{"id":"575c5f41-4a05-4b7a-b578-b590d668679c","arxiv_id":"2607.27463","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"FADEx derives per-instance feature attributions, distortion, and directional influence for any dimensionality-reduction embedding from a locally fitted Jacobian matrix and its singular value decomposition.","lead":"FADEx explains why points land where they do in a 2D projection by fitting a local linear model to each point's neighborhood and using the SVD of the resulting Jacobian to score every original feature. It also outputs a distortion measure and directional influence arrows, and works for any dimensionality-reduction algorithm without needing to map new points.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (6)'s h_j = x_j step makes FADEx attribution scale-dependent without justification or test; the central claim that φ_j reliably ranks feature influence is therefore not yet established.","rationale":"I read the paper's central claim as: the scalar φ_j from Eq. (6) reliably ranks how much each original feature drives the placement of an instance. The most load-bearing step is the transition from the local linear model J to a per-feature scalar. The authors justify the linear model (Sec. 3.2/3.3) but the SVD-to-attribution step is under-determined. The reader's weakest_assumption identifies the same step, and I agree. I would not move the verdict: this is fixable by either standardization, a clear definition of the reference point, or validation on heterogeneous-scale synthetic data. It does not invalidate the method's other contributions (agnosticism, distortion, speed), but it does mean the headline accuracy claim is unproven for real data. Hence CONDITIONAL remains appropriate.","tokens_in":29375,"tokens_out":10258,"duration_ms":115368,"concrete_test":"On a synthetic set X∈R^{N×6} and fixed A∈R^{2×6}, set y=Ax. Run FADEx with k=N and α=0 on (X,y) and on (X'=XD, y), where D=diag(c_j) with c_j spanning 10^{-3}..10^{3} and A'=A D^{-1} (so y=A'x' and A'_{:,j}x'_j = A_{:,j}x_j for every j). Compare the top-3 φ_j rankings and, if available, the Spearman correlation with ||A_{:,j}x_j||. If the ranking changes between the two runs, Eq. (6) is not a well-defined function of the per-feature output contributions, and the scale assumption is load-bearing. If it is unchanged and matches ground truth, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on φ_j = Σ_i (λ_i/λ_1)|v_ij x_j|, introduced in Sec. 3.1 via the unstated choice h_j = x_j. This is not a neutral normalization: it says importance scales linearly with the raw feature value, and it is combined with an L1-style collapse over SVD directions rather than the actual Euclidean norm of the contribution vector A_{:,j} x_j (which would be sqrt(Σ_i λ_i^2 (v_ij x_j)^2)). The paper gives no invariance argument, no reference-point justification, and no experiment in which features have heterogeneous scales; the synthetic validation in Sec. 4.1 generates all features on the same scale, so the confound is invisible. On real data (e.g., Breast Cancer, where area is hundreds while smoothness is ~0.1), large-magnitude features can dominate the ranking even if the DR mapping is insensitive to them. The ablation test in Sec. 4.3.1 is similarly confounded because ablating high-variance features will disrupt any layout. If Eq. 6 is simply a heuristic, it must be validated against a ground truth that separates sensitivity from feature magnitude; currently the paper claims 'robust and reliable explanations' without addressing this.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"FADEx is a local feature-attribution method for explaining dimensionality reduction (DR) mappings. It estimates the Jacobian of the DR map at each instance by a weighted ridge least-squares fit over high-dimensional neighbors and their embeddings, avoiding out-of-sample mappings. The estimated Jacobian is decomposed by SVD, and the attribution score for feature j is defined as φ_j = Σ_{i=1}^d (λ_i/λ_1)|v_{ij} x_j| (Eq. 6). The same Jacobian also yields feature influence vectors (columns of the Jacobian) and a distortion metric SND (spectral norm). The authors claim that this single per-feature score is model-agnostic, requires no OOS data, is computationally efficient, and reliably identifies features that drive instance placement in the embedding. Validation includes a synthetic ground-truth experiment, comparisons with LXDR, ClusterShapley, and Corbugy, an ablation study, distortion validation against δ=d/D, and three case studies on tabular and image data.","tokens_in":29706,"tokens_out":5681,"duration_ms":61550,"significance":"If the central attribution claim holds, FADEx would be a practically valuable contribution: it is model-agnostic, avoids the out-of-sample problem that limits several DR explanation methods, assigns a single attribution per feature, and integrates attribution with distortion and directional analysis in one framework. The paper also ships an open-source implementation, which aids reproducibility. However, the central formula in