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Signal or Noise? Auditing Rotation-Induced Saliency Drift in Medical and Aerial Imaging
Khawaja Murad ul Hassan, Mehran Ebrahimi
TL;DR
Rotation can make Grad-CAM explanations drift even when predictions remain unchanged, weakening their use in auditing orientation-free imagery. The paper measures equivariance throughout the CAM operator and introduces training-free aligned multi-view averaging; across ImageNet backbones, it substantially improves equivariance and supports more reproducible explanations, while remaining limited in scope and not guaranteeing correctness.
Problem
Rotation-induced saliency drift makes post-hoc explanations difficult to use as evidence in domains without a canonical orientation, motivating a test of whether the drift is faithful signal or CAM-operator noise.
Method
The paper measures equivariance at every Grad-CAM stage and introduces EquiGrad-CAM, which inverse-rotates saliency from T views into a common frame before averaging.
Results
+36.0% to +247% equivariance over Grad-CAM was reported across ResNet-50, VGG-16, and ViT-B/16 on full ImageNet-1K validation, with gains also reported for CLIP and rotation-natural domains.
Takeaways & Limitations
The drift is mostly operator noise carried by spatial degrees of freedom discarded by pooling, so aligned removal can improve explanation consistency without retraining.
Takeaways & Limitations
The evaluation covers in-plane rotation only, equivariance is an approximate empirical metric, and EquiGrad-CAM does not universally improve faithfulness or establish that explanations are correct.
Abstract
from arXiv · showhide
Post-hoc saliency maps such as Grad-CAM are increasingly used to audit why a deployed vision model made a decision, yet the heatmap drifts when the input is rotated, even when the prediction is unchanged. In domains with no canonical orientation, such as histopathology and aerial imagery, this undermines using saliency as evidence. We ask whether that drift is faithful signal or noise introduced by the CAM operator, and answer it by measuring equivariance at every stage of the operator rather than inferring it from the network's output. The instability is not where one would guess: the channel weights are the most rotation-stable stage, and on ResNet-50 exactly stable, because a GAP+linear head makes the class gradient field spatially constant. What moves is the spatial activation tensor, and the classifier's own pooling discards that movement. A causal test confirms the consequence: occluding the pixels whose saliency drifts costs the model less than occluding random pixels, at either orientation. The drift is carried by degrees of freedom the classifier throws away, which is what makes removing it faithful rather than destructive. EquiGrad-CAM is a training-free wrapper that takes T rotated views, inverse-rotates each view's saliency into a common canonical frame, and averages. On the full ImageNet-1K validation set it raises equivariance over single-view Grad-CAM by +36.0% (ResNet-50), +87.5% (VGG-16) and +247% (ViT-B/16); a scale-matched ablation isolates alignment before averaging, not the locus of aggregation, as the driver. It beats rotation-augmented training without retraining, lifts zero-shot CLIP by +145%, and yields rotation-consistent explanations on PatchCamelyon and RESISC45. Its by-product PEUM ranks explanations by how reproducible they are, at no cost beyond the views already taken. Code: https://github.com/Khawaja-Murad/EquiGrad-CAM
1. Introduction
The paper argues that rotation-induced Grad-CAM drift undermines saliency-based auditing in orientation-free domains, then identifies the drift as mostly operator noise and proposes aligned multi-view averaging.
- Motivation: Rotating an input can qualitatively change Grad-CAM while leaving the prediction unchanged, challenging its use as audit evidence.This problem is especially acute for histopathology and aerial imagery, where inputs lack a canonical orientation.
- Research question: The central question is whether saliency drift reflects faithful changes in model attention or noise introduced by the CAM operator.The paper treats this as an empirical question rather than assuming that consistency is always correct.
- Evidence: Internal representations remain relatively stable under rotation, while drift persists on rotations that preserve predictions and is uncorrelated with confidence change.Feature and logit cosine similarities are 0.90 and 0.85, respectively.
- Method: EquiGrad-CAM inverse-rotates saliency maps from T rotated views into a common canonical frame before averaging.The alignment step is presented as the missing ingredient for cancelling operator noise while reinforcing consistent evidence.
- Results: +36.0%, +87.5%, and +247% equivariance gains over Grad-CAM were reported for ResNet-50, VGG-16, and ViT-B/16, respectively.The evaluation used the full ImageNet-1K validation set, and a scale-matched ablation attributed the improvement to alignment rather than the aggregation locus.
2. Related Work
The paper positions EquiGrad-CAM as a training-free, post-hoc alternative to architectural or retraining-based approaches, centered on alignment and reproducibility of explanations.
