{"id":"444ee833-f7f3-4f94-ad47-dd21579a3fae","arxiv_id":"2502.02279","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"PDisVAE replaces the total-correlation penalty with a group-wise partial-correlation penalty, letting VAEs learn independent groups of entangled latent factors.","lead":"This paper introduces PDisVAE, a variational autoencoder that penalizes dependence between groups of latent variables instead of requiring every latent dimension to be independent. It replaces the total-correlation term with a partial-correlation term that reduces to standard VAE or fully disentangled VAE at the extremes, with synthetic and real-world tests.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"User-supplied (G,H) is the load-bearing assumption: the PC penalty in Eq. (6) enforces independence relative to a chosen group partition, yet no experiment tests misspecified group counts, and Section 5.2 admits there is no guidance for choosing them.","rationale":"The reader's weakest assumption identifies exactly the concern I consider most load-bearing: the user must supply the number of groups G and group rank H, and Eq. (4) defines groups as contiguous coordinate blocks. My reading of the paper confirms that this choice is what determines the target independence pattern, and Section 5.2 admits there is no guidance or automatic selection. I considered whether a more technical objection was available, such as the circularity of evaluating with the same PC objective or the overbroad logcosh-novelty claim. The circularity is real but not decisive, because the synthetic experiments also report latent R2 after alignment, which is independent of the PC objective. The batch approximation derivation in Appendix A.3 appears internally consistent and the IS estimator is unbiased. The logcosh novelty claim is tangential to the main contribution. I also considered the absence of an identifiability theorem, but the paper's central claim is primarily empirical and the synthetic oracle experiments do provide some support; the missing robustness-to-misspecification evidence is a sharper gap. Since the reader already returned CONDITIONAL and my concern is the same one, no verdict adjustment is needed. The concrete test I propose would settle whether the concern actually lands: if wrong (G,H) configurations still recover the true groups with high latent R2, the method is more flexible than the concern assumes; if they collapse, the central claim genuinely depends on oracle knowledge of the latent group structure.","tokens_in":1171,"tokens_out":1112,"duration_ms":100384,"concrete_test":"Run the Section 4.1 synthetic generator (true latent K=6, G=3, H=2, known linear map to D=20 with Gaussian noise) and train PDisVAE for every admissible configuration with K=6: (G,H) = (1,6), (2,3), (3,2), (6,1), using the same beta, optimizer, and number of seeds as the paper. Report PC and latent R2 after Procrustes alignment to the true latents for each configuration. The concern lands if only the oracle (3,2) configuration achieves high latent R2 and low PC, while wrong configurations achieve low PC but markedly lower latent R2; the concern is weakened if PDisVAE recovers the correct grouping even from misspecified G/H, e.g., by detecting dummy dimensions as in Appendix A.4.3. To test rank mismatch separately, also run K=4 with (G,H)=(2,2) on the same true K=6 data and check whether the method either degrades gracefully or forces an incorrect union/split of true groups.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that PDisVAE enforces group-wise independence flexibly and, on partially entangled data, recovers latent groups more accurately than fully disentangled VAEs and ISA-VAE. What must be true for that claim to hold is that the user can supply a group configuration (G, H, with K = G x H) that is compatible with the true latent structure. The objective in Eq. (6) is defined relative to a specific partition of the latent coordinates into G contiguous blocks. If G or H is wrong, the penalty enforces the wrong independence pattern: the model can drive PC to zero by making the chosen groups independent, even when that grouping is not the true one, e.g., by splitting a true group across two supplied groups or by using dummy near-Gaussian dimensions to satisfy an oversized group rank. Thus a low PC value is not by itself evidence that the recovered grouping is correct. The paper's strongest quantitative evidence is the synthetic experiment in Section 4.1, where the true structure (K=6, G=3, H=2) is known and PDisVAE is run with the oracle configuration. The pdsprites experiment similarly fixes K=4, G=2, H=2 to match the assumed (z1,z2) and (z3,z4) grouping. No synthetic experiment varies G or H away from the true values while measuring latent R2, so the method's advertised flexibility under realistic misspecification is untested. Section 5.2 explicitly concedes that 'we may not have guidance on this information' and defers automatic group-rank reduction to future work. Because the group configuration is not a nuisance hyperparameter but defines the very independence structure being learned, this is the least secure link in the argument. The self-referential PC metric is a secondary concern, but it is partially mitigated by the independent latent R2 results on synthetic data; the batch estimator also appears unbiased, so no attack is needed there. The unaddressed sensitivity to (G,H) is the load-bearing issue.