{"id":"c53852c8-0ad1-4765-822e-31f0023739bf","arxiv_id":"2412.02399","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"OMENN exactly decomposes a network's output into pixel contributions by composing per-layer input-dependent affine transformations into a single matrix.","lead":"OMENN rewrites a trained neural network into one matrix per input, so that the sum of pixel attributions exactly equals the model's score. It matches or beats common explainability methods on ViT benchmarks, but trails some baselines on CNNs and its code is not yet public.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Benchmark tables likely use post-processed OMENN maps, so the exact completeness result (Eq. 27) is not what is measured; raw and processed scores are not reported separately.","rationale":"The central mathematical construction appears sound: composing input-dependent affine layers yields an exact completeness identity for the listed layers. The weakest link is the bridge from that theory to the empirical claims. The paper's own Section 4 introduces post-processing that destroys sum(C)=f(x), and the manuscript never clarifies which quantity is benchmarked. This is load-bearing because the paper's stated contribution is that OMENN provides locally exact explanations; if the reported competitiveness comes from a post-processed variant whose exactness is forfeited, the empirical support for the central claim collapses. The reader's conditional verdict already identifies this, and my stress-test does not find a more fundamental mathematical error. I would keep the verdict CONDITIONAL, contingent on the authors specifying and releasing the pipeline and reporting raw and post-processed results separately. A secondary gap is that residual connections are not explicitly derived in the augmented bias-free form, though they can be handled by aggregating the affine forms, so I do not treat that as the primary concern.","tokens_in":17488,"tokens_out":17764,"duration_ms":210613,"concrete_test":"Run the Table 1 faithfulness protocol and the FunnyBirds benchmark on ViT-B/16 with two versions of OMENN: (i) the raw matrix C from Eq. 26, first verifying numerically that sum(C)-f(x) is within 1e-4 on a held-out sample; (ii) C after the Section 4 post-processing, with the quantile and mean-filter parameters reported. Report both sets of scores and the completeness residual for version (ii). If the raw scores are substantially lower than the post-processed scores, the headline results are driven by post-processing rather than by the exact completeness property.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 states that after computing C the authors 'disregard all elements with negative contributions' and apply 'quantile-based outlier removal and smoothing using a mean filter.' These steps break the completeness identity sum(C)=f(x) from Eq. 27, yet the paper never states whether the FunnyBirds results (Figure 4, Table 3) and faithfulness scores (Table 1) use the raw matrix or the post-processed matrix, nor does it report the quantile threshold or filter kernel. Because the raw maps are acknowledged as noisy, the benchmark numbers are likely based on the post-processed maps. If so, the empirical claims evaluate 'OMENN + clipping + smoothing' rather than the exact OMENN decomposition, so the central theoretical guarantee is not what is validated. The code footnote says the code will be published only after acceptance, so the exact pipeline cannot currently be checked.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces OMENN, a post-hoc attribution method that represents a neural network as a single input-dependent matrix for a given input, based on the 'dynamic linearity' property that each layer can be expressed as an affine or input-dependent affine transformation. The authors derive how fully-connected, convolutional, normalization, attention, and activation layers (including GELU and SWISH) can be reformulated, and show that the resulting explanation matrix C satisfies the completeness property sum(C) = f(x) (Eq. 27). The method is evaluated on the FunnyBirds and Quantus faithfulness benchmarks with ViT and CNN backbones, where the authors claim competitive or superior performance. The theoretical derivations in Sections 3.2-3.5 are mathematically sound for the listed layers, and the completeness identity is a clean contribution. However, the paper suffers from a major ambiguity about whether the reported experiments use the raw matrix or the post-processed version described in Section 4, and the main text's claim of consistent outperformance is contradicted by the supplementary