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The paper sets out to determine which ingredients actually drive targeted instruction selection for LLM fine-tuning, and concludes that the data representation—not the selection algorithm—is the decisive component: only gradient-based repre

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2026-08-02 23:05 UTC pith:GBEBBKCK

load-bearing objection A genuinely useful empirical comparison, but the abstract's 'consistently predicts' overstates downstream evidence; worth a serious referee after a revision. the 4 major comments →

arxiv 2602.14696 v2 pith:GBEBBKCK submitted 2026-02-16 cs.LG

A Critical Look at Targeted Instruction Selection: Disentangling What Matters (and What Doesn't)

Nihal V. Nayak , Paula Rodriguez-Diaz , Neha Hulkund , Sara Beery , David Alvarez-Melis This is my paper
classification cs.LG
keywords instruction tuningdata selectiontargeted instruction selectiongradient-based representationdistance minimizationoptimal transportgeneralization boundLLM fine-tuning
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.

Targeted instruction selection means picking a small subset of candidate training examples to fine-tune a language model for a specific task, guided by a handful of query examples. This paper disentangles the two ingredients that prior work mixes together—how examples are encoded (representation) and how examples are picked (selection algorithm)—and tests each separately. It finds that only gradient-based representations, such as the low-rank gradient features used by LESS, create distances to the query set that consistently predict query-set loss and downstream performance; text-embedding and hidden-state representations often fail or invert this relationship. It also finds that greedy round-robin selection is the strongest method at small budgets, unbalanced optimal transport takes over at large budgets, and random sampling is a surprisingly strong baseline that becomes competitive as the budget grows. The paper unifies these algorithms as approximate distance minimizers and proves generalization bounds explaining both when selection helps and why its benefit decays with budget.

Core claim

The paper's central claim is that targeted instruction selection is best understood as approximate distance minimization between the selected subset and the query set, and that the data representation used to compute that distance is the decisive component. Concretely, only gradient-based representations—low-dimensional projections of Adam update vectors computed during warm-up training, as in LESS—produce subset-query distances that correlate monotonically with query-set loss and downstream performance. Under these representations, greedy round-robin selection is the strongest method at small budgets, while unbalanced optimal transport offers modest gains at larger budgets. The advantage ov

What carries the argument

The central object is the subset-to-query distance computed in a representation space. The paper's key representation is gradient-based: each instruction-response pair becomes a low-dimensional random projection of Adam update vectors, aggregated across checkpoints of a warm-up-trained LoRA model (the LESS representation). Selection algorithms are then viewed as approximate minimizers of a distributional distance—chiefly the 1-Wasserstein distance between the empirical distributions of the selected subset and the query set. Theorem 6.1 bounds test loss by the sum of the subset-query Wasserstein distance, an irreducible query-test mismatch term, training error, and an ideal joint error; Theor

Load-bearing premise

The load-bearing premise is that the small query set (8–81 examples per task) faithfully represents the true target-test distribution; if the query set is unrepresentative or contaminated, minimizing distance to the query set is untethered from actual test performance.

What would settle it

Construct a benchmark where the query set is drawn from an easy or distributionally close slice of a task while the held-out test set comes from a hard or shifted slice; then run LESS-based greedy round-robin at a 500-example budget. If selection then fails to beat random sampling, or if the Spearman correlation between LESS distance quantiles and query loss is near zero, the paper's central claim that gradient representations make distance predictive would be refuted.

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

If this is right

  • At small budgets, practitioners should use gradient-based representations (LESS) with greedy round-robin selection; it beats hidden-state and embedding-based methods on most of the five tasks and several models.
  • At large budgets, optimal-transport selectors (UOT, KNN-KDE) become competitive, but no method reliably beats random sampling.
  • A subset's distance to the query set should not be trusted as a selection signal unless it is computed with gradient-based representations.
  • Cheap proxy models with about 135M parameters can produce LESS representations that match or beat full-model representations, cutting the compute cost of selection.
  • The theoretical bounds imply that the advantage of any query-aware method over random has a hard ceiling set by pool-query mismatch and the dimension-driven B^{-1/d} decay.

