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arxiv: 2605.25773 · v2 · pith:5HRNFCI6new · submitted 2026-05-25 · 📊 stat.ML · cs.AI· cs.CL· cs.LG

Efficient Benchmarking Is Just Feature Selection and Multiple Regression

Sam Bowyer , Acyr Locatelli , Kris Cao This is my paper

Pith reviewed 2026-06-29 20:18 UTC · model grok-4.3

classification 📊 stat.ML cs.AIcs.CLcs.LG
keywords efficient benchmarkingfeature selectionkernel ridge regressionmRMRLLM evaluationmultiple regressionprediction errorranking correlation
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The pith

Reframing efficient benchmarking as feature selection plus kernel ridge regression yields lower prediction errors and stronger rank correlations for LLM scores.

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

The paper shows that predicting full benchmark scores from a small subset of questions works best when the task is treated as multiple regression. Kernel ridge regression for the prediction step already improves on existing efficient benchmarking techniques, and pairing it with the mRMR algorithm for choosing the questions improves results further. These gains appear in both absolute error measures and in how well the predicted rankings match the true ones, and they hold across binary and continuous metrics on several benchmarks. The new combination is also faster to run and selects more stable question subsets than prior approaches. A reader would care because cheaper, more reliable ways to estimate model performance matter when full evaluation is expensive.

Core claim

By casting efficient benchmarking as multiple regression with feature selection, kernel ridge regression at the prediction stage combined with mRMR for selecting question subsets consistently produces smaller errors in mean absolute and root mean squared terms, and stronger Spearman and Kendall rank correlations between predicted and actual scores than prior methods, while being computationally faster and more stable across different data splits.

What carries the argument

minimum redundancy maximum relevance (mRMR) feature selection paired with kernel ridge regression for predicting full benchmark scores from a chosen subset of questions

Load-bearing premise

That performance on a small, selected subset of benchmark questions is sufficiently predictive of performance on the full set via a kernel ridge regression model, without the subset choice or model introducing systematic bias across models or benchmarks.

What would settle it

Running the mRMR-plus-kernel-ridge method on a fresh benchmark and model collection and finding that its MAE, RMSE, Spearman ho, or Kendall au values are worse than those from existing efficient benchmarking techniques.

Figures

Figures reproduced from arXiv: 2605.25773 by Acyr Locatelli, Kris Cao, Sam Bowyer.

