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REVIEW 4 major objections 6 minor 58 references

Advancing Attribution-Based Neural Network Explainability through Relative Absolute Magnitude Layer-Wise Relevance Propagation and Multi-Component Evaluation

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that changing one denominator in layer-wise relevance propagation—normalizing by the absolute total pre-activation of each neuron rather than by the sum of its positive contributions—fixes misattributions between neurons…

desk verdict A plausible but unproven LRP variant with a self-proposed metric; the algorithm/equation mismatch and non-conservation need fixing before the claims hold. read the letter →

arxiv 2412.09311 v1 pith:G7YKEMDB submitted 2024-12-12 cs.CV cs.AI

Davor Vukadin , Petar Afrić , Marin Šilić , Goran Delač This is my paper · ORCID
classification cs.CVcs.AI
keywords explainableartificialintelligencelayer-wiserelevancepropagationvisiontransformerattribution-basedevaluationcontrastiveexplanationsabsolutemagnitudenormalizationpixel-levelattributionimageclassification
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

This paper claims that a single change to layer-wise relevance propagation—dividing by the absolute value of a neuron's total incoming signal instead of by the sum of its positive contributions—fixes a real error in how credit is shared between neurons of different activation magnitudes. On that basis it introduces absLRP and shows it produces sparse, noise-free, class-specific attribution maps on three architectures, including the Vision Transformer. It also introduces Global Attribution Evaluation (GAE), a single score that folds faithfulness, robustness, and localization together, and uses it to rank more than a dozen attribution methods on ImageNet and PascalVOC. In those comparisons absLRP outscores every method on VGG and ViT-Base and statistically ties contrastive LRP on ResNet50, while the authors acknowledge the ViT margin is smaller and leaves room for improvement. If the claim is correct, deep-network explanations can be obtained from a simple, architecture-agnostic rule that works at pixel resolution even when a Vision Transformer has very few patches.

What carries the argument

The load-bearing object is the absLRP rule in Eq. (12), which redistributes neuron $j$'s relevance to input $i$ as $(x_i w_{ij})_+ / (|\sum_k x_k w_{kj}| + \epsilon) R_j^l$: positive contributions in the numerator, absolute pre-activation magnitude in the denominator. It is implemented through automatic differentiation, where the ratio of incoming relevance to the absolute output of a layer is used as the gradient scaling, so the same code works for convolutions, residual branches, normalizations, and attention blocks with only layer-specific bookkeeping. The second mechanism is the Global Attribution Evaluation (GAE) metric, which multiplies a local consistency score—obtained by correlating MoRF/LeRF output-drop curves with attribution-map similarity curves, plus a faithfulness term from gradient-based impact maps—by a contrastiveness score derived from four-image mosaics.

What would settle it

Build two small networks with identical input–output behavior, one obtained from the other by scaling a hidden neuron's incoming weights and compensating in the next layer; if absLRP assigns different attribution maps to the two (as Figure 1's toy example suggests it would), then the method tracks parameter magnitude rather than functional importance, and the claimed 'correction' becomes a design choice that a reader can test in minutes.

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Extended reading notes

Core claim

The central discovery on the paper's own terms is that existing LRP rules misallocate relative relevance when neurons in the same layer have different absolute activation magnitudes, and that replacing the denominator with the absolute value of the whole pre-activation corrects this. Concretely, LRP-$\alpha_1\beta_0$ uses $\sum_k (x_k w_{kj})_+$ as the normalizer, so two toy networks that share the same input, hidden, and output values but differ in the magnitude of one hidden neuron's incoming weights receive identical attributions $[0.5, 0.5]$; absLRP, defined by $R_i^{l-1} = \sum_j (x_i w_{ij})_+ / (|\sum_k x_k w_{kj}| + \epsilon) R_j^l$, changes the split to $[0.25, 0.75]$, which the paper argues better reflects the network's internal dynamics. From there the paper builds a full recipe for convolutional, residual, batch-normalized, layer-normalized, and self-attention layers, seeds the top layer with contrastive relevance (1 for the target class, $-1/N$ for the others), and reports that the resulting maps are the top-scoring ones under its GAE metric on VGG and ViT-Base, tying contrastive LRP on ResNet50.

Load-bearing premise

Everything rests on the premise that the absolute magnitude of a neuron's total incoming signal is the right yardstick for splitting credit among its inputs; the paper motivates this with a toy example but supplies no conservation, axiomatic, or independent empirical justification for that particular denominator.