Where Pith is reading between the lines

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

  • A practical extension the paper leaves implicit: use distance-based selection only under a critical budget threshold, then fall back to random sampling to save compute once the B^{-1/d} catch-up becomes visible.
  • The paper excludes saturated tasks where zero-shot performance is already high; an implicit corollary is that targeted selection is only worth doing when the base model has clear headroom on the target task, and skipping selection entirely is a legitimate option.
  • LESS-selected subsets are shorter on average than those from embedding-based methods, so part of its advantage may come from length regularization rather than pure gradient influence; a testable follow-up is to control for token length before comparing selection methods.
  • The theory suggests a new algorithm family: directly minimize the 1-Wasserstein distance between subset and query while explicitly tolerating the measured pool-query mismatch, which could outperform both round-robin and current OT heuristics.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper presents a systematic, disentangled evaluation of targeted instruction selection for LLM fine-tuning, separating data representations (RDS+, EMBED, LESS) from selection algorithms (round-robin, doubly greedy, KNN-Uniform, KNN-KDE, and a proposed UOT method). It evaluates these components across five target tasks and several base models, with three-seed averaged experiments for the main budget sweeps. The authors report that gradient-based LESS representations give the most consistent relationship between subset-query distance and query loss, that greedy round-robin performs best at small budgets, that UOT/KNN-KDE become competitive at larger budgets, and that random sampling is a surprisingly strong baseline. The paper also contributes a theoretical unification of selection methods as approximate Wasserstein-distance minimizers, with two generalization bounds and a discussion of diminishing returns.

Significance. If the results hold, this is a valuable empirical contribution. The paper addresses a real fragmentation in the instruction-selection literature by controlling representation and selection algorithm separately, and it provides a rare multi-model, multi-task comparison with released code, three-seed averaging, and a strong random baseline. The finding that random sampling is competitive at larger budgets is practically important and helps explain conflicting results in prior work. The theoretical unification, while not the main contribution, offers a useful conceptual framing. The main risk is that the headline claim of consistent prediction is broader than the reported evidence supports, especially for downstream performance on newer models; the paper's own appendix contains multiple wrong-sign correlations. The theory also has proof gaps that need attention.

major comments (4)
  1. [Abstract; Section 5.1; Appendix M] The abstract claims that only gradient-based representations choose subsets whose similarity to the query 'consistently predicts performance across datasets, models, and candidate pools.' The downstream Spearman correlations in Figure 3 and Appendix M (Figures 15-18) contradict this for a substantial fraction of model-task pairs: positive (wrong-sign) or weak correlations for LESS appear in 7 of 25 pairs, including Llama-2 Codex (+0.72), Llama 3.2 Codex (+0.28), SmolLM3 BBH (+0.88), SmolLM3 Codex (+0.68), SmolLM3 MMLU-Pro (+0.28), Qwen3 BBH (+0.18), and Olmo3 BBH (+0.58). The manuscript itself concedes in Section 5.1 that 'trends are less consistent on downstream performance with newer, over-trained models.' Please restrict the 'consistently predicts' claim to query loss, or explicitly scope it to downstream performance and temper the practical guidance accordingly.
  2. [Section 5.1, Figures 2-3] The central correlation analysis rests on single training runs. Figures 2 and 3 report Spearman correlations over 10 distance quantiles, but there are no confidence intervals, seed repetitions, or significance tests for these correlations. This is unlike the budget experiments in Sections 5.2-5.3, which average over three seeds. Given that the paper's central claim is about consistency of correlation, please provide seed-resampled uncertainty estimates or at minimum state explicitly that the quantile experiment is single-run and therefore should be interpreted with caution.
  3. [Theorem 6.1, Eq. (1), Lemma L.1] The proof of Theorem 6.1 is not justified by the cited lemma. Lemma L.1 (Appendix L.1) is a high-probability bound for samples S and T drawn i.i.d. from underlying measures P_S and P_T. In Theorem 6.1, S is an arbitrary deterministic subset of the candidate pool D, and the proof applies Lemma L.1 twice treating S and then Q as source samples. Without an i.i.d. or exchangeability assumption on S, the probabilistic statement does not follow from Lemma L.1. Additionally, Eq. (1) contains L_S(theta_S) and a term lambda-tilde that depends on S (through the L_S term in its definition), so the sentence 'only W1(P_S, P_Q) is directly affected by the choice of S' is not consistent with the displayed bound. Please repair the proof or state clearly the additional conditions under which the bound is valid.
  4. [Section 6.2, Theorem 6.2, Figure 8] Theorem 6.2's assumptions (mu-strong convexity of the empirical risk, K-Lipschitzness of L_T, and Gtheta_z-Lipschitz gradients) are not verified for the LoRA fine-tuning setup used in the experiments. The qualitative statement about diminishing returns is plausible and empirically supported, but the quantitative reference to a B^{-1/d} decay with d=8192 in Figure 8 is illustrative only; the constants and residual terms in the bound are not measured. Please clarify that the empirical agreement is qualitative and that the theorem does not provide a fitted decay law for the actual training setup.
minor comments (4)
  1. [Section 3.2, Appendix D] The term 'gradient-based representations' is used throughout, but LESS actually combines LoRA gradients with Adam update vectors and random projections. Please make this explicit in the main text to avoid confusion with full-gradient influence methods.
  2. [Table 1] The budget for Xia et al. is written as '13,533' while the text elsewhere uses '13,533' consistently; please harmonize comma styling across tables and text.
  3. [Figures 2, 3, 9, 10] TyDiQA is rendered as 'T yDiQA' in the figure panels and captions; please fix the spacing.
  4. [Appendix B, Table 2] The Codex split is described as '164 examples' in Appendix B, and Table 2 lists 16 query + 148 test = 164; please verify the arithmetic and clarify the split in one place.