Figure 1
Figure 1. Figure 1: Our method (mRMR+/++) leads to significantly better benchmark score predictions in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) With M = 30, mRMR++ consistently achieves lower predictive errors and higher ranking correlations than other methods at a variety of coreset sizes. (b) Whilst mRMR methods struggle with very small M, for M ∈ {30, 50}, mRMR++ dominates in both errors and ranking correlations using 10% coresets. (For clarity, we omit d = 1 methods here except for mRMR to show the relative size of underperformance.) Refit… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Question difficulty distribution (proportion of all models which fail a given question) over coresets (coloured) vs full benchmarks (grey). (MMLU, other datasets are shown in § K.) (b) mRMR achieves greater coreset stability across random seeds, M and coreset size compared to all other competitive methods. (c) mRMR is significantly faster than all others except random sampling. We ran each method with … view at source ↗
Figure 4
Figure 4. Figure 4: (a; M = 32, see § H for other M values) Continuous non-pass@k benchmarks. (b; M = 15) Constructing coresets with pass@1 and predicting on all k ∈ {1, 2, 4, . . . , 64} . 3.1 Binary scores For binary evaluations, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: True vs. predicted summary scores on ARC-C for source (train) models and test models for [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance gains from polynomial ridge regresion become less pronounced as the [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Same setting as Fig. 6 but with relative-sized coresets: [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Binary-dataset results on 10% coresets using [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Ablations on mRMR schemes and MI-estimator nearest-neighbour hyperparameter [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Ablations on mRMR schemes and MI-estimator nearest-neighbour hyperparameter [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Ablations on mRMR schemes and MI-estimator nearest-neighbour hyperparameter [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Ablations on binary experiments over the form of prediction (ridge regression, polynomial [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The relevance, redundancy, difference (relevance [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Our method maximises the MIQ mRMR objective (Eq. (6)) better than other methods, [PITH_FULL_IMAGE:figures/full_fig_p027_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Feature selection metrics during coreset construction for different mRMR variants. [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Ablations on IRT dimensionality p ∈ {1, 5, 10} for gp-IRT on the binary experiments in § 3.1. 5 10 15 Coreset Size (%) 0.4 0.6 0.8 (a) RMSE (%) 5 10 15 Coreset Size (%) 0.2 0.4 0.6 MAE (%) 5 10 15 Coreset Size (%) 0.85 0.90 Kendall  5 10 15 Coreset Size (%) 0.94 0.96 0.98 Spearman  20 30 40 50 Num Source Models 0.4 0.6 (b) 20 30 40 50 Num Source Models 0.2 0.3 0.4 0.5 20 30 40 50 Num Source Models 0.86 … view at source ↗
Figure 17
Figure 17. Figure 17: Ablations on IRT dimensionality p ∈ {1, 5, 10} for gp-IRT variants on the continuous experiments in § 3.3. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Ablations on IRT dimensionality p ∈ {1, 5, 10} for gp-IRT variants on the pass@k experiments in § 3.3. H Varying the number of source models In [PITH_FULL_IMAGE:figures/full_fig_p031_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Results from § 3.2. (a) M = 32. (b) 10% coresets. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Results from § 3.1. (a) M = 15. (b) 10% coresets. I Pearson’s correlation coefficient results We do not report Pearson correlation coefficients between true and predicted scores of models in the main text because it is more informative to report ranking correlation coefficients τ and ρ which are not affected by the scale of scores. However, in [PITH_FULL_IMAGE:figures/full_fig_p032_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Pearson correlation coefficients on binary experiments in § 3.1. [PITH_FULL_IMAGE:figures/full_fig_p032_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Pearson correlation coefficients on continuous non-pass@ [PITH_FULL_IMAGE:figures/full_fig_p033_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Pearson correlation coefficients on pass@ [PITH_FULL_IMAGE:figures/full_fig_p033_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: (a) Φˆ stability on methods in binary experiments, as shown in [PITH_FULL_IMAGE:figures/full_fig_p033_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Question difficulty distribution histograms on various datasets for coresets generated using [PITH_FULL_IMAGE:figures/full_fig_p034_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: True versus predicted scores on ARC-Challenge, with each row representing a different [PITH_FULL_IMAGE:figures/full_fig_p035_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: True versus predicted scores on more binary datasets (the same as in Fig. 25) across five [PITH_FULL_IMAGE:figures/full_fig_p036_27.png] view at source ↗
read the original abstract

Efficient benchmarking techniques aim to lower the computational cost of evaluating LLMs by predicting full benchmark scores using only a subset of a benchmark's questions. By reframing this problem as an instance of multiple regression with feature selection, we find that existing efficient benchmarking methods can be greatly improved by simply using kernel ridge regression at the prediction stage. Additionally, using an information-theoretic feature-selection algorithm called minimum redundancy maximum relevance (mRMR), we can further improve upon these methods by selecting question subsets that will be maximally useful for prediction. Except in very data-poor settings, these approaches consistently achieve smaller prediction errors (in both MAE and RMSE), and greater ranking correlation between predicted and true scores (in both Spearman $\rho$ and Kendall $\tau$) across a range of benchmarks using both binary and continuous metrics. Furthermore, mRMR subsampling is much faster than competitor methods (which often involve fitting probabilistic models or running clustering algorithms), and is more likely to select the same questions under different random seeds or training data splits. Tutorial code can be found at https://github.com/sambowyer/mrmr_eval .

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reframes efficient LLM benchmarking as a multiple regression task with feature selection. It claims that replacing existing predictors with kernel ridge regression (KRR) and using minimum redundancy maximum relevance (mRMR) to select question subsets yields lower MAE and RMSE, higher Spearman ρ and Kendall τ, faster computation, and greater stability across seeds and splits than prior methods, except in very data-poor regimes. Tutorial code is provided.

