable AI","saliency maps","multiple explanations","Dice loss","model interpretability"],"falsifier":"Train the INR as described, then evaluate the mask at a dense grid of area parameters such as 0.025, 0.04, 0.06, 0.08, 0.1, 0.15, 0.2 and compute both the true mask area and the pairwise overlap of consecutive masks. If the true area does not rise monotonically with the requested area, or if adjacent masks differ discontinuously by swapping to a different image region, the central continuity claim is disproved. A direct test of generalization is to train on a few discrete area values only and evaluate at held-out values in between.","tokens_in":10859,"feed_emoji":"🎯","tokens_out":7161,"duration_ms":63868,"temperature":0.7,"pith_summary":"The paper aims to show that implicit neural representations (INRs) are a natural home for visual explanation, not just for image synthesis. It recasts extremal perturbations as a single coordinate-based network conditioned on a mask-area parameter, so one trained network can produce an attribution mask for any requested area instead of re-optimizing from scratch. Adding a soft Dice loss makes the same setup produce a sequence of non-overlapping masks, exposing that a classifier may rely on object context such as sky and water as much as on the object itself. The reported precision scores on ImageNet-S and PASCAL VOC indicate the method is competitive with or better than existing baselines while offering the new continuity and multi-explanation properties.","feed_headline":"Implicit networks make attribution masks smooth across areas","feed_subtitle":"One trained model answers any mask-area query and exposes the context cues a classifier relies on.","key_machinery":"The load-bearing mechanism is the conditioned implicit neural representation of the attribution mask: an MLP whose input is the pair of pixel coordinates and a scalar area value, with a Fourier feature encoding of both, and whose output is filtered through a radial-basis-function smoothing step. The area conditioning ties coordinates and area together so the network must interpolate masks across the whole area range. A soft Dice loss is added for the multi-mask variant, enforcing that newly generated masks avoid already explained regions.","core_discovery":"The central discovery is that a mask over the input image can be represented as an implicit function of pixel coordinates and an area. A multilayer perceptron with Fourier feature encoding takes $(x, a)$ and outputs a scalar mask value, which is then smoothed; during training $a$ is sampled uniformly, so the result is a continuum of masks rather than a set of discrete solutions. The same implicit function, retrained with a soft Dice penalty against previous masks, yields non-overlapping explanations. On ImageNet-S the method reaches a mean precision of 0.68 and a hit rate of 0.73; on PASCAL VOC it is statistically tied with extremal perturbations, and the iterative procedure shows that later masks drift outside the object while the best of the first three iterations reaches 0.73 precision.","pith_inferences":["Beyond the paper's experiments, the area-conditioned INR could power a real-time 'explanation slider' for debugging interfaces, since the same weights answer arbitrary area queries without re-optimization.","The non-overlap mechanism could be turned into a quantitative bias score by measuring how much of each successive mask falls outside the reference segmentation, giving a per-class context-dependence measure.","If the continuity claim holds at higher resolutions, combining the INR with a learned initialization could bring per-case training time down enough for clinical or interactive use.","The same mask representation already uses a segmentation-style Dice loss, so attribution and semantic segmentation could plausibly be optimized jointly in one implicit network."],"forward_implications":["A single trained INR per image can be queried at any mask area without retraining, making area sweeps and interactive explanation tools practical.","The iterative Dice-loss procedure provides a concrete way to surface contextual biases: masks outside the reference segmentation reveal what scene elements, such as sky and water for boats, the classifier uses.","Reported ImageNet-S precision of 0.68 and a combined first-three-iterations maximum of 0.73 suggest the method can recover the object region while also mapping the object's surroundings.","Because the same network architecture handles both single and multiple masks by changing only the loss, the approach slots into existing INR toolchains for joint tasks like segmentation."],"supporting_citations":[{"why":"Supplies the extremal perturbations formulation and area-regularization loss that the INR-based method reformulates and compares against.","marker":"[10]"},{"why":"Supplies the Fourier feature input encoding that lets the MLP represent high-frequency mask