{"id":"15e6eac6-20d6-4045-831e-31fad0f35138","arxiv_id":"1908.06871","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A linear projection plus k-nearest-neighbor averaging is proposed for regression and classification, with reported accuracy gains on a handful of LIBSVM datasets.","lead":"This paper proposes a machine learning method that projects data with a linear function, then predicts by averaging the k nearest neighbors in the projected space. The author reports accuracy gains over Spark MLlib algorithms on a few datasets, but the evaluation lacks key baselines and error bars.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The empirical superiority claim is unreproducible: the published algorithm omits required parameters (inc, pas) and optimization details, and Table 1 lacks a protocol, the promised random-forest baseline, and definitions for regression 'accuracy'.","rationale":"Reading in good faith, the paper proposes a local ratio-scaling estimator: after projecting the data onto a linear function f', each new prediction is a weighted consensus of neighbor labels, with weights y'/y'_jt. That idea could in principle be evaluated, and the GitHub repository may contain a working implementation. However, the central claim is an empirical one, and the published evidence for it is the table in the Discussion. The table cannot be trusted because the algorithm is underspecified at the exact points needed for reproduction: inc, pas, the meaning of '>> 0', and the regression optimizer are all undefined. The comparison methodology is also missing: no train/test split, no hyperparameter settings, no error bars, no random-forest baseline despite the abstract, and no explanation of how regression datasets were scored as classification accuracy. These are internal inconsistencies, not disagreements with outside consensus, so they directly undermine the soundness of the empirical claim. I agree with the reader's verdict of reject; the weakest formal assumption identified by the reader (smoothness of the ratio y_j/y'_j) is real but secondary to the lack of a reproducible evaluation. The reader's rationale covers much of this ground, but the cleanest load-bearing concern is the unreproducibility of the experiment, not the smoothness assumption alone.","tokens_in":3400,"tokens_out":3634,"duration_ms":36648,"concrete_test":"Clone the published repository (github.com/stuenofotso/LinearizationML) and run the end-to-end pipeline on breast-cancer, a1a, and the square-root dataset using a pre-registered train/test split, a fixed random seed, and the exact configuration described in the paper. Compare the resulting accuracies against Spark MLlib MLP and logistic regression on identical folds. If implementing §1.2.3 requires choosing inc and pas, or if any reported accuracy changes by more than the rounding shown, Table 1 is not reproducible. Separately, check the repository for any random-forest comparison; if none exists, the abstract's promised baseline is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that 'linearization machine learning implementations are in many cases more accurate' than Spark MLlib methods. For that claim to hold, the evaluated algorithm must be precisely defined, the comparison protocol fair, and the reported numbers reproducible. None of these is established. The Learn procedure in §1.2.3 uses undefined constants 'inc' and 'pas' and an undefined threshold predicate '>> 0', so the recursion cannot be executed as written. The regression algorithm in §1.2.1 instructs the reader to 'estimate the best parameter values using an optimization algorithm' without naming the optimizer, loss, initialization, or stopping rule. The binary classification algorithm initializes every p_i with random(]0,0.5[) or random(]0.5,1[); since final predictions depend on p_i, Table 1 could change with the random seed. Table 1 omits the random-forest baseline promised in the abstract, reports only point accuracies with no error bars or fold structure, and lists 'square root' and 'exp' (regression-like datasets) under classification accuracy without explaining how continuous targets were binarized or how the 3507/4010 test counts relate to the 'thousand randomly picked points' described for the square-root dataset. A reader cannot tell whether the linearization method was tuned, whether MLP/logistic parameters were tuned, or whether the same train/test split was used. Therefore the published evidence does not support the claimed improvement; the claim is currently unverified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a supervised learning approach in which an unknown function f(x) is approximated by a linear (or multilinear) projection f'(x), and prediction for a new point x is obtained by taking a weighted consensus among the k nearest neighbors of f'(x) in the projected space, using the formula y = (1/k) * sum(y' * y_jt / y'_jt). Algorithms are sketched for regression and binary classification, and a table of accuracies on five datasets compares the method against Spark MLlib's multilayer perceptrons, logistic regression, and (in the abstract and introduction) random forests. The central claim is that the linearization approach is often more accurate than these baselines, even without parameter tuning.","tokens_in":3732,"tokens_out":6195,"duration_ms":60287,"significance":"If the approach were fully specified and validated, the idea of replacing the original feature-space distance with a one-dimensional projected-space distance and applying a ratio-based consensus rule would be a simple and potentially interesting