{"id":"70e9c77b-d5e9-4ebd-bc75-733e35e48adb","arxiv_id":"2507.03884","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The Rashomon Effect, the existence of many equally accurate models, suppresses the accuracy-simplicity tradeoff, making simple models as accurate as complex ones for noisy problems.","lead":"This perspective argues that Leo Breiman's accuracy-simplicity tradeoff, the Occam Dilemma, is nullified by the Rashomon Effect: when many equally good models exist, some of them are likely to be simple. It reinterprets Breiman's notion of simplicity and argues that interpretable models can match black boxes on noisy problems.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Rashomon-to-simplicity step lacks quantitative condition; without it the central claim is a non-sequitur, not a proof.","rationale":"The reader's CONDITIONAL verdict is appropriate because the paper does not provide a self-contained proof of the central claim. Our concern sharpens this: the missing condition is not merely a technicality but could be violated in natural settings, so the paper's headline claim is not established. The concrete test would settle whether the concern lands by constructing an explicit counterexample or showing that the condition holds empirically. If the test finds R < D, the paper's universal phrasing should be weakened to a conditional claim about datasets where the approximation gap is small enough. If R >= D across settings, the paper's intuition is supported, but a formal theorem is still needed. We agree partially with the reader's weakest assumption: both point to the unquantified step from a large Rashomon set to the existence of a simpler model, but we add a concrete failure mode and a test. The verdict should remain CONDITIONAL because the paper's contribution as a perspective is still interesting, but its central logical claim requires either a precise theorem or a caveat.","tokens_in":10098,"tokens_out":6875,"duration_ms":73242,"concrete_test":"Synthetic experiment: generate data from f(x)=x^10 with Gaussian noise (n=200, sigma=0.1). Fit degree-10 polynomials (complex class) and degree-1 polynomials (simple class). Define the Rashomon radius R as the largest radius around the best degree-10 coefficient vector for which every model inside has validation loss within one standard error of the best complex model's loss. Compute the distance D (in L2 function space) from the best degree-10 fit to the nearest degree-1 polynomial. If R < D for any sigma in {0.01, 0.1, 1} or for other non-smooth targets (e.g., sinusoids), the paper's universal claim is refuted; if R >= D in all cases, the claim's condition holds in the tested regimes but a formal theorem is still absent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.2 argues that a large Rashomon set contains a ball of functions and that 'if the ball is large enough, the simplest models in the ball may be polynomials of a smaller degree.' The phrase 'large enough' is never quantified or tied to dataset properties. The central claim—the Rashomon effect causes the accuracy/simplicity tradeoff to vanish—therefore lacks a logical foundation. To see the gap, take target f(x)=x^10, noise sigma, complex class degree-10 polynomials, simple class degree-1. For moderate sigma, the set of degree-10 models within one standard error of the best fit can be large (many near-optimal coefficient vectors), yet the nearest degree-1 polynomial is a distance of order 1 away in function space, far exceeding sigma. Thus a large Rashomon set and a tradeoff coexist. The paper's escape clause, 'as long as ... functions from a simpler class can represent those from the more complex class sufficiently well,' is precisely the condition that fails here; the paper gives no basis for believing it holds broadly. Since the proof from [SRP22] is not reproduced, the assertion that the Rashomon effect nullifies the Occam dilemma is unsupported: it is either tautological if 'large enough' is defined to include reaching simpler models, or false if 'large enough' means merely many equally good models.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This perspective paper revisits Leo Breiman's \"Two Cultures\" dichotomy and argues that Breiman's accuracy/simplicity tradeoff, the Occam Dilemma, is generally false. The paper's central claim is that the Rashomon Effect—the existence of many approximately equally good models—does not coexist with an accuracy/simplicity tradeoff; rather, a sufficiently large Rashomon set forces the appearance of simpler models that are also accurate. The paper attributes Breiman's contrary observation to his narrow notion of simplicity (linear models and unoptimized CART trees), presents Bruce Hoadley's 2001 credit-scoring experience as early empirical evidence, and argues that causal questions can be addressed without fitting a single interpretable data model, citing model-free methods such as Rashomon Importance Distributions and Almost Matching Exactly.","tokens_in":10265,"tokens_out":4229,"duration_ms":44650,"significance":"If the central claim were rigorously established, it would substantially reframe a foundational debate in statistics and machine learning, strengthening the case for interpretable modeling in noisy tabular settings and converting the Occam Dilemma from a presumed law into a symptom of restricted model classes and insufficient computation. The paper is valuable as a synthesis: it crisply identifies the