VGG-16 faithfulness table.","tokens_in":1718,"tokens_out":2072,"duration_ms":106022,"significance":"If the exactness and completeness properties are taken as the core contribution, OMENN offers a principled way to obtain pixel-level attributions that exactly reconstruct the logit for modern architectures with smooth activations. The derivation is clear and the completeness property is a rigorous, parameter-free guarantee for the raw matrix. This distinguishes OMENN from heuristic gradient-based methods and provides a potential tool for exact decomposition in ViTs. The authors also correctly identify the limitations of gradient-based attributions at near-stationary points. However, the empirical evaluation does not currently establish that the proposed method, as actually used, retains these guarantees: the post-processing steps in Section 4 break the completeness identity, and the benchmark numbers may reflect a different pipeline than the theoretical object. The missing comparison with FullGrad, the closest related exact method, is a significant gap. Thus the theoretical contribution is promising but the empirical evidence, as presented, is not yet convincing.","major_comments":[{"comment":"The paper claims a completeness property sum(C) = f(x) for the explanation matrix C, but Section 4 states that, after computing C, the authors 'disregard all elements with negative contributions' and apply 'quantile-based outlier removal and smoothing using a mean filter.' These operations change the matrix, so the post-processed map no longer satisfies Eq. (27). The manuscript never states whether the reported FunnyBirds results (Table 3, Figure 4) and faithfulness scores (Tables 1-2) use the raw matrix or the post-processed one, nor does it report the quantile threshold and filter kernel. If the evaluations use the post-processed maps, then the empirical validation is of 'OMENN + clipping + smoothing', not of the exact decomposition that is the paper's central theoretical contribution. The authors must report raw and post-processed results separately and provide the post-processing hyperparameters, or modify the method to preserve completeness under post-processing (e.g., by redistributing discarded contributions). Without this, the connection between theory and experiments is unsubstantiated.","section":"Section 4, Efficient Implementation; Eq. (27)"},{"comment":"The main text states that OMENN 'consistently outperforms all competing approaches' on the faithfulness benchmark, based on the ViT-B/16 results in Table 1. However, the supplementary Table 2 for VGG-16 reports an OMENN faithfulness score of 0.023 ± 0.003, which is lower than GradCAM (0.065), LRP (0.057), and Integrated Gradients (0.045). The main text only remarks that 'results for convolutional model are provided in the Supplementary Materials,' without acknowledging that the reported numbers are not superior for VGG-16. This is a direct contradiction of the 'consistently outperforms' claim. The authors should either revise the claim to make it backbone-specific, or provide a discussion explaining the VGG-16 result and what it implies for the applicability of OMENN.","section":"Section 5, Comparison of Faithfulness; Supplementary Table 2"},{"comment":"The paper motivates OMENN partly by contrast with FullGrad (Gradient NN Representation, cited as [53]), which provides an exact gradient+bias explanation but is restricted to ReLU/LeakyReLU networks. FullGrad is the most closely related method to OMENN, and it is directly applicable to the VGG-16 and ResNet-50 backbones used in the FunnyBirds and faithfulness experiments. Yet FullGrad is not included in any benchmark comparison (Tables 1-3, Figure 4). Without comparing to FullGrad, the claimed advantage of OMENN — extension to smooth activations while maintaining exactness — is not empirically tested. The authors should either include FullGrad in the evaluations or explicitly justify its absence.","section":"Sections 2 and 5; related work [53]"}],"minor_comments":[{"comment":"The post-processing hyperparameters (quantile cutoff, mean filter size) are not reported anywhere in the manuscript or supplementary material. Please specify these values, as the benchmark results depend on them.","section":"Section 4"},{"comment":"The word 'tremnedous' in the caption should be 'tremendous'.","section":"Supplementary, Figure 9 caption"},{"comment":"There is a typo: 'SWISH (Self-Gated Activation Funstion)' should be 'Self-Gated Activation Function'.","section":"Section 3.2"},{"comment":"The paper uses 'exact' and 'precise' to describe OMENN, but the post-processing in Section 4 breaks the