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes PDisVAE, a variational auto-encoder objective that replaces the total correlation (TC) penalty in fully disentangled VAEs with a partial correlation (PC) penalty, KL(q(z) || ∏_g q(z_g)), defined with respect to a user-specified partition of the latent space into G groups of rank H (Eq. 6). The objective reduces to the standard VAE when G=1 and to a TC-penalized VAE when G=K. The paper also introduces an importance-sampling batch approximation for estimating PC/TC, claims it is unbiased and lower-variance than minibatch stratified sampling, and validates PDisVAE on synthetic group-wise independent data, a partially entangled dsprites variant, CelebA, and mouse voltage imaging data. The central claimed contribution is a flexible, penalty-based way to enforce group-wise independence that can also accommodate dummy latent dimensions within groups.","tokens_in":18853,"tokens_out":7211,"duration_ms":75699,"significance":"If the central claim holds, PDisVAE is a natural and potentially useful generalization of TC-based disentanglement, and the reduction property (G=1 and G=K) is elegant. The paper gives real evidence for the core mechanism: in synthetic experiments with known ground truth, PDisVAE achieves higher latent R2 than VAE, logcosh ICA, ISA-VAE, and beta-TCVAE, and the full-independence experiment in Appendix A.4.3 shows that PDisVAE can reduce to a fully disentangled solution when the true rank is deficient. The importance-sampling estimator, if correctly analyzed, would also be a practical contribution. However, the advertised flexibility is tested only under oracle group configurations, and the optimality claim for the estimator is not rigorously supported, so the strength of the contribution is currently below what the paper claims.","major_comments":[{"comment":"The flexibility of PDisVAE is demonstrated only under oracle group configurations. Equation (4) fixes a partition into G contiguous blocks of equal rank H, and every controlled experiment uses the true (K,G,H): K=6, G=3, H=2 in Section 4.1; K=4, G=2, H=2 in Section 4.2; and K=6, G=3 with true underlying K=3 in Appendix A.4.3. No experiment varies G or H away from the true values, and Section 5.2 explicitly concedes that 'we may not have guidance on this information.' This matters because, with a misspecified partition, the PC penalty can be minimized by a wrong grouping, for example by splitting one true group across two supplied groups or by placing a dummy near-Gaussian dimension in an oversized group, so a low PC value alone would not certify that the recovered grouping is correct. I ask for misspecification experiments with over- and under-specified G, unequal true group ranks, and non-contiguous true groups, with latent R2 as the primary metric; these experiments are needed to support the paper's central flexibility claim.","section":"Sections 4.1, 4.2, 5.2"},{"comment":"The PC metric used as a headline comparison is the same objective that PDisVAE minimizes, so comparisons on PC are partly circular; beta-TCVAE minimizes TC, not PC, and standard VAE does not minimize either. The paper does provide independent evidence through latent R2 against known true latents in the synthetic experiments, and that is the strongest part of the empirical support. To avoid the appearance of circularity, the paper should present PC as a diagnostic of the objective and make latent R2 (or another equally independent metric such as MIG) the primary basis for cross-method claims, especially because the real-world conclusions in Section 4.3 are qualitative and are not supported by repeated-seed statistics.","section":"Fig. 2(b), Table 5"},{"comment":"The optimality claim for the IS batch estimator is not established. The variance comparison computes the variances of the inverse importance weight sets IS0 and MSS0, not the variances of the estimators \\hat q(z); the latter depend on the conditional densities q(z|n), which are not constant across n, and on the distribution of the sampled latent z. The paper also announces a 'theoretical proof of its optimality' in Section 3.5, but no minimization over proposal distributions appears in the appendix. Either provide a correct variance bound for the actual estimator, or revise the claim to state only that the estimator is unbiased and has lower weight variance than MSS.","section":"Appendix A.3, Eqs. (17)-(19)"},{"comment":"The real-world experiments on CelebA and mouse voltage imaging are used to support the versatility claim, but they are presented through selected qualitative reconstructions and brain maps, with no repeated seeds, no quantitative comparison across group configurations, and no uncertainty quantification. Since these data have no ground-truth latent structure, the 'valuable information' claim