{"id":"f9ee1ecb-6629-4da4-b43c-e2b75b8350f3","arxiv_id":"2608.12903","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"GBKNN replaces fixed k with a neighborhood size derived from the nearest granular ball and uses a Fisher criterion to guide ball splitting, reporting higher accuracy and speed than 13 KNN baselines on 12 datasets.","lead":"Granular-ball KNN (GBKNN) first splits a dataset into coarse balls and then adapts the neighborhood size around each test point instead of using a fixed k. The paper claims higher accuracy and speed than 13 KNN variants on 12 benchmark datasets and reports stable behavior on large datasets.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (15) cannot be a purity threshold, so the quality-optimization stage credited in the ablation is not reproducible as written.","rationale":"I read the paper as proposing a complete two-stage pipeline, with the central claim resting on the empirical superiority reported in Tables II and V. The reader's weakest-assumption analysis identifies the same load-bearing defect: Eq. (15) is not a valid purity threshold and is insufficiently specified, so the T_L component that the ablation credits with real accuracy gains cannot be enacted from the paper as written. This is a correctness and reproducibility concern, not a disagreement with the community consensus about KNN or granular-ball methods. It is serious enough to keep the verdict at CONDITIONAL, but not to reject: the open-source code is genuine independent support and makes a direct check feasible. If the code's actual formula is a sensible per-class purity bound, the issue reduces to a documentation fix; if the code reproduces the reported ablation only with a different formula, the paper's account of its own method is incomplete. I considered other weaknesses, such as missing error bars and the absence of baselines in Table IV, but the Eq. (15) defect is more load-bearing because it concerns a component explicitly credited with improvements and is stated as a formal definition rather than an analysis choice. My recommendation is UNCHANGED: the reader's conditional verdict is the right one, pending the concrete check above.","tokens_in":23300,"tokens_out":6330,"duration_ms":69211,"concrete_test":"Extract the exact T_L predicate from the released repository at https://github.com/lianxiaoyu724/Adaptive-GBKNN, then run the implementation on haberman and rssi with line 13 disabled and enabled, using the same fixed initial centers described in Section V-F. If the code's predicate differs from Eq. (15), the paper must document the actual formula; if the reported row-5 versus row-6 differences of 2.05% and 1.32% are not reproducible, the ablation's attribution of those gains to T_L is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (15) defines T_Lj as (Σ_{i=1}^N |GB_i^*|) / |L_j|. Since L_j is a class subset of the samples contained in the granular-ball set, the denominator is at most the numerator, so T_Lj ≥ 1 whenever the class is non-empty. Purity (Definition 3) never exceeds 1. Therefore the predicate \"purity lower than T_Lj\" in Algorithm 1, line 13 is true for every non-pure ball; the documented threshold cannot act as the category-adaptive purity lower bound described in Section IV-B. The quantities GB_i^* and |L_j| are also not defined precisely (GB_i^* appears only here), so the formula is not merely mis-normalized but incomplete. This matters because the central claim is for the complete GBKNN pipeline, and Table V explicitly credits T_L with accuracy gains, for example 2.05% on haberman and 1.32% on rssi. If the released code uses a different predicate, the paper does not document the real mechanism, and the ablation cannot be reproduced from the text. Conversely, if line 13 is executed with the formula exactly as written, the method degenerates to a final split of all impure balls, which is a different algorithm from the one whose components are described.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes GBKNN, a two-stage adaptive k-nearest-neighbor classifier based on granular-ball computing. In the training stage, the dataset is first split into sqrt(n) initial granular balls by k-means, then each ball is recursively refined with the GBG++ splitting procedure; a split is accepted only when the weighted Fisher criterion of the child balls exceeds that of the parent. A further 'category-adaptive purity lower bound' T_L is introduced to re-split low-quality balls, and a global de-overlap step is applied. In the prediction stage, GBKNN selects the nearest granular ball by a sample-count-weighted boundary distance, constructs an adaptive neighborhood around the test point using the distance to the farthest sample inside that