{"id":"c33b1104-e80e-44f0-9b10-58c69d06720e","arxiv_id":"2505.12897","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"EPIC fits an invertible channel-disentangling transform on top of a frozen pretrained classifier to produce prototype-based explanations while exactly preserving the original predictions.","lead":"EPIC adds a learnable linear transformation to a pretrained image classifier so that its feature channels become pure and can be explained with prototype image patches, without changing the model's predictions. It aims to give post-hoc prototype explanations, a capability usually reserved for specially trained interpretable models.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper never specifies whether U is orthogonal or merely invertible; if invertible is used, a diagonal scaling U=diag(1,...,lambda,...,1) drives purity to 1 while leaving predictions and explanations unchanged, so the reported disentanglement could be vacuous.","rationale":"The reader's weakest assumption is exactly the orthogonal-versus-invertible ambiguity in U, and this is the most load-bearing issue in the paper. The central claim is that EPIC produces meaningful prototype-based disentanglement without changing predictions; that claim is only non-vacuous if U is constrained to preserve norms, because otherwise the purity objective can be satisfied by rescaling a single channel. The paper provides no experimental detail resolving the constraint, so the reported purity and explanation quality cannot be evaluated from the manuscript alone. Other concerns, such as the overstatement in 'fully replicating the core explanatory power' and the lack of error bars in the FunnyBirds evaluation, are secondary and addressable. Since the core mechanism can still be valid if the released code uses orthogonal U, the appropriate outcome is to require the authors to specify and justify the constraint, rather than to reject outright. The reader's CONDITIONAL verdict already captures this, so no verdict change is needed.","tokens_in":11717,"tokens_out":5993,"duration_ms":70411,"concrete_test":"Inspect the released code at github.com/piotr310100/EPIC to determine whether U is parameterized as orthogonal (e.g., via QR, Cayley transform, or orthogonal regularization) in all experiments reported in Tables 1-5 and Fig. 7. If it is not orthogonal, run a control experiment on CUB-200-2011 or ImageNet with U fixed to a diagonal matrix diag(lambda_k) chosen to match the learned per-channel amplification, and compare the resulting purity, FunnyBirds center score, and user-study accuracy with the reported EPIC values; if the diagonal control matches, the reported disentanglement is not attributable to the learned U.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3 (Disentanglement Module) defines U as a learnable invertible matrix and then says it is trained 'with a restriction to either the class of invertible or orthogonal matrices,' but no experiment or appendix states which restriction is used. This choice is load-bearing: the purity objective is p_k/||p|| at the max-activation pixel. For any prototype pixel p, a non-orthogonal U can set U = diag(1,...,lambda,...,1), giving (Up)_k/||Up|| -> 1 as lambda -> infinity. Remark 3.1 still holds, so predictions are exactly preserved, and since A' = A U^{-1}, the per-class contributions A'_k ReLU(v_k) = A_k ReLU(avg Z_k) are unchanged; EPIC's explanations are identical to the original model's. Thus the purity metric can be trivially saturated without any semantic disentanglement, and the prototype figures could reflect only a learned rescaling. If the experiments used an orthogonal constraint, the trivial diagonal is excluded and the reported purity is meaningful; but the paper as written does not say so, so the central claim rests on an unstated assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes EPIC, a post-hoc explanation method for pretrained image classifiers with a global-average-pooling and linear classification head. EPIC inserts a learnable invertible matrix U before pooling and multiplies the classification weights by U^{-1}, which preserves the network's predictions exactly (Remark 3.1). U is trained to maximize the 'purity' of channel prototypes, defined as the normalized k-th coordinate of the feature vector at the max-activation pixel of channel k. After training, the authors select top-k contributing channels to explain a prediction and display the corresponding prototype patches. Experiments on CUB-200-2011, Stanford Cars/Dogs, and ImageNet compare EPIC with Grad-CAM, LRP, InfoDisent, and other