{"id":"ff275a64-8233-429f-9ebc-213b846195a1","arxiv_id":"2607.28386","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Sparse-autoencoder Concept Activation Vectors, perturbed in embedding space, yield concept importances that explain image-pair and group similarity more faithfully than pixel-space baselines.","lead":"The paper explains why two images look similar to a neural network by automatically finding semantic concepts with sparse autoencoders and measuring how each concept changes the similarity score. It offers pair- and group-level explanations plus a new retrieval task that finds images similar for the same reasons.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the reader's already-flagged LRH dependence.","rationale":"The strongest claim is empirical and multi-faceted (manifold faithfulness of latent CAV perturbations + linear recoverability of similarity + qualitative utility of the resulting importances). The single condition that must hold for clean attribution is the Linear Representation Hypothesis / exact dictionary reconstruction used in Eq. 1–3 and the Completeness Theorem. The reader already isolates this; the authors themselves flag recent counter-evidence and note that abstract/relational similarities may be missed. Supporting tables are consistent across six backbones, the synthetic control set isolates concept presence, and statistical tests are reported. Qualitative sections (Exemplar Retrieval, group UMAPs) are illustrative rather than user-validated, but that is already reflected in the CONDITIONAL verdict and does not constitute an independent load-bearing flaw. Consequently no verdict adjustment is warranted; the existing CONDITIONAL (accept-shaped once LRH caveats and artifacts are treated as open) stands.","tokens_in":20015,"tokens_out":511,"duration_ms":10306,"concrete_test":"Re-run the linear-recoverability protocol of Table 3 on the same 3 000 pairs after replacing the Top-K SAE dictionary with a matched-dimensionality non-negative matrix factorization (or PCA) basis; if mean R^{2} falls below ~0.7 while W1/OOD remain comparable, the claim that SAE-derived CAVs specifically (rather than any linear basis) are necessary for faithful importance vectors is weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest assumption (exact sparse linear reconstruction of embeddings by SAE CAVs, Eq. 1 and the Completeness Theorem) is correctly identified as the structural hinge. The paper already surfaces the same caveat (Limitations; citations to Hindupur et al. 2025 and Bhalla et al. 2026) and treats linearity as a first-order approximation. Empirical supports for the strongest claim—lower W1/OOD versus pixel masks (Table 1, Fig. 4) and high linear recoverability of similarity (Table 3, R^{2} ≳ 0.87)—are multi-backbone, significance-tested, and partially controlled by the synthetic Multi-CIFAR-10 collage. No additional internal inconsistency, hidden assumption, or unacknowledged failure mode rises to load-bearing status that would further weaken the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","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.","tokens_in":20191,"tokens_out":1289,"duration_ms":39655,"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":[{"comment":"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.","section":"Table 3; Appendix Tables 6–7; Linearly Recoverable"},{"comment":"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.","section":"Exemplar Retrieval; Figure 6; Contributions"},{"comment":"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.","section":"Supplementary Theory, Theorem 1; Eqs. (2)–(3); Table 3"}],"minor_comments":[{"comment":"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).","section":"Methodology, Eq. (2)"},{"comment":"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”).","section":"Figure 1; Case Study"},{"comment":"Related work: briefly position against Integrated Jacobians for Siamese encoders (already cited) on what concept-level importances add beyond pairwise input attributions.","section":"Related work"},{"comment":"Typos and spacing artifacts from PDF extraction appear throughout (e.g., “Imagesimilarityunderlies”, “forsimilarity”); a careful copy-edit pass is needed before camera-ready.","section":"Throughout"},{"comment":"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).","section":"Case Study Setup; Experiment Details"}],"recommendation":"minor_revision","confidential_remarks":"Central empirical pillars (latent W1/OOD superiority; recoverability at the chosen c) look solid enough for a methods venue after the dictionary-size and Exemplar Retrieval fixes. No integrity concerns. Scope fits cs.CV xAI; novelty relative to the authors’ own CSIM citation should stay clearly delineated in the camera-ready (perturbation-based importances vs assuming concepts intrinsically explain similarity)."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","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.\n\nWhat 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.\n\nThey 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.\n\nSoft 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.\n\nWho 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.","headline":"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.","tokens_in":20866,"tokens_out":620,"would_cite":true,"duration_ms":16979,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Image similarity can be explained by removing automatically found concept directions from embeddings and measuring how the similarity score changes.","keywords":["image similarity","concept activation vectors","sparse autoencoders","explainable AI","latent perturbation","exemplar retrieval","group explanations","embedding faithfulness"],"falsifier":"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.","tokens_in":20847,"feed_emoji":"🔍","tokens_out":882,"duration_ms":21065,"temperature":0.7,"pith_summary":"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.","feed_headline":"Strip concepts from embeddings to explain image similarity","feed_subtitle":"Latent edits beat pixel masks and nearly rebuild the similarity score from ranked concepts alone.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["SAE concepts subtracted from embeddings explain image similarity","Latent CAV edits rank what drives pairwise image similarity","Concept importances from SAE directions recover similarity scores","Perturb embeddings along auto-found CAVs to explain similarity","Group and pair similarity explained by SAE concept ablation"],"cache_read_input_tokens":128,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["SAE concepts subtracted from embeddings explain image similarity","Latent CAV edits rank what drives pairwise image similarity","Concept importances from SAE directions recover similarity scores","Perturb embeddings along auto-found CAVs to explain similarity","Group and pair similarity explained by SAE concept ablation"]},"model":"grok-4.5","effort":"low","cost_usd":0.003248,"raw_usage":{"total_tokens":1079,"prompt_tokens":752,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":32484000,"prompt_tokens_details":{"text_tokens":752,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":264,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":752,"tokens_out":63,"duration_ms":5134,"temperature":1.0,"reasoning_tokens":264,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T09:02:55.667010+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"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.","supporting_citations":[],"review_version":1}