{"id":"8ef27324-e89b-47d2-8144-624dc24a4493","arxiv_id":"2412.01354","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Integrative CAM weights multiple CNN layers with a perturbation-based importance score and adds a classifier bias, but the supporting derivation and experiments are incomplete.","lead":"This paper introduces Integrative CAM, a Class Activation Mapping variant that fuses layers with adaptive importance weights, adds a bias term, and generalizes the Grad-CAM++ alpha formula. The reported gains rest on a small subjective survey and a missing quantitative table, and the alpha generalization requires an assumption that fails for intermediate layers.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation 24 misapplies the chain rule: softmax is a multivariate function of all logits, so ∂Y^c/∂A includes cross-class terms; the simplified alpha and I-CAM weights are therefore not justified.","rationale":"The reader identifies Eq. 24 as the load-bearing step, and I agree that the generalized alpha is the paper's main theoretical hook. However, the precise failure mode is not the one stated in the reader's weakest_assumption. For a standard ResNet-50 with ReLU, the pre-softmax logits S^j are piecewise linear functions of any intermediate activation map, so the higher derivatives of S^j with respect to that activation vanish almost everywhere; the piecewise-linear approximation in Section 2.4 is actually exact for such networks. The real problem is that the paper chooses softmax as the smooth function f. Softmax is a function of the entire logit vector, not of S^c alone, so even the first-order chain rule in Eq. 23 drops cross-class terms. Those terms persist at second and third order even when the S^j are linear. Eq. 24 is therefore not a valid generalization to 'any smooth function' — it only holds for univariate f such as the exponential used in Grad-CAM++. This error invalidates the simplified alpha in Eq. 25 and the I-CAM weights in Eq. 31, which are central to the method's claimed superior fidelity. I also note the empirical support is thin: Section 3.2 refers to 'Table 1' for IoU results, but the table is absent from the manuscript, and the saliency-score numbers are reported for only a handful of selected images; the blind surveys are small and not statistically analyzed. Those omissions would already justify rejecting the empirical claim, but the analytical error is the more fundamental problem because it attacks the method's construction rather than its evaluation. I therefore keep the reader's REJECT verdict. The proposed check — comparing Eq. 23 and Eq. 24 against autodiff on a two-class softmax model — is decisive and cheap.","tokens_in":20535,"tokens_out":8523,"duration_ms":67733,"concrete_test":"Use automatic differentiation on a minimal two-class softmax model. Let A be a scalar activation, S1 = w1 A + b1, S2 = w2 A + b2, Y1 = softmax(S1, S2). Compute ∂Y1/∂A by autodiff and compare with Eq. 23's f'(S1)∂S1/∂A = Y1(1−Y1)w1; with w1≠w2 the two values differ by −Y1Y2(w2−w1). Repeat for the second derivative: compare autodiff ∂²Y1/∂A² with f''(S1)(∂S1/∂A)²; even with piecewise-linear S, the autodiff value includes cross terms and is nonzero, while the simplified expression is a different number. This one-dimensional check settles the validity of Eq. 24. Alternatively, on a real ResNet-50 image, compare Eq. 31's weight map with autograd-computed weights; any nonzero difference confirms the flaw.","verdict_should_be":"REJECT","load_bearing_attack":"Section 2.4 derives Eq. 24 from the univariate chain rule: for Y^c = f(S^c), ∂^n Y^c/∂A^n = f^(n)(S^c)(∂S^c/∂A)^n, dropping all derivatives of S^c of order ≥2. Two problems compound. First, the chosen f is the softmax (Eq. 29), which is not a function of the single logit S^c; it depends on every logit S^j. The correct first derivative is ∂Y^c/∂A = Σ_j (∂Y^c/∂S^j)(∂S^j/∂A) = Y^c(1−Y^c)∂S^c/∂A − Σ_{j≠c} Y^cY^j ∂S^j/∂A. Equation 23 keeps only the c term. The error propagates to the second and third derivatives: even when every S^j is piecewise linear in A (so second derivatives of S^j vanish a.e.), the cross terms ∂²Y^c/∂S^j∂S^k times (∂S^j/∂A)(∂S^k/∂A) remain and are nonzero. Hence Eq. 24 is false for softmax, and the simplified alpha (Eq. 25) and the weight formula (Eq. 31) do not follow. This is not rescued by the piecewise-linearity argument in Section 2.4, which addresses only derivatives of S^c, not the multivariate structure of softmax. Since the generalized alpha is a principal novelty and is used in every I-CAM weight, the method's theoretical foundation collapses. The reader's linearity concern is related but secondary; for standard ReLU CNNs the map A→S^j is piecewise linear, so the missing terms from ∂²S^j/∂A² vanish a.e., whereas the missing cross-logit terms do not.