prototype methods, and include FunnyBirds scores and two user studies.","tokens_in":11914,"tokens_out":11218,"duration_ms":104306,"significance":"The mathematical identity in Remark 3.1 is correct and clean: an invertible linear transform applied to each spatial location and compensated by U^{-1} in the final layer leaves the logits exactly unchanged. If the disentanglement training is meaningful—that is, if U is constrained to be orthogonal and the purity loss is well defined—EPIC would be a valuable post-hoc prototype method applicable to a broad class of pretrained CNNs. The paper includes a code link and reports FunnyBirds and user-study evaluations that provide some independent grounding beyond the internal purity metric. However, as written, the manuscript does not specify the constraint set for U or the training loss, so the validity of the reported disentanglement cannot be assessed; the DenseNet-121 accuracy discrepancy further weakens confidence. The significance of the contribution is therefore conditional on resolving these load-bearing points.","major_comments":[{"comment":"The paper states that U is trained 'with a restriction to either the class of invertible or orthogonal matrices' but never specifies which restriction is used in the experiments, nor does it give the parameterization of the constrained matrix. This choice is load-bearing for the paper's central claim. If U is allowed to be an arbitrary invertible matrix, the purity objective can be trivially saturated: for any prototype pixel p, a diagonal U = diag(1,...,lambda,...,1) with lambda > 1 makes purity(I,k) = (Up)_k/||Up|| approach 1, while leaving the selected prototypes, their spatial locations, and the top-k contribution scores exactly unchanged (A'_{pred,k} v_k = A_{pred,k} avg_pool(Z)_k). The reported disentanglement and the visual improvements in Fig. 3 would then be vacuous. The authors must state which constraint was used, define the purity loss computed on the transformed representation, and provide the concrete optimization setup. As written, the method is not reproducible and the main claim is unsupported.","section":"Section 3 (Disentanglement Module)"},{"comment":"In the DenseNet-121 row of Table 4, EPIC is reported to achieve 75.4% accuracy on Stanford Dogs while the original DenseNet-121 achieves 84.1%. This contradicts the paper's assertion that EPIC preserves the original model's predictions exactly (Section 3, Remark 3.1, and the 'Classification Performance' section). The value 75.4% also coincides with the ProtoPNet entry in the same column, suggesting a typographical error. Regardless, as printed, the table undermines the numerical validation of prediction preservation and must be corrected.","section":"Appendix A.3, Table 4"},{"comment":"The training objective is not specified. The text says only that 'the training stage focuses on the maximization of prototypes purity,' but no loss function is given, and the definition of purity in the 'Purity of prototype' paragraph involves an argmax over spatial locations, which is non-differentiable as written. The paper does not state how the purity of a set of prototypes is aggregated, how gradients are obtained through the argmax, what optimizer or learning rate is used, or how the prototype recalculation interacts with the loss. Without this information, the experimental results cannot be reproduced and it is impossible to verify that the reported disentanglement is due to a meaningful optimization rather than the trivial scaling described in the first comment.","section":"Section 3 (Training)"}],"minor_comments":[{"comment":"The text says Fig. 5 'illustrates ... on the imput images from CUB200-2011 and Stanford Dogs datasets,' but the caption identifies the image as a Hognose Snake from ImageNet; please reconcile the text and the figure caption.","section":"Section 4 and Fig. 5"},{"comment":"Reference [15] lists incorrect author names for PIPNet; the correct authors are Meike Nauta, Ron van Bree, and Christin Seifert. Please fix the citation.","section":"References"},{"comment":"The text says Table 2 'reports ... p-values', but Table 2 contains no p-value column; p-values appear only in Table 3. Please correct the text or the table.","section":"Section 4 (User study results)"},{"comment":"The function name avg_pool_over_channels is misleading: it performs global average pooling over spatial dimensions, not over channels (see Eq. (3) and Fig. 2). Please rename it (e.g., avg_pool_over_spatial) or clarify the terminology.","section":"Section 3 (Eq. (3))"},{"comment":"There are several typos: 