is difficult to verify, and the text's own Section 5.1 acknowledges that semantic-statistical correspondences cannot be rigorously certified. Please either add quantitative, replicated comparisons or explicitly mark Section 4.3 as exploratory illustration rather than validation.","section":"Section 4.3"}],"minor_comments":[{"comment":"The word 'expecially' should be 'especially'.","section":"Section 5.2"},{"comment":"The name 'β-BTCV AE' in Section 4.2 is inconsistent with the 'β-TCVAE' notation used elsewhere, and Fig. 14's caption says 'fully entangled VAE' where it appears to mean 'fully disentangled VAE'.","section":"Section 4.2 and Fig. 14"},{"comment":"The 'adapted mutual information gap (MIG)' is not defined; please specify how it is computed and over how many seeds the means and standard deviations are reported.","section":"Table 5"},{"comment":"The horizontal axis labels in Fig. 6 are rendered as '100 102' and should be displayed as powers of 10.","section":"Fig. 6"},{"comment":"In the related-work discussion, the sentence 'This approach has been proven to be worse than β-VAE and FactorVAE' is likely missing a 'TC' qualifier and is confusing as written.","section":"Appendix A.1"},{"comment":"Reference [9] (Bhowal et al.) lacks a year and venue, and reference [10] (Hsu et al.) would benefit from the full publication venue; also, the appendix says 'see code for details' but no code repository URL is provided.","section":"References"},{"comment":"The empirical evaluation of the batch estimators reports variances over 1000 repeats for a toy 10-point dataset, but the text does not specify how the 'true' TC/PC value is computed or why the empirical variance of IS is lower than MSS; a short explanation would improve reproducibility.","section":"Appendix A.3.3"}],"recommendation":"major_revision","confidential_remarks":"The central objective in Eq. (6) is a clean and defensible generalization, and the synthetic latent-R2 evidence is genuinely informative. My main reservations are that the flexibility claim is not tested under misspecified group counts and that the IS optimality proof is incomplete; both are fixable within the scope of a revision. I do not see grounds for rejection, but the manuscript's current claims overstate the evidence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The core idea is simple and clean: replace the TC penalty in beta-TCVAE with KL(q(z) || prod_g q(z_g)), giving group-wise independence that reduces to standard VAE at G=1 and to fully disentangled VAE at G=K. The IS batch estimator derived in Appendix A.3 is a genuine contribution—it is unbiased, provably lower variance than MSS, and the derivation is rigorous. The synthetic experiments with known ground truth back the core mechanism: PDisVAE gets higher latent R2 after alignment than beta-TCVAE, ISA-VAE, ICA, and VAE. That is independent evidence, not just the training loss.\n\nThe soft spots. The load-bearing assumption is the user-supplied (G,H): the penalty enforces independence relative to a specific contiguous partition, and no experiment varies G or H away from the true values while measuring latent R2. The paper explicitly concedes in Section 5.2 that there is no guidance for choosing the number of groups. That is not a minor nuisance hyperparameter; it defines the independence structure being learned. If the supplied partition is wrong, a low PC value does not mean the recovered grouping is correct. The paper's own counterexample (Section 3.1) shows marginal pairwise independence is not sufficient, which makes the sensitivity to the group partition even more salient. Second, the PC metric used in headline comparisons (Fig. 2b, Table 5) is the same quantity being minimized, so part of the reported advantage is circular. The latent R2 results mitigate this, but the real-world neural and CelebA results are qualitative and lack repeated-seed error bars. Minor: the claim of being 'first to recognize the logcosh-priored VAE as nonlinear ICA' is overbroad given existing nonlinear ICA literature, and no code or data is released despite a 'see code' reference.\n\nOverall, this is a solid within-subfield paper with a real formal component (the IS estimator) and honest synthetic validation. The central argument holds up insofar as the oracle group configuration is provided. Who it is for: practitioners and researchers working on disentangled representation learning, especially those applying VAEs to neural data where group-wise structure is plausible. It deserves a serious referee; the main revision should confront the (G,H) sensitivity head-on—either with misspecification experiments or with a clearly scoped claim that the method assumes a known compatible grouping. I would send it to review.","headline":"A clean PC generalization of TC-VAE with a solid IS batch estimator and honest synthetic evidence, but the user-supplied group configuration is load-bearing and its misspecification is never tested.","tokens_in":19441,"tokens_out":2539,"would_cite":true,"duration_ms":23419,"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":"A variational auto-encoder can enforce group-wise