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes Integrative CAM (I-CAM), a class activation mapping method that fuses features from multiple CNN layers using a perturbation-based layer importance score, a bias term in the saliency map, and a generalized alpha term derived from a claimed chain-rule simplification. The authors claim that I-CAM provides a more comprehensive and faithful visualization of CNN decisions than Grad-CAM, Grad-CAM++, and LayerCAM, supported by a qualitative survey, IoU localization results, and case studies on ImageNet with ResNet-50.","tokens_in":21001,"tokens_out":2285,"duration_ms":22220,"significance":"If the method were sound, the idea of principled multi-layer fusion with automatic layer weighting and a bias term would be a useful contribution to the interpretability literature. The paper also aims to provide a parameter-light alpha formula for any smooth output function, which could simplify higher-order gradient computations. However, the central theoretical derivation in Section 2.4 is incorrect for softmax outputs, the main quantitative evidence (Table 1) is missing from the manuscript, and the qualitative evaluation is based on a small, biased image selection with no statistical analysis. As presented, the central claims of superior fidelity and a generalized alpha formula are not established.","major_comments":[{"comment":"Equation (24) misapplies the chain rule for the softmax case used in Section 2.6. The softmax output Y^c depends on all logits S^j, not only on S^c, so the first derivative with respect to a layer activation A is ∂Y^c/∂A = Y^c(1−Y^c)∂S^c/∂A − Σ_{j≠c} Y^c Y^j ∂S^j/∂A. Equation (23) and the subsequent derivation in Eq. (24) keep only the diagonal term. Even under piecewise linearity of each S^j in A, the second derivative of softmax contains cross-logit terms such as ∂²Y^c/∂S^j∂S^k times products of first derivatives, which do not vanish. Therefore the simplified alpha in Eq. (25) and the weight formula in Eq. (31), which are used in every layer fusion, are not justified for the softmax function.","section":"§2.4, Eq. (24)"},{"comment":"The claim that any nonlinear function can be approximated as piecewise linear, and that the alpha simplification becomes valid if the approximation error is low, is not supported by any error bound or analysis of the multi-layer case. For intermediate layers, S^c depends on the layer activation through several subsequent nonlinear layers, so ∂S^c/∂A^k is not constant even when each individual activation function is piecewise linear; the derivative changes at the boundaries of the linear regions. The paper does not quantify the resulting error in the alpha term, so the central novelty of the method is asserted rather than proven.","section":"§2.4, final paragraph"},{"comment":"The central quantitative claim that I-CAM achieves superior IoU localization accuracy is unverifiable because Table 1 is not included in the manuscript. The text states 'Table 1 presents the IoU evaluation results' but no such table appears. Since the paper's headline result is that I-CAM outperforms existing methods, the missing table is a load-bearing omission.","section":"§3.2, Table 1"},{"comment":"The qualitative evaluation is not sufficient to support the claim of superior fidelity. The 50 images are drawn from only five classes selected by highest F1-scores, with the ten highest-confidence images per class, which biases the evaluation toward easy, unambiguous examples. The surveys involve 10 participants each, with no reported inter-rater agreement, statistical significance test, confidence intervals, or comparison against chance. The normalized scores (e.g., I-CAM 24.4 vs. LayerCAM 11.37) are presented as conclusive, but the experimental design does not rule out selection bias or participant noise.","section":"§3.1.1 and §3.1.2"},{"comment":"The bias term in Eq. (27) is defined as the residual S^c minus the weighted sum of activations. By construction, adding this bias term makes the layer's contribution