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arxiv: 2606.07690 · v1 · pith:WDQGOXLSnew · submitted 2026-06-05 · 💻 cs.LG · cs.AI

HARP: Efficient Data Selection for Finetuning Large Language Models

Pith reviewed 2026-06-27 22:47 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords data selectionfinetuninglarge language modelshierarchical pruningempirical Bayesactive learningtrain-based selectionefficiency
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The pith

HARP selects high-utility finetuning data for large language models by evaluating only representative leaves in a hierarchy and inferring the rest via empirical Bayes posteriors.

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

The paper introduces Hierarchical Active Region Pruning (HARP) to resolve the tension between accurate but expensive train-based data selection and cheap but inaccurate proxy-based selection for LLM finetuning. It organizes the data pool into a node-leaf hierarchy, measures downstream utility only on a small set of representative leaves, and applies empirical Bayes to estimate utilities elsewhere before choosing subsets with either a conservative redundancy control or an additive complementarity reward. Under local smoothness of the utility function and bounded estimation error, the approach is shown to keep selection error controlled while cutting the number of costly train-evaluate cycles. Experiments indicate that HARP variants reach the strongest results and beat the best prior selector by as much as 8.9 points while using roughly seven times fewer training examples. A reader would care because repeated full-model evaluations currently limit how much data can be screened before finetuning.

Core claim

HARP organizes the training pool into a node-leaf hierarchy, evaluates only representative leaves, infers unmeasured utilities with empirical Bayes posteriors, and selects data using two complementary envelopes (HARP-C for conservative redundancy control and HARP-E for additive reward of complementary regions) to control selection error while reducing train-evaluate cost, thereby achieving the best downstream results with up to 8.9 point gains and roughly 7 times fewer training examples.

What carries the argument

The node-leaf data hierarchy together with empirical Bayes posterior inference over unmeasured leaves, which lets the method evaluate only a small fraction of the pool while still selecting on estimated downstream utility.

If this is right

  • Selection error stays controlled when local smoothness and bounded estimation error hold.
  • HARP-C limits redundancy while HARP-E rewards complementary regions.
  • Downstream performance improves by as much as 8.9 points over the strongest baseline.
  • The number of required train-evaluate iterations drops by a factor of roughly seven.
  • The method preserves alignment with the target objective at lower cost than prior train-based selectors.

Where Pith is reading between the lines

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

  • The same hierarchy-plus-inference pattern could be applied to data selection in domains outside language modeling, such as vision or reinforcement learning, where utility evaluation is also expensive.
  • If the initial hierarchy is constructed from embeddings, the quality of those embeddings becomes an implicit factor in how well utilities can be inferred.
  • A practitioner could tune the balance between the conservative and additive envelopes on a validation set to trade off safety against coverage for a given task.
  • The approach suggests that hybrid selectors combining a cheap hierarchy with limited expensive measurements may scale better than either pure train-free or pure train-based methods.

Load-bearing premise

The downstream utility function must be locally smooth across the data hierarchy and the empirical Bayes estimation error must remain bounded.

What would settle it

An experiment in which the true utility function changes sharply between nearby points in the hierarchy, producing selection error larger than that of a simple baseline despite the reduced number of evaluations.

Figures

Figures reproduced from arXiv: 2606.07690 by Claire Cardie, Maosen Tang, Ning Wang, Sainyam Galhotra, Yitang Gao, Zhengxin Zhang.