Circularity Check

0 steps flagged

No circularity found: the central claims rest on empirical forks and explicit-assumption bounds, not on fitted inputs or load-bearing self-citations.

full rationale

The paper's main empirical claims are genuine empirical forks. Section 5.1 trains models on distance-stratified quantiles and measures Spearman correlations; Sections 5.2-5.3 train on selected subsets and compare against random and zero-shot baselines. The selection representations (RDS+, EMBED, LESS) and most selection algorithms are adopted from prior external work rather than fit to the reported trends, and the new UOT algorithm is presented with fixed hyperparameters rather than tuned to the results. LESS is itself an influence estimator, so finding that LESS distance correlates with query loss validates an approximation rather than being forced by construction: the paper trains full models and observes whether the ordering holds after nonlinear fine-tuning. The theoretical results (Theorems 6.1 and 6.2) are derived from explicit assumptions (strong convexity, Lipschitzness, loss form, bounded support) and do not assume the conclusion; the bounds explicitly include irreducible terms such as W1(P̂_Q, P̂_T), L_S(θ_S), and λ̃. The 'distance minimization' unification is an interpretive framing and does not feed back into the empirical comparisons. The only self-citations (Alvarez-Melis & Fusi 2020 in Appendix C; Hulkund et al. 2025 in Related Work) are non-load-bearing, and the central derivation is independent of them. The paper itself flags a genuine limitation in Appendix M: LESS query-loss correlations are consistent but downstream correlations are 'less consistent with newer, over-trained models.' This weakens the abstract's universal phrasing but is a robustness/correctness concern, not circularity. No equation or fitted parameter reduces to the paper's conclusions by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities; the new UOT algorithm is a method, not an entity. The central claim relies on hands-selected hyperparameters (τ2, ε, KNN-KDE settings, LoRA rank) and on domain assumptions about query representativeness, strong convexity, and the meaning of Wasserstein distance in embedding space. These are stated clearly in the text and appendices, but they limit the theory's applicability to LLM fine-tuning.

