{"id":"d9507df0-49b7-40b5-aa0c-29af4da47924","arxiv_id":"2412.13550","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"MGBCC performs multi-view contrastive clustering at the granular-ball level, linking overlapping balls within and across views and reporting state-of-the-art or competitive accuracy on seven datasets.","lead":"MGBCC is a multi-view clustering method that first groups each view's samples into coarse 'granular balls', then runs contrastive learning on ball centers rather than individual samples. It tries to keep overlapping balls within a view and sufficiently overlapping balls across views close in a shared space, reporting strong results on seven benchmark datasets.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (12) lacks the negative sign and logarithm needed for contrastive learning; minimizing it repels associated granular balls and attracts unrelated ones, inverting the paper's central claim.","rationale":"The reader's rejection is based on the same central defect I identify. I read the full manuscript and looked for an alternative interpretation of Eq. (12) that would make minimization attractive. There is none: no negative sign appears anywhere in the loss, no log is present, and the denominator is restricted to non-associated balls (Φ_i = {z | Miz = 0}), so the expression is a positive ratio of exponentials of positives to exponentials of negatives. In standard contrastive losses, the numerator contains the positive pair and the denominator contains all candidates including the positive; minimizing -log of that ratio raises positive similarity. Here, because the numerator is the associated set and the denominator is the unrelated set, the monotonicity is reversed. This is not merely a concern about tuning or baselines; it undermines the causal attribution of every reported improvement to granular-ball contrastive learning. The self-referential overlap count in Eq. (2) is a second definitional gap, but I do not need it to reach the same verdict. I also considered whether the unusual expression could be a typographical error in the preprint while the experiments used the intended InfoNCE loss; if so, the paper can be repaired by rewriting Eq. (12) and releasing code, but the submitted text as it stands cannot support the strongest claim. No independent verification (machine-checked proof, code, or variance estimates) is present to offset this. Verdict unchanged: REJECT.","tokens_in":12035,"tokens_out":3984,"duration_ms":37571,"concrete_test":"Take a minimal three-ball case (k=3) with only M12=M21=1 and ball 3 unrelated; fix the unrelated similarity and compute dL/ds for s=cos(c1,c2) from Eq. (12). The derivative is positive, so minimizing the printed objective lowers s, separating the associated pair. Empirically, re-run the published procedure with Eq. (12) exactly as printed on MNIST-USPS and monitor the mean cosine similarity of associated ball-center pairs across epochs: if it increases, the code does not implement the printed loss; if it decreases, the objective demonstrably separates positive granular balls. Either outcome settles whether the reported results come from the mechanism claimed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that minimizing Lcon brings associated granular balls closer and pushes unrelated balls apart. In Eq. (12), L(m,n) = (1/k) Σ_i Σ_{j∈Ω_i} exp(cos(c_i,c_j)) / Σ_{z∈Φ_i} exp(cos(c_i,c_z)). Every term in the numerator is positive for an associated pair, and the denominator sums only over non-associated balls. Holding unrelated similarities fixed, the partial derivative of the summand with respect to the cosine similarity of an associated pair is exp(cos(c_i,c_j))/denominator > 0. Gradient descent therefore decreases that similarity, i.e., associated balls are pushed apart and the denominator's unrelated balls become relatively closer. This is exactly opposite to the stated objective and to the description in Section 'Granular-ball Contrastive Learning' and Figure 2. The missing minus sign and log are not cosmetic: if the authors instead optimize L = -(1/k) Σ_i log Σ_{j∈Ω_i} exp(cos(c_i,c_j)) / Σ_z exp(cos(c_i,c_z)), the gradient flips, but that is not the equation in the manuscript. As printed, Table 2, Figure 3, and the ablation study cannot be interpreted as evidence for granular-ball contrastive learning. Eq. (2) also has a definitional circularity (pi and pj are defined as overlap counts while simultaneously determining overlaps), but the Eq. (12) sign error alone is decisive.