Explaining Image Similarity with Automatically Extracted Concept Activation Vectors

Alexander Schulz; Barbara Hammer; Isaac Roberts; Petra Bevandic

REVIEW 3 major objections 5 minor 49 references

Explaining Image Similarity with Automatically Extracted Concept Activation Vectors

T0 review · 3 major / 5 minor · reviewed 2026-07-31 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Image similarity can be explained by removing automatically found concept directions from embeddings and measuring how the similarity score changes.

desk verdict Solid methods paper: SAE-CAV latent interventions for similarity XAI, with real multi-backbone evidence and an honest LRH caveat—not a theory breakthrough, but worth referee time. read the letter →

arxiv 2607.28386 v1 pith:YUXLZEAX submitted 2026-07-30 cs.CV

Isaac Roberts , Petra Bevandic , Alexander Schulz , Barbara Hammer This is my paper · ORCID

classification cs.CV

keywords imagesimilarityconceptactivationvectorssparseautoencodersexplainableAIlatentperturbationexemplarretrievalgroupexplanationsembeddingfaithfulness

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

Deep models score how similar two images are, but the score alone does not say whether the match is about stripes, neckline, color, or something else. This paper argues that you can recover those reasons without hand-labeled attributes. Sparse autoencoders break a model’s embeddings into concept directions; each concept is then stripped from a pair of embeddings and the drop in similarity becomes that concept’s importance. The same importances work for single pairs, whole clusters, and a new task the authors call Exemplar Retrieval—finding other pairs that are similar for the same reasons. Experiments on a controlled collage dataset and real fashion images show the latent edits stay closer to the data manifold than pixel masking and that the importance vectors nearly reconstruct the original similarity score by linear regression. A sympathetic reader cares because the method is model- and metric-agnostic, needs no concept labels, and turns opaque similarity into ranked, localizable factors a designer can act on.

What carries the argument

Latent concept perturbation: for each automatically extracted CAV, remove its contribution from both embeddings (a_i − u_{i,k} v_k) and define importance as the resulting drop in similarity on both sides; group importances are averages of these pairwise vectors.

What would settle it

Train a linear regressor from the concept-importance vectors to the true similarity on held-out pairs; if mean R² collapses well below the reported ~0.87–0.94 range, or if latent removals no longer beat pixel masks on Wasserstein and OOD scores across the six backbones, the central claim fails.

Watch

Extended reading notes

Core claim

Concept importances obtained by subtracting SAE-extracted Concept Activation Vectors from image embeddings, then measuring the change in any chosen similarity function, are more faithful to the embedding distribution than pixel-space baselines and linearly recover the true pairwise similarity. The same local importance vectors aggregate into group explanations and support Exemplar Retrieval of pairs that share the same similarity drivers.

Load-bearing premise

An embedding can be treated as a sparse linear mix of concept directions, so subtracting one direction cleanly isolates that concept’s share of the similarity score.

Editorial extensions

If this is right

Pairwise similarity scores become ranked lists of named concepts with heatmaps, without any hand-defined attribute vocabulary.
Cluster-level similarity and dissimilarity can be explained by averaging the same importance vectors over all pairs in a group.
Exemplar Retrieval can surface other image pairs that match for the same conceptual reasons rather than merely similar overall scores.
Model designers can identify and down-weight unwanted background or domain-mismatch concepts that inflate similarity.
The procedure applies to any frozen vision backbone and any embedding-space similarity metric.

Reading between the lines

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

If completeness holds only for linear similarities such as the dot product, non-linear metrics may need a different attribution identity before importances can be trusted as a full decomposition.
The same importance vectors could serve as a cheap steering signal: subtract high-ranking unwanted concepts at retrieval time without retraining the backbone.
Failure modes on abstract relational similarity (e.g., “same outfit composition”) would mark the practical boundary of linear CAVs and motivate hierarchical or non-linear dictionaries.
Exemplar Retrieval suggests a label-free route to conditional similarity datasets: mine pairs whose explanation vectors align and treat those shared concepts as soft conditions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Punchline: this is a competent, usable post-hoc toolkit for explaining embedding similarity with automatically extracted SAE concepts, plus group aggregation and a neat Exemplar Retrieval task. The load-bearing empirical claims hold up better than average for this subfield.