free parameters (4)
  • UOT marginal relaxation τ2 = 0.0001
    Chosen by hand (Appendix F.2) without sensitivity analysis; controls how much candidate-pool marginal may deviate, directly affecting which candidates get mass.
  • UOT entropy regularization ε = 0.01
    Hand-set in Appendix F.2; affects the sharpness of the transport plan and hence the selected subset.
  • KNN-KDE hyperparameters (L, KKDE, σ, C) = L=5000, KKDE=1000, σ=0.75, C=5.0
    Taken from Liu et al. (2024) without re-tuning; selected subsets and downstream results may depend on these values.
  • LoRA rank/α/dropout = rank=128, α=512, dropout=0.1
    Taken from Xia et al. (2024) for the main model; used for all LESS representations and proxy models.
axioms (4)
  • domain assumption Query set Q is an i.i.d. sample from the target task distribution T.
    Used in the objective in Section 2 and in Theorem 6.1; if Q is a poor proxy (e.g., tiny sizes 8-81), selection by query similarity is not guaranteed to help.
  • standard math Loss ℓ is symmetric, convex, bounded, satisfies triangle inequality, and has form |y-fθ(x)|^q for some q>0.
    Assumed in Lemma L.1 and Theorem 6.1 to apply the Redko et al. domain-adaptation bound; cross-entropy does not satisfy symmetry/boundedness/triangle inequality, so the theorem does not literally cover LLM fine-tuning.
  • domain assumption A1-A3: empirical risk µ-strongly convex, gradient Lipschitz in data, and ERM loss K-Lipschitz in parameters.
    Assumed in Lemma L.2 and Theorem 6.2; these are violated by modern LLM loss landscapes, so the diminishing-returns bound is a toy-model result, not a description of the actual experiments.
  • domain assumption Wasserstein distance in embedding space is a meaningful proxy for task-relevant similarity.
    The entire selection framework postulates that candidates close to the query in representation space (LESS/RDS+/EMBED) improve target performance; the empirical section tests this, but the theoretical bounds take W1 as the relevant metric without justifying the embedding.

pith-pipeline@v1.3.0-alltime-deepseek · 34045 in / 16282 out tokens · 159262 ms · 2026-08-02T23:05:25.634618+00:00 · methodology

0 comments
read the original abstract

Instruction fine-tuning of large language models (LLMs) often involves selecting a subset of instruction training data from a large candidate pool, using a small query set from the target task. Despite growing interest, the literature on targeted instruction selection remains fragmented and opaque: methods vary widely in selection budgets, often omit zero-shot baselines, and frequently entangle the contributions of key components. As a result, practitioners lack actionable guidance on selecting instructions for their target tasks. In this work, we aim to bring clarity to this landscape by disentangling and systematically analyzing the two core ingredients: data representation and selection algorithms. Our framework enables controlled comparisons across models, tasks, and budgets. We find that only gradient-based data representations choose subsets whose similarity to the query consistently predicts performance across datasets, models, and candidate pools. While no single method dominates, gradient-based representations paired with greedy round-robin selection often perform best on average at low budgets, but these gains diminish at larger budgets. Finally, we unify several existing selection algorithms as forms of approximate distance minimization between the selected subset and the query set, and support this view with new generalization bounds. More broadly, our findings provide critical insights and a foundation for more principled data selection in LLM fine-tuning. The code is available at https://github.com/dcml-lab/targeted-instruction-selection.

Figures

Figures reproduced from arXiv: 2602.14696 by David Alvarez-Melis, Neha Hulkund, Nihal V. Nayak, Paula Rodriguez-Diaz, Sara Beery.