exactness of the raw matrix. It would be clearer to explicitly state that the theoretical exactness applies only to the raw decomposition, and that the reported qualitative and quantitative results may use a modified map.","section":"Section 3.6"}],"recommendation":"major_revision","confidential_remarks":"The theoretical core of the paper (Sections 3.2-3.5) is sound and the completeness property is a valuable contribution. However, the empirical evaluation is compromised by the ambiguity about whether raw or post-processed maps are used, and by the main-text claim that is contradicted by the authors' own supplementary table. The missing comparison with FullGrad also weakens the novelty claim. The issues are fixable within the scope of the paper, so I recommend major revision rather than rejection. The authors should provide raw and post-processed benchmark numbers, disclose hyperparameters, and either add FullGrad or justify its exclusion."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"OMENN is a solid incremental result: it gives an exact, completeness-preserving attribution for modern architectures with smooth activations. The empirical section, as written, overclaims, though the underlying method deserves a serious look.\n\nThe core construction is sound. Composing layerwise input-dependent affine maps into a single matrix with an augmented ones channel is a clean way to turn a ViT or ConvNeXt into one linear operator per input. The x·ξ(x) trick for GELU/SWISH is the genuinely new piece; for ReLU it collapses to gradient·input plus biases, which the authors admit. The completeness identity (sum(C)=f(x)) is a theorem, not a heuristic. The supplementary derivations for convolutions, normalization, attention, and residuals are thorough and check out.\n\nWhat the paper does well: it is honest about the ReLU reduction, the gradient-vs-OMENN toy example in Figure 3 is instructive, and the statement of limitations is fair. This is a useful addition to the XAI toolbox.\n\nNow the soft spots, in proportion.\n\nFirst, the empirical overclaim. The main text says OMENN 'consistently outperforms all competing approaches,' but Supplement Table 2 shows on VGG-16 faithfulness OMENN gets 0.023 while GradCAM gets 0.065, IG 0.045, LRP 0.057. That is a decisive loss on one of the two backbones tested, and it is hidden in the supplementary. The paper needs to reconcile this with the 'consistently outperforms' language.\n\nSecond, FullGrad is cited but never compared. That is the most relevant baseline, since FullGrad is exactly the ReLU special case of this construction. Without that comparison, the reader cannot tell whether the smooth-activation extension actually buys anything.\n\nThird, and most important for reproducibility: Section 4 states the authors discard negative contributions, apply quantile-based outlier removal, and mean-filter smoothing. Those operations break the completeness identity that is the paper's headline theoretical result, yet the paper never states whether the FunnyBirds and faithfulness numbers use raw or post-processed maps, nor does it give the quantile threshold or filter size. Code is withheld until acceptance. The stress-test note's suspicion that the benchmarks use the post-processed, non-complete maps is plausible; I cannot rule it out. This is not a fatal flaw—post-processing for visualization is legitimate—but it turns the empirical validation into a test of 'OMENN plus a smoothing pipeline' rather than the exact decomposition, and must be disclosed.\n\nThe math itself is solid, and the failure on VGG faithfulness actually suggests the authors did not cherry-pick successful runs. But the write-up needs major revision: add FullGrad, report raw and processed scores separately, fix the overclaim, and release code. I would send this to peer review, expecting heavy revision but not rejection.","headline":"OMENN's exact completeness for smooth activations is real and worth knowing, but the empirical paper as written overclaims and hides a VGG failure in the supplementary.","tokens_in":18230,"tokens_out":3860,"would_cite":true,"duration_ms":42712,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that a neural network can be collapsed into a single matrix per input whose entries sum exactly to the model's output logit.","keywords":["explainable AI","attribution methods","dynamic linearity","neural network interpretability","Vision Transformer","convolutional neural network","completeness property","post-hoc explanation"],"falsifier":"Evaluate OMENN on the reported benchmarks using the raw matrix before post-processing; if the raw version scores no