Editorial extensions

If this is right

  • If absLRP's advantage holds, Vision Transformer explanations need no longer be upscaled from patch resolution: the method delivers sparse pixel-level maps even for a model with 49 patches.
  • The same rule transfers to non-image domains without modification; the authors demonstrate BERT sentiment attributions, so text and other discrete-input models inherit the recipe.
  • GAE offers a single-number ranking that unifies faithfulness, robustness, and localization, replacing the common practice of reporting several possibly conflicting metrics.
  • Because the last-layer seed is contrastive (target class positive, all others negative), the maps change with the queried class, making multi-class image analysis practical.
  • The ResNet50 tie with contrastive LRP implies the new denominator matters most in architectures with less normalized activation scales, which is consistent with the smaller margins the authors report for ViT-Base.

Reading between the lines

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

  • AbsLRP does not conserve total relevance across layers, because its numerator sums only positive contributions while its denominator is the absolute total; the paper does not discuss this departure from LRP's conservation tradition.
  • The motivating toy example changes the network's weights without changing its input–output function; an alternative reading is that a good attribution should be invariant to such re-parameterizations, which would make absLRP's sensitivity to weight scale a testable weakness rather than a clear correction.
  • Because GAE's faithfulness term is built from gradient-based impact maps, the metric systematically favors methods whose maps align with input-gradients; attention-only methods such as Rollout are disadvantaged by construction, so GAE is best read as a comparison within gradient-aligned families.
  • The ViT results suggest a testable extension: on models with stronger normalization of internal activations the new denominator should matter less, so one could predict smaller absLRP gains on other LayerNorm-heavy transformer variants beyond ViT.
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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

4 major / 6 minor

Summary. The paper proposes a new layer-wise relevance propagation rule, absLRP, defined in Eq. (12) as propagating relevance through a layer by normalizing each positive contribution (x_i w_ij)_+ by the absolute value of the total pre-activation |\sum_k x_k w_kj| + epsilon. The authors argue this corrects a relative-attribution issue in LRP-\alpha1\beta0 when neurons differ in absolute activation magnitude, and they apply the rule to VGG, ResNet50, and ViT-Base using a contrastive output initialization. They also introduce a new evaluation metric, Global Attribution Evaluation (GAE), which combines a local-consistency score (robustness plus faithfulness via gradient-guided masking) with a contrastiveness score based on mosaics, and they report large GAE improvements for absLRP over many baselines on ImageNet and PascalVOC. The paper additionally reports ROAD, Lipschitz, and Focus scores, and performs ablations and qualitative comparisons for Transformers.

Significance. If the proposed rule is taken at face value, absLRP is an attractively simple and architecture-agnostic LRP variant, and the paper deserves credit for tackling Vision Transformer explainability at pixel level and for attempting a multi-component evaluation metric. The authors provide code, compare a large set of attribution methods, and include ablation studies. However, the central quantitative claim rests mainly on GAE, a metric introduced in the same paper, and the independent standard metrics give only mixed support, especially for ViT. The manuscript contains no conservation or axiomatic analysis of Eq. (12), and there is an apparent mismatch between the formal rule and the provided pseudocode. These issues currently leave the headline contribution under-supported, although the core idea is plausible and the requested fixes appear addressable.

