Algorithmic Blindness in Large Language Models: A Calibration Study of Performance Prediction

Ashish Mahendran Kurapath; Sohan Venkatesh; Tejas Melkote

REVIEW 3 major objections 4 minor 7 references

Frontier LLMs cannot produce calibrated predictions of causal discovery algorithm performance, scoring 15.9% calibrated coverage with most models below random guessing.

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2026-08-02 20:50 UTC pith:IW3VIUTT

load-bearing objection Strong negative result on LLM coverage, but the paper's strongest claim—that Claude's edge is memorization—is not supported by the design. the 3 major comments →

arxiv 2602.21947 v5 pith:IW3VIUTT submitted 2026-02-25 cs.CL

Algorithmic Blindness in Large Language Models: A Calibration Study of Performance Prediction

Sohan Venkatesh , Ashish Mahendran Kurapath , Tejas Melkote This is my paper

classification cs.CL

keywords algorithmic blindnesscalibrated coveragelarge language modelsperformance predictioncausal discoveryalgorithm selectionmemorizationuncertainty calibration

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper asks whether large language models can predict how well a causal discovery algorithm will perform on a given dataset, in the form of calibrated ranges. Across 1,664 comparisons with eight frontier LLMs, the answer is no: the models' predicted intervals contain the true algorithmic mean only 15.9% of the time, and seven of eight models do worse than a random-range baseline. The single model that edges past random (Claude at 39.4%) appears to do so by recalling benchmark-associated statistics rather than by reasoning about algorithm-data interactions. The authors name this failure 'algorithmic blindness' and argue it reflects a structural gap between declarative knowledge about algorithms and calibrated procedural prediction. If correct, the result rules out zero-shot LLMs as trustworthy uncertainty-aware algorithm selectors and motivates empirical evaluation or learned performance predictors instead.

Core claim

The central claim is that frontier LLMs are algorithmically blind: they cannot translate their verbal knowledge of algorithmic assumptions into numerical expectations about empirical performance. Using causal discovery as a testbed, the paper measures calibrated coverage, the fraction of cases where a model's stated range contains the true mean from 100 bootstrap algorithm runs, and finds 15.9% mean coverage across 1,664 model-dataset-algorithm-metric comparisons. Seven of eight models fall below a uniform random baseline of 36.5%, and the best model's 39.4% coverage is marginally above random and attributed to memorization of benchmark statistics rather than principled reasoning. The wide-b

What carries the argument

The central object is 'calibrated coverage' (Eq. 3): for each model, dataset, algorithm, and metric, whether the LLM's aggregated predicted range [l, u] contains the empirical algorithmic mean from 100 bootstrap runs of the algorithm. The paper builds its argument around this interval-coverage metric plus three behavioral memorization probes: range-width compression (tighter predictions on familiar benchmarks than on synthetic data), cross-model agreement collapse (models agree on benchmarks but diverge on synthetic data), and algorithm-specific degradation (LiNGAM uniquely collapses on synthetic data). Together these are intended to separate genuine reasoning from retrieval of benchmark-ass

Load-bearing premise

The paper's claim that the best model's edge is memorization, not reasoning, rests on the assumption that genuine algorithmic reasoning would show similar synthetic-data performance across all four algorithms; but the synthetic data are linear Gaussian, which happens to match one algorithm's objective and violate another's, so the observed pattern does not distinguish reasoning from memorization.

What would settle it

Generate held-out synthetic datasets with a linear non-Gaussian data-generating process (satisfying LiNGAM's identifiability condition) and with a nonlinear Gaussian process (challenging NOTEARS's linear objective), rerun the 52-condition calibration protocol, and check whether LiNGAM's synthetic coverage collapse persists and NOTEARS's boost disappears. If coverage tracks assumption fit rather than benchmark fame, the memorization inference is falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Practitioners should not use zero-shot LLM intervals to choose among causal discovery algorithms; a uniform random range is better calibrated than most frontier models.
Simple dataset-level heuristics outperform seven of eight models, so cheap statistical baselines should be the reference floor for any LLM-based algorithm selector.
The coverage failure is not a confidence-calibration artifact: intervals are far too wide and still miss the true mean, implying absence of a performance model rather than miscalibrated uncertainty.
The memorization account predicts that above-random performance should concentrate on algorithms and metrics with dense benchmark literature; new or obscure algorithms should show the largest degradation.
If algorithmic blindness is general, LLM-assisted algorithm selection in other domains (optimization, SAT solving) should be treated as unvalidated until the same calibration test is run.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The synthetic-data evidence for memorization is confounded: the held-out synthetic graphs are linear Gaussian, which satisfies NOTEARS's optimization objective and violates LiNGAM's non-Gaussian identifiability condition. LiNGAM's synthetic collapse and NOTEARS's stability are exactly what assumption-aware reasoning would predict, so the dissociation may not demonstrate memorization.
A cleaner test of the memorization hypothesis would hold algorithmic assumptions fixed: generate synthetic data that respects each algorithm's identifiability conditions (non-Gaussian for LiNGAM, linear Gaussian for NOTEARS) and check whether collapse persists.
The 36.5% random baseline is inflated by the wide valid metric domains; a more decision-relevant baseline would be a heuristic that always guesses the unconditional mean or median range from training data, which the paper shows scores near Claude.
The paper's protocol (bootstrap ground truth, three prompt formulations, aggregated coverage) is directly transferable to other algorithm-selection tasks; running the same 1,664-comparison calibration test on SAT solvers or graph algorithms would show whether algorithmic blindness is a general LLM property or specific to causal discovery's statistical nuance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Strong negative result on LLM coverage, but the paper's strongest claim—that Claude's edge is memorization—is not supported by the design.