sum exactly to the class score S^c, so any improvement in the resulting saliency map is not an independent test of the bias term's value. The paper reports that channel bias outperforms spatial bias but does not compare against a no-bias baseline where the residual is not added, so the claimed benefit of including a bias term is asserted rather than demonstrated.","section":"§2.5, Eq. (27)"}],"minor_comments":[{"comment":"Equation (3) is difficult to parse: the norm subscripts and the summation indices are not fully defined, and the role of the weight α_i in the inner sum is unclear. Please clarify the notation.","section":"§2.1, Eq. (3)"},{"comment":"The text says MDS 'diverges from traditional metrics such as JSD' but then states that MDD can also be conceptualized as symmetric Jensen-Shannon Divergence. This is contradictory and should be reconciled.","section":"§2.1.4, Eqs. (8)–(10)"},{"comment":"The description of the survey scoring is incomplete: the text says 'Each method was scored based on the participants' evaluations' but does not specify the scale, the instructions given to participants, or whether participants were asked to rank or rate the outputs.","section":"§3.1.1"},{"comment":"The examples in Figures 6–9 are presented as evidence that training-set similarity causes misclassification, but the comparisons are anecdotal and not quantified. Please provide a more systematic analysis or temper the causal language.","section":"§3.1.3, Case 3 and Case 4"},{"comment":"The paper repeatedly claims that I-CAM is 'comprehensive' and 'superior' without defining a precise notion of comprehensiveness or fidelity. A formal definition or at least an operationalized metric would help make these claims testable.","section":"Abstract and Introduction"},{"comment":"There are numerous typographical and rendering issues in the equations (e.g., missing subscripts, garbled symbols in Eqs. (3), (8), and (27)). The manuscript would benefit from a careful proofreading pass.","section":"Throughout"}],"recommendation":"reject","confidential_remarks":"The manuscript's central theoretical contribution is not valid for the softmax function it employs, and the primary quantitative evidence is missing from the submitted text. Even setting aside the derivation issue, the experimental evaluation is far too weak to support the claimed superiority. The paper may contain a useful empirical idea, but as it stands the flaws are load-bearing and cannot be fixed by local revisions within the current scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, the central theoretical claim—a generalized alpha for any smooth function—is invalid as written, because the derivation treats softmax as a function of one logit. Second, the quantitative evidence is missing: Table 1, where the IoU comparison supposedly lives, never appears in the manuscript. These are load-bearing parts, and both are soft.\n\nWhat's genuinely useful: the layer importance score via perturbed inputs is a sensible idea, and the bias term is a simple addition that could improve CAM variants. The paper is clearly written and unusually honest about its own limitations—it flags heatmap resizing artifacts, the bounding-box compromise in IoU, and the open question of class-level layer prominence. The related-work discussion of LayerCAM and Grad-CAM++ is accurate.\n\nNow the specifics. Eq. 24 claims ∂^nY^c/∂A^n = f^(n)(S^c)(∂S^c/∂A)^n. That only holds if Y^c is a function of S^c alone. But with softmax, Y^c = exp(S^c)/Σ_j exp(S^j), so the derivative w.r.t. A includes cross-logit terms: Y^c(1−Y^c)∂S^c/∂A − Σ_{j≠c} Y^cY^j∂S^j/∂A. The cross terms persist even when each S^j is piecewise linear in A. So the simplified alpha in Eq. 25 and the weights in Eq. 31 don't follow from the stated assumptions. The piecewise-linearity argument in Section 2.4 addresses a different issue—the second derivatives of S^c—and doesn't rescue the multivariate softmax structure.\n\nThe bias term (Eq. 27) is defined as the residual S^c minus the weighted activation sum, so including it makes the map sum to the class score by construction. That may be useful, but it is not tested on its own.\n\nAnd the evidence: the qualitative survey is 50 images from 5 high-F1 classes, all high-confidence, judged by 10 anonymous participants, with no error bars or significance test. That's a weak basis for \"superior fidelity.