{"id":"8ac92395-4e13-4878-be9b-c2411fc89e74","arxiv_id":"2509.02084","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"CIML combines a Gács-Körner-style common-representation objective with per-view information-bottleneck unique representations and independence constraints, reporting state-of-the-art accuracy on six multi-view datasets.","lead":"The paper proposes CIML, a multi-view learning framework that learns both shared and view-unique representations using information-bottleneck objectives and a squared-error objective it calls Gács-Körner common information. The authors report accuracy improvements on six datasets, but the proposed theoretical guarantee is not actually proven.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (B7) assumes additive mutual information across independent components; the proof gives no argument against synergistic label dependence, so predictive sufficiency (Thm 3.1) is unproven.","rationale":"The reader identified exactly the weakest step. The paper's central novel contribution is the proof of predictive sufficiency; without it, the framework is an ad hoc combination of IB and independence penalties. The empirical results are not enough to establish the theoretical claim, especially given zero-variance perfect accuracy on MSRC-v1, but the proof flaw is the load-bearing issue. The additivity assumption is not just a technical gap; it is mathematically false in general, and the training objective does not enforce the required condition. Thus the theoretical guarantee is unsupported. The suggested test would settle whether an additional assumption (e.g., no synergy) is needed; if the authors can prove Eq. (B7) under a reasonable stated condition, a conditional acceptance might be possible, but no such condition is present in the manuscript.","tokens_in":17553,"tokens_out":3196,"duration_ms":35331,"concrete_test":"Independently re-derive Eq. (B7) from the stated constraints. Concretely, simulate the exact independence conditions by drawing Zc~Bern(0.5), Zu1~Bern(0.5), and set Y=Zc XOR Zu1 (add Zu2 if v>2). Compute I(Zc;Y)+I(Zu1;Y) vs I(Zc,Zu1;Y); they are 0 and 1 bit. If the discrepancy persists, Eq. (B7) is not a consequence of the model's penalty terms. Optionally, train CIML on this synthetic view/label pair and check whether H(Y|Z) approaches H(Y|X); the proof predicts it should, but the XOR counterexample shows the information-theoretic inequality fails without an additional non-synergy assumption.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Appendix B's proof of predictive sufficiency hinges on the decomposition I(Zc,Zu1..;Y) ≈ I(Zc;Y)+ΣI(Zu_i;Y) in Eq. (B7). This additivity is the load-bearing step. The preceding independence penalties (Eq. 12) ensure only pairwise independence among unique representations and between unique and common; they do not imply that Y's dependence on the joint representation decomposes as a sum. Pairwise independence does not rule out synergistic information: if Y = Zc XOR Zu1 with Zc, Zu1 independent Bernoulli(0.5), then I(Zc;Y)=I(Zu1;Y)=0, yet I(Zc,Zu1;Y)=1 bit. Eq. (B4) is also invalid: I(Zu1,..;Y|Zc) ≠ Σ I(Zu_i;Y|Zc), and independence of Zc and Zu does not make the conditional MI equal the marginal (the same XOR example gives 1 bit vs 0). Since Eq. (B7) is assumed rather than derived, Theorem 3.1's conclusion H(Y|Z)≈H(Y|X) does not follow from the training objective. The theorem's statement is close to a restatement of approximate sufficiency; the proof is what carries the claim, and it fails at this step.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes CIML, a multi-view representation learning method that explicitly models both shared information across views and view-specific information. The common representation is learned by maximizing a heuristic Gács-Körner (GK) common-information objective followed by an information-bottleneck compression step; the unique representations are learned via IB objectives penalized by mutual information terms that encourage pairwise independence among unique representations and between unique and common representations. The central advertised result is Theorem 3.1, which claims that the concatenated joint representation Z=(Zc,Zu^1,...,Zu^v) is predictively sufficient for target Y. Experiments are reported on six datasets against a number of existing multi-view methods, together with ablation, hyperparameter, convergence, and visualization analyses. The main theoretical claim is, however, not established by the proof in Appendix B, and the GK interpretation of Eq. (1) is asserted rather than derived.","tokens_in":17983,"tokens_out":3532,"duration_ms":43318,"significance":"The motivation is timely: relaxing the multi-view redundancy assumption and treating unique information as predictive is an active research problem, and the proposed framework is modular enough to be of interest if its claims were sound. Strengths include the explicit common/unique decomposition, ablations, parameter sensitivity analysis, and release of code. However, the advertised predictive-sufficiency theorem is the paper’s main conceptual contribution, and the proof in Appendix B assumes the additivity that the theorem needs to show. The connection between Eq. (1) and Gács-Körner common information is also not justified. These are load-bearing issues rather than presentation defects. If the proof could be repaired under explicit nontrivial assumptions, the framework would be worth revisiting, but