structure.","marker":"[37]"},{"why":"Supplies the soft Dice loss used to push successive attribution masks apart.","marker":"[17]"},{"why":"Establishes the meaningful perturbation objective that extremal perturbations and this work build on.","marker":"[11]"},{"why":"Provides ImageNet-S, the dataset with detailed semantic segmentations used for precision evaluation.","marker":"[12]"},{"why":"Provides PASCAL VOC test sets and bounding-box-based segmentations used for evaluation.","marker":"[8]"},{"why":"Provides GradCAM, an activation-based attribution baseline for comparison.","marker":"[26]"},{"why":"Provides RISE, a perturbation-based attribution baseline for comparison.","marker":"[22]"},{"why":"Motivates generating multiple explanations for one image, which the iterative Dice-loss method targets.","marker":"[27]"}],"fun_headline_variants":["Implicit networks turn attribution masks into a continuous function of area","One implicit model yields any-size attribution mask and reveals context cues","Attribution masks as implicit functions: smooth, area-controllable, and context-aware","Implicit neural reps explain deep nets with smooth, area-tunable masks","Continuous attribution masks via implicit representations expose hidden context"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method's claimed advantage depends on a single INR, trained with area values sampled uniformly, generalizing smoothly and monotonically between those values; if the network merely memorizes the sampled areas, the masks will not be well-behaved for unseen area queries.","fun_headline_variants_meta":{"raw":{"variants":["Implicit networks turn attribution masks into a continuous function of area","One implicit model yields any-size attribution mask and reveals context cues","Attribution masks as implicit functions: smooth, area-controllable, and context-aware","Implicit neural reps explain deep nets with smooth, area-tunable masks","Continuous attribution masks via implicit representations expose hidden context"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000238,"raw_usage":{"total_tokens":1485,"prompt_tokens":892,"completion_tokens":593,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":508,"completion_tokens_details":{"reasoning_tokens":502}},"tokens_in":508,"tokens_out":593,"duration_ms":5955,"temperature":1.0,"reasoning_tokens":502,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T17:52:39.106657+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the INR as described, then evaluate the mask at a dense grid of area parameters such as 0.025, 0.04, 0.06, 0.08, 0.1, 0.15, 0.2 and compute both the true mask area and the pairwise overlap of consecutive masks. If the true area does not rise monotonically with the requested area, or if adjacent masks differ discontinuously by swapping to a different image region, the central continuity claim is disproved. A direct test of generalization is to train on a few discrete area values only and evaluate at held-out values in between.","supporting_citations":[{"cited_title":"Un- derstanding deep networks via extremal perturbations and smooth masks","cited_arxiv_id":null,"evidence_quote":"Supplies the extremal perturbations formulation and area-regularization loss that the INR-based method reformulates and compares against."},{"cited_title":"Fourier features let networks learn high frequency functions in low dimen- sional domains","cited_arxiv_id":null,"evidence_quote":"Supplies the Fourier feature input encoding that lets the MLP represent high-frequency mask structure."},{"cited_title":"V-net: Fully convolutional neural networks for volumetric medical image segmentation","cited_arxiv_id":null,"evidence_quote":"Supplies the soft Dice loss used to push successive attribution masks apart."},{"cited_title":"Interpretable explana- tions of black boxes by meaningful perturbation","cited_arxiv_id":null,"evidence_quote":"Establishes the meaningful perturbation objective that extremal perturbations and this work build on."},{"cited_title":"Large-scale unsu- pervised semantic segmentation","cited_arxiv_id":null,"evidence_quote":"Provides ImageNet-S, the dataset with detailed semantic segmentations used for precision evaluation."},{"cited_title":"The pascal visual object classes challenge: A retrospective","cited_arxiv_id":null,"evidence_quote":"Provides PASCAL VOC test sets and bounding-box-based segmentations used for evaluation."},{"cited_title":"Rise: Random- ized input sampling for explanation of black-box models","cited_arxiv_id":null,"evidence_quote":"Provides RISE, a perturbation-based attribution baseline for comparison."},{"cited_title":"One explanation is not enough: structured attention graphs for image classification.Advances in Neural Information Processing Systems, 34:11352–11363, 2021","cited_arxiv_id":null,"evidence_quote":"Motivates generating multiple explanations for one image, which the iterative Dice-loss method targets."}],"review_version":1}