Eq. (6) is an ad-hoc modeling choice that couples feature importance to raw feature magnitude. The validation evidence does not yet separate sensitivity from magnitude, and the real-data case studies use features with very different scales (e.g., Breast Cancer). Since the abstract and conclusion claim 'robust and reliable explanations,' this scale dependence is a load-bearing issue. The paper notes in Sec. 6 that explanations degrade when local PCA is unreliable, but the sensitivity of attributions to the pipeline's hyperparameters (α, PCA threshold, k) is not quantified. Thus the contribution is promising but the central claim needs additional support or a reformulated attribution rule.","major_comments":[{"comment":"The attribution formula is not derived from the Taylor expansion; it is introduced by the unstated step 'we set h_j = x_j.' This makes the importance score scale linearly with the raw feature value. The natural local-sensitivity-based measure for a perturbation along feature j would involve the norm of the j-th column of the Jacobian (e.g., sqrt(Σ_i λ_i^2 v_ij^2)|h_j|), not the L1-style weighted sum with λ_i/λ_1 and an additional factor |x_j|. Under feature rescaling x_j → c x_j, φ_j changes by |c| even when the embedding (e.g., on standardized data) is unchanged. No invariance argument, axiomatic justification, or test with heterogeneous feature scales is provided. The synthetic validation in §4.1 uses features all drawn from [0,1] with identical shift sizes, so the confound is invisible. The ablation study in §4.3.1 is also confounded: ablating high-magnitude features removes high-vari","section":"§3.1, Eq. (6)"},{"comment":"The experimental validation does not isolate sensitivity from feature magnitude. In the synthetic experiment, all ground-truth-relevant features are shifted by the same amount and initialized on the same interval, so any scale-dependent heuristic trivially recovers the 'important' features. The Jacobian approximation quality study (§3.3) only measures directional agreement of displacement vectors, not whether the estimated Jacobian's singular vectors yield correct attribution rankings. The paper should include an experiment where the ground-truth important feature has a deliberately small raw magnitude (or where features are standardized after ground truth is defined), and show that Eq. (6) still recovers it. Without such a test, Figures 3 and 6 do not establish that FADEx 'correctly identifies' the driving features beyond the same-scale scenario.","section":"§4.1 / §3.3"},{"comment":"The FADEx pipeline introduces several free parameters — Gaussian kernel scale σ (set to median distance), ridge term α=0.1, constant-feature variance threshold 10^{-6}, local PCA explained-variance threshold 0.95, and neighborhood size k (default 'roughly 10% of the dataset'). The paper acknowledges in Sec. 6 that the method's reliability depends on the PCA step, but no sensitivity analysis of the final attributions with respect to these parameters is reported. The supplementary partially analyzes k, but α and the PCA threshold are fixed without discussion. Since these are part of the method, the 'robust' claim requires at least a stability analysis over these hyperparameters, especially for high-dimensional datasets where local PCA is always applied.","section":"§3.2 / §6"}],"minor_comments":[{"comment":"The notation 'h = h_j = [0,...,0,h_j,0,...,0]' is confusing: h is used as both a vector and a scalar component. Write h = h_j e_j for clarity.","section":"§3.1"},{"comment":"The vertical red line in panel (A) is not described in the caption. Please state what it marks (the 'optimum' neighborhood size) and how it was chosen.","section":"Fig. 2"},{"comment":"The statement that FADEx is 'nearly one order of magnitude faster' than the other methods is not supported for Breast Cancer, where FADEx and Corbugy both report 0.02 s. Please qualify the claim or report full distributions.","section":"§4.3 / Table 3"},{"comment":"The 'Speed' entries 'Fast' and 'Faster' are vague; define them operationally (e.g., relative to Table 3) or remove the column.","section":"Table 1"},{"comment":"The image case study would benefit from specifying how VGG16 fine-tuning was performed (learning rate, epochs, which layers were updated) and whether the attribution maps were quantitatively evaluated or only qualitatively inspected.","section":"§5.3"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable candidate for TVCG if the authors address the scale-dependence of Eq. (6). The concern raised in the stress-test note is valid and lands on the central claim: the attribution score is not derived from the Taylor expansion but from the extra choice h_j=x_j. This is fixable within the manuscript's scope, either by adding a justified normalization/invariance axiom or by adding experiments with heterogeneous feature scales and a sensitivity-only baseline. I would also ask the authors to temper the 'robust and reliable' wording until the hyperparameter sensitivity is assessed. The code release and the ablation comparison are strengths."