Figure 1
Figure 1. Figure 1: Disentangled view of targeted instruction selection. First, the query set (stars) and candidate pool (dots) are encoded as data representations. Then, for a given budget, using the data representations for the query and candidates, we perform targeted selection (denoted by the dotted line) using a selection algorithm such as greedy round-robin. 3. A Disentangled View of Instruction Selection In this sectio… view at source ↗
Figure 2
Figure 2. Figure 2: Query loss vs. subset-query distance quantile. We stratify candidates into 10 distance quantiles (1 = closest, 10 = farthest) using each representation, select 500 examples per quantile using the RR selection algorithm, and train the Llama 2 7B model. We report query-set cross-entropy loss and Spearman correlation per target task. LESS (RR) exhibits a strong monotonic increase in loss with distance (high p… view at source ↗
Figure 3
Figure 3. Figure 3: Downstream performance vs. subset-query distance quantile. Using the same quantile construction and training protocol as [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Query loss vs. budget for different data representations (fixed selection algorithm). Using greedy round-robin selection and the query-candidate pool similarity, we select subsets of size B ∈ {500, 1000, 2500, 5000, 10000}, train Llama 2 7B on them, and report average cross entropy loss averaged across three seeds and the standard error. Random averages over three uniformly sampled subsets from the candida… view at source ↗
Figure 5
Figure 5. Figure 5: Downstream performance vs. budget for different data representations (fixed selection algorithm). With the same greedy round-robin selection and budgets as [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Query loss vs. budget for different selection algorithms (fixed data representation). Using LESS representations and the query-candidate pool cosine similarity (or distance), we select subsets of size B ∈ {500, 1000, 2500, 5000, 10000} with each selection algorithm, train Llama 2 7B on them, and report average cross entropy loss on the query set averaged across three seeds and the standard error. Random av… view at source ↗
Figure 7
Figure 7. Figure 7: Downstream performance vs. budget for different selection algorithms (fixed data representation). With the same data representation and the budgets as [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: shows the change in performance gap between LESS variants and random sampling as the budget increases on MMLU-Pro. As B increases, the gap shrinks, and the performance approaches the random sampling, which is qualitatively aligned with Theorem 6.2. While B−1/d refer￾ence rate shows a slow worst-case decay in high dimensions, we see that LESS (KNN-Unif.), LESS (KNN-KDE), and LESS (UOT) exhibit a slower or a… view at source ↗
Figure 9
Figure 9. Figure 9: Query loss across subset-query distance sub-quantiles and Spearman correlation. We further stratify the first distance quantile from Section 5.1 into 10 sub-quantiles (1 = closest, 10 = farthest), select 500 examples per sub-quantile, and train the Llama 2 7B model. We report loss on the query set and Spearman correlation per dataset. LESS (RR) maintains a strong monotonic increase in loss with distance (h… view at source ↗
Figure 10
Figure 10. Figure 10: Downstream performance across subset-query distance sub-quantiles and Spearman correlation. Using the same sub-quantile construction and training protocol as [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Average token length of the query set and the selected subsets with different data representations. We find that LESS (RR) is biased towards shorter sequences, whereas RDS+ (RR) and EMBED (RR) select subsets with longer sequences. 0.0 0.2 0.4 0.6 0.8 1.0 Jaccard index RDS+ (RR) EMBED (RR) EMBED (RR) LESS (RR) 0.14 0.07 0.04 BBH RDS+ (RR) EMBED (RR) EMBED (RR) LESS (RR) 0.34 0.02 0.02 Codex RDS+ (RR) EMBED… view at source ↗
Figure 12
Figure 12. Figure 12: Jaccard index between selected subsets created using different data representations. We find that model-based representations (RDS+ and EMBED) have a higher Jaccard index compared to LESS. embeddings share greater similarity in the examples they select. J. Cheaper Proxies for LESS LESS data representations are computationally expensive as they require a forward and a backward pass over all the candidate s… view at source ↗
Figure 13
Figure 13. Figure 13: Cheaper proxies for LESS (fixed selection algorithm). With the same greedy round-robin selection procedure and the budgets from Section 5.2, we report downstream performance of Llama 2 7B when LESS representations are computed using proxy models, averaged across three seeds and the standard error. SmolLM-135M and SmolLM2-135M consistently match or outperform the Random baseline across target tasks, wherea… view at source ↗
Figure 14
Figure 14. Figure 14: KNN-Uniform and KNN-KDE with L2 distance (fixed data representation). With the same Llama 2 7B LESS represen￾tations and the budgets from Section 5.3, we report downstream performance for KNN-Uniform and KNN-KDE when distances are computed with L2 (following Liu et al. (2024b)), averaged across three seeds and the standard error. We compare against cosine distance variants and find similar performance tre… view at source ↗
Figure 15
Figure 15. Figure 15: Ablation experiments with Llama 3.2 3B. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Ablation experiments with SmolLM3 3B. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Ablation experiments with Qwen3 4B. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Ablation experiments with Olmo 3 7B. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗

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