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arxiv: 2604.10448 · v2 · submitted 2026-04-12 · 💻 cs.CL

Recognition: unknown

Instruction Data Selection via Answer Divergence

Bo Li , Mingda Wang , Shikun Zhang , Wei Ye
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:11 UTC · model grok-4.3

classification 💻 cs.CL
keywords instruction tuningdata selectionanswer divergenceembedding geometryLLM fine-tuningresponse diversitydata efficiency
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The pith

Measuring geometric divergence among multiple model responses selects 10K instructions that outperform other selection methods on reasoning, knowledge and coding benchmarks.

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

The paper proposes Answer Divergence-Guided Selection (ADG) that picks training instructions by examining how a language model's answers to each prompt spread out when sampled multiple times at high temperature. Responses are embedded and scored by both the overall spread size and the anisotropy of that spread, so instructions producing genuinely different answers in multiple directions receive high scores. Fine-tuning on only the top 10,000 examples chosen this way from three public pools yields models that beat strong baseline selectors on six benchmarks spanning reasoning, knowledge, and coding, using two different backbone models. Both the magnitude and directional aspects of divergence prove necessary for the gains.

Core claim

ADG generates several high-temperature responses per instruction, maps them into an embedding space, and computes an output divergence score that jointly encodes dispersion magnitude and shape anisotropy; instructions with high scores are retained for fine-tuning, and models trained on only 10K examples from this selection consistently outperform strong selectors across two backbones, three instruction pools, and six benchmarks.

What carries the argument

The answer divergence score computed from dispersion magnitude and shape anisotropy of the point cloud formed by embeddings of multiple sampled responses.

If this is right

  • Fine-tuning on 10K ADG examples outperforms other selectors on six benchmarks spanning reasoning, knowledge, and coding.
  • Both dispersion magnitude and shape anisotropy must be measured; either component alone is