addition to the non-parametric classification and regression literature. The paper's strengths include a concrete prediction formula and a link to a Scala implementation, both of which could facilitate further investigation. However, the manuscript in its current form does not establish the claimed improvements: the learning algorithm is incompletely specified, the empirical comparison lacks a recoverable protocol, and the key modeling assumptions are neither stated nor tested. The contribution is therefore not yet sufficient for publication.","major_comments":[{"comment":"The Learn procedure is not executable as written: the constants 'inc' and 'pas' are never defined, and the predicates '>> 0', '>>', and '<<' are not defined. The recursion also lacks a precise termination condition—'If (p_i) has not changed' does not specify how equality is tested—and no convergence argument is given. Because the final prediction rule for classification depends on the p_i produced by this procedure, the central empirical claim cannot be checked.","section":"§1.2.3 (Function Learn)"},{"comment":"The binary classification algorithm does not describe how the projection f' (i.e., the coefficients a,b or W) is estimated. The only fitting instruction appears in §1.2.1, where the author writes 'estimate the best parameter values using an optimization algorithm' without specifying the objective function, the optimizer, the initialization, or the stopping rule. Since both the training-time neighbors in Learn and the test-time prediction require f'(x), the algorithm is incomplete as published.","section":"§1.2.2 (Binary Classification)"},{"comment":"The empirical evaluation in Table 1 is not reproducible. There are no error bars, no number of runs, no description of the train/test split, and no hyperparameter settings for the linearization method or for the Spark MLlib baselines. The random-forest baseline promised in the abstract and introduction is missing from the table. Moreover, the rows 'square root' and 'exp' appear to be regression tasks, yet they are reported as classification accuracies without explaining how continuous targets were converted to classes; the test counts 3507 and 4010 also conflict with the statement that the square-root dataset uses 'a thousand randomly picked points.'","section":"Table 1"},{"comment":"The prediction formula y = (1/k) * sum_t (y' * y_jt / y'_jt) divides by each neighbor's projected value y'_jt; if any y'_jt is zero (or very small), the estimate is undefined or numerically unstable, and no safeguard is described. More fundamentally, the method relies on the assumption that the ratio y_jt / y'_jt is approximately constant among nearby projected points, but this assumption is not stated formally or validated on the datasets. A poor local fit of the linear projection could amplify errors rather than correct them.","section":"Eq. (1) (prediction rule)"},{"comment":"The Learn procedure initializes each p_i with a random draw from (0,0.5) or (0.5,1) and then iteratively updates p_i using the same training data. Because the test-time prediction in step 3 of §1.2.2 depends on the fitted p_jt, the results in Table 1 are potentially seed-dependent, yet no variance or ensemble results are reported. There is also no proof of convergence to a fixed point, nor any argument that the fixed point, if reached, would generalize to new data.","section":"§1.2.3 (random initialization and convergence)"}],"minor_comments":[{"comment":"The manuscript uses nonstandard notation such as 'k∈ 1..n' and 'random(]0, 0.5[)'; these should be replaced with conventional mathematical notation (e.g., k ∈ {1,...,n} and uniform draws from intervals).","section":"Throughout"},{"comment":"The abstract states that the implementations 'have demonstrated improvements in prediction accuracies,' but the discussion in Section 2 concedes 'without proper parameter tuning' and 'must be further investigated.' The strength of the claim should match the actual evidence presented.","section":"Abstract and Discussion"},{"comment":"The summation notation in Eq. (1) is unclear: the index t is not defined in the text, and the meaning of the limits j1 and jk is ambiguous. The author should define the indexing used for the k nearest neighbors.","section":"Eq. (1) and notation"},{"comment":"The 'square root' and 'exp' datasets are not standard LIBSVM datasets and no URL or generation procedure is provided beyond a brief footnote; the manuscript should state how these data were created and preprocessed.","section":"Datasets"},{"comment":"The paper cites the GitHub repository [9] as the implementation, but it does not specify the exact commit, runtime environment, or data-processing steps needed to reproduce Table 1.","section":"Reproducibility"}],"recommendation":"major_revision","confidential_remarks":"The paper is a very early-stage preprint with a potentially interesting idea, but it is far from the standard expected for a journal publication. The main concerns are the incomplete algorithm specification and the lack of a rigorous experimental protocol. If the author can provide a complete, executable algorithm and a careful empirical study with proper baselines and uncertainty quantification, the approach may be worth revisiting. Editors may also want to check that the claim of superiority over random forests is not based on an accidental omission of that baseline from the experiments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper proposes a local correction rule: fit a linear projection, then for a new point find k nearest projected neighbors and