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Honestly, this paper has more substance than the usual DR-explainability submission. FADEx combines local Jacobian estimation via weighted ridge regression, an SVD-based single per-feature attribution, a distortion metric, and feature influence vectors in one model-agnostic framework. It does not need out-of-sample mappings, which makes it usable with t-SNE and UMAP, and it comes with open-source code. The synthetic experiment with three clusters and known ground-truth features gives the expected diagonal block structure, and the ablation study shows that FADEx-ranked features disrupt cluster structure as much as ClusterShapley's. That is real evidence of usefulness.\n\nThe main soft spot is exactly where the stress test lands. Equation (6) defines phi_j = sum_i (lambda_i/lambda_1) |v_ij x_j|, and the paper arrives at this by setting h_j = x_j with no justification. That is a modeling choice, not a derivation: it makes the attribution scale linearly with raw feature magnitude. On a dataset like Breast Cancer, where area is hundreds and smoothness is ~0.1, the score can be dominated by large-magnitude features even if the DR map ignores them. The paper never tests this. The synthetic data is generated with features on a common scale, so the confound never shows. The ablation test is similarly confounded: removing high-variance features will disrupt any layout, so that experiment does not isolate sensitivity from magnitude.\n\nThis is not a rejection-level flaw. The local-linear approximation itself is sound, and the paper validates it with a sensible hold-out cosine similarity protocol. The fix is feasible: standardize features or give a principled reason for h_j = x_j, and then rerun the ablation on data with heterogeneous feature scales. Also, several headline numbers (the Fig. 5 silhouette scores, for example) have no error bars, so the 'robust and reliable' claim is overstated.\n\nThis is a conditional accept. The method is new enough, the code is there, and the empirical evidence, while incomplete, is not fabricated. The paper deserves a serious referee and probably a revision.","headline":"A genuinely useful DR explanation framework with a real scale-dependence problem in its core attribution score; worth reviewing carefully.","tokens_in":30166,"tokens_out":3077,"would_cite":true,"duration_ms":28058,"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":"FADEx gives every original feature a single importance score per instance, explaining why a dimensionality-reduction method places each point where it does — using only the already-computed embedding, with no need to rerun the DR algorithm.","keywords":["feature attribution","dimensionality reduction explainability","Jacobian estimation","singular value decomposition","local linear approximation","t-SNE","UMAP","distortion metric"],"falsifier":"Construct a dataset with two features of very different scales whose true DR mapping depends only on the small-scale feature, compute FADEx attributions, and check whether the large-scale feature still receives the higher score. Simpler: rerun FADEx after rescaling every feature to unit variance and see whether the per-instance ranking changes; if it does, Eq. (6)'s dependence on raw |x_j| is driving the result rather than the mapping's actual sensitivity.","tokens_in":29271,"feed_emoji":"📍","tokens_out":11065,"duration_ms":102754,"temperature":0.7,"pith_summary":"FADEx sets out to make any dimensionality-reduction embedding explainable at the level of individual points and features. The idea is to approximate the DR mapping around each point by a local linear map — a Jacobian — fit with weighted least squares to the point's nearest neighbors and their known projections, so the method never has to rerun t-SNE, UMAP, Isomap, or LLE on new samples. A singular value decomposition of that local operator yields one attribution score per feature, a measure of local stretching or shrinking, and directional influence vectors, all from the same computation. If the method works as claimed, an analyst can ask not just where an embedding puts a point, but which original features put it there and how much the projection distorts the neighborhood. The paper supports the claim with synthetic ground-truth data, ablation tests against other attribution methods, and case studies, arguing FADEx matches or beats cluster-based and gradient-based alternatives while being faster and model-agnostic.","feed_headline":"One score per feature explains why points land where they do","feed_subtitle":"FADEx reads local linear structure, needs no rerun of t-SNE or UMAP, and maps distortion per point.","key_machinery":"Load-bearing is the estimated Jacobian Ĵ_M(x) — the local linear map of the DR transformation at each point — fitted with Gaussian-weighted ridge least squares (Eq. 11) over displacement pairs of neighbors, in the original and projected spaces. Its SVD, Ĵ = UΣV^T, splits the local map into projection directions v_i, singular-value scalings λ_i, and output