'LPR' should be 'LRP' (Section 4), 'usy studies' should be 'user studies' (Appendix A.2), 'distributative' should be 'distributive' (Remark 3.1 proof), and 'future space' should be 'feature space' (Section 3, Purity of prototype).","section":"Throughout"},{"comment":"Algorithm 1 overloads the symbol ⊛: it is used both for the matrix application U⊛Z (Eq. (2)) and for element-wise multiplication in line 9. Please use different symbols for these operations.","section":"Algorithm 1"},{"comment":"The claim that EPIC 'fully replicat[es] the core explanatory power of inherently interpretable models' is stronger than what the user studies support: in Table 3, EPIC's accuracy (0.568 ImageNet, 0.55 CUB) is below that of InfoDisent (0.593, 0.647) and only barely above random. Please temper the claim or add discussion of this limitation.","section":"Abstract and Section 5"}],"recommendation":"major_revision","confidential_remarks":"The paper is an arXiv preprint under review. The central issue is that the authors never specify the constraint set for U; given the dramatic visual differences in Fig. 3, it is likely they used orthogonal matrices, but the text allows arbitrary invertible matrices, which would make the reported disentanglement vacuous. The authors must confirm the constraint and provide the exact training loss. The DenseNet-121 accuracy discrepancy in Table 4 and the incorrect PIPNet reference also suggest the manuscript needs a careful revision before it can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: EPIC is a real step for XAI practice — it gives you prototype explanations for a pretrained pooling-plus-linear classifier without changing the model's predictions. The core trick (Remark 3.1) is just linear algebra: an invertible linear map on feature channels composed with an inverse on the head leaves logits unchanged. That's simple but correct, and applying it to prototype extraction is a sensible extension of ProtoPNet/PIPNet/InfoDisent. The paper does the right kind of evaluation: FunnyBirds, two user studies, accuracy preservation tables. The code is on GitHub. Credit where due: the qualitative figures show cleaner prototypes after EPIC, and the FunnyBirds center score is competitive.\n\nThe soft spot is load-bearing. Section 3 says U is trained 'with a restriction to either the class of invertible or orthogonal matrices' but the experiments never say which. This matters a lot. If arbitrary invertible U is allowed, a diagonal scaling U=diag(1,...,λ,...,1) drives purity to 1 for any pixel, and since A'=A U^{-1}, the logits and the per-channel contributions to the explanation are exactly identical to the original model. So the reported 'disentanglement' could be vacuous — pure by construction, not by semantic content. The authors need to state plainly that they used orthogonal U, and how they parameterize and enforce orthogonality during training. If they did use orthogonal, the purity numbers are meaningful; if not, the central claim collapses. The paper as written leaves this open, so the verdict has to be conditional.\n\nOther concerns are milder. The paper defines purity, optimizes purity, and then shows enhanced purity as evidence — that's circular in the internal evaluation, but the FunnyBirds and user studies provide independent grounding, so it's not fatal. The claim in the abstract that EPIC 'fully replicates the core explanatory power of inherently interpretable models' is too strong; the user study numbers are above chance but not dramatically so (e.g., 0.568 for ImageNet in Table 3). And EPIC still needs access to the original training data, which post-hoc purists would note.\n\nNet: the method is worth engaging with, and the ambiguity is fixable with an explicit statement and an ablation. A serious referee should ask for the U constraint, error bars on FunnyBirds, and a more measured version of the abstract. I'd send it to review. It's not a desk reject.","headline":"EPIC is a genuinely useful post-hoc prototype method, but the unstated choice of whether U is orthogonal or merely invertible determines whether the central purity claim means anything.","tokens_in":12522,"tokens_out":2507,"would_cite":true,"duration_ms":26449,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"EPIC gives pretrained image classifiers prototype-based explanations while leaving every prediction exactly unchanged.","keywords":["explainable AI","prototype-based explanations","post-hoc interpretability","feature disentanglement","channel purity","image classification","pretrained models"],"falsifier":"Inspect the learned $U$ in a released