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes MGBCC, a multi-view clustering method that performs contrastive learning at the granular-ball level. Granular balls are formed in each view's latent space via k-means, intra-view associations are defined by a geometric overlap criterion, cross-view associations are defined by the proportion of shared sample indices, and a contrastive loss over granular-ball centers is minimized jointly with reconstruction losses. Experiments on seven multi-view datasets report state-of-the-art or competitive ACC/NMI/PUR, and an ablation on Caltech101-20 is used to argue that granular-ball-level contrastive learning outperforms instance-level contrastive learning.","tokens_in":12284,"tokens_out":6008,"duration_ms":56605,"significance":"If the method were correctly specified, the proposal of an intermediate granularity between instances and clusters for multi-view contrastive learning would be a useful contribution, and the experimental suite is broad. The paper is also among the first to connect granular-ball computing to deep multi-view contrastive clustering. However, the central objective as printed in Eq. (12) does not do what the text claims: minimizing it repels associated granular balls and relatively attracts unrelated ones. Because this equation is the defining mechanism of the method, the theoretical description, the ablation, and the interpretation of the experimental results are not supported as written. The circularity in Eq. (2) further means that the overlap matrix used to build the contrastive mask is not well defined.","major_comments":[{"comment":"Equation (12) defines the granular-ball contrastive loss as L(m,n) = (1/k) sum_i sum_{j in Omega_i} exp(cos(c_i,c_j)) / sum_{z in Phi_i} exp(cos(c_i,c_z)), with no negative sign and no logarithm. Since every term in the numerator is positive, the partial derivative of the summand with respect to the cosine similarity of an associated pair is exp(cos(c_i,c_j)) / sum_{z in Phi_i} exp(cos(c_i,c_z)) > 0. Gradient descent therefore makes associated granular balls less similar, while the denominator makes non-associated balls relatively more similar. This is exactly the opposite of the objective stated in the text and in Figure 2. As a result, Table 2, Figure 3, and Table 3 cannot be interpreted as evidence for granular-ball contrastive learning unless the actual loss used in the experiments is different from Eq. (12) and is stated explicitly.","section":"Granular-ball Contrastive Learning, Eq. (12)"},{"comment":"Equation (2) defines the overlap criterion using omega = min(ri, rj) / min(pi, pj), where pi and pj are described as the total numbers of overlaps with adjacent granular balls for GBi and GBj. Whether two balls overlap is precisely the relation being defined, so pi and pj are not available before the overlap matrix Av is computed. The manuscript provides no fixed-point iteration, initialization rule, or alternative definition. Therefore Av in Eq. (6), the mask M in Eq. (11), and the contrastive loss in Eq. (12) are not well defined for an arbitrary input.","section":"Within-view Granular-ball Generation, Eq. (2)"},{"comment":"The ablation compares Lrec, Lrec + Lcon with p=1, and Lrec + Lcon with p=2, and uses the improvement of the p=2 setting to conclude that granular-ball contrastive learning is effective. This conclusion is load-bearing for the paper's central claim. Because Eq. (12) is not a contrastive objective, the difference between the two settings cannot be attributed to the claimed mechanism. The authors need to specify the actual loss minimized in the experiments and provide the corrected equation; otherwise the ablation cannot support the granular-ball hypothesis.","section":"Ablation Studies, Table 3"}],"minor_comments":[{"comment":"The heading contains a typo: 'granular-ball asociation' should be 'granular-ball association'.","section":"Methodology heading"},{"comment":"The text says 'classical multi-view constrastive learning methods'; 'constrastive' should be 'contrastive'.","section":"Experimental Results"},{"comment":"The coefficient in Eq. (13) is rendered as '2 V (V - 1)'; it should be written as 2 / (V(V - 1)) to avoid ambiguity.","section":"Equation (13)"},{"comment":"The sum symbol in Eq. (12) appears as 'P' in the rendering; it should be a proper summation symbol (\\sum) over z in Phi_i.","section":"Equation (12)"},{"comment":"For BBCSport and Cora, lambda is set to 0, so the reconstruction loss is disabled; the manuscript should clarify what prevents the encoder from collapsing or drifting when the only loss is the contrastive term.","section":"Implementation Details"}],"recommendation":"reject","confidential_remarks":"The central equation of the method is inconsistent with the stated objective, and the overlap definition is circular. These are load-bearing issues, not presentation problems. If the authors resubmit, they should provide the corrected loss, a well-defined construction of the overlap matrix, and ideally code or a clear statement of the exact objective actually optimized to produce the reported numbers."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know the central contrastive loss in Eq. (12) is written backwards. It has no negative sign or log, so minimizing it makes associated granular balls farther apart and unrelated balls relatively closer — the exact opposite of what the text says. The gradient of each term with respect to the cosine similarity of an associated pair is positive, so gradient descent decreases that similarity. This is not cosmetic; it inverts the method's objective.