What is actually new is the package, not any single ingredient. Prior similarity XAI is mostly saliency or hand-labeled attributes (SANE, Sim2Word, Integrated Jacobians, LRP-for-similarity). Here they train SAEs on penultimate activations, define concept importance as the change in an arbitrary similarity score after subtracting u_k v_k from both embeddings, aggregate to groups via Eq. 4, and retrieve pairs whose explanation vectors align. Multi-CIFAR-10 collages give them controllable concept swaps; that design choice is smart and underused elsewhere.

They do the empirical work carefully. Six backbones, W1 and OOD vs several pixel masks (Table 1, Fig. 4), symmetry recovery under concept swap (~90%), similarity-drop checks, and linear recoverability with R² ≳ 0.87 beating CSIM/blur/gradient baselines (Table 3), plus Wilcoxon tests. The Completeness Theorem is a clean identity for linear dot-product under exact dictionary reconstruction—not deep theory, but correctly scoped. Limitations section flags the Linear Representation Hypothesis and cites the recent skepticism (Hindupur, Bhalla); they treat linearity as a first-order approximation rather than hiding it. Qualitative case study on VITON-HD (stripes, necklines, background contrast, cluster UMAPs) is readable and actionable for retrieval/debugging.

Soft spots, in proportion: the whole story rests on sparse linear CAVs isolating semantic factors. They know this; if LRH fails for abstract/relational similarity, importances get muddy. No user study, so “usefulness” is author-illustrated. At 2000 concepts the recoverability numbers collapse in the appendix—worth a referee question on dictionary size. Reproducibility is mid-tier (hyperparams and hardware listed; no public commit cited in the text). None of that sinks the central claim.

Who it is for: people building or auditing retrieval, fashion/face matching, or cluster inspection in vision embeddings. Not for someone hunting a new representation theorem. I would bring it to reading group, cite it when I need a baseline for concept-level similarity explanations, and send it to peer review. Accept-shaped with the usual revision asks on LRH framing and artifact release.

Referee Report

3 major / 5 minor

Summary. The paper proposes a model- and metric-agnostic post-hoc framework for explaining image similarity by decomposing pretrained embeddings with Sparse Autoencoders into Concept Activation Vectors, then measuring each concept’s importance via the change in a chosen similarity score under latent removal of that concept (Eqs. 2–3). It extends pair-level importances to group explanations (Eq. 4), concept attribution maps, and a new Exemplar Retrieval task that ranks pairs by explanation-vector similarity. Faithfulness is argued via Multi-CIFAR-10 collage controls and VITON-HD: latent interventions yield lower W1/OOD than several pixel masks across six backbones (Table 1, Fig. 4), induce consistent similarity drops (Table 2), and produce explanation vectors that linearly recover cosine and Euclidean scores with high R² (Table 3). A Completeness Theorem in the supplement shows that, under exact linear reconstruction and dot-product similarity, concept importances sum to twice the score.

Significance. If the empirical claims hold, the work meaningfully advances explainability for two-input similarity functions beyond saliency and hand-labeled attributes, with automatic concepts, multi-backbone evidence, a controllable synthetic benchmark, and a clean completeness identity for the linear-dot-product case. The latent-vs-pixel manifold comparison (W1/OOD) and linear recoverability tests are concrete, falsifiable contributions; Exemplar Retrieval and group explanations point to actionable uses in retrieval and model auditing. Strengths include multi-backbone significance testing, the Multi-CIFAR-10 design, and explicit acknowledgment of Linear Representation Hypothesis limits. The result is of clear interest to the vision xAI and metric-learning communities even if some applications remain qualitative.

major comments (3)

[Table 3; Appendix Tables 6–7; Linearly Recoverable] Appendix Tables 6–7 vs main Table 3: linear recoverability is reported as strong at 1500 Top-K concepts (R² ≈ 0.94/0.87), but at 2000 concepts the same “Ours” regressor collapses (R² ≈ −14.8 / −230). With ~2400 training pairs and c features, unregularized OLS is near-saturated; the main claim that “concept importances linearly recover the true similarity score” therefore depends on a narrow dictionary-size regime that is not analyzed or stabilized (e.g., ridge, feature selection, or reporting across c with error bars). Please either regularize/justify the operating point or qualify the recoverability claim by the full c sweep.
[Exemplar Retrieval; Figure 6; Contributions] Exemplar Retrieval is listed among the contributions and motivated as an actionable task, yet evaluation is limited to four qualitative rows in Figure 6 against a cosine-score baseline. Without a quantitative protocol (e.g., concept-consistency of top-k, human preference, or retrieval metrics conditioned on shared top concepts), the claim that explanation vectors recover “samples with similar reasons” is not yet substantiated at the same standard as Tables 1–3. Add a controlled metric on Multi-CIFAR-10 or VITON-HD, or move Exemplar Retrieval to exploratory discussion.
[Supplementary Theory, Theorem 1; Eqs. (2)–(3); Table 3] The Completeness Theorem (Supplementary Materials) assumes exact dictionary reconstruction and f(x,y)=x⊤y, yielding ∑Δc_i = 2f. Main experiments and Table 3 use cosine and −Euclidean, for which the identity does not hold and importances are not guaranteed to be a complete decomposition. Either extend the analysis (e.g., local linearization of cosine) or clearly separate the theorem as motivational for the linear case so readers do not over-read completeness for the reported metrics.