logical tension in Breiman's position, brings forward Hoadley's striking field evidence, and connects the discussion to concrete modern tools such as optimized sparse decision trees, sparse GAMs, and risk scores. However, the paper's primary theoretical assertion is not derived here; it is cited to the author's earlier work, and the conditions under which the assertion holds are only stated qualitatively. The significance is therefore conditional on the cited theorem and on the breadth of the empirical claim being better quantified.","major_comments":[{"comment":"The inference from \"a large Rashomon Effect\" to \"there exist simpler accurate models\" is not established in this manuscript. The text states that \"if the ball is large enough, the simplest models in the ball may be polynomials of a smaller degree,\" but \"large enough\" is never quantified, and the later condition that \"functions from a simpler class can represent those from the more complex class sufficiently well\" is also left qualitative. This is the load-bearing step of the paper's main claim. A concrete counterexample shows why quantification matters: take target f(x)=x^10, complex class of degree-10 polynomials, and simple class of degree-1 polynomials. For moderate noise, the set of degree-10 models within one standard error can be large (many near-optimal coefficient vectors), yet the nearest degree-1 polynomial is far outside the error tolerance, so a large Rashomon set and a tradeoff coexist. The paper's escape clause is exactly the condition that fails in this example, but no argument is given that the clause holds broadly. If the theorem in [SRP22] contains precise conditions, those conditions should be stated here; otherwise the central claim is a non-sequitur.","section":"Section 2.2"},{"comment":"The paper's key explanatory mechanism—that noise in the world causes increased variance, which forces simpler models and a larger Rashomon set—is presented narratively rather than formally. Neither \"sufficient noise\" nor \"sufficiently well\" is defined in terms of loss functions, model classes, or dataset properties. As a result, the central assertion is not falsifiable in its current form. To make the claim testable, the paper should specify the hypothesis class, the loss, the error tolerance defining the Rashomon set, and a quantitative condition under which the distance between the complex and simple classes is smaller than the Rashomon set's radius. Without such a specification, the statement that the Rashomon Effect causes the Occam Dilemma to vanish cannot be distinguished from a tautology about a specially chosen notion of \"large enough.\"","section":"Sections 2.2-2.3"},{"comment":"The empirical generalization \"For most tabular data problems with noise in the outcomes, very sparse models perform similarly to complicated black box models\" is supported in the manuscript mainly by a series of studies from the author's group and by the single historical case of Hoadley. While these are suggestive, the breadth of the claim exceeds the evidence shown here. The paper would be strengthened by a small systematic comparison table listing datasets, model classes, and accuracy differences, or by explicitly framing the statement as a research hypothesis rather than an established fact. This matters because the paper's conclusion about the nonexistence of the tradeoff in practice depends on this generalization.","section":"Section 2.3"}],"minor_comments":[{"comment":"The abstract and Section 1 state that the Rashomon Effect \"causes\" the accuracy/simplicity tradeoff to vanish, while Section 2.2 concludes only under two qualitative conditions (sufficient noise and sufficient representability). The wording should be aligned so that the earlier statements match the conditional nature of the later argument.","section":"Abstract and Section 1"},{"comment":"The phrase \"its 2 δ-packing number\" should be typeset as \"its 2δ-packing number,\" and the symbol δ should be defined in the caption or nearby text.","section":"Figure 1 caption"},{"comment":"In the sentence \"If we want to estimate the effect that a chosen variablev has on the outcome,\" there is a missing space: \"variable v.\"","section":"Section 5"},{"comment":"The quotation from Breiman contains \"more accurate predictors in classification and regression then neural nets\"; if this is a direct quote the spelling should be checked against the original, and if it is the author's own sentence, \"then\" should be \"than.\"","section":"Section 3.2"},{"comment":"The phrase \"They haven't made a dent on a multitude of noisy problems – because they can't\" is rhetorically strong but overstated. A more precise phrasing, such as \"they have not been shown to improve accuracy over simpler methods in many noisy problems,\" would better match the evidence presented.","section":"Section 2.3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is clearly written and the historical synthesis is useful, but the central theoretical claim rests on the author's own prior work without the relevant conditions being restated, and much of the supporting empirical evidence is self-referential. The editor should weigh whether the journal expects an original technical contribution; as a perspective, the paper can be acceptable if the authors either state the precise conditions from the cited theorem or visibly soften the central claim. The Hoadley case and the section on model-free causality are the most distinctive contributions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a perspective essay, not a new technical result. The paper reads well and does something genuinely useful: it argues Breiman's 'simple' meant linear models and off-the-shelf CART, and it resurrects Hoadley's comment as early evidence against the tradeoff. That historical framing is the real contribution. I also credit the paper for openly saying the formal argument follows [SRP22] rather than trying to reproduce it here.