the manuscript as written does not provide a valid theoretical guarantee.","major_comments":[{"comment":"The proof’s load-bearing step is the assertion that, under the independence constraints, I(Zu^1,...,Zu^v; Y | Zc) ≈ Σ_i I(Zu^i; Y | Zc) ≈ Σ_i I(Zu^i; Y). This is false in general. Pairwise or even mutual independence among Zc and the Zu^i does not imply that their mutual information with Y decomposes additively, nor does it make the conditional mutual information equal to the marginal. A standard counterexample is Y = Zc XOR Zu^1 with Zc and Zu^1 independent Bernoulli(1/2): I(Zc;Y)=I(Zu^1;Y)=0 but I(Zc,Zu^1;Y)=1 bit, and I(Zu^1; Y | Zc)=1 bit. Thus Eq. (B5) is not a consequence of the training constraints.","section":"Appendix B, Eqs. (B4)–(B5)"},{"comment":"Even if Eq. (B5) were granted, Eq. (B7) states that I(Zc;Y) + Σ_i I(Zu^i;Y) ≈ I(X;Y). This is essentially the conclusion to be proven: it asserts that the joint representation retains approximately all predictive information from the original views. The training objectives in Eqs. (10)–(17) do not force this equality; the independence penalties at most enforce pairwise independence, and the IB terms are variational lower bounds. The theorem therefore reduces to an assumption about the learned representation rather than a guarantee, and its statement is close to tautological ('Z approximately determines Y if Z approximately determines Y').","section":"Appendix B, Eq. (B7)"},{"comment":"The paper claims that maximizing H(C) − Σ_i ||fi(X^(i)) − C||^2 realizes Gács-Körner common information. This is not demonstrated. GK common information is a zero-error notion based on common randomness reconstructable from each source; an l2 reconstruction discrepancy does not by itself correspond to maximizing the entropy of a common part. No derivation, theorem, or reference in the manuscript establishes this equivalence. Since the common-representation module is a central component of the framework, the connection needs to be made precise or the claim should be weakened.","section":"Section III-B, Eq. (1)"},{"comment":"The experimental protocol is not sufficiently rigorous to support the claimed superiority. Hyperparameters β3 and β4 are tuned over predefined sets to 'achieve optimal performance' on the same datasets used for final reporting, with no validation split described and no significance tests. In such a setup, the reported gains (e.g., 100.00±0.00 on MSRC-v1) may reflect selection on test performance. A proper train/validation/test protocol and statistical comparison are needed before the empirical claims can be accepted.","section":"Section IV-A and IV-B"}],"minor_comments":[{"comment":"Step 7 says 'Calculate unique representation loss Lu by Eq. (18)', but the unique loss is in Eq. (17); Eq. (18) is the cross-entropy loss.","section":"Algorithm 1, Step 7"},{"comment":"Typographical errors include 'accouts', 'minmizing', 'uniqe', and 'down-steam'. 'NoisyMINST' in Table II and in the Section IV-B heading is inconsistent with 'NoisyMNIST' used elsewhere.","section":"Throughout"},{"comment":"The notation “Σ_{j=k}” in the second displayed line should presumably be “Σ_{k=1}”.","section":"Equation (9)"},{"comment":"The figure captions are confusing: Fig. 4 appears to have duplicated subcaptions, and the caption lists multiple '(a)–(f)' blocks. Please clarify which panels refer to Zc and which to Zu.","section":"Figures 2–4"}],"recommendation":"reject","confidential_remarks":"The paper’s central theoretical claim is not proven and, as stated, is close to a restatement of the objective. The experimental section lacks a validation protocol. These are core issues rather than local fixes. I would be open to reconsidering a substantially revised version with an explicit and non-tautological theoretical statement, a valid proof or clearly stated assumptions, and a properly designed experimental evaluation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe bottom line: the paper's central theoretical claim—predictive sufficiency of the joint (common + unique) representation—is not proven. Appendix B steps from the training objective to the theorem by assuming the very additivity the objective is meant to enforce. Specifically, Eq. (B7) assumes I(X;Y) ≈ I(Zc;Y) + Σ I(Zu^i;Y). That requires that the unique representations, even if pairwise independent of each other and of Zc, carry no synergistic information about Y. That is false in general—XOR is the standard counterexample. The step from conditional to marginal MI in Eq. (B4) is also invalid. The proof is a restatement of the objective, not a derivation.\n\nWhat is genuinely useful here is the engineering framing. Combining Gács–Körner common information with IB compression for both shared and view-specific representations, plus explicit pairwise independence penalties, is a reasonable recipe for multi-view classification. The paper is honest that it is discarding the multi-view redundancy assumption and builds on FACTORCL and IMC. The ablation study shows both modules contribute. That part is worth reading.\n\nThe empirical section is much weaker. There is no clear validation protocol—no mention of train/test splits, hyperparameter selection procedure on test data, or how the 10 trials are run. The 100.00 ± 0.00 on MSRC-v1 (210 samples) is a red flag for overfitting or leakage. The GK objective in Eq. (1) is asserted without derivation or citation; presumably it is meant as an approximation, but it is not justified. Also, the complexity table is sketchy but that is minor.