ball, and classifies by majority vote over the neighborhood samples. Experiments on 12 UCI datasets and 5 large-scale datasets report accuracy, noise robustness, runtime, and an ablation study, alongside open-source code.","tokens_in":23571,"tokens_out":7772,"duration_ms":81169,"significance":"If the claims are correct, the paper offers a practically useful adaptive-k KNN variant: the coarse-to-fine granular-ball representation plus neighborhood construction could reduce both sensitivity to k and computational cost on medium and large datasets. The manuscript has genuine strengths: the code is public, the experimental design covers multiple datasets and noise levels, and the ablation study explicitly attributes gains to individual modules. However, the contribution is not yet established as written. The purity threshold in Eq. (15) is not a well-defined quantity, the density theorem in Section IV-E is asserted rather than proved, and the accuracy comparisons lack statistical support. These issues are local and fixable, but they are load-bearing for the central claims, so a major revision is needed.","major_comments":[{"comment":"Equation (15) cannot be a purity threshold as written. The term T_{L_j} is defined as the sum of |GB_i^*| over all granular balls divided by |L_j|, but GB_i^* is never defined and the expression is not normalized to lie between 0 and 1. If L_j is the class-j subset of the samples contained in the granular-ball set, the denominator is a subset of the samples counted in the numerator, so T_{L_j} >= 1 for any nonempty class; if L_j instead denotes all class-j samples in the dataset, the same inequality holds. Since purity (Definition 3) is at most 1, the predicate 'purity lower than T_{L_j}' in Algorithm 1 line 13 is true for every non-pure ball. The documented quality-optimization stage therefore degenerates into a rule that splits all impure balls, which is not the adaptive threshold described in the text and which Table V explicitly credits with accuracy gains. The paper must define GB_i^*, replace Eq. (15) with a correctly normalized purity threshold, and reconcile the formula with the implementation in the released code.","section":"Section IV-B, Eq. (15) and Algorithm 1 line 13"},{"comment":"The density comparison theorem is not rigorously established. The proof asserts that direct global k-means produces centers in higher-density regions and smaller radii than recursive 2-means, but that is precisely the claim to be proved; no comparison of the two partition methods under a Lipschitz-continuous density is actually carried out. Equation (29) presents an estimate rho_i = n f(c_i) + n L_i r_i that mixes a leading term with a worst-case upper bound on the bias, and the sign of the error term is not handled consistently when the text argues that smaller radii lead to higher density. Equation (17) is also ill-defined because it puts a summation over all balls inside the definition of rho_i. If the theorem is kept, either provide a complete proof with well-defined density quantities and controlled approximation errors, or explicitly label the argument as a heuristic motivation rather than a theorem.","section":"Section IV-E, Theorem 1 and Eqs. (17)-(31)"},{"comment":"The central empirical claim that GBKNN outperforms existing KNN variants is not supported by statistical evidence. Table II reports single accuracy averages over one 8:2 split per noise level, with no standard deviations, no repeated random splits, and no significance tests. On several datasets GBKNN is numerically below GBKNN_p (for example, mushroom 0.9896 vs 0.9924 and Skin NonSkin 0.9766 vs 0.9922), so the reported average advantage of 0.0114 over GBKNN_p could plausibly arise from split variance. Table IV reports only GBKNN results with no baselines, making the large-scale section descriptive rather than comparative. The paper should provide statistics over repeated trials, significance tests, and explicit statements about which baselines could not be run on the large-scale datasets.","section":"Section V-B, Tables II and IV"}],"minor_comments":[{"comment":"The checkmark rows in Table V are not labeled with a legend, and the text refers to rows by number without making it easy to identify which module combination each row corresponds to; please add explicit row labels or a legend.","section":"Section V-F, Table V"},{"comment":"The column header 'phonme' is a typo for 'phoneme', and the dataset name 'Skin Nonskin' appears with inconsistent spacing and capitalization across tables and text.","section":"Table II"},{"comment":"The method in reference [23] is called MGKNN in the related-work section and MGNR in the experiments and baseline tables; please use one consistent name