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REVIEW 5 major objections 6 minor 42 references

Integrative CAM: Adaptive Layer Fusion for Comprehensive Interpretation of CNNs

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A heatmap method that reads every layer of a CNN, not just the last, claims sharper and more faithful saliency maps.

desk verdict Salvageable layer-scoring idea wrapped in a flawed softmax derivation and missing quantitative table. read the letter →

arxiv 2412.01354 v1 pith:GOVXTXPP submitted 2024-12-02 cs.CV cs.AI

Aniket K. Singh , Debasis Chaudhuri , Manish P. Singh , Samiran Chattopadhyay This is my paper · ORCID
classification cs.CVcs.AI
keywords classactivationmappingCNNinterpretabilitygradient-basedsaliencylayerfusionfeatureattributionweaklysupervisedlocalizationexplainableAI
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

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.

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 (5)
  1. [§2.4, Eq. (24)] 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.
  2. [§2.4, final paragraph] 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.
  3. [§3.2, Table 1] 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.
  4. [§3.1.1 and §3.1.2] 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.
  5. [§2.5, Eq. (27)] 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.
minor comments (6)
  1. [§2.1, Eq. (3)] 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.
  2. [§2.1.4, Eqs. (8)–(10)] 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.
  3. [§3.1.1] 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.
  4. [§3.1.3, Case 3 and Case 4] 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.
  5. [Abstract and Introduction] 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.
  6. [Throughout] 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.

Circularity Check

1 steps flagged · score 4.0 of 10

The bias term of I-CAM is defined as the residual S^c minus the same weighted activation sum used in the map, so its claimed benefit is an accounting identity rather than an independently tested component; the alpha simplification is mathematically unsupported but not circular.

  1. self definitional [Section 2.5, Eq. 27 (bias definition); applied in Eq. 20 and Eq. 21]
    "considering that the model output S^c depends on a linear combination of activations from the k-th layer, we can express it as: S^c = Σ_{i,j} w_{ij,k}^c Σ_{i,j} A_{ij,k} + b_k^c ... b_k^c = S^c − Σ_{i,j} w_{ij,k}^c Σ_{i,j} A_{ij,k} (27)"

    The bias term is not a separately estimated or independently validated model quantity; it is defined as the exact residual between the class score S^c and the same weighted activation sum that appears in the I-CAM layer map (Eq. 20). Substituting Eq. 27 into Eq. 20 therefore makes the layer map reproduce S^c by construction (up to the spatial fluctuation of the weighted activations around their summed value), and Eq. 21 then recombines these score-forced maps. The paper's claim that the bias term is 'essential' and 'captures more nuanced aspects' is not tested against I-CAM without the bias: Section 3.1.1 compares channel bias against spatial bias only, both of which already contain the residual construction.

full rationale

The only step that reduces to its own input by construction is the residual bias term: Eq. 27 defines b^c as S^c minus the weighted activation sum used in Eq. 20, so any saliency map built with that bias is partially forced to encode the class score. This is a real self-definitional component, but it does not make the whole method circular, because the spatial localization still comes from gradients and activations, and the paper reports independent IoU and human-survey evaluations. The generalized alpha derivation in Section 2.4 is not a circularity: it is an explicit, though mathematically incorrect, assumption that higher derivatives of S^c vanish and that the softmax can be treated as a univariate function of S^c. That is a correctness/validity risk rather than a reduction of a prediction to its input. There are no load-bearing self-citations in the reference list, and the layer importance score is computed from the very model being explained, which is by design for CAM methods rather than circular. Overall, the central empirical claim has independent content, so the circularity is partial rather than total.