\n\nThe granular-ball idea itself is genuinely new and worth taking seriously. An intermediate scale between instances and clusters makes sense for multi-view contrastive learning: it can reduce false negatives from instance-level sampling while preserving local structure that cluster-level alignment misses. The k-means-based ball construction with overlap/intersection associations is simple and reasonable, and the related work coverage is adequate.\n\nBeyond the sign error, Eq. (2) is self-referential: the overlap matrix is defined using p_i and p_j, which are the overlap counts that the matrix itself defines, with no fixed-point argument. The experiments lack error bars, mix quoted and rerun baselines, and tune the granularity parameter p per dataset without a validation protocol. No code is released. But the sign error is the load-bearing problem. As printed, Tables 2 and 3 and the ablation study cannot be interpreted as evidence for granular-ball contrastive learning.\n\nFor a reader: this is a paper to fix, not to cite. If the authors replace Eq. (12) with a proper InfoNCE-style loss, resolve the overlap definition, and add proper experimental rigor, the idea could become a solid contribution. As is, I would not trust the numbers.\n\nRecommendation: I would still send this to peer review with the strong expectation of major revision, because the granular-ball concept deserves expert engagement and the flaw is specific and correctable. But the current manuscript does not support its central claim and should not be accepted in this form.","headline":"Granular-ball contrastive clustering has a promising intermediate-scale idea, but Eq. (12) is missing its negative sign and log, so the printed loss repels associated balls and attracts unrelated ones, inverting the paper's central claim.","tokens_in":12821,"tokens_out":4177,"would_cite":false,"duration_ms":37117,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Multi-view contrastive clustering works better when the contrast units are granular balls—compact local groups of samples—rather than individual instances, and the paper supports this with strong results on seven benchmarks.","keywords":["multi-view clustering","contrastive learning","granular-ball computing","deep clustering","representation learning","unsupervised learning","local structure"],"falsifier":"One can settle the central claim by training MGBCC with the loss exactly as written in Eq. (12) and measuring whether the average cosine similarity between associated granular-ball pairs increases or decreases over training; if it decreases, the stated objective implements the opposite of the claimed contrastive behavior.","tokens_in":11781,"feed_emoji":"📊","tokens_out":11424,"duration_ms":88314,"temperature":0.7,"pith_summary":"This paper argues that multi-view contrastive clustering should operate at an intermediate scale between individual instances and whole clusters: on 'granular balls,' or compact groups of similar samples. The authors propose MGBCC, a deep clustering method that first constructs these balls in each view's learned latent space, then links balls within a view if they overlap and across views if they share enough of the same samples. A contrastive loss then pulls linked balls together and pushes unlinked balls apart, so the shared representation learns both local topology and cross-view agreement. On seven standard multi-view datasets, the method reports accuracy, normalized mutual information, and purity that are best or second-best in most cases, and it substantially improves on instance-level contrastive baselines such as SURE on three datasets.","feed_headline":"Granular-ball contrastive learning improves multi-view clustering","feed_subtitle":"New method contrasts groups of samples instead of single instances, preserving local structure and improving on strong baselines.","key_machinery":"The load-bearing objects are granular balls: local clusters of latent-space representations with a center and radius, obtained by a direct $k$-means partition with a granularity parameter $p$ rather than the classical recursive splitting. The mechanism is a dual-association contrastive step: intra-view associations come from an overlap matrix $A^v$ (two balls overlap if their center distance minus the sum of radii is below a threshold related to their overlap counts), and cross-view associations come from a matrix $P^{(m,n)}$ (two balls in different views are linked if the fraction of common sample indices over the smaller ball's size exceeds $\\tau$). These are merged into a unified mask matrix $M$ that feeds a contrastive loss on ball centers, so that the shared latent space preserves within-view topology and cross-view agreement at the ball level.","core_discovery":"MGBCC claims that contrastive learning at the granular-ball level yields highly discriminative multi-view representations. Instead of pairing individual samples across views (which creates false negatives) or aligning whole cluster assignments (which ignores local structure), the method segments each view's latent space into a number of granular balls set by a granularity parameter $p$ (roughly $N/p$ balls) via $k$-means, computes