EPIC model: if its singular values are not all equal, the purity gain is confounded by scaling. A direct null test is to apply $U = \\mathrm{diag}(1,\\dots,\\lambda,\\dots,1)$ to a single channel of an arbitrary feature map: this preserves predictions (Remark 3.1) yet drives the channel's purity toward 1, showing that the disentanglement score alone does not certify semantic separation. If the released implementation restricts $U$ to the orthogonal group, the null test is blocked and the claim survives.","tokens_in":11475,"feed_emoji":"🧩","tokens_out":10948,"duration_ms":105656,"temperature":0.7,"pith_summary":"EPIC tries to close the gap between two families of explainable AI: post-hoc methods that work on any trained model but give only coarse heatmaps, and prototype methods that give intuitive part-level explanations but require specially designed architectures trained from scratch. The paper proposes a plug-in module for an already-trained classifier that leaves its predictions unchanged and produces prototype explanations for individual feature channels. The mechanism is a learnable invertible matrix applied to the final feature map, trained to maximize a purity score so that each channel responds to a single dominant concept. If the claim holds, prototype-based explanations become available for deployed models without retraining, including large-scale settings where ante-hoc prototype models struggle. The paper reports exact accuracy preservation and user studies showing that EPIC's explanations let people identify the model's class better than chance.","feed_headline":"Pretrained classifiers get prototype explanations","feed_subtitle":"EPIC fits an invertible transform to the last layer, so predictions stay exactly the same.","key_machinery":"The Disentanglement Module is a learnable $D \\times D$ matrix $U$, restricted to invertible or orthogonal matrices, applied per pixel to the feature map by $\\widehat{Z}[x,y] = U Z[x,y]$ at each spatial location $(x,y)$, with the final linear layer's weights replaced by $A' = A U^{-1}$ so the output logits are exactly preserved. The purity measure is $purity(I,k) = p_k / \\|p\\|$, where $p = Z_I[h,w] \\in \\mathbb{R}^D$ is the feature vector at the spatial location of the maximal activation of channel $k$; a value of 1 means every other channel is zero at that location. Prototypes are the top-$m$ training images by channel activation, and training maximizes the purity of these prototypes while periodically recomputing them as $U$ evolves.","core_discovery":"EPIC's central discovery is that prototype explanations do not require an inherently interpretable architecture. By inserting a learnable square matrix $U$ into the feature map just before global average pooling and replacing the classification weight $A$ with $A U^{-1}$, the pretrained network's logits are exactly preserved (Remark 3.1). Training $U$ to maximize the purity $p_k / \\|p\\|$ of each channel's prototype pixel yields a disentangled feature space in which each channel corresponds to a single dominant concept, and the top contributing channels to the predicted class can be shown as prototype images. The authors state that this makes EPIC the first post-hoc method able to fully replicate the core explanatory power of inherently interpretable prototype models.","pith_inferences":["(Editorial inference) If the effectiveness of EPIC depends on the orthogonal restriction, the method is best understood as a learned rotation of the final feature space; the same purity objective could then be applied to intermediate layers to yield hierarchical concept explanations.","(Editorial inference) A natural stress test not reported in the paper is channel ablation: removing or strongly suppressing one disentangled channel should produce a predictable drop in the probability of the classes that rely on it, which would confirm that the channels carry independent concepts.","(Editorial inference) The purity score is computed at a single spatial location per channel; a complementary check for global disentanglement would measure whether the winning channel dominates across the whole feature map, not only at its maximum, since local purity alone does not rule out redundant or overlapping channels."],"forward_implications":["For architectures with a pooled feature map followed by a linear classification head, prototype explanations can be added to an already-trained model with zero change in its outputs.","EPIC's construction preserves the pretrained model's accuracy exactly, so the accuracy-interpretability tradeoff usually associated with