\n\nNet: this is a plausible heuristic method with an overclaimed theoretical wrapper. The core idea is not novel enough to be a breakthrough—shared/unique factorization already exists—but the specific combination of GK and IB penalties is new as a system. If the theorem were removed and the experiments redone with a proper protocol, this could be a decent workshop paper or a small contribution. As it stands, the main claim fails, and the experiments do not support the headline results.\n\nIf the journal wants a referee to push for a cleaner empirical setup and an honest theorem (or no theorem), I'd send it. Otherwise, it's a desk reject or major revision. I would not cite it for the theory, but I'd keep it in mind as related work for the method design.","headline":"The predictive-sufficiency theorem is assumed rather than proven, and the perfect MSRC-v1 score looks suspicious, but the common/unique IB+GK design is a sensible heuristic.","tokens_in":18366,"tokens_out":2215,"would_cite":false,"duration_ms":24649,"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 proposes a multi-view learning framework that keeps both shared and view-specific information and proves the combined representation stays predictively sufficient for the downstream label.","keywords":["multi-view learning","information bottleneck","Gács-Körner common information","predictive sufficiency","view-unique information","mutual information","representation learning","multi-view redundancy"],"falsifier":"Train CIML on a constructed multi-view dataset where the label is the XOR of one unique bit from view 1 and one unique bit from view 2, plus any shared bits. If the model makes the unique representations independent, a classifier reading Zc, Zu1, and Zu2 cannot recover the XOR correlation unless the joint representation preserves the pair, so accuracy will drop far below a classifier with access to raw views; measuring I(X;Y) versus I(Z;Y) directly would settle whether Eq. (B7) holds.","tokens_in":17456,"feed_emoji":"🧩","tokens_out":5920,"duration_ms":63821,"temperature":0.7,"pith_summary":"This paper proposes CIML, a multi-view learning framework that rejects the common 'multi-view redundancy' assumption that only information shared by all views matters for prediction. It learns two kinds of representation: a common representation extracted with Gács-Körner common information and then compressed by the information bottleneck, and per-view unique representations compressed separately while being pushed to be independent of the common part and of each other. The authors prove that the combined representation is predictively sufficient: if the original views fully determine the label, the learned joint representation retains essentially the same predictive information. On six benchmark datasets, CIML beats or matches state-of-the-art baselines, and ablation studies show both common and unique parts contribute.","feed_headline":"Shared plus unique clues keep multi-view prediction intact","feed_subtitle":"A new learner drops the 'only shared information matters' assumption and beats strong baselines on six datasets.","key_machinery":"The load-bearing object is the joint representation Z=(Zc, Zu^(1),...,Zu^(v)), split into a common part Zc and per-view unique parts. Zc is learned by maximizing Gács-Körner common information, the largest latent variable reconstructable from every view, and then compressing through an information-bottleneck objective I(Zc;Y) - beta1 I(Zc;C). Each unique part Zu^(i) is learned with IB plus penalties minimizing I(Zu^(i);Zc) and cross-view I(Zu^(i);Zu^(j)); mutual-information terms are bounded variationally, with MINE used for the independence penalties. The argument's workhorse is the additivity identity I(Zc,Zu^1,...,Zu^v;Y) is approximately I(Zc;Y) plus the sum of I(Zu^i;Y), asserted to fol","core_discovery":"The central claim is that a representation can use both the information shared by all views and the information unique to each view, and still retain all predictive information about the target. Concretely, Theorem 3.1 asserts that if the raw multi-view input X fully determines label Y, then the trained joint representation Z=(Zc,Zu^1,...,Zu^v) approximately determines Y, so H(Y|Z) is close to H(Y|X). The construction makes the claim work: Gács-Körner common information pins down the shared part, information bottleneck compresses both common and unique parts to task-relevant signal, and independence penalties separate the parts so their predictive contributions add.","pith_inferences":["If the additivity step in Eq. (B7) is tested directly, XOR-like label functions are the natural probe: two unique bits that are each useless alone but decisive together should reveal whether the independence penalties sacrifice joint predictive information.","The common/unique decomposition could be extended to incomplete multi-view learning, the paper's stated future direction, by using Gács-Körner common information as a reconstruction target for missing views; this follows from the modularity of the two loss terms.","A practitioner should verify that the MINE-based near-zero mutual-information penalties correspond to true near-independence at the dataset's finite sample size, since the predictive-sufficiency proof relies on those penalties actually holding.","The independence constraints create a representation where each view's