major comments (4)
  1. [Section 3.1, Eq. (12) and Algorithm 1] Algorithm 1 does not implement Eq. (12). For a linear or convolutional layer, the gradient of h + ha with respect to x_i is w_ij + sign(x_i)|w_ij|, and after multiplication by x_i and rel_scaling this yields 2 (x_i w_ij)_+ R_j^l / (|s_j| + epsilon), not (x_i w_ij)_+ R_j^l / (|s_j| + epsilon). Each layer processed by Algorithm 1 therefore introduces an extra factor of 2, and across a deep network the implemented rule differs from the defined rule by a factor exponential in depth. Because all experiments, ablations, and qualitative figures are produced with the implementation, the paper must reconcile Eq. (12), Algorithm 1, and the released code; as written, the claim that absLRP is the rule in Eq. (12) is not supported.
  2. [Section 3.1, Eq. (12)] Eq. (12) does not conserve relevance. Summing R_i^{l-1} over i gives sum_j [ (sum_i (x_i w_ij)_+) / (|sum_k x_k w_kj| + epsilon) ] R_j^l. The numerator equals |sum_k x_k w_kj| only when all contributions x_i w_ij have the same sign; in general sum_i (x_i w_ij)_+ differs from |sum_k x_k w_kj|, so relevance is systematically amplified or suppressed layer by layer. The paper motivates LRP through the redistribution property in Eq. (1) but never states whether absLRP is intended to be conservative, and the toy example in Figure 1 involves only positive contributions and cannot reveal this behavior. The authors should prove conservation under stated conditions, add a normalization that restores it, or explicitly characterize and justify the non-conservation.
  3. [Section 4.1, Tables 7-9 and 11-13] The claim of consistent superiority is not supported by the external metrics. On ViT-Base/ImageNet (Table 9), absLRP has lower Focus (0.826) than GradCAM and HiResCAM (0.913) and worse ROAD_MoRF (0.457 vs 0.317); on ViT-Base/PascalVOC (Table 13) the same pattern holds (Focus 0.689 vs 0.800/0.785; ROAD_MoRF 0.195 vs 0.131). On VGG and ResNet absLRP is competitive, but the "significant margin" claimed in the abstract appears only on GAE, a metric defined by the same authors. Since GAE is also aligned with the method's design goals (sparse, contrastive, pixel-level maps), the paper should provide a sensitivity analysis of GAE to its parameters and normalization choices, and should either temper the abstract or justify why GAE should override the standard metrics where they disagree.
  4. [Section 3.2, Local consistency definition] The GAE metric is incompletely specified. Section 3.2 states that "we select the top k percent of input features" but neither the value of k nor the feature-block granularity (pixel-wise versus patch-wise) is given anywhere in the paper or appendices; only T=10 is reported in Section 4.1. Without k and the masking implementation, the experiments are not reproducible, and the metric's sensitivity to these choices is unknown. Given that GAE carries the paper's main quantitative conclusion, this omission blocks verification of the primary result.
minor comments (6)
  1. [Section 2.1, Eq. (5)] The definition of R^{l-1}_{i in P,N} is hard to parse, and the sentence "where Psi^{l-1}_i is the mean value of non-zero-neurons in the layer l-1" does not explain how a per-neuron subtraction term is computed from a mean; please clarify the notation.
  2. [Table 8] The GradCAM++ Focus score is printed as "747" rather than "0.747", which appears to be a typographical error.
  3. [References] References [46] and [47] are the same paper (Smilkov et al. 2017); please remove the duplicate.
  4. [Section 4.1] The paragraph following Table 9 contains the doubled phrase "Additionally, Additionally".
  5. [Figure 1 caption] The caption uses the acronym "RAMP" while the text and the rest of the paper use "absLRP"; the shorter acronym is never defined.
  6. [Algorithm 1] In the pseudocode, the variable x is used both as the function input and inside autograd.grad(ha + h, x, rel_scaling), while the parameter is named input; this makes the intended dependence of rel on the layer's input ambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular step: absLRP and GAE are defined independently, and external ROAD/Lipschitz/Focus results provide non-circular corroboration.

full rationale

The absLRP rule in Eq. (12) is a direct definition in terms of the layer's pre-activations and weights; it is not defined in terms of GAE, nor is any parameter fitted to the evaluation data. GAE's local-consistency and contrastiveness components are constructed from model outputs, input×gradient impact maps, and a mosaic scoring map; none of these components presuppose the absLRP rule, and the same protocol is applied to all baseline methods. The paper also reports independent external metrics (ROAD, Local Lipschitz, Focus) from prior work, and absLRP is top or near-top on several of them, so the central claim does not reduce to a self-defined score. There are no self-citations or imported uniqueness theorems in the reference list. A separate, non-circular correctness concern exists: Algorithm 1's autograd of h+ha yields twice the Eq. (12) contribution per linear layer, so the experiments may implement a scaled variant; this affects validity but not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

Core claim rests on the heuristic absLRP normalization and on GAE, a metric proposed in the same paper; external standard metrics provide partial independent support.

free parameters (3)
  • GAE masking step count T = 10
    Number of perturbation steps in Local consistency, set to 10 in all experiments without sensitivity analysis (Section 4.1).
  • GAE top-k percent for gradient masking = unspecified
    The paper states 'top k percent of input features' but does not specify k; the choice affects MoRF/LeRF curves (Section 3.2).
  • absLRP epsilon = 1e-9
    Numerical stability constant in Algorithm 1; not fitted but necessary for implementation.
assumptions (5)
  • ad hoc to paper Relevance should be proportional to (x_i w_ij)_+ normalized by |sum_k x_k w_kj|
    Eq. (12) defines absLRP; this normalization is motivated by the toy example in Figure 1 but not derived from conservation or other principles.
  • domain assumption Gradient-based masking selects features whose removal changes model output most/least
    Section 3.2 uses input*gradient magnitudes as impact estimates; this is assumed to be a good proxy for feature impact.
  • domain assumption Attribution maps should change in step with model output under perturbation
    The LC_R robustness component (Eq. 14) assumes a correlation between output difference curves and attribution similarity curves.
  • domain assumption Softmax scores in the mosaic define class similarity for contrastiveness
    The scoring map S_mosaic sets negative quadrants based on softmax ratio 2*s_p[c_ni]/s_p[c_p]-1, assuming this reflects class overlap.
  • domain assumption Self-attention softmax denominator can be detached and treated as constant
    Section 3.1 detaches softmax denominator during LRP pass, following prior transformer XAI practice; this is a modelling choice.