throughout.","section":"Section II-A and Section V-B"},{"comment":"The algorithm description states that the method achieves 'threshold-free and adaptive splitting', but Algorithm 1 line 13 applies the purity threshold T_L; please clarify whether the claim of threshold-freeness excludes this quality-optimization stage, and align the wording with the actual algorithmic flow.","section":"Section IV-D"},{"comment":"The runtime analysis assumes that the de-overlapping cost is negligible and that the GBG++ splitting is O(n), but these assumptions are not justified in the text; a brief remark on when de-overlap could become non-negligible would improve the analysis.","section":"Section IV-F"},{"comment":"The runtimes in Table IV are not accompanied by a description of whether they cover all noise levels, a single train-test split, or the full experimental protocol; please specify what the reported times include.","section":"Section V-E, Table IV"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the journal's scope and the open-source code is a clear strength. The main risk is not novelty but rigor: the purity threshold in Eq. (15) must be corrected, the density theorem needs either a real proof or a downgrade to a heuristic, and the experimental claims require statistical support. The manuscript also leans heavily on the authors' own prior granular-ball papers; this is acceptable, but the comparison against GBKNN_p should be scrutinized to ensure the baseline is implemented fairly and is not a straw man."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nRead GBKNN. The core idea is a sensible combination of known parts: √n k-means coarse balls, Fisher-criterion splitting, weighted boundary distance, and a neighborhood-based adaptive k from the nearest ball. That combination is new relative to the cited granular-ball KNN line, and the open-source code plus the 12-dataset noise sweep give the empirical claim a real basis. If the reported gains hold, this is a practical threshold-free KNN variant, though the average improvement over the closest baseline (GBKNN_p) is about 1.3 points, so \"outperforms\" is true but modest.\n\nThe paper's main soft spot is not the incremental gains; it's the purity lower bound in Eq. (15). As written, T_Lj is (total samples in all balls)/|L_j|, which is ≥1 for any non-empty class. Purity (Definition 3) is at most 1. So the predicate \"purity lower than T_Lj\" in Algorithm 1 line 13 is true for every non-pure ball; the documented threshold cannot act as a per-class quality gate. The ablation (Table V) explicitly credits T_L with gains (2.05% on haberman, 1.32% on rssi), so this is load-bearing. Either the code uses a different formula not documented in the text, or the implementation splits all impure balls at the final stage—a different algorithm than the one described. This is a reproducibility defect, not a style nit.\n\nOther issues are more conventional. The noise-injection protocol is underspecified (how are labels flipped? which samples?), the reported accuracies have no error bars or significance tests across different train/test splits, and the large-scale section (Table IV) reports only GBKNN, so there's no evidence it beats anything there. Theorem 1 is asserted rather than proved: the Lipschitz argument bounds an error term, but the conclusion that Method 1 has higher average density than Method 2 is not derived rigorously; the \"k-means tends to generate balanced sizes\" step is hand-waving.\n\nStill, the Fisher-controlled splitting and the adaptive neighborhood are coherent, and the code is public, so a referee can check whether Eq. (15) is a typo or a real discrepancy. The circularity burden is low: k is determined by local structure, not fitted to test labels, and the heavy citation of the authors' own granular-ball line is not itself a flaw.\n\nWho is this for? Someone working on parameter-free KNN variants or granular-ball classifiers will want to engage. It deserves a serious referee—conditional on a corrected Eq. (15), error bars or at least multiple splits, and a specified noise protocol. I'd send it to review, but I'd expect major revision.","headline":"A useful adaptive KNN variant with a genuine reproducibility hole: Eq. (15) cannot be a purity threshold as written, and the ablation credits that step—so the paper needs a correction before the headline claims can be checked.","tokens_in":24070,"tokens_out":2972,"would_cite":false,"duration_ms":27332,"reading_group":"yes","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that replacing KNN's fixed $k$ with a granular-ball-induced adaptive neighborhood yields both higher accuracy and lower runtime across benchmark datasets.","keywords":["adaptive k-nearest neighbors","granular-ball