unique contribution is individually decodable, which could be useful for interpretability and per-view attribution, though the paper does not explore this."],"forward_implications":["If predictive sufficiency holds, downstream classifiers can use the concatenated common-plus-unique representation instead of raw views without losing label information.","The multi-view redundancy assumption can be dropped without paying a predictive price; on reported benchmarks CIML meets or exceeds methods built on that assumption.","The framework is not limited to two views: Gács-Körner common information gives a shared representation across any number of views instead of pairwise averages.","Ablations show common and unique modules are complementary: removing either loss lowers accuracy, and on LandUse-21 the unique module contributes more than the common module."],"supporting_citations":[{"why":"Defines the multi-view redundancy assumption and the MIB baseline that the paper explicitly discards and compares against.","marker":"[12]"},{"why":"Introduces Gács-Körner common information, the shared-information measure used to extract common representations across all views.","marker":"[44]"},{"why":"Supplies the deep variational information bottleneck and Monte Carlo variational bounds used for compressing common and unique representations.","marker":"[9]"},{"why":"Provides the MINE estimator used to bound mutual information between unique and common representations and between unique pairs.","marker":"[48]"},{"why":"FACTORCL, a recent model that relaxes the redundancy assumption but only captures pairwise shared information and lacks the cross-unique independence constraint; serves as a key comparison.","marker":"[49]"},{"why":"IMC, an information-theoretic multi-view clustering model that also relaxes redundancy and is contrasted as pairwise and computationally costly.","marker":"[39]"},{"why":"DCP, a representative method relying on the multi-view redundancy assumption for consistency learning; used as baseline and example of the assumption.","marker":"[7]"}],"fun_headline_variants":["Shared and unique view info combined: full predictive power kept","Multi-view learning that uses both common and unique signals","Drop the redundancy assumption: learn from every view's data","CIML proves both shared and unique info preserve prediction","One learner, all view information: no more ignoring unique data"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The proof assumes that once the common and per-view unique pieces are made mutually independent, their separate contributions to predicting the label sum exactly; independent pieces can still carry information about the label only when combined, so this additivity can fail.","fun_headline_variants_meta":{"raw":{"variants":["Shared and unique view info combined: full predictive power kept","Multi-view learning that uses both common and unique signals","Drop the redundancy assumption: learn from every view's data","CIML proves both shared and unique info preserve prediction","One learner, all view information: no more ignoring unique data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000598,"raw_usage":{"total_tokens":2629,"prompt_tokens":735,"completion_tokens":1894,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":479,"completion_tokens_details":{"reasoning_tokens":1813}},"tokens_in":479,"tokens_out":1894,"duration_ms":15376,"temperature":1.0,"reasoning_tokens":1813,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T11:52:38.555155+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train CIML on a constructed multi-view dataset where the label is the XOR of one unique bit from view 1 and one unique bit from view 2, plus any shared bits. If the model makes the unique representations independent, a classifier reading Zc, Zu1, and Zu2 cannot recover the XOR correlation unless the joint representation preserves the pair, so accuracy will drop far below a classifier with access to raw views; measuring I(X;Y) versus I(Z;Y) directly would settle whether Eq. (B7) holds.","supporting_citations":[{"cited_title":"Learning robust representations via multi-view information bottleneck,","cited_arxiv_id":null,"evidence_quote":"Defines the multi-view redundancy assumption and the MIB baseline that the paper explicitly discards and compares against."},{"cited_title":"Common information is far less than mutual information","cited_arxiv_id":null,"evidence_quote":"Introduces Gács-Körner common information, the shared-information measure used to extract common representations across all views."},{"cited_title":"Factorized contrastive learning: Going beyond multi- view redundancy,","cited_arxiv_id":null,"evidence_quote":"FACTORCL, a recent model that relaxes the redundancy assumption but only captures pairwise shared information and lacks the cross-unique independence constraint; serves as a key comparison."},{"cited_title":"Generalized information-theoretic multi-view clustering,","cited_arxiv_id":null,"evidence_quote":"IMC, an information-theoretic multi-view clustering model that also relaxes redundancy and is contrasted as pairwise and computationally costly."},{"cited_title":"Dual contrastive prediction for incomplete multi-view representation learning,","cited_arxiv_id":null,"evidence_quote":"DCP, a representative method relying on the multi-view redundancy assumption for consistency learning; used as baseline and example of the assumption."}],"review_version":1}