minor comments (5)

[Methodology, Eq. (2)] Wording around Eq. (2): “asymmetric explanation such that e_l(a_i,a_j)=e_l(a_j,a_i)” is contradictory; the construction is symmetric in the pair. Clarify intended meaning (joint vs one-sided ablation).
[Figure 1; Case Study] Figure 1 and several case-study figures are hard to parse in grayscale; ensure concept IDs, heatmaps, and bar importances remain legible and consistently labeled (e.g., c1184 “stripe”).
[Related work] Related work: briefly position against Integrated Jacobians for Siamese encoders (already cited) on what concept-level importances add beyond pairwise input attributions.
[Throughout] Typos and spacing artifacts from PDF extraction appear throughout (e.g., “Imagesimilarityunderlies”, “forsimilarity”); a careful copy-edit pass is needed before camera-ready.
[Case Study Setup; Experiment Details] State explicitly whether SAE training uses only train-split activations on VITON-HD and whether test images used for explanations were held out from dictionary learning (Setup says test-set activations for the case study—potential leakage relative to the faithfulness splits).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: importances are operationally defined interventions, Completeness is an identity under stated LRH assumptions, and empirical claims are externally validated.

full rationale

The paper defines concept importance as the measured change in a chosen similarity function after removing a SAE concept direction from one or both embeddings (Eqs. 2–3). That is a methodological definition, not a claim that X derives Y while being defined as Y. The Completeness Theorem (Supplementary Materials) then shows that, if activations admit exact linear reconstruction and f is the bilinear dot product, the sum of those importances equals 2f—an algebraic identity under the Linear Representation Hypothesis, analogous to completeness for Integrated Gradients, not a fitted “prediction” of the target claim. Empirical load-bearing results—lower W1/OOD versus pixel-space masks (Table 1, Fig. 4) and high held-out linear recoverability of cosine/Euclidean similarity (Table 3, R² ≳ 0.87)—are multi-backbone, significance-tested comparisons against external baselines (blur, gradient, CSIM product), not quantities forced by construction from the same fit. The mild self-citation to CSIM (Roberts et al. 2026) positions prior SAE concept work and supplies a baseline; it does not supply a uniqueness theorem or force the faithfulness/recoverability numbers. Multi-CIFAR-10 symmetry-recovery and distributional checks further probe the method against controlled ground truth rather than recycling inputs as outputs. Under the stated hard rules, there is no self-definitional loop, no fitted-input-called-prediction, and no load-bearing self-citation chain. Score 0 with empty steps is the honest finding.

Assumptions & free parameters 4 free parameters · 5 assumptions · 3 invented entities

The framework rests on standard embedding + SAE machinery plus the domain assumption that sparse linear concept directions are the right units for explaining similarity. Free choices are dictionary size, SAE type/hyperparameters, and which layer is decomposed. No new physical entities; invented constructs are methodological (Multi-CIFAR-10 collage, Exemplar Retrieval task, group explanation average).

free parameters (4)

Number of SAE concepts c = 1500 (main tables); sweeps 100–2000
Chosen experimentally (often 1500 for main claims; sweeps 100–2000). Linear recoverability and OOD both depend strongly on c; performance breaks at 2000.
SAE architecture and training hyperparameters = Per-backbone best configs in Appendix Table 4
Top-K vs JumpReLU vs Vanilla, batch size, LR, epochs, top-k, sparsity λ selected by grid search on class-identifiability accuracy on synthetic data.
Perturbation localization threshold (VITON-HD) = top 10%
Top 10% activating pixels used for fair image-space baseline heatmaps; affects W1/OOD comparison.
Domain-adaptation reweighting matrix M (appendix) = trained 10 epochs, lr 1e-3, bs 32
Optional learned linear map aligning cosine similarities to Jaccard concept overlap; changes absolute W1/OOD but is not the main claim path.