better than the gradient baseline, the completeness property does not carry the empirical results.","tokens_in":17305,"feed_emoji":"🧮","tokens_out":9325,"duration_ms":95288,"temperature":0.7,"pith_summary":"This paper introduces OMENN (One Matrix to Explain Neural Networks), a post-hoc method that represents a trained neural network as a single matrix for each input. The authors show that every layer of a Vision Transformer or CNN—convolutions, attention, normalization, residual connections, and GELU or SWISH activations—can be rewritten as an input-dependent affine transformation. Composing these transformations collapses the whole network into one matrix, and the paper's central claim is that the sum of all entries in the explanation matrix equals the network's output logit for the explained class. This exact completeness, if it holds, would make OMENN's pixel attributions faithful by construction rather than approximate, and it would apply to already-trained models without retraining or architectural changes. The authors also report benchmark results on FunnyBirds and a faithfulness metric where OMENN is competitive with or exceeds existing attribution methods.","feed_headline":"One matrix per input sums exactly to a network's logit","feed_subtitle":"OMENN collapses ViTs and CNNs into a single affine map, making pixel attributions locally exact without retraining.","key_machinery":"The key machinery is dynamic linearity: each layer $l_i(x)=W_i(x)x + b_i(x)$ acts as an affine transformation whose parameters depend on the input. The paper establishes this form for fully-connected layers, convolutions via doubly block-Toeplitz matrices and im2col, normalization, residual connections, multi-head self-attention, and dynamic activations such as GELU and SWISH, which factor as $\\phi(x)=x\\,\\xi(x)$ and become diagonal linear maps. To absorb additive biases, the input is augmented with an extra channel of ones and layer parameters are merged into augmented matrices, so that a whole network collapses into a single matrix $\\tilde{\\Omega}_w$. The explanation matrix $C$ is the Hadamard-product decomposition of that collapse, and equation (27) states that its entries sum exactly to the network output, which is the completeness property that carries the method's claims of exactness.","core_discovery":"The central discovery is that a broad class of modern networks can be exactly re-expressed as one input-dependent affine map, yielding an attribution matrix whose entries sum to the output. The construction augments the input with a constant channel of ones so that biases become part of a combined weight matrix, then multiplies the per-layer linear maps together. For the explanation matrix $C$ defined as $C = \\sum_d (C_w \\odot X)[:,d] + C_b$, with $C_w$ the input-multiplying part and $C_b$ the bias part, the identity $\\sum C = f(x)$ holds. The paper contrasts this with gradient-based saliency, which assigns zero contribution to a GELU input at $x=-0.75$ even though the function value is $-0.17$, while OMENN's local linear coefficient captures that contribution exactly.","pith_inferences":["Because the raw matrix preserves exact completeness while the post-processed maps do not, a natural extension is to evaluate whether the reported benchmark gains survive when using the raw matrix; this would separate the value of the exact decomposition from the value of the smoothing step.","The same dynamic-linearity collapse should extend to other architectures built from GELU/SWISH and attention, such as transformer decoders or hybrid models; testing OMENN on a text or audio model would check whether the proof's assumptions travel beyond vision.","The paper's completeness identity suggests a new diagnostic: the difference between the raw OMENN sum and a post-processed map's sum measures how much information the visualization pipeline discards, which could guide the design of explanation displays that preserve faithfulness.","Another testable extension is to use the OMENN matrix directly in perturbation-based faithfulness evaluations, since the raw matrix gives exact per-pixel contributions; comparing raw versus smoothed maps on existing benchmarks would quantify the cost of interpretability post-processing."],"forward_implications":["OMENN can be applied to pre-trained ViTs and CNNs without any retraining or architecture change, unlike B-Cos or QSENN, which require modifying the model.","For piecewise-linear activations such as ReLU, OMENN's explanation coincides with image times gradient; for GELU and SWISH it departs from the gradient, correcting cases where the gradient is zero despite a