prototype models disappears.","The method scales to large datasets such as ImageNet and to modern backbones, where training dedicated prototype architectures from scratch is impractical.","User studies in the paper indicate that people who see EPIC explanations identify the model's predicted class above chance, so the explanations convey decision-relevant information.","Because the original training data is not needed for the explanation step, EPIC can be applied to models already in deployment."],"supporting_citations":[{"why":"Supplies the channel-as-prototype interpretation of the final feature map and the prototype-selection scheme on which EPIC builds.","marker":"[15]"},{"why":"Closest prototype-based method on a pretrained backbone; EPIC's main comparison and the antecedent for ImageNet-scale prototype explanations.","marker":"[21]"},{"why":"Introduced class-specific prototype explanations; EPIC positions itself against this ante-hoc paradigm and uses it as a user-study baseline.","marker":"[5]"},{"why":"Provides the part-level evaluation benchmark used to assess whether explanations identify object parts.","marker":"[10]"},{"why":"Saliency-map baseline used to argue that EPIC provides concept-level rather than purely region-level explanations.","marker":"[18]"},{"why":"Additional saliency-map baseline used in qualitative comparisons.","marker":"[2]"}],"fun_headline_variants":["Post-hoc prototypes for pretrained classifiers, no retraining","EPIC gives any pretrained network prototype-based explanations","Transform enables prototype explanations for pretrained models","First post-hoc method to fully replicate prototype explainability","Prototype explanations without changing pretrained architecture"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Whether EPIC's disentanglement is genuine rests on the unstated restriction that the learned matrix $U$ is an orthogonal (norm-preserving) rotation rather than an arbitrary invertible matrix, because an unrestricted transform can inflate the purity score simply by rescaling channels.","fun_headline_variants_meta":{"raw":{"variants":["Post-hoc prototypes for pretrained classifiers, no retraining","EPIC gives any pretrained network prototype-based explanations","Transform enables prototype explanations for pretrained models","First post-hoc method to fully replicate prototype explainability","Prototype explanations without changing pretrained architecture"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000184,"raw_usage":{"total_tokens":1323,"prompt_tokens":955,"completion_tokens":368,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":571,"completion_tokens_details":{"reasoning_tokens":295}},"tokens_in":571,"tokens_out":368,"duration_ms":4212,"temperature":1.0,"reasoning_tokens":295,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:24:09.458121+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Inspect the learned $U$ in a released EPIC model: if its singular values are not all equal, the purity gain is confounded by scaling. A direct null test is to apply $U = \\mathrm{diag}(1,\\dots,\\lambda,\\dots,1)$ to a single channel of an arbitrary feature map: this preserves predictions (Remark 3.1) yet drives the channel's purity toward 1, showing that the disentanglement score alone does not certify semantic separation. If the released implementation restricts $U$ to the orthogonal group, the null test is blocked and the claim survives.","supporting_citations":[{"cited_title":"Pipnet: Prototypical part network for interpretable fine-grained recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023","cited_arxiv_id":null,"evidence_quote":"Supplies the channel-as-prototype interpretation of the final feature map and the prototype-selection scheme on which EPIC builds."},{"cited_title":"This looks like that: Deep learning for interpretable image recognition.Advances in Neural Information Processing Systems, 32, 2019","cited_arxiv_id":null,"evidence_quote":"Introduced class-specific prototype explanations; EPIC positions itself against this ante-hoc paradigm and uses it as a user-study baseline."},{"cited_title":"FunnyBirds: A synthetic vision dataset for a part-based analysis of explainable AI methods","cited_arxiv_id":null,"evidence_quote":"Provides the part-level evaluation benchmark used to assess whether explanations identify object parts."},{"cited_title":"On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation.PLoS One, 10(7):e0130140, 2015","cited_arxiv_id":null,"evidence_quote":"Additional saliency-map baseline used in qualitative comparisons."}],"review_version":1}