predict by averaging y' times the ratio y_jt / y'_jt. That rule is clean and I have not seen it in the cited literature. The self-consistent pseudo-probability training for classification is also unusual. The author states the algorithm in pseudocode and points to a public repo, which is useful. The soft spots are substantial. The pseudocode uses undefined constants ('inc', 'pas') and an undefined threshold ('>> 0'), and it says tune parameters with an optimization algorithm without naming the optimizer, loss, or stopping rule. Classification initializes p_i randomly, so results could change with the seed. A reader cannot reconstruct the exact algorithm, and the accuracy table is therefore not reproducible. The evaluation is too thin to support the abstract's claim of improvements over Spark MLlib. There are no error bars, no statistical tests, no split description, and no random forest baseline despite the abstract promising one. Regression datasets are listed under classification accuracy without explaining how continuous targets were binarized. The natural baselines for a kNN-style method, plain kNN and linear regression, are missing. The citation pattern also omits local linear regression and label propagation, which are the closest relatives. The author is appropriately cautious in the discussion, saying 'without proper parameter tuning' and 'must be further investigated.' So this is a promising direction rather than a demonstrated win. But the paper does not yet provide enough to verify the central claim. It reads like a preliminary technical report. Who is this for? Someone interested in a simple alternative to kNN with a global linear anchor. It is not publishable in its current form. A serious editor would desk-reject, though a referee's report could help the author tighten the algorithm and evaluation. I would not cite it.","headline":"A clean but incremental local-correction rule that is too under-specified to verify and whose reported accuracy gains are unsupported.","tokens_in":717,"tokens_out":1572,"would_cite":false,"duration_ms":46760,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper proposes that supervised learning can be reduced to a linear projection of the target function followed by a ratio-weighted consensus among k nearest neighbors, and reports accuracy gains over standard neural, linear, and…","keywords":["linearization machine learning","multilinear projection","k nearest neighbors","supervised learning","regression","binary classification","ratio-weighted consensus","baseline comparison"],"falsifier":"Evaluate the method on a smooth but strongly nonlinear target such as $y=\\sin(10x)$ with dense, noise-free samples; if the ratio-weighted consensus is less accurate than plain k-nearest-neighbors on the original inputs, or if the largest errors occur where projected training values $y'_{jt}$ are near zero, the central assumption fails.","tokens_in":3166,"feed_emoji":"📈","tokens_out":8662,"duration_ms":80233,"temperature":0.7,"pith_summary":"This paper introduces a supervised learning method that first approximates an unknown target function $f$ by a linear (or multilinear) projection $f'(X)=W^tX$, then predicts a new input's output as a consensus among the $k$ nearest neighbors of $f'(x)$ in the projected space. The prediction rule is $y = \\frac{1}{k}\\sum_{t} y'\\, y_{jt}/y'_{jt}$, where each neighbor's true label is rescaled by the ratio of projected values. For binary classification, labels are converted to pseudo-probabilities and the same consensus rule decides the class by a $0.5$ threshold. The author reports that implementations of this approach achieved higher accuracies than standard multilayer perceptron, logistic regression, and random forest classifiers on several benchmark datasets, even without parameter tuning.","feed_headline":"Linear projection plus k-nearest-neighbor vote beats standard baselines","feed_subtitle":"Method rescales neighbor labels by a linear fit; tests on benchmark sets show higher accuracy in many cases.","key_machinery":"The central object is the multilinear projection $f'(X)=W^tX$ together with the ratio-weighted consensus formula $y = \\frac{1}{k}\\sum_{t} y'\\, y_{jt}/y'_{jt}$. The projection maps each training point $(X_i, y_i)$ to $(X_i, y'_i)$, and the ratio $y'/y'_{jt}$ rescales each neighbor's true label so that the average reflects the local scaling of the projected output space. Nearest-neighbor search is performed on the projected outputs, so the quality of the linear fit determines whether nearby projected points correspond to nearby true outputs. For classification, the recursive Learn procedure iteratively adjusts pseudo-probability targets, making the classification algorithm a wrapper around the same regression machinery.","core_discovery":"The central claim is that an unknown function can be estimated by projecting it onto a linear function in a new space and then performing a ratio-weighted average of neighbor labels. Concretely, after fitting $f'(X)=W^tX$, the algorithm finds the $k$ nearest neighbors of $y' = f'(x)$ among the projected training outputs and computes $y = \\frac{1}{k}\\sum_{t=j_1}^{j_k} y'\\, y_{jt}/y'_{jt}$. The same formula underlies regression and binary classification: for classification, each label $c_i$ is first assigned a random value $p_i$ in $(0,0.5)$ or $(0.5,1)$, a recursive procedure adjusts these pseudo-targets until they are consistent with the consensus rule, and the final prediction is $1$ if the consensus exceeds $0.5$ and $0$ otherwise. The paper's evidence is a set of accuracy comparisons on a dozen