independence of latent factors by replacing total correlation with partial correlation, recovering entangled groups that full disentanglement misses and reducing to standard VAE at one…","keywords":["partial disentanglement","variational auto-encoder","total correlation","partial correlation","group-wise independence","importance sampling batch approximation","independent component analysis","disentangled representation learning"],"falsifier":"Generate synthetic data with true group-wise independence $(z_1,z_3) \\perp (z_2,z_4)$ and train PDisVAE with $G=2$, $H=2$ using the contiguous groups $(z_1,z_2)$ and $(z_3,z_4)$. The paper's formulation assumes groups are contiguous blocks, so it predicts the partial correlation cannot be driven to zero; observing it driven to zero would show the penalty is more flexible than its derivation, while observing it remain high would confirm the contiguous-block limitation.","tokens_in":18291,"feed_emoji":"🧩","tokens_out":10111,"duration_ms":87303,"temperature":0.7,"pith_summary":"The paper develops PDisVAE, a variational auto-encoder that replaces the total correlation (TC) penalty—which forces all K latent dimensions to be independent—with a partial correlation (PC) penalty that forces only user-specified groups of dimensions to be independent. The PC term is the KL divergence between the aggregated posterior q(z) and the product of group marginals; it vanishes exactly when groups are independent and leaves within-group dependence untouched. The authors argue that on data where factors are entangled in non-separable ways, this is the right prior, and they show that the method reduces to the standard VAE when there is one group and to a fully disentangled VAE when each group is a single dimension. They further derive an importance-sampling batch estimator for TC and PC and prove it has lower variance than the existing minibatch stratified sampling estimator.","feed_headline":"VAE penalty recovers latent groups full disentanglement misses","feed_subtitle":"Partial correlation between groups, not within them, matches data where factors entangle non-separably.","key_machinery":"The machinery is the partial correlation (PC) term, $\\mathrm{PC} = \\mathrm{KL}\\big(q(z) \\,\\|\\, \\prod_{g=1}^G q(z_g)\\big)$, a generalization of total correlation ($\\mathrm{TC} = \\mathrm{KL}(q(z) \\| \\prod_{k=1}^K q(z_k))$). Added to the ELBO with weight $\\beta$, it drives the aggregated posterior $q(z) = \\frac{1}{N}\\sum_n q(z|x^{(n)})$ to factorize across groups while permitting arbitrary dependence inside each group. The second piece is an importance-sampling (IS) batch estimator that replaces the minibatch weighted and stratified sampling estimators used in earlier TC-VAEs: when a latent $z$ is drawn from a specific example's posterior, the other $M-1$ batch points are reweighted to represent the rest of the dataset. The paper proves the IS estimator is unbiased with variance $(N-M)^2/(M^2(M-1))$, which is strictly smaller than the MSS estimator's variance for $M>2$.","core_discovery":"The central claim is that optimizing a VAE objective with the additional penalty $-\\beta \\, \\mathrm{KL}(q(z) \\| \\prod_{g=1}^G q(z_g))$ enforces group-wise independence of the latent representation. For $G=1$ the penalty is identically zero and the objective is the standard VAE; for $G=K$ it is exactly the TC penalty, so the fully disentangled VAE appears as a special case. In synthetic experiments with three independent but internally entangled latent groups, PDisVAE attains lower partial correlation and higher latent recovery $R^2$ than standard VAE, logcosh-prior ICA, ISA-VAE, and $\\beta$-TCVAE. On the partial-dsprites dataset, PDisVAE is the only method whose groups align with the true entangled location group and the independent size factor; on CelebA it expresses attributes such as background color as multi-dimensional manifolds rather than forced one-dimensional codes, and on voltage imaging data a six-group configuration separates cortical regions more clearly than full disentanglement.","pith_inferences":["Outside the paper's setup, the same PC penalty could be attached to any VAE-style objective that uses an aggregated posterior, and the variance comparison suggests existing TC-based VAEs could improve stability by switching to the IS estimator.","The contiguous-coordinate-block definition of groups (Eq. 4) is a real constraint; if true latent groups interleave coordinates, a learned permutation or grouping layer would be needed, and the paper gives no guidance there.","The rank-deficiency experiments imply a simple automatic-group-selection heuristic: monitor within-group PCA explained variance or Gaussianity to trim $H$ during training, which the paper explicitly leaves to future work.","The semantic-vs-statistical discussion suggests that even when a single semantic label exists, it may live in a group of several latent dimensions; evaluating disentanglement by matching one dimension to one label could systematically misjudge group-based methods."],"forward_implications":["On synthetic data with three independent rank-2 groups, PDisVAE recovers the