assumptions (5)

domain assumption Linear Representation Hypothesis: activations admit (approximate) sparse linear reconstruction A ≈ UV^T from concept dictionary V.
Eq. 1 and Completeness Theorem; paper cites Costa et al. 2025 and notes challenges in Hindupur/Bhalla.
domain assumption Removing the rank-one contribution u_{i,k} v_k isolates the effect of concept k on similarity without destroying other factors.
Core of local importance e^k_l in Eqs. 2–3; fails if concepts are entangled or non-linear.
domain assumption Similarity of interest is a function f of a pair of embeddings from a frozen pretrained backbone g.
Stated in Fundamentals; method is metric-agnostic within that class (cosine, Euclidean used).
domain assumption Frobenius dictionary learning / SAE training recovers monosemantic concept directions usable as CAVs.
Section Methodology (1); verified only approximately via class-identifiability on Multi-CIFAR-10.
standard math Bilinearity of the dot product yields completeness Σ Δc_i = 2 f(a1,a2) under exact reconstruction.
Appendix Completeness Theorem; holds only for linear f = dot product and exact reconstruction.

invented entities (3)

Multi-CIFAR-10 Collage dataset
purpose: Provide ground-truth concept presence/overlap for controlled perturbation and symmetry-recovery tests.
Synthetic 2×2 CIFAR grids with fixed class images; enables fairer latent vs pixel comparison.
Exemplar Retrieval task
purpose: Retrieve pairs/samples that share the same concept-level reasons for similarity as a query–reference pair.
Defined via ranking by dot product of explanation vectors; qualitative demos only.
Group explanation vector e_G
purpose: Average pairwise local explanation vectors over a cluster to explain group similarity/dissimilarity.
Eq. 4; operational aggregate, not an external natural kind.

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Pith. "Pith review of Explaining Image Similarity with Automatically Extracted Concept Activation Vectors." pith.science (2026). https://pith.science/paper/YUXLZEAX

@misc{pith2026260728386,
  author       = {Pith},
  title        = {Pith review of: Explaining Image Similarity with Automatically Extracted Concept Activation Vectors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YUXLZEAX}},
  note         = {Machine review of arXiv:2607.28386}
}

read the original abstract

Image similarity underlies many computer vision applications, yet it is often unclear why two images receive a high or low similarity score. Existing explainability methods often rely on gradient-based attribution maps to provide local justifications for similarity. These approaches struggle to provide global insights into what specifically drives similarity in regions of an embedding space, such as texture, shape, or color. We introduce a model- and metric-agnostic framework that explains image similarity using Concept Activation Vectors (CAVs) extracted automatically via Sparse Autoencoders (SAEs). Given a pair of images, we perturb their embeddings along discovered concept directions and measure the resulting change in a chosen similarity function, yielding concept importances. For image pairs, we provide localization with concept attribution maps. We extend this procedure to group-level settings, explaining what drives similarity across a cluster of images rather than a single pair, and further, we introduce Exemplar Retrieval, aiming to recover samples with similar reasons contributing to similarity. Our experiments show that our latent perturbations are more faithful to the underlying data distribution than pixel-space baselines, and that concept importances linearly recover the true similarity score. Qualitative results further confirm the usefulness of our methods in understanding a model's individual and group similarity judgments.

Figures

Figures reproduced from arXiv: 2607.28386 by the authors.

**Figure 3.** We report the average difference between the base [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Average W1 and OOD scores (y-axis) over number of concepts (x-axis) for all pretrained models on VITON-HD. Curves illustrate various perturbation strategies. The y-axis is normalized to range from 0 to 1. f(ak, aj ) for two functions. Note: full score recovery is impossible since concepts do not encode spatial information. The results in [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: UMAP of the explanation vectors produced with respect to Query image, with red indicating high-similarity samples [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Exemplar Retrieval Example (selecting images sim [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: UMAP of DINOv3 embeddings with respect to cosine distance for 250 images that activate the stripes concept the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: Dissimilarity is difficult to track due to underlying similarities. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: We illustrate the impact of perturbation severity on [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed July 31, 2026 · model on record in the stance chip above.

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