- Gradient-based CAM: Existing CAM variants change channel weighting but still condition each heatmap on one input orientation.The paper contrasts this shared limitation with its alignment-based approach.
- Alignment: Inverse-rotating each view’s saliency to a common canonical frame before averaging is the paper’s key distinction from averaging finished maps.The authors report that unaligned averaging can fall below the single-view baseline on fragile backbones.
- Equivariant architectures: Unlike group-equivariant architectures, EquiGrad-CAM audits pretrained non-equivariant networks without training or retraining.Its contribution is complementary to feature-level architectural equivariance.
- Explanation invariance and equivariance: The paper measures explanation equivariance in the approximately invariant regime instead of assuming that model invariance holds.This follows prior guidance that consistency should be enforced when the model itself is invariant, while making that condition empirical.
- Saliency consistency and uncertainty: PEUM provides an image-level explanation-reliability signal using no computation beyond the views already taken.The paper distinguishes this from uncertainty methods requiring model modification.
- Operator analysis: Stage-wise analysis finds that channel weights are the most rotation-stable Grad-CAM stage, while spatial activations and gradients carry the movement.On ResNet-50, the channel weights are exactly stable; channel summation nevertheless cancels some per-channel error.
3. Is the Drift Signal or Noise?
The paper measures rotation equivariance throughout Grad-CAM to determine whether saliency drift reflects changing model evidence or operator noise. The evidence localizes drift to spatial activations that pooling discards, and a causal occlusion test shows these drifting pixels are less consequential than random pixels.
- Operator-level diagnosis: Measuring every CAM stage, rather than relying on output similarity, addresses whether rotation drift is faithful signal or operator noise.This tests the objection that rotated inputs may induce genuinely different computations and that CAM reads quantities not captured by pooled features or logits.
- Operator-level diagnosis: The channel weights are rotation-stable, while the spatial activation tensor carries ResNet-50’s rotation drift.The decomposition reproduces published Grad-CAM within 0.003, validating the stage-wise analysis.
- Operator-level diagnosis: Global pooling discards the spatial arrangement disturbed by rotation, making activation changes invisible to the classifier but visible to Grad-CAM.For a GAP+linear classifier, the decision depends on GAP(A), so rearrangements preserving the pooled vector are discarded by construction.
- Causal validation: 0.100/0.038 probability loss follows occluding the drift region in canonical/rotated frames, versus 0.152/0.121 for random pixels and 0.264/0.225 for agreement pixels.The drift region is the least consequential of the three tested regions on ResNet-50 with n=1,000 images.
- Causal validation: The drift-region test is asymmetric by construction and therefore favors finding faithful signal, but the below-random causal importance remains the load-bearing observation.The authors treat the asymmetry result as informative while relying primarily on the below-random causal effect.
- Robustness: Conditioning equivariance on model stability changes Grad-CAM by at most +0.067 and EquiGrad-CAM by less than 0.017, without closing the 0.25–0.61 gap.The conclusion is reported as insensitive to the conditioning choice.
4. Method
EquiGrad-CAM aggregates Grad-CAM across rotated views after inverse-rotating each view’s quantities into a common computational frame. The method supports feature- or output-space aggregation, with alignment identified as the essential design choice and PEUM obtained from aligned-map variability.
- Grad-CAM: Grad-CAM forms a class-specific heatmap by weighting target-layer activations with spatially averaged class gradients, then applying ReLU and upsampling.Maps are min–max normalised to [0, 1].
- Aligned multi-view aggregation: EquiGrad-CAM samples T=18 rotated views, runs each through the frozen backbone, inverse-rotates per-view quantities to the canonical frame, and averages them.The target class is fixed as the unrotated image’s top-1 class across views.
- Aligned multi-view aggregation: Alignment precedes averaging so consistent explanations reinforce and view-specific operator noise cancels; unaligned finished-map averaging is not equivariant.The wrapper can instantiate aligned aggregation in feature space or output space.
- PEUM: PEUM is an aligned per-view weighted-variance score that ranks how reproducible each image’s explanation is under rotation.It requires no computation beyond the views already used for aggregation and is validated as an image-level instability signal.
- Aggregation loci: Feature-space aggregation averages aligned activations and gradients before forming one map, while output-space aggregation averages finished per-view maps.The full-scale comparison makes alignment, rather than aggregation locus, the central design choice.
- View weighting: Uniform weighting gives every view equal contribution, while prediction-conditioned weighting excludes views whose top-1 changes or confidence falls below τ.The headline EquiGrad-CAM setting uses τ=0 and uniform weights.