true latent structure with lower partial correlation and higher latent $R^2$ than VAE, ICA, ISA-VAE, and $\\beta$-TCVAE.","PDisVAE automatically handles rank deficiency: if a group's true rank is below $H$, it learns dummy components, so it reduces smoothly to full disentanglement when the data are fully independent.","The importance-sampling batch estimator is unbiased and has lower variance than minibatch stratified sampling, which should make TC and PC penalties more stable during training.","On CelebA, grouping dimensions allows attributes like background color to be represented by a 2D or 3D manifold, which a fully disentangled single-component code cannot express.","On mouse dorsal cortex voltage imaging, a six-group configuration separates cortical regions (S1-bf, M2-m, M1) into independent groups more clearly than coarser or fully disentangled configurations."],"supporting_citations":[{"why":"Defines the total-correlation penalty and the minibatch weighted/stratified batch estimators that PDisVAE's PC term generalizes and its IS estimator improves.","marker":"Chen et al., 2018"},{"why":"FactorVAE, the penalty-based fully disentangled baseline that PDisVAE extends to groups.","marker":"Kim & Mnih, 2018"},{"why":"Introduced the beta-VAE penalty from which the TC interpretation grew.","marker":"Higgins et al., 2017"},{"why":"ISA-VAE, the prior-based group-wise independence baseline that PDisVAE compares against and argues is too rigid.","marker":"Stühmer et al., 2020"},{"why":"Source of the 'non-Gaussian is independent' ICA baseline used as a comparison method.","marker":"Hyvärinen & Oja, 2000"},{"why":"Defines the aggregated posterior q(z) used to compute TC and PC.","marker":"Makhzani et al., 2015"},{"why":"Provides the understanding of beta-VAE disentanglement and the image CNN architecture used in experiments.","marker":"Burgess et al., 2018"},{"why":"Supports the motivation that unsupervised full disentanglement is fundamentally hard, motivating the weaker group-wise assumption.","marker":"Locatello et al., 2019"}],"fun_headline_variants":["Group-wise VAE penalty uncovers latent groups full TC misses","Partial disentanglement: VAE relaxes independence to groups","PDisVAE: group independence beats full disentanglement","When factors entangle, VAE with partial correlation wins"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method presupposes that the user knows the number of latent groups G and the group rank H (with K = G × H), that the true latent structure can be expressed by contiguous coordinate blocks, and that the chosen partition matches that structure; the paper states in Section 5.2 that there is no guidance for this choice and automatic group-rank reduction is left to future work.","fun_headline_variants_meta":{"raw":{"variants":["Group-wise VAE penalty uncovers latent groups full TC misses","Partial disentanglement: VAE relaxes independence to groups","PDisVAE: group independence beats full disentanglement","When factors entangle, VAE with partial correlation wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001167,"raw_usage":{"total_tokens":4823,"prompt_tokens":936,"completion_tokens":3887,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":552,"completion_tokens_details":{"reasoning_tokens":3819}},"tokens_in":552,"tokens_out":3887,"duration_ms":28588,"temperature":1.0,"reasoning_tokens":3819,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T12:41:02.254038+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate synthetic data with true group-wise independence $(z_1,z_3) \\perp (z_2,z_4)$ and train PDisVAE with $G=2$, $H=2$ using the contiguous groups $(z_1,z_2)$ and $(z_3,z_4)$. The paper's formulation assumes groups are contiguous blocks, so it predicts the partial correlation cannot be driven to zero; observing it driven to zero would show the penalty is more flexible than its derivation, while observing it remain high would confirm the contiguous-block limitation.","supporting_citations":[{"cited_title":"The only difference between these two papers is their implementations of minimizing TC","cited_arxiv_id":null,"evidence_quote":"Defines the total-correlation penalty and the minibatch weighted/stratified batch estimators that PDisVAE's PC term generalizes and its IS estimator improves."},{"cited_title":"However, the choice of the non-Gaussian prior is critical and might be too rigid, hurting the flexibility of the method","cited_arxiv_id":null,"evidence_quote":"Source of the 'non-Gaussian is independent' ICA baseline used as a comparison method."},{"cited_title":"This approach has been proven to be worse than β-V AE and FactorV AE","cited_arxiv_id":null,"evidence_quote":"Provides the understanding of beta-VAE disentanglement and the image CNN architecture used in experiments."},{"cited_title":"This also gives us a hint that full disentanglement might be a strong and inappropriate assumption and could result in poor latent interpretation","cited_arxiv_id":null,"evidence_quote":"Supports the motivation that unsupervised full disentanglement is fundamentally hard, motivating the weaker group-wise assumption."}],"review_version":1}