read the letter

You should know two things about this paper. First, the core empirical finding is solid and worth taking seriously: across 1,664 comparisons, eight frontier LLMs produce intervals that contain the true algorithmic mean only 15.9% of the time, and seven of eight do worse than a random baseline. That is a genuinely new and important negative result for anyone thinking about LLM-assisted algorithm selection. Second, the paper's secondary claim—that the best model's marginal above-random performance is “attributable to benchmark memorization rather than principled reasoning”—is not established by the experiments as designed. The synthetic datasets are linear Gaussian, which satisfies NOTEARS's objective and violates LiNGAM's identifiability condition. So the observed dissociation, with LiNGAM collapsing and NOTEARS improving, is exactly what assumption-aware reasoning would predict. The authors even note this in Appendix A, and then in Section 6 concede that their memorization inference relies on indirect behavioral signals. The claim may be true, but the paper's current evidence does not rule out the more parsimonious explanation that some models reason from algorithm-data assumptions.

What the paper does well: the methodology is transparent, the baselines are sensible, the prompt-robustness analysis is a good practice, and the aggregate tables are consistent with the headline coverage figure. The distinction between declarative knowledge and calibrated procedural prediction is a useful framing, and the “algorithmic blindness” label, though a bit grandiose, points at a real phenomenon. The paper is also honest about limitations—it flags the indirectness of the memorization signal and the correlation among metrics.

Where it's softer: the memorization attribution is the main weakness, and it is load-bearing for the abstract's strongest sentence. A simple fix would be to drop or weaken that claim and instead report the algorithm-specific dissociation as an open question. It would also help to report a significance test for Claude versus the random baseline, since the 2.9-point gap is currently described as not meaningful but no test is given. Minor issues: the random baseline's 36.5% is high, which is explained but still worth a sensitivity check; and the paper treats metrics as independent without much discussion of how that affects coverage interpretation.

This paper deserves a serious referee. The central negative result is important, the experimental design is reproducible in principle, and the weak spot is a well-defined interpretational flaw, not a structural one. I would send it out, with the expectation that the memorization claim be revised or re-tested on non-Gaussian synthetic data. For a reading group, it would generate a good methodological discussion.

Referee Report

3 major / 4 minor

Summary. The paper evaluates whether eight frontier LLMs can provide calibrated interval predictions for the performance of four causal-discovery algorithms on thirteen datasets. Ground-truth means are obtained from 5,200 bootstrap algorithm runs, and LLM ranges are elicited with three prompt formulations per condition, yielding 1,664 coverage comparisons. The primary empirical finding is a mean calibrated coverage of 15.9%, with seven of eight models below a uniform-random baseline of 36.5%; the best model, Claude, reaches 39.4% but the authors attribute this edge to benchmark memorization rather than reasoning. The paper proposes the term 'algorithmic blindness' for the observed failure.

Significance. If the primary coverage finding is accepted, this is a useful and timely negative result: it suggests that current LLMs cannot serve as calibrated zero-shot performance predictors for causal-discovery algorithm selection. The evaluation is unusually explicit about protocol: multiple prompt formulations, external ground truth from repeated runs, and uninformed baselines. No fitted parameters are recycled into the evaluation, and the aggregate coverage result is internally consistent. However, the paper's strongest interpretive claim—that Claude's above-random coverage is memorization—is not supported by the reported experiments, because the synthetic-data design is confounded with the algorithms' own identifiability assumptions. The primary contribution can stand after reanalysis or softening of the memorization claim, but the current abstract overstates what the data establish.

major comments (3)