nonzero contribution.","The exact sum-to-logit property provides a built-in consistency check: any explanation that does not sum to the logit can be identified immediately, and the raw OMENN matrix can serve as ground truth for evaluating other attribution methods.","On the FunnyBirds benchmark, OMENN achieves the highest mean score on ViT-B/16 and VGG-16 among the compared methods, and on the Quantus faithfulness metric it roughly doubles the score of the second-best method for ViT-B/16."],"supporting_citations":[{"why":"supplies the dynamic-linearity idea of input-dependent linear model representations that OMENN generalizes.","marker":"[8]"},{"why":"the B-Cos follow-up that OMENN contrasts with, since it requires specialized architectures without biases.","marker":"[9]"},{"why":"FullGrad, a prior single-matrix attribution method restricted to ReLU/LeakyReLU that OMENN extends to GELU/SWISH and attention.","marker":"[53]"},{"why":"defines the Vision Transformer architecture used as a target backbone for OMENN.","marker":"[15]"},{"why":"introduces GELU, the activation whose $x\\cdot\\xi(x)$ factorization underlies OMENN's dynamic linearity treatment.","marker":"[25]"},{"why":"provides the FunnyBirds benchmark used to evaluate attribution quality across multiple dimensions.","marker":"[26]"},{"why":"defines the faithfulness correlation metric used in the Quantus evaluation.","marker":"[6]"},{"why":"provides the Quantus toolkit and its faithfulness evaluation protocol.","marker":"[22]"},{"why":"the Chefer LRP method, the strongest baseline that OMENN is compared against in the benchmarks.","marker":"[11]"}],"fun_headline_variants":["OMENN: one matrix per input explains any network exactly","No gradients needed: one matrix gives exact attributions","One matrix per input sums to the network output, exactly","OMENN: replace a network with one matrix, attributions exact","One matrix per input: the exact explanation for any network"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper's reported benchmarks treat the post-processed explanation maps as OMENN, even though the post-processing steps (dropping negative entries, quantile clipping, smoothing) break the exact sum-to-logit equality that the method's completeness guarantee depends on.","fun_headline_variants_meta":{"raw":{"variants":["OMENN: one matrix per input explains any network exactly","No gradients needed: one matrix gives exact attributions","One matrix per input sums to the network output, exactly","OMENN: replace a network with one matrix, attributions exact","One matrix per input: the exact explanation for any network"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000785,"raw_usage":{"total_tokens":3448,"prompt_tokens":909,"completion_tokens":2539,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":525,"completion_tokens_details":{"reasoning_tokens":2469}},"tokens_in":525,"tokens_out":2539,"duration_ms":16587,"temperature":1.0,"reasoning_tokens":2469,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:30:53.424856+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate OMENN on the reported benchmarks using the raw matrix before post-processing; if the raw version scores no better than the gradient baseline, the completeness property does not carry the empirical results.","supporting_citations":[{"cited_title":"B-cos net- works: Alignment is all we need for interpretability","cited_arxiv_id":null,"evidence_quote":"supplies the dynamic-linearity idea of input-dependent linear model representations that OMENN generalizes."},{"cited_title":"B-cos alignment for inherently interpretable cnns and vision transformers","cited_arxiv_id":null,"evidence_quote":"the B-Cos follow-up that OMENN contrasts with, since it requires specialized architectures without biases."},{"cited_title":"Full-gradient represen- tation for neural network visualization","cited_arxiv_id":null,"evidence_quote":"FullGrad, a prior single-matrix attribution method restricted to ReLU/LeakyReLU that OMENN extends to GELU/SWISH and attention."},{"cited_title":"An image is worth 16x16 words: Transformers for image recognition at scale, 2021","cited_arxiv_id":null,"evidence_quote":"defines the Vision Transformer architecture used as a target backbone for OMENN."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defines the faithfulness correlation metric used in the Quantus evaluation."},{"cited_title":"Quantus: An explain- able ai toolkit for responsible evaluation of neural network explanations and beyond","cited_arxiv_id":null,"evidence_quote":"provides the Quantus toolkit and its faithfulness evaluation protocol."}],"review_version":1}