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Cite this review

Pith. "Pith review of Advancing Attribution-Based Neural Network Explainability through Relative Absolute Magnitude Layer-Wise Relevance Propagation and Multi-Component Evaluation." pith.science (2026). https://pith.science/paper/G7YKEMDB

@misc{pith2026241209311,
  author       = {Pith},
  title        = {Pith review of: Advancing Attribution-Based Neural Network Explainability through Relative Absolute Magnitude Layer-Wise Relevance Propagation and Multi-Component Evaluation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G7YKEMDB}},
  note         = {Machine review of arXiv:2412.09311}
}
read the original abstract

Recent advancement in deep-neural network performance led to the development of new state-of-the-art approaches in numerous areas. However, the black-box nature of neural networks often prohibits their use in areas where model explainability and model transparency are crucial. Over the years, researchers proposed many algorithms to aid neural network understanding and provide additional information to the human expert. One of the most popular methods being Layer-Wise Relevance Propagation (LRP). This method assigns local relevance based on the pixel-wise decomposition of nonlinear classifiers. With the rise of attribution method research, there has emerged a pressing need to assess and evaluate their performance. Numerous metrics have been proposed, each assessing an individual property of attribution methods such as faithfulness, robustness or localization. Unfortunately, no single metric is deemed optimal for every case, and researchers often use several metrics to test the quality of the attribution maps. In this work, we address the shortcomings of the current LRP formulations and introduce a novel method for determining the relevance of input neurons through layer-wise relevance propagation. Furthermore, we apply this approach to the recently developed Vision Transformer architecture and evaluate its performance against existing methods on two image classification datasets, namely ImageNet and PascalVOC. Our results clearly demonstrate the advantage of our proposed method. Furthermore, we discuss the insufficiencies of current evaluation metrics for attribution-based explainability and propose a new evaluation metric that combines the notions of faithfulness, robustness and contrastiveness. We utilize this new metric to evaluate the performance of various attribution-based methods. Our code is available at: https://github.com/davor10105/relative-absolute-magnitude-propagation

Figures

Figures reproduced from arXiv: 2412.09311 by the authors.

Figure 1
Figure 1. Toy examples illustrating key differences between LRP- [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Change curves for an example from ImageNet - VGG - absLRP: [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Impact maps on an example from ImageNet - VGG network: [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: (a) Example mosaic image - ImageNet (b) Our method’s attribution map (positive only) - selected bottom left image as target class (c) LRP-𝛼2𝛽1 attribution map (positive only), example of an attribution method with poor contrastive properties randomly chosen. Next we de…
Figure 5
Figure 5. Figure 5: absLRP attribution maps for VGG - ImageNet [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 6
Figure 6. Figure 6: absLRP attribution maps for ViT-Base - PascalVOC [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: Class-specific visualizations for multiple attribution methods - ImageNet VGG [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: Class-specific visualizations for multiple attribution methods - ImageNet ViT-Base [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 10
Figure 10. Figure 10: Attribution maps produced by absLRP and HiResCAM for ViT-Base patch size 16 image size 384 (576 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Top five (top row) and bottom five (bottom row) scored attribution maps for our method in randomly [PITH_FULL_IMAGE:figures/full_fig_p022_11.png]
Figure 12
Figure 12. Figure 12: AbsLRP attribution maps for VGG - PascalVOC [PITH_FULL_IMAGE:figures/full_fig_p026_12.png]
Figure 13
Figure 13. Figure 13: AbsLRP attribution maps for ViT-Base - ImageNet [PITH_FULL_IMAGE:figures/full_fig_p026_13.png]
Figure 14
Figure 14. Figure 14: Top five (top row) and bottom five (bottom row) scored attribution maps for our method in randomly [PITH_FULL_IMAGE:figures/full_fig_p027_14.png]
Figure 15
Figure 15. Figure 15: AbsLRP attribution maps for ResNet50 - ImageNet (top), PascalVOC (bottom) [PITH_FULL_IMAGE:figures/full_fig_p027_15.png]
Figure 16
Figure 16. Figure 16: Class-specific visualizations for multiple attribution methods - ImageNet ResNet50 [PITH_FULL_IMAGE:figures/full_fig_p028_16.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.