[§4.1, §4.4, Appendix A] The synthetic datasets are generated from linear Gaussian DAGs (Section 3.1). Appendix A states that NOTEARS's optimization objective in Eq. (8) is exactly the linear-Gaussian least-squares problem, while LiNGAM's identifiability requires non-Gaussian noise (Eqs. 5–6). The observed dissociation—LiNGAM collapses on synthetic data (−23.2% across all models; −16.0% for Claude) while NOTEARS does not (+1.7%; +24.3% for Claude)—is therefore exactly what assumption-aware reasoning would predict. It cannot be used as 'the hallmark of pattern matching against benchmark statistics' (§4.1) nor as support for the Abstract's claim that Claude's 39.4% is 'attributable to benchmark memorization.' Section 6 concedes that alternative explanations cannot be ruled out. This load-bearing inference should either be removed from the headline or tested with non-Gaussian synthetic data and/or direct training-d
[§4.5, Tables 7–8, Figures 5–6] The three memorization probes are confounded with graph size and algorithmic difficulty. The benchmark-versus-synthetic comparison mixes 5–70-node benchmarks with 12–60-node synthetic graphs, so the observed 2.26× range-width compression and the 2.6× cross-model disagreement gap partly reflect that larger graphs have more possible structures and a wider SHD range. The monotonic 15× collapse in cross-model agreement with synthetic network size is not decisive against principled reasoning: any reasonable estimator would show larger uncertainty and wider disagreement on larger, more complex instances. The authors should supply size-matched controls, or normalize by graph order/edge density and SHD scale, before interpreting these patterns as memorization signals.
[§3.4, Tables 1 and 4] The random baseline is not a no-reasoning floor: a predictor that always returns the full valid range for every metric would trivially achieve 100% coverage while carrying no information. The claim that seven models are 'worse than random guessing' is only meaningful under a scoring rule that trades coverage against interval width. The 'Mean Score' columns in Tables 1 and 4 are never defined, nor is any proper interval score (e.g., Winkler score or CRPS) reported. Please define the mean score and either report width-matched baseline comparisons or restrict the random-baseline claim to the specific uniform-interval construction described.

minor comments (4)

[§3.3] The aggregation step averages lower and upper bounds across the three prompt formulations, which can create an interval that no single prompt produced. Reporting per-formulation coverage in addition to the aggregated coverage would clarify how much of the result depends on this arithmetic averaging.
[References] Several reference entries contain formatting errors (e.g., 'V owels' in the D'ya like DAGs entry; 'Bühlman' should be 'Bühlmann'). The 'and 1 others' placeholders should be resolved with full author lists.
[Reproducibility] No code or data release is mentioned. Given the study is empirical and prompt-sensitive, releasing the exact prompts, raw model outputs, and ground-truth tables would substantially strengthen the paper's contribution.
[§4.3] The statement that models with true understanding 'would provide consistent estimates regardless of minor phrasing variations' is stronger than warranted. Prompt sensitivity alone is not a direct measure of understanding; it is compatible with genuine competence plus sensitivity to surface form. The evidence of instability is interesting, but the interpretive language should be more cautious.

Circularity Check

0 steps flagged

No significant circularity: the study is an external empirical evaluation with ground truth from independent algorithm runs, not a derivation from its own outputs or fitted parameters.

full rationale

The paper's central numeric claims -- 15.9% calibrated coverage, per-model coverage, baseline comparisons -- are measured against ground truth computed from 100 bootstrap algorithm runs per condition (Section 3.1), an external target that does not incorporate any LLM output or fitted model. No parameter is fitted and then renamed as a prediction; no equation makes the result equal to its input by construction; and there are no self-citations from the authors carrying the argument (the reference list contains no works by Venkatesh, Kurapath, or Melkote). The memorization attribution for Claude in Sections 4.1 and 4.4 is an interpretive inference from indirect behavioral signals (algorithm-specific synthetic degradation, range-width compression, cross-model agreement collapse). Section 6 explicitly concedes: 'Our memorization inference relies on indirect behavioral signals such as range width compression, cross-model agreement collapse and algorithm-specific degradation rather than direct training data attribution, so we cannot rule out alternative explanations for these patterns.' The skeptical concern that linear-Gaussian synthetic data advantage NOTEARS and disadvantage LiNGAM by the algorithms' own assumptions (Appendix A, Eqs. 5-8) is a confound/validity critique of the memorization interpretation, not a circularity: the observed dissociation does not reduce by construction to the conclusion 'memorization.' The empirical evaluation is self-contained against external benchmarks; any weakness in the strongest claim is a correctness or interpretation risk, not a circular derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 1 invented entities