Assumptions & free parameters 4 free parameters · 3 assumptions · 2 invented entities

The method rests on several hand-chosen constants and unvalidated model assumptions. The most consequential is the linearity assumption behind the alpha simplification, which is only true for the final layer of a GAP-based CNN. The perturbation-based importance scoring also depends on newly proposed SVIM and MDS metrics that are not independently validated.

free parameters (4)
  • layer retention threshold k = 0.95
    Manually chosen in Section 2.2 to retain top layers; not justified by data or theory.
  • SVIM Gaussian width sigma = not specified
    The SVIM metric in Eq. 6 depends on sigma, but the paper never reports its value or how it is set.
  • perturbation noise and masking intensity beta = 0.4 used in Fig 1
    Controls how strongly images are perturbed in Section 2.1.1; no sensitivity analysis is provided.
  • number of perturbations N = 8 in Fig 1
    Layer scores are computed from N perturbed inputs; N is not varied or justified.
assumptions (3)
  • ad hoc to paper dS^c/dA^k is constant, so all higher-order derivatives of S^c with respect to layer activations vanish
    Section 2.4, Eqs. 23-25. Stated for linear psi(A) but applied to all layers, including intermediate layers where S depends non-linearly on A through subsequent layers.
  • ad hoc to paper Any non-linear function can be approximated as piecewise linear with negligible error
    Section 2.4: used to extend the alpha simplification to non-linear activation functions; the error term epsilon is neglected without a bound.
  • domain assumption Perturbation-based layer importance scores with SVIM and MDS weighting reliably rank layer relevance
    Section 2.1: this is the basis for layer selection and weighting but is not validated against any ground truth.
invented entities (2)
  • SVIM metric
    purpose: Quantifies structural variability between original and perturbed images for perturbation weighting
    Newly introduced metric in Eq. 6; no external validation or comparison to other perceptual metrics.
  • MDS metric
    purpose: Measures agreement between output probability distributions for perturbation weighting
    Newly introduced similarity measure in Eqs. 8-10; presented as a substitute for JSD but not validated.

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Pith. "Pith review of Integrative CAM: Adaptive Layer Fusion for Comprehensive Interpretation of CNNs." pith.science (2026). https://pith.science/paper/GOVXTXPP

@misc{pith2026241201354,
  author       = {Pith},
  title        = {Pith review of: Integrative CAM: Adaptive Layer Fusion for Comprehensive Interpretation of CNNs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GOVXTXPP}},
  note         = {Machine review of arXiv:2412.01354}
}
read the original abstract

With the growing demand for interpretable deep learning models, this paper introduces Integrative CAM, an advanced Class Activation Mapping (CAM) technique aimed at providing a holistic view of feature importance across Convolutional Neural Networks (CNNs). Traditional gradient-based CAM methods, such as Grad-CAM and Grad-CAM++, primarily use final layer activations to highlight regions of interest, often neglecting critical features derived from intermediate layers. Integrative CAM addresses this limitation by fusing insights across all network layers, leveraging both gradient and activation scores to adaptively weight layer contributions, thus yielding a comprehensive interpretation of the model's internal representation. Our approach includes a novel bias term in the saliency map calculation, a factor frequently omitted in existing CAM techniques, but essential for capturing a more complete feature importance landscape, as modern CNNs rely on both weighted activations and biases to make predictions. Additionally, we generalize the alpha term from Grad-CAM++ to apply to any smooth function, expanding CAM applicability across a wider range of models. Through extensive experiments on diverse and complex datasets, Integrative CAM demonstrates superior fidelity in feature importance mapping, effectively enhancing interpretability for intricate fusion scenarios and complex decision-making tasks. By advancing interpretability methods to capture multi-layered model insights, Integrative CAM provides a valuable tool for fusion-driven applications, promoting the trustworthy and insightful deployment of deep learning models.

Figures

Figures reproduced from arXiv: 2412.01354 by the authors.

Figure 1
Figure 1. Perturbations on an image using random noise and pixel-masking [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Examples of I-CAM outputs using channel bias and spatial bias overlayed on their corresponding images [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Examples of outputs of all methods overlayed on their corresponding images [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Case 1 scenarios where model gives correct prediction with high confidence [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 6
Figure 6. Figure 6: Case 3 scenarios where model gives incorrect prediction with high confidence [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 8
Figure 8. Figure 8: Case 4 scenarios where model performs the worst with incorrect prediction and poor confidence [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: Images from ImageNet training dataset for understanding model’s behavior for respective classes in Case 4 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Heatmaps of different layers of ResNet along with their respective layer weights [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

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