\" The IoU results are referenced but not shown. That alone would stop me from accepting.\n\nVerdict: the layer scoring and bias ideas are worth a look, but this version's central derivation is wrong and the experiments as reported don't support the claims. I'd still send it to a careful referee rather than desk-reject, because the chain-rule issue is exactly what a referee should catch and the layer importance idea could be salvageable. But it will need major revision.","headline":"Salvageable layer-scoring idea wrapped in a flawed softmax derivation and missing quantitative table.","tokens_in":21472,"tokens_out":3358,"would_cite":false,"duration_ms":28760,"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":"A heatmap method that reads every layer of a CNN, not just the last, claims sharper and more faithful saliency maps.","keywords":["class activation mapping","CNN interpretability","gradient-based saliency","layer fusion","feature attribution","weakly supervised localization","explainable AI"],"falsifier":"Take a trained ResNet-50, pick an intermediate layer, and numerically compute both sides of Eq. 24, the true $n$-th derivative of the softmax output with respect to that layer's activations versus $f^{(n)}(S^c)$ times the first-derivative power. If they differ by more than numerical noise, the $\\alpha$ simplification is not an identity for real networks.","tokens_in":20352,"feed_emoji":"🔍","tokens_out":3743,"duration_ms":32750,"temperature":0.7,"pith_summary":"The paper claims that class activation maps should not come from the final convolutional layer alone. It introduces Integrative CAM (I-CAM), which scores every layer's relevance from perturbed copies of the input, keeps the top 95% of layers, and fuses their saliency maps with adaptive weights plus an explicit bias term. The authors also generalize the Grad-CAM++ alpha coefficient to any smooth function, so the method can work with softmax outputs. If correct, I-CAM gives a fuller view of where a CNN looks and which layers actually drive a prediction.","feed_headline":"A heatmap method that reads every CNN layer","feed_subtitle":"Integrative CAM weights each layer’s contribution and adds bias, claiming clearer maps than Grad-CAM and its variants.","key_machinery":"The load-bearing object is Eq. 24, the derivative-reduction identity $\\partial^n Y^c / (\\partial A)^n = f^{(n)}(S^c)\\,(\\partial S^c/\\partial A)^n$, justified by the assumption that the pre-softmax score $S^c$ is linear in each layer's activations. On top of it sit three mechanisms: a perturbation-based layer importance score that uses Gaussian-noise plus Bernoulli-mask perturbed images weighted by a structural variability metric and a probability-similarity metric; a 95% cumulative-importance filter with normalized layer weights; and a fusion formula that sums layer-specific CAMs weighted by those layer scores, with a channel bias term derived from the classification score. Together these convert a single-image CAM into an adaptively weighted multi-layer map.","core_discovery":"On its own terms, the paper's central discovery is that a CAM built from all layers, with each layer weighted by a perturbation-based importance score and combined with an explicit bias term, represents a CNN's decision better than maps drawn only from the last layer. The authors derive a derivative-reduction identity, claiming that for any smooth function $f$ and any layer activation $A$, the $n$-th derivative of the class output $Y^c$ with respect to $A$ equals $f^{(n)}(S^c)\\,(\\partial S^c/\\partial A)^n$, and use it to reduce the $\\alpha$ term of Grad-CAM++ to a simpler closed form. They support the method with qualitative surveys and IoU localization numbers on ImageNet with ResNet-50, and they show that the final convolutional layer is often not the most influential one for an image.","pith_inferences":["The identity in Eq. 24 is exact only when the pre-softmax score is linear in the layer's activations; for intermediate layers that linearity fails, making I-CAM's alpha an approximation whose error the paper does not quantify.","If the layer scoring truly reflects causal relevance, it could be reused as a pruning or architecture-search signal, an application the paper mentions but does not develop.","The same perturbation-scoring and fusion scheme could be tested on vision transformers or non-CNN architectures, where the notion of a layer differs and the bias term may behave