The evaluation relies on no fitted free parameters. The load-bearing assumptions are bootstrap ground-truth stability, the validity of coverage as a calibration measure, the adequacy of a uniform-in-domain random baseline, and—for the memorization conclusion—that benchmark-vs-synthetic gaps are driven by training-data exposure rather than by algorithm-data mismatch. The linear-Gaussian synthetic design makes the last assumption questionable.

axioms (4)

domain assumption 100 bootstrap runs per condition yield empirical means stable enough to serve as the coverage target.
Section 3.1: ground truth is the empirical mean over 100 runs; the authors note in Limitations that for high-variance algorithms this may be unstable.
domain assumption Calibrated coverage—whether an LLM range contains the empirical mean—is a valid operational measure of predictive calibration.
Section 3.3 defines coverage using the Gneiting and Raftery interval-prediction framework.
domain assumption A uniformly random range over each metric's valid domain is an appropriate uninformed baseline for calibration.
Section 3.4 uses this baseline; its elevated coverage is acknowledged to reflect wide valid domains rather than predictive skill.
ad hoc to paper Synthetic and benchmark datasets are matched in difficulty, so benchmark-vs-synthetic differences indicate memorization rather than algorithm-data mismatch.
This load-bearing premise for the memorization claim is undermined by Section 3.1's linear-Gaussian synthetic generation, which matches NOTEARS and violates LiNGAM's assumptions.

invented entities (1)

algorithmic blindness no independent evidence
purpose: Conceptual label for the claimed inability of LLMs to translate declarative algorithmic knowledge into calibrated procedural performance expectations.
The term is defined and operationalized only through calibrated coverage in this paper; there is no separate external evidence for the construct.

pith-pipeline@v1.3.0-alltime-deepseek · 16783 in / 13112 out tokens · 120296 ms · 2026-08-02T20:50:51.475484+00:00 · methodology

0 comments

read the original abstract

Large language models (LLMs) demonstrate remarkable breadth of knowledge, yet their ability to reason about computational processes remains poorly understood. Closing this gap matters for practitioners who rely on LLMs to guide algorithm selection and deployment. We address this limitation using causal discovery as a testbed and evaluate eight frontier LLMs against ground truth derived from algorithm executions. We find systematic, near-total failure across models. The predicted ranges are far wider than true confidence intervals yet still fail to contain the true algorithmic mean in most cases. Most models perform worse than random guessing. The best model's marginal improvement points to benchmark memorization rather than principled reasoning. We term this failure algorithmic blindness and argue it reflects a fundamental gap between declarative knowledge about algorithms and calibrated procedural prediction.

Figures

Figures reproduced from arXiv: 2602.21947 by Ashish Mahendran Kurapath, Sohan Venkatesh, Tejas Melkote.

**Figure 2.** Figure 2: Illustration of our methodology. LLMs are prompted with dataset characteristics and algorithmic [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: (a) Mean calibrated coverage on benchmark [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: (b) Coverage collapse across synthetic net [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Predicted range width: benchmark vs. syn [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: (a) Cross-model pairwise distance on benchmark versus synthetic datasets. (b) Mean cross-model pairwise [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Three prompt formulations used across all experimental conditions. Formulation 1 elicits direct numerical [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

7 extracted references · 5 linked inside Pith

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In The Twelfth International Conference on Learning Representations

Large language models as optimizers. In The Twelfth International Conference on Learning Representations. Xun Zheng, Bryon Aragam, Pradeep K Ravikumar, and Eric P Xing. 2018. Dags with no tears: Continu- ous optimization for structure learning.Advances in neural information processing systems, 31. Yujia Zheng, Biwei Huang, Wei Chen, Joseph Ramsey, Mingmin...

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Shohei Shimizu, Patrik O Hoyer, Aapo Hyvärinen, Antti Kerminen, and Michael Jordan

Bayesian networks with examples in r. Shohei Shimizu, Patrik O Hoyer, Aapo Hyvärinen, Antti Kerminen, and Michael Jordan. 2006. A linear non- gaussian acyclic model for causal discovery.Journal of Machine Learning Research, 7(10). David J Spiegelhalter, A Philip Dawid, Steffen L Lau- ritzen, and Robert G Cowell. 1993. Bayesian anal- ysis in expert systems...

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Pith/arXiv arXiv 2006

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Nicholas Carlini, Daphne Ippolito, Matthew Jagielski, Katherine Lee, Florian Tramer, and Chiyuan Zhang

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arXiv preprint arXiv:2410.05229

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An Yang, Enrui Yang, Bohan Zhang, Kai Hui, Kangfei Zheng, Hongyi Yu, Jipeng Li, Yuzhen Liu, Donghao Zhao, Yingqiang Ge, and 1 others

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