\n\nWhere I part company with the reader's conditional verdict is only on severity. The paper's central sentence—'the Rashomon Effect causes the accuracy/simplicity tradeoff to vanish'—is considerably stronger than the 'as long as' condition later in Section 2.2. The stress-test note identifies the exact gap. 'Large enough' is never tied to the noise level or to an approximation error between function classes. The degree-10/degree-1 example is a legitimate counterexample to the unqualified statement: you can have many near-equally-good complex models and still have no simple model within tolerance. The paper's own escape clause, 'functions from a simpler class can represent those from the more complex class sufficiently well,' is the missing assumption, and the paper gives no quantitative reason to believe it holds broadly. So a reader cannot use this preprint to establish the nullification claim; they need [SRP22] and related papers, and even those are not checked here.\n\nIs that fatal? For a perspective paper, not entirely. The paper is honest about most of these qualifications. My main editorial gripe is that the abstract and introduction don't carry the same caveats as Section 2.2. The self-citation pattern is heavy but not misleading—the cited work is the relevant work.\n\nBottom line: if you want a readable, historically grounded argument for why interpretable models should often be the default on noisy tabular data, this is a fine piece. If you want a proof that the Occam dilemma vanishes, you don't get it here. I would send it to peer review as a perspective, with the expectation that the authors either add a formal statement of sufficient conditions or soften the abstract.","headline":"A clear, well-written perspective, but the nullification claim rests on an unquantified 'large enough' inherited from prior work; the stress-test counterexample is a fair hit.","tokens_in":10826,"tokens_out":2706,"would_cite":false,"duration_ms":27134,"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 claims that a large Rashomon effect—many equally good models—and an accuracy-simplicity tradeoff cannot coexist; the effect makes the tradeoff vanish.","keywords":["Rashomon effect","Occam dilemma","accuracy-simplicity tradeoff","interpretable machine learning","Rashomon set theory","noisy tabular data","sparse decision trees","Two Cultures"],"falsifier":"For a synthetic problem where the true complexity is known, increase the label noise and measure the smallest model that still reaches near-best accuracy. The paper's logic says that size should not grow with noise; if it does, the central claim fails.","tokens_in":9820,"feed_emoji":"","tokens_out":8059,"duration_ms":84543,"temperature":0.7,"pith_summary":"The paper revisits Leo Breiman's 2001 'Two Cultures' essay and challenges one of its central warnings, the Occam Dilemma: that accurate predictive models must be complicated and hard to interpret. It argues that a large Rashomon effect—many different models with nearly equal accuracy—is incompatible with an accuracy-simplicity tradeoff. If many models fit the data almost equally well, then, under the Rashomon Set Theory the paper relies on, some of those models will be simple as well as accurate. The author concludes that for noisy tabular data, interpretable models such as sparse additive models and optimized decision trees can match black-box performance, and that causality can be sought without fitting a single explanatory model.","feed_headline":"Rashomon effect cancels accuracy-versus-simplicity tradeoff","feed_subtitle":"When noise yields many good models, interpretable models can match black-box accuracy without a performance penalty.","key_machinery":"The central object is the Rashomon set, the collection of all models whose predictive loss is within a chosen tolerance of the best loss on a dataset. The argument uses the geometry of function balls in that set: if the set is large enough to contain whole neighborhoods of functions, and if simpler function classes approximate complex ones well, then at least one delta-close simpler model sits inside each neighborhood. This converts noise-driven variance in the loss into an abundance of equally good models, and the abundance forces simpler models into the set. The size of the set can be measured by packing numbers, the number of separated balls of models it contains.","core_discovery":"On the paper's own terms: the Rashomon effect does not coexist with the Occam Dilemma. A dataset with sufficiently noisy outcomes admits a large Rashomon set, the collection of models whose loss is within a small tolerance of the best achievable loss. Within that set, function classes are often nested and approximating, so a ball of complex models contains at least one model from a simpler class. Hence a large Rashomon set contains simpler, accurate models, and the supposed tradeoff between accuracy and simplicity disappears. Breiman's contrary observation