directions u_i. The attribution φ_j = Σ_i (λ_i/λ_1)|v_{ij} x_j| reads feature j's importance off the right singular vectors, normalized by the dominant singular value and weighted by the raw feature value x_j; the operator's columns are the Feature Influence Vectors; and the spectral norm λ_1 is the SND distortion score. One operator carrie","core_discovery":"The central claim is that a single scalar per feature, φ_j = Σ_i (λ_i/λ_1)|v_{ij} x_j|, computed from the SVD of a locally estimated Jacobian, captures how much each original feature drives an instance's placement in a DR embedding. That Jacobian is fitted by Gaussian-weighted ridge least squares over each point's neighbors and their known embeddings, removing the need for out-of-sample mapping and making the method agnostic to the DR algorithm. The same operator's columns yield the Feature Influence Vectors and its largest singular value yields the SND distortion score — attribution, distortion, and directional analysis from one computation. Ablation tests argue the scores are load-bearing:","pith_inferences":["The attribution multiplies sensitivity by the raw feature value |x_j|, so on data with features on different scales the ranking may reflect feature magnitudes rather than the mapping's true sensitivity; rescaling features to a common scale before computing φ_j is a natural variant the paper neither tests nor discusses.","The Dry Bean case study finds strong agreement in feature importance across t-SNE, UMAP, Isomap, and LLE (Spearman 0.65–0.84); if that agreement is general, FADEx scores on a fixed dataset could predict which features any DR method will rely on — a claim the paper leaves open.","As the paper notes in its limitations, when local PCA does not reduce dimensionality without distorting neighborhood structure, the estimated Jacobian and everything derived from it inherit that error; the method's reliability is therefore conditioned on neighborhoods being locally reducible.","The Feature Influence Vectors are, in effect, a per-feature displacement field; they could power an interactive perturb-and-see tool — or a test of attribution stability across random restarts of stochastic DR methods — neither of which the paper builds."],"forward_implications":["FADEx explains any embedding produced by any DR method, including t-SNE and UMAP, which cannot map out-of-sample points; only the original data and its embedding are required.","Each feature receives exactly one attribution per instance, avoiding the two-scores-per-feature ambiguity of dimension-wise surrogate models and the per-cluster scores of cluster-based Shapley methods.","Ablating FADEx's top-ranked features degrades cluster structure in UMAP and t-SNE layouts far more than random ablation, and comparably to methods that use predefined clusters, indicating the scores mark features the embedding actually depends on.","The SND distortion score — the local operator's largest singular value — correlates with an established distance-preservation ratio across datasets, giving a per-point expansion/shrinkage map at no extra computational cost.","Per-instance explanations are about an order of magnitude faster and more memory-efficient than the compared methods on larger datasets, making the analysis practical at scale."],"fun_headline_variants":["One score per feature explains DR placements","Attribution and distortion from one SVD","Local Taylor trick explains any DR method","Per-feature scalar keys to t-SNE and UMAP","FADEx: one score tells why points land"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"Equation (6) assumes a feature's importance scales with its raw value: the sensitivity terms v_{ij} are multiplied by x_j, so on features with different units or scales the attribution can be dominated by large-magnitude features even when the DR mapping barely uses them — a modeling choice the paper makes without testing.","fun_headline_variants_meta":{"raw":{"variants":["One score per feature explains DR placements","Attribution and distortion from one SVD","Local Taylor trick explains any DR method","Per-feature scalar keys to t-SNE and UMAP","FADEx: one score tells why points land"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000114,"raw_usage":{"total_tokens":936,"prompt_tokens":806,"completion_tokens":130,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":60}},"tokens_in":550,"tokens_out":130,"duration_ms":2524,"temperature":1.0,"reasoning_tokens":60,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T07:33:26.758201+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a dataset with two features of very different scales whose true DR mapping depends only on the small-scale feature, compute FADEx attributions, and check whether the large-scale feature still receives the higher score. Simpler: rerun FADEx after rescaling every feature to unit variance and see whether the per-instance ranking changes; if it does, Eq. (6)'s dependence on raw |x_j| is driving the result rather than the mapping's actual sensitivity.","supporting_citations":[],"review_version":1}