intra-view overlap from ball center distances and radii, and computes inter-view overlap from the fraction of shared sample indices. The resulting association masks are combined into a unified mask matrix, and a contrastive loss on ball centers encourages associated balls to attract and unassociated balls to repel in a shared space. The paper demonstrates on BBCSport, Cora, MNIST-USPS, and other benchmarks that this intermediate-scale contrastive objective matches or exceeds state-of-the-art instance-level and cluster-level methods, and an ablation on Caltech101-20 shows granular-ball contrast ($p=2$) far outperforms instance-level contrast ($p=1$) when both are added to the reconstruction loss.","pith_inferences":["The same granular-ball idea could be transplanted to single-view contrastive learning, where augmentations of the same image could define ball membership and negative pairs could be drawn from other balls; the paper does not test this, but it follows directly from the mechanism.","Because the contrastive loss operates on ball centers rather than all $N$ samples, memory use scales with the number of balls $k$, opening the way to very large datasets when $p$ is chosen moderately; this scaling is not demonstrated in the paper.","The parameter $p$ sensitivity suggests an adaptive granularity schedule: starting with large balls early in training and refining to smaller $p$ later could give a curriculum that the paper does not explore."],"forward_implications":["The granular-ball construction can be added to any multi-view contrastive pipeline that uses instance-level negatives, because it only requires computing ball centers and masks from the latent representation.","Because negatives are defined between whole balls rather than individual samples, the method reduces the impact of false negative pairs that come from putting two samples of the same class into a negative pair.","The granularity parameter $p$ provides a continuous interpolation between instance-level contrast ($p=1$) and cluster-level contrast (large $p$), so a single framework covers both existing regimes.","The reported Cora accuracy (65.44%) against the best baseline (49.07%) suggests ball-level contrast is especially effective when views are high-dimensional and sparse."],"supporting_citations":[{"why":"introduced the multi-granularity cognitive computation framework that motivates the granular-ball perspective.","marker":"Wang 2017"},{"why":"developed the granular-ball computing method whose ball construction MGBCC adapts.","marker":"Xia et al. 2019"},{"why":"supplies the $k$-means algorithm used to generate granular balls in each view.","marker":"Lloyd 1982"},{"why":"proposed the cluster-level contrastive framework MFLVC, a key baseline and motivation for ball-level contrast.","marker":"Xu et al. 2022"},{"why":"proposed SURE, the instance-level false-negative-aware baseline the paper's results are set against.","marker":"Yang et al. 2023a"},{"why":"proposed DealMVC, another instance-level contrastive baseline in the empirical comparison.","marker":"Yang et al. 2023b"}],"fun_headline_variants":["Granular balls outperform instance pairs in multi-view clustering","Ball-level contrastive learning improves multi-view clustering","Ditch instance pairs: use granular balls for multi-view contrast","Granular-ball contrast: a new scale for multi-view clustering","Multi-view clustering via granular-ball contrastive learning"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method relies on the printed contrastive loss actually pulling associated granular balls together and pushing unassociated ones apart, and on the overlap definition being computable rather than circular; if either assumption fails, the claimed feature learning would not follow from the stated objective.","fun_headline_variants_meta":{"raw":{"variants":["Granular balls outperform instance pairs in multi-view clustering","Ball-level contrastive learning improves multi-view clustering","Ditch instance pairs: use granular balls for multi-view contrast","Granular-ball contrast: a new scale for multi-view clustering","Multi-view clustering via granular-ball contrastive learning"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000325,"raw_usage":{"total_tokens":1820,"prompt_tokens":942,"completion_tokens":878,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":558,"completion_tokens_details":{"reasoning_tokens":800}},"tokens_in":558,"tokens_out":878,"duration_ms":7561,"temperature":1.0,"reasoning_tokens":800,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T13:01:28.494736+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"One can settle the central claim by training MGBCC with the loss exactly as written in Eq. (12) and measuring whether the average cosine similarity between associated granular-ball pairs increases or decreases over training; if it decreases, the stated objective implements the opposite of the claimed contrastive behavior.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the $k$-means algorithm used to generate granular balls in each view."}],"review_version":1}