is attributed to his narrow notion of simplicity: linear models and unoptimized CART trees, both of which are stunted compared to modern sparse generalized additive models and optimized sparse decision trees. The paper maintains Breiman's goals—accuracy, simplicity, causal insight—but argues they can be reached by model-free causal methods and interpretable prediction models instead of a single explanatory data model.","pith_inferences":["If the claim is right, benchmark competitions on noisy tabular data that report tiny accuracy differences among methods are largely measuring noise within the Rashomon set; the more consequential objective is to find the simplest member of the set.","This suggests a practical design rule: on any noisy tabular dataset, first enumerate or approximate the Rashomon set, then choose the simplest model inside it, rather than optimize a single regularized objective.","A testable extension would be to measure the minimal complexity of an epsilon-optimal model as noise increases on controlled datasets; the paper's logic predicts that complexity should stay flat while the Rashomon set grows.","The noisy/non-noisy split implies that claims about the Occam Dilemma should be stratified by noise level; a tradeoff may reappear in near-deterministic problems even if it vanishes in noisy ones."],"forward_implications":["On noisy tabular problems, practitioners should expect sparse GAMs, optimized decision trees, and risk scorecards to match more complex black-box models, so interpretable models can be used in high-stakes decisions without an accuracy penalty.","The accuracy-simplicity tradeoff that motivated black-box model use is not a general law; it appears only when simplicity is defined so narrowly that the intermediate class of expressive but interpretable models is excluded.","Non-noisy problems, such as image classification, behave differently: the Rashomon effect is weaker, so the arguments that erase the tradeoff for noisy data do not transfer unchanged to deterministic-label settings.","Causal insight does not require a single simple model: variable-importance distributions over many good models and case-based matching methods can give interpretable causal information without claiming to model the data-generation process."],"supporting_citations":[{"why":"Defines the Two Cultures framing, the Rashomon Effect, and the Occam Dilemma that the paper's argument targets.","marker":"[Bre01]"},{"why":"Supplies the Rashomon Set Theory proof that a sufficiently large Rashomon set contains simpler accurate models.","marker":"[SRP22]"},{"why":"The companion paper whose talk this perspective accompanies; it develops the consequences of many good models and illustrates the geometric argument.","marker":"[RZS+24]"},{"why":"Shows that the entire Rashomon set of sparse decision trees can be enumerated, providing empirical evidence of many equally good interpretable trees.","marker":"[XZC+22]"},{"why":"Representing Rashomon sets for generalized linear and additive models provides evidence that simple model classes achieve comparable accuracy.","marker":"[ZCL+23]"},{"why":"Argues that for high-stakes problems interpretable models should replace black-box models, supporting the paper's no-tradeoff position.","marker":"[Rud19]"},{"why":"Introduces the noise-to-simplicity mechanism by which noise increases variance in loss and leads to a larger, simpler-containing Rashomon set.","marker":"[SCPR23]"},{"why":"Extends the noise-based explanation of how simpler models emerge without learning, reinforcing the core mechanism.","marker":"[BCS+24]"},{"why":"Defines CART, which the paper identifies as Breiman's unoptimized decision-tree baseline that should not be conflated with all decision trees.","marker":"[BFSO84]"}],"fun_headline_variants":["Rashomon effect nullifies accuracy-simplicity tradeoff","Many good models mean simple ones can match black boxes","The Occam Dilemma is a myth under Rashomon effect","When noise creates many models, simple models suffice","Accuracy and simplicity can coexist via Rashomon sets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument depends on the assumption that whenever there is enough noise to create many equally good models, at least one accurate model in that crowd is simple enough to be interpretable; the paper gives no quantitative test for when that must happen.","fun_headline_variants_meta":{"raw":{"variants":["Rashomon effect nullifies accuracy-simplicity tradeoff","Many good models mean simple ones can match black boxes","The Occam Dilemma is a myth under Rashomon effect","When noise creates many models, simple models suffice","Accuracy and simplicity can coexist via Rashomon sets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000417,"raw_usage":{"total_tokens":2219,"prompt_tokens":1082,"completion_tokens":1137,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":698,"completion_tokens_details":{"reasoning_tokens":1073}},"tokens_in":698,"tokens_out":1137,"duration_ms":9735,"temperature":1.0,"reasoning_tokens":1073,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:00:00.813953+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For a synthetic problem where the true complexity is known, increase the label noise and measure the smallest model that still reaches near-best accuracy. The paper's logic says that size should not grow with noise; if it does, the central claim fails.","supporting_citations":[],"review_version":1}