computing","Fisher criterion","neighborhood construction","noise robustness","classification","large-scale data","parameter-free k selection"],"falsifier":"Run the implementation accompanying the paper on the 12 benchmark datasets with the documented 8:2 split and 0–30% training-label noise, and inspect the value of $T_{L_j}$ from Eq. (15) at line 13 of Algorithm 1: if the average accuracy does not reach the reported 0.8736, or if the threshold is not between 0 and 1 and therefore cannot be compared with a purity value, the central claim fails.","tokens_in":23107,"feed_emoji":"📊","tokens_out":11743,"duration_ms":108233,"temperature":0.7,"pith_summary":"The paper aims to remove the fixed $k$ from $k$-nearest-neighbor classification by representing the training set as a small set of granular balls (spherical clusters labeled by their majority class) and letting each test point's neighborhood size emerge from the ball next to it. In training, the data is first coarsely split into $\\sqrt{n}$ balls and then refined under a Fisher-criterion control that balances between-class separation against within-class compactness. In prediction, the method finds the nearest ball by a weighted distance, sets the neighborhood radius to the distance from the test point to the farthest sample inside that ball, and takes $k$ as the number of training samples captured in that neighborhood. On 12 benchmark datasets it reports an average accuracy of 0.8736, above 0.8622 for a purity-controlled variant and 0.8195 for the 2019 granular-ball KNN, with lower runtimes on medium and large datasets. A sympathetic reader would take the central claim to be that coarse ball representation plus a locally adaptive neighbor count can be both more accurate and more efficient than existing KNN variants.","feed_headline":"Adaptive KNN lifts average accuracy to 0.8736 across 12 datasets","feed_subtitle":"The method grows the neighbor count from the nearest granular ball, removing manual k tuning and cutting runtime.","key_machinery":"The load-bearing object is the granular ball, a spherical cluster with center $c$ and radius $r$ that covers the samples within distance $r$ of $c$ and carries the majority class label of those samples. The mechanism that carries the argument is a two-level adaptive pipeline: coarse $\\sqrt{n}$-ball initialization by $k$-means, Fisher-criterion-controlled splitting with a category-adaptive purity lower bound and overlap removal during generation, and then a prediction stage in which a weighted boundary distance selects the nearest ball and the distance to its farthest sample sets the neighborhood radius, making $k$ equal to the number of samples caught in that neighborhood. This pipeline is what converts KNN's global $k$ into a local, data-determined value while shrinking the search from all $n$ points to $N$ balls plus a few candidate balls.","core_discovery":"The central discovery claimed is that replacing both the fixed $k$ and the point-level nearest-neighbor search with a two-level granular-ball representation improves KNN's accuracy and efficiency at once. The training stage first runs $k$-means with $k=\\sqrt{n}$ to coarsely partition the data, then repeatedly splits each ball with an attention-based fast splitting procedure, accepting a split only when the weighted Fisher value of the child balls exceeds the parent's; a category-adaptive quality lower bound and overlap removal then refine the balls. For a test point, the method selects the nearest ball using a sample-count-weighted boundary distance, constructs a neighborhood of radius $R_{kNN}(x)=\\max_{x_i\\in GB^*}\\Delta(x,x_i)$, and classifies by majority vote over the samples inside that neighborhood. The paper reports that this yields average accuracy 0.8736 on the 12 benchmark datasets, versus 0.8622 for a purity-based variant and 0.8195 for GBKNN 2019, with substantially shorter runtimes on datasets from about five thousand samples upward.","pith_inferences":["The same two-level ball-plus-neighborhood design could be carried over to $k$-NN regression, outlier detection, or imbalanced classification, where a fixed neighbor count is also known to be problematic; the paper does not test these settings.","Since the neighborhood is induced by a single nearest ball, a natural variant would blend the two nearest balls' neighborhoods or cap the radius; this is an untested extension rather than a claim in the paper.","The printed formula for the category-adaptive purity lower bound, Eq. (15), is not a purity value between 0 and 1, so the ablation gains credited to that mechanism should be checked against the released implementation before being taken at face value."],"forward_implications":["The reported 0.8736 versus 0.8622 and 