differently.","A concrete test would compare the approximate alpha of Eq. 25 with exact higher-order derivatives on a small network; large discrepancies would show the simplification is not generally valid."],"forward_implications":["I-CAM's heatmaps localize objects better than Grad-CAM, Grad-CAM++, and LayerCAM on ImageNet with ResNet-50, as measured by IoU on correct predictions.","Layer importance scores reveal that the final convolutional layer is often not the primary contributor, so interpretation should weight intermediate layers rather than relying on the last one.","The alpha simplification allows the method to apply to any smooth output function, such as softmax, rather than only exponentials, so long as the score is linear in the activations.","The layer scoring system can guide model optimization tasks such as pruning or simplifying less critical layers, and combining I-CAM with example-based comparisons can explain high-confidence misclassifications."],"supporting_citations":[{"why":"Introduces the original CAM formulation linking global average pooling with linear classification weights, the paradigm being extended.","marker":"[21]"},{"why":"Defines Grad-CAM, the gradient-weighted baseline that I-CAM compares against and builds on.","marker":"[22]"},{"why":"Defines Grad-CAM++ and its alpha term involving higher-order derivatives, which the paper generalizes.","marker":"[23]"},{"why":"Defines LayerCAM's element-wise gradient weighting, which I-CAM adopts, and the layer-averaging approach I-CAM claims to improve.","marker":"[24]"},{"why":"Supplies the ImageNet dataset used for all experiments and evaluation.","marker":"[31]"},{"why":"Supplies the ResNet-50 architecture on which the method is implemented and tested.","marker":"[17]"}],"fun_headline_variants":["All-layer CAM outshines Grad-CAM","Heatmaps from every CNN layer, not just the last","Adaptive fusion of all layers for clearer heatmaps","A bias-aware CAM for complete CNN interpretation","New CAM method weighs each layer's contribution"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole simplification of the alpha term assumes the model's pre-softmax score changes at a constant rate as you vary any layer's activations; for middle layers that rate itself changes, so the simplification is an approximation with no measured error.","fun_headline_variants_meta":{"raw":{"variants":["All-layer CAM outshines Grad-CAM","Heatmaps from every CNN layer, not just the last","Adaptive fusion of all layers for clearer heatmaps","A bias-aware CAM for complete CNN interpretation","New CAM method weighs each layer's contribution"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000189,"raw_usage":{"total_tokens":1344,"prompt_tokens":960,"completion_tokens":384,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":312}},"tokens_in":576,"tokens_out":384,"duration_ms":3658,"temperature":1.0,"reasoning_tokens":312,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:25:29.805194+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a trained ResNet-50, pick an intermediate layer, and numerically compute both sides of Eq. 24, the true $n$-th derivative of the softmax output with respect to that layer's activations versus $f^{(n)}(S^c)$ times the first-derivative power. If they differ by more than numerical noise, the $\\alpha$ simplification is not an identity for real networks.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the original CAM formulation linking global average pooling with linear classification weights, the paradigm being extended."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines Grad-CAM, the gradient-weighted baseline that I-CAM compares against and builds on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines Grad-CAM++ and its alpha term involving higher-order derivatives, which the paper generalizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines LayerCAM's element-wise gradient weighting, which I-CAM adopts, and the layer-averaging approach I-CAM claims to improve."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the ImageNet dataset used for all experiments and evaluation."},{"cited_title":"Miller, Explanation in artificial intelligence: Insights from the social sciences, Artificial intelligence 267 (2019) 1-38","cited_arxiv_id":null,"evidence_quote":"Supplies the ResNet-50 architecture on which the method is implemented and tested."}],"review_version":1}