standard binary datasets, in which the linearization approach often outperforms standard multilayer perceptron, logistic regression, and random forest classifiers.","pith_inferences":["The formula behaves like locally adaptive k-nearest-neighbors: where the linear fit is accurate, the ratios are near $1$ and the estimate reduces to plain neighbor averaging; where the fit is poor, small projected values amplify errors, so the method's practical success hinges on the projection capturing the global trend.","The classification procedure's recursive pseudo-label updates form a fixed-point iteration whose convergence and dependence on initialization are not analyzed; testing different update rules could change accuracy substantially.","A natural extension is to replace the mean with the median or to apply the ratio correction to distances as well as labels, which would soften the influence of neighbors with very small projected values.","Comparing this method against kernel ridge regression or Gaussian processes could isolate whether the gain comes from the linear projection itself or from the locally linear correction that the ratio provides."],"forward_implications":["Regression and binary classification share one prediction rule, so improvements to the consensus estimator apply to both settings.","Training cost is dominated by fitting a linear projection and organizing projected points for nearest-neighbor queries, avoiding iterative deep or ensemble training.","If the reported comparisons hold, the approach can beat multilayer perceptrons, logistic regression, and random forests on datasets where projected neighborhoods are informative, even without tuning.","Multiclass problems can be handled by reducing to binary problems via one-against-all, as the paper notes.","The prediction rule is inspectable: each neighbor contributes a rescaled vote, so a wrong prediction can be traced to specific neighbors and their projected values."],"supporting_citations":[{"why":"Supplies the linear regression model $Y=W^tX$ that the projection step generalizes.","marker":"[3]"},{"why":"Serves as the logistic regression baseline whose accuracy is compared on the assessment datasets.","marker":"[4]"},{"why":"Serves as the random forest baseline whose accuracy is compared.","marker":"[5]"},{"why":"Serves as the multilayer perceptron baseline whose accuracy is compared.","marker":"[7]"},{"why":"Provides the implementation and datasets used for the reported assessments.","marker":"[9]"},{"why":"Supplies the benchmark datasets used in the accuracy comparison.","marker":"[13]"},{"why":"Describes the distributed machine learning library whose implementations are used as baselines.","marker":"[14]"}],"fun_headline_variants":["Linear projection then neighbor-vote consensus beats standard baselines","Project data linearly, let k neighbors vote, and accuracy improves","Linear-map plus k-NN consensus outperforms MLP, logistic, and forests","Linear projection plus k-NN vote: better than MLP, logistic, and forests"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the target function is locally smooth enough that, for nearby points, the ratio of projected values $y'/y'_{jt}$ tracks the ratio of true values; if the linear projection is a poor fit in a region, the ratio weighting can amplify a neighbor's label into a large, wrong correction.","fun_headline_variants_meta":{"raw":{"variants":["Linear projection then neighbor-vote consensus beats standard baselines","Project data linearly, let k neighbors vote, and accuracy improves","Linear-map plus k-NN consensus outperforms MLP, logistic, and forests","Linear projection plus k-NN vote: better than MLP, logistic, and forests"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00101,"raw_usage":{"total_tokens":4231,"prompt_tokens":869,"completion_tokens":3362,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":485,"completion_tokens_details":{"reasoning_tokens":3283}},"tokens_in":485,"tokens_out":3362,"duration_ms":26515,"temperature":1.0,"reasoning_tokens":3283,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:23:48.672149+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the method on a smooth but strongly nonlinear target such as $y=\\sin(10x)$ with dense, noise-free samples; if the ratio-weighted consensus is less accurate than plain k-nearest-neighbors on the original inputs, or if the largest errors occur where projected training values $y'_{jt}$ are near zero, the central assumption fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the linear regression model $Y=W^tX$ that the projection step generalizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Serves as the logistic regression baseline whose accuracy is compared on the assessment datasets."},{"cited_title":"Breiman, Random forests, Machine learning 45 (1) (2001) 5–32","cited_arxiv_id":null,"evidence_quote":"Serves as the random forest baseline whose accuracy is compared."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Serves as the multilayer perceptron baseline whose accuracy is compared."},{"cited_title":"URL https://github.com/stuenofotso/LinearizationML","cited_arxiv_id":null,"evidence_quote":"Provides the implementation and datasets used for the reported assessments."},{"cited_title":"URL https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/ binary.html","cited_arxiv_id":null,"evidence_quote":"Supplies the benchmark datasets used in the accuracy comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the distributed machine learning library whose implementations are used as baselines."}],"review_version":1}