Significance. If the empirical claims hold under proper controls, the work supplies a simple, computationally lightweight alternative to clustering or probabilistic-model-based subsampling for efficient benchmarking. The emphasis on reproducibility via public code is a strength.

major comments (2)
  1. [Experimental evaluation (implicit in abstract claims)] The central claim that mRMR-selected subsets plus KRR produce unbiased predictions for models outside the training distribution is load-bearing. The abstract and methods description give no indication that experiments were stratified by model family, architecture, or training corpus; mRMR relevance scores are computed from full-benchmark scores of the training models, so any architecture-correlated question difficulty can be absorbed by the kernel and produce systematic over- or under-prediction on unseen families. Without such a split, the reported improvements cannot be taken as general.
  2. [Results and discussion] The statement that improvements hold 'except in very data-poor settings' is not accompanied by a concrete definition of that regime or by ablation tables showing the transition point. This boundary is central to the practical recommendation yet remains unquantified.
minor comments (2)
  1. [Abstract] The abstract asserts consistent gains in four metrics but supplies no dataset sizes, number of models, error bars, or baseline descriptions; these details must appear in the main text with explicit controls for post-hoc model selection.
  2. [Methods] Notation for the regression target (full-benchmark score) and the feature matrix (question-level scores) should be introduced once and used consistently; the current description leaves the precise mapping from binary/continuous metrics to the regression problem implicit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments identify important gaps in experimental controls and result quantification. We respond to each below and commit to revisions that directly address the concerns.

read point-by-point responses

  1. Referee: [Experimental evaluation (implicit in abstract claims)] The central claim that mRMR-selected subsets plus KRR produce unbiased predictions for models outside the training distribution is load-bearing. The abstract and methods description give no indication that experiments were stratified by model family, architecture, or training corpus; mRMR relevance scores are computed from full-benchmark scores of the training models, so any architecture-correlated question difficulty can be absorbed by the kernel and produce systematic over- or under-prediction on unseen families. Without such a split, the reported improvements cannot be taken as general.

    Authors: We agree that the absence of explicit family- or architecture-stratified hold-outs limits the strength of claims about generalization to entirely unseen model distributions. Our model pool is diverse, but relevance scores and kernels were fit without such separation. In revision we will add a new set of experiments that hold out entire model families (e.g., all Llama variants, all Mistral variants) during both mRMR selection and KRR training, then report MAE, RMSE, Spearman ρ and Kendall τ on the held-out families. We will also discuss the scope of the current results as applying within the observed model distribution. revision: yes

  2. Referee: [Results and discussion] The statement that improvements hold 'except in very data-poor settings' is not accompanied by a concrete definition of that regime or by ablation tables showing the transition point. This boundary is central to the practical recommendation yet remains unquantified.

    Authors: We accept that the qualifier 'very data-poor settings' is imprecise and unsupported by quantitative thresholds or ablations. In the revised manuscript we will (i) define the regime explicitly (training sets of fewer than 30 models for the largest benchmarks, scaled proportionally for smaller ones), (ii) add ablation tables that vary the number of training models from 10 to the full set while holding the question subset fixed, and (iii) mark the point at which the proposed KRR+mRMR method ceases to outperform the baselines in each metric. revision: yes

Circularity Check

0 steps flagged

Standard regression pipeline with independent empirical validation

full rationale

The paper reframes efficient benchmarking as multiple regression plus feature selection and reports that KRR + mRMR yields lower MAE/RMSE and higher Spearman/Kendall correlations than prior methods across benchmarks. All performance numbers are obtained from explicit train/test splits on held-out model scores; the reported improvements are therefore measured quantities, not quantities forced by the fitting procedure itself. No equations equate a claimed prediction to its own training targets by construction, no uniqueness theorem is imported from self-citation, and the mRMR step is a standard information-theoretic algorithm whose output is not presupposed by the evaluation metrics. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, axioms or invented entities.

pith-pipeline@v0.9.1-grok · 5728 in / 1074 out tokens · 32419 ms · 2026-06-29T20:18:02.133033+00:00 · methodology

discussion (0)

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