0.8195 averages imply the Fisher-controlled ball splitting plus adaptive neighborhood is worth about 5.4 points and 1.1 points of average accuracy over the two granular-ball baselines.","The stated complexity $O(n\\sqrt{n}+M(N+\\bar{s}))$ means the method trades an $O(n\\sqrt{n})$ training cost for a prediction cost far below the $O(Mn)$ scan of plain KNN, which is why the paper reports runtimes on datasets with up to roughly a million samples.","Because $k$ is computed per test point as the number of samples in a ball-derived neighborhood, the classifier is free of global $k$ tuning; users no longer need to search a $k$ grid.","The group-based ball neighborhood is claimed to absorb label noise better than point-based neighbors, and the reported accuracy on several datasets remains stable even with 30% training-label noise."],"supporting_citations":[{"why":"Defines the classic KNN baseline whose fixed $k$ and $O(Mn)$ cost the paper targets.","marker":"[1]"},{"why":"Introduces natural-neighbor methods, a baseline and the adaptive-$k$ idea the paper extends.","marker":"[19]"},{"why":"Supplies the original granular-ball KNN baseline that the new method compares against and improves upon.","marker":"[21]"},{"why":"Provides the adaptive granular-ball generation via weighted purity that the Fisher criterion is meant to replace.","marker":"[22]"},{"why":"Gives the multi-granularity neighbor relationship baseline and motivation for adaptive neighborhood construction.","marker":"[23]"},{"why":"Supplies the fast splitting procedure used inside the proposed granular-ball generation.","marker":"[33]"}],"fun_headline_variants":["Adaptive KNN auto-tunes k via granular balls, boosts accuracy","Granular-ball KNN adapts k, slashes runtime, lifts accuracy","Nearest-neighbor no longer needs manual k: granular-ball adaptive KNN","Adaptive KNN: granular balls set k, beat static-k variants","From fixed k to granular-ball neighborhoods: adaptive KNN wins"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the category-adaptive purity lower bound in Eq. (15) works as a per-class splitting threshold, even though as written $T_{L_j}$ is a sum of granular-ball sample counts divided by a class-set cardinality, not a purity value, so if the implementation follows the printed formula, Algorithm 1 line 13 cannot gate splitting as claimed.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive KNN auto-tunes k via granular balls, boosts accuracy","Granular-ball KNN adapts k, slashes runtime, lifts accuracy","Nearest-neighbor no longer needs manual k: granular-ball adaptive KNN","Adaptive KNN: granular balls set k, beat static-k variants","From fixed k to granular-ball neighborhoods: adaptive KNN wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00063,"raw_usage":{"total_tokens":2929,"prompt_tokens":984,"completion_tokens":1945,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":1849}},"tokens_in":600,"tokens_out":1945,"duration_ms":15107,"temperature":1.0,"reasoning_tokens":1849,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:54:00.713157+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the implementation accompanying the paper on the 12 benchmark datasets with the documented 8:2 split and 0–30% training-label noise, and inspect the value of $T_{L_j}$ from Eq. (15) at line 13 of Algorithm 1: if the average accuracy does not reach the reported 0.8736, or if the threshold is not between 0 and 1 and therefore cannot be compared with a purity value, the central claim fails.","supporting_citations":[{"cited_title":"A simple knn algorithm for text catego- rization,","cited_arxiv_id":null,"evidence_quote":"Defines the classic KNN baseline whose fixed $k$ and $O(Mn)$ cost the paper targets."},{"cited_title":"Natural neighbor: A self-adaptive neighborhood method without parameter k,","cited_arxiv_id":null,"evidence_quote":"Introduces natural-neighbor methods, a baseline and the adaptive-$k$ idea the paper extends."},{"cited_title":"An efficient and adaptive granular-ball generation method in classification problem,","cited_arxiv_id":null,"evidence_quote":"Provides the adaptive granular-ball generation via weighted purity that the Fisher criterion is meant to replace."},{"cited_title":"Mgnr: A multi- granularity neighbor relationship and its application in knn classification and clustering methods,","cited_arxiv_id":null,"evidence_quote":"Gives the multi-granularity neighbor relationship baseline and motivation for adaptive neighborhood construction."},{"cited_title":"Gbg++: A fast and stable granular ball generation method for clas- sification,","cited_arxiv_id":null,"evidence_quote":"Supplies the fast splitting procedure used inside the proposed granular-ball generation."}],"review_version":1}