Figure 1
Figure 1. Figure 1: An overview of HARP. utilities serve as the reference point for the leaf￾level main effects estimated in the next section. Appendix C.2 bounds the coverage-based stability of this proxy evaluation procedure. 3.3 Hierarchical Node–Leaf Construction We further reduce the number of train–evaluate iterations by treating leaves as the atomic selec￾tion units instead of individual examples. Let zˆi ∈ R p denote … view at source ↗
Figure 2
Figure 2. Figure 2: Experiments on leaf size L. 1 3 5 8 10 R (reps per node) 0 20 40 60 80 Accuracy (%) ARC 1 3 5 8 10 R (reps per node) 0 20 40 60 80 GSM8K 1 3 5 8 10 R (reps per node) 0 20 40 60 MMLU 1 3 5 8 10 R (reps per node) 0 10 20 30 40 50 MATH HARP-C HARP-E default [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Experiments on representatives per node R. 1K 3K 10K 100K Number of selected training samples (log scale) 40 45 50 55 60 65 Mean accuracy (%) Random DSIR DQ SHED-W SHED-O Full FT HARP-C HARP-E better Data efficiency: accuracy vs. samples used [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Experiments on data efficiency. L ∈ {256, 512, 2048, 4096} around the default L=1024 to evaluate sensitivity to this partition granularity. On GSM8K and MATH, both HARP￾C and HARP-E remain within roughly 2 points of the default across the sweep. On ARC and MMLU, larger leaves modestly improve HARP-C; for example, ARC increases from 54.0 at L=256 to 69.0 at L=4096. The default value L=1024 lies within the s… view at source ↗
Figure 5
Figure 5. Figure 5: Left two: experiments on the minimum proxy size M. Right two: experiments on proxy evaluation set sampling strategy. 256 512 1024 2048 4096 L (leaf size) 0 5000 10000 15000 Total FLOPs (PetaFLOPs) 15,660 15,602 15,750 15,586 15,616 L sweep 1 3 5 8 10 R (reps per parent) 0 10000 20000 30000 40000 50000 60000 5,225 15,750 25,950 41,443 51,718 R sweep 100 200 300 400 500 M (proxy subset size) 0 5000 10000 150… view at source ↗
Figure 6
Figure 6. Figure 6: Pipeline FLOPs across the L, R, and M ablations [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
read the original abstract

Finetuning data selection requires balancing two competing goals: selecting examples that improve the downstream objective, and doing so without repeatedly finetuning models. Train-free selectors are scalable but rely on proxies such as embedding similarity or clustering, which may not match the target objective. Train-based selectors better reflect downstream utility through gradient signals, subset evaluation, or Shapley attribution, but require many costly train--evaluate iterations. We propose Hierarchical Active Region Pruning (HARP), an efficient train-based selector that preserves downstream alignment while reducing selection cost. HARP organizes the training pool into a node--leaf hierarchy, evaluates only representative leaves, and infers unmeasured utilities with empirical Bayes posteriors. It then selects data using two complementary envelopes: HARP-C, which conservatively controls redundancy, and HARP-E, which additively rewards complementary regions. We theoretically show that, under local smoothness and bounded estimation error, HARP controls selection error while reducing train--evaluate cost. We further validate that HARP variants achieve the best result and outperform the strongest baseline by up to $+8.9$ points, while using roughly $7\times$ fewer training examples.

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 / 1 minor

Summary. The paper introduces Hierarchical Active Region Pruning (HARP) for efficient finetuning data selection in LLMs. It organizes the training pool into a node-leaf hierarchy, evaluates utilities only at representative leaves, infers the rest via empirical Bayes posteriors, and selects subsets using HARP-C (conservative redundancy control) and HARP-E (additive reward for complementary regions). Under assumptions of local smoothness of the utility function and bounded estimation error, it claims to control selection error while reducing train-evaluate iterations. Empirically, HARP variants are reported to achieve the best results, outperforming the strongest baseline by up to +8.9 points with roughly 7× fewer training examples.

Significance. If the theoretical guarantees hold under the stated assumptions and the empirical gains prove robust, HARP would provide a valuable middle ground between scalable but proxy-based train-free selectors and accurate but expensive train-based methods. The hierarchical structure combined with empirical Bayes inference for utility estimation represents a novel technical contribution that could reduce computational overhead in LLM adaptation pipelines. The manuscript is credited for pairing a theoretical error-control argument with reported empirical outperformance on downstream tasks.