- ViT extension: For ViT-B/16, the method hooks the final pre-residual-normalization spatial representation; later locations can yield constant heatmaps.The aggregation wrapper is architecture-agnostic, but transformer CAM extraction requires a hook producing a non-degenerate map.
- Evaluation protocol: Equivariance compares a rotated-image heatmap with the rotated original heatmap using Pearson correlation across seven evaluation angles.Five evaluation angles lie off the internal T=18 sampling grid.
5. Application: Auditing in Rotation-Natural Domains
EquiGrad-CAM restores rotation-consistent explanations training-free in histopathology and aerial imagery, while PEUM helps auditors prioritize unstable explanations. Alignment improves stability without making saliency more localized or predicting model error.
- Rotation-natural domains: EquiGrad-CAM restores equivariant explanations training-free on PatchCamelyon and RESISC45.The application evaluation uses rotation-naive fine-tuned ResNet-50 classifiers, attributing explanation gains to the wrapper rather than retrained weights.
- Rotation-natural domains: Unaligned averaging falls below single-view Grad-CAM on histopathology, isolating canonical-frame alignment as the mechanism.Histopathology equivariance is 0.484 for Grad-CAM and 0.412 for unaligned averaging.
- Visual audit: Figure 3 contrasts drifting Grad-CAM maps in rotated frames with EquiGrad-CAM maps inverse-rotated into a canonical frame.The aligned maps remain the same across the displayed rotation row.
- Faithfulness and localization: No CAM strongly concentrates saliency in PatchCamelyon’s label-defining centre region; EquiGrad-CAM instead minimizes energy loss under rotation.The uniform-map null is 0.145, while EquiGrad-CAM’s label-region level is 0.179 and its rotational energy loss is 0.0019 versus 0.0060 for Grad-CAM.
6. Generality: ImageNet-Scale Validation
ImageNet-1K experiments show that EquiGrad-CAM generalizes across CNNs and ViTs, with alignment—not aggregation locus—driving the gain. The method improves consistency without retraining, but its multi-view cost scales with the number of rotations.
- ImageNet-1K results: EquiGrad-CAM is highest on rotational equivariance across all ImageNet-1K backbones in Table 5.The evaluation covers the official 10,000-image validation set with ResNet-50, VGG-16, and ViT-B/16.
- ImageNet-1K results: +36.0% raises equivariance from 0.703 to 0.956 on ResNet-50, while VGG-16 rises 0.511 to 0.958 (+87.5%) and ViT-B/16 0.250 to 0.867 (+247%).Every comparison is significant after correction.
- Ablation: Alignment, not the aggregation locus, drives equivariance: aligned averaging performs similarly whether aggregation occurs in feature or output space.Without alignment, averaging barely changes the baseline and falls below it on both CNNs.
- Training comparison: Rotation augmentation raises Grad-CAM equivariance but lowers clean accuracy, whereas post-hoc EquiGrad-CAM reaches 0.978 on CUB without retraining.On CUB/ResNet-50, augmentation changes equivariance 0.82 to 0.88 and accuracy 0.81 to 0.78.
- Scope of gains: EquiGrad-CAM improves equivariance broadly while faithfulness remains comparable to CAM peers and localization is not uniformly best.The authors explicitly claim consistency, not localization.
- Cost: T=6 retains 93.8% of ResNet-50’s and 86.4% of ViT-B/16’s full T=18 gain at 6.4–6.9× single-pass cost.The paper recommends T=6 for deployment and T=18 as the reference configuration.
7. Limitations and Conclusion
The paper finds that rotation drift is mostly operator noise and removes it training-free, while emphasizing that reproducibility does not establish correctness. Its scope is limited to in-plane rotation and post-hoc auditing, with several evaluation caveats.
- Limitations: The evaluation covers in-plane rotation only, and EquiGrad-CAM is assessed as a post-hoc audit rather than as a training signal.The equivariance metric is approximate, and the method does not universally improve faithfulness across model families.
- Conclusion: EquiGrad-CAM produces rotation-consistent explanations in histopathology and aerial imagery, but rotation-consistency makes explanations reproducible, not correct.The paper warns that consistent-but-wrong maps may be more persuasive than visibly unstable ones.
- Limitations: PEUM and EquiGrad-CAM are positioned as repeatable audit tools that route irreproducible explanations to human review rather than proving model correctness or detecting errors.
- Conclusion: +36 to +247% equivariance improvement is reported across three ImageNet backbones, alongside +145% on zero-shot CLIP.The conclusion also reports gains in two rotation-natural domains and against rotation-augmented training without retraining.
- Conclusion: A scale-matched ablation identifies alignment, rather than the aggregation locus, as the mechanism behind the improvement.