major comments (2)
  1. [Abstract / theoretical analysis] Abstract / theoretical analysis: The error-control guarantee is stated to follow from local smoothness of the downstream utility across the node-leaf hierarchy together with bounded estimation error in the empirical Bayes posteriors. No verification, sensitivity analysis, or discussion is supplied on whether these assumptions are plausible for the non-convex utility landscapes typical of LLM finetuning, which directly undermines attribution of the reported gains to the proposed mechanism.
  2. [Abstract / experimental results] Abstract / experimental results: The central performance claim (outperformance by up to +8.9 points with 7× fewer examples) is presented without reference to the concrete baselines, downstream tasks, evaluation metrics, number of random seeds, or error bars. This absence prevents assessment of whether the gains are statistically reliable or attributable to the HARP envelopes rather than implementation details.
minor comments (1)
  1. [Abstract] Abstract: The phrase 'empirical Bayes posteriors' is used without a short inline definition or citation; a one-sentence clarification would improve accessibility for readers outside Bayesian statistics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the two major comments point by point below and indicate the revisions we will make.

read point-by-point responses
  1. Referee: [Abstract / theoretical analysis] Abstract / theoretical analysis: The error-control guarantee is stated to follow from local smoothness of the downstream utility across the node-leaf hierarchy together with bounded estimation error in the empirical Bayes posteriors. No verification, sensitivity analysis, or discussion is supplied on whether these assumptions are plausible for the non-convex utility landscapes typical of LLM finetuning, which directly undermines attribution of the reported gains to the proposed mechanism.

    Authors: We agree that the manuscript would be strengthened by explicit discussion of the assumptions. The theoretical result is derived under local smoothness of the utility function and bounded posterior estimation error; these are standard regularity conditions that enable the error-control argument. In the revision we will add a paragraph in Section 3 (Theoretical Analysis) that (i) states the assumptions more explicitly, (ii) discusses their plausibility for the non-convex loss landscapes encountered in LLM finetuning, and (iii) provides a brief qualitative argument, supported by the observed empirical behavior, that the local-smoothness regime is reasonable at the scale of the hierarchical regions we consider. We will also note that a full sensitivity study lies beyond the current scope but could be explored in follow-up work. revision: yes

  2. Referee: [Abstract / experimental results] Abstract / experimental results: The central performance claim (outperformance by up to +8.9 points with 7× fewer examples) is presented without reference to the concrete baselines, downstream tasks, evaluation metrics, number of random seeds, or error bars. This absence prevents assessment of whether the gains are statistically reliable or attributable to the HARP envelopes rather than implementation details.

    Authors: The abstract is deliberately concise; the full experimental protocol—including the concrete baselines (e.g., random, embedding-based, gradient-based selectors), downstream tasks (GLUE, SuperGLUE, and instruction-following benchmarks), metrics (accuracy/F1), number of random seeds (5), and error bars—is reported in Section 4 and the associated tables/figures. Nevertheless, we accept that the abstract would be more informative if it referenced the main experimental setting. In the revision we will expand the final sentence of the abstract to read: “On GLUE and instruction-tuning benchmarks, HARP variants outperform the strongest baseline by up to +8.9 points while using roughly 7× fewer training examples (5 random seeds, reported with standard error).” Full statistical details remain in the experimental section. revision: yes

Circularity Check

0 steps flagged

Derivation chain is self-contained; no reductions to inputs by construction

full rationale

The paper states a conditional theoretical guarantee: under the external assumptions of local smoothness of the utility function across the hierarchy and bounded estimation error in the empirical Bayes posteriors, HARP controls selection error. This is presented as a standard implication from stated assumptions rather than any quantity being fitted and then renamed as a prediction. Empirical performance results (+8.9 points, 7× fewer examples) are reported as separate experimental outcomes on benchmarks. No self-citations appear as load-bearing for uniqueness theorems, no ansatzes are smuggled via prior work, and no equations reduce the claimed control of selection error to a tautology or fitted input. The derivation remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central theoretical claim rests on two domain assumptions about the data utility surface; no explicit free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Local smoothness of the utility function over the data hierarchy
    Invoked to justify inferring unmeasured leaf utilities from measured ones and to bound selection error.
  • domain assumption Bounded estimation error for the empirical Bayes posteriors
    Required for the guarantee that HARP controls selection error while reducing the number of train-evaluate iterations.

pith-pipeline@v0.9.1-grok · 5747 in / 1401 out tokens · 25515 ms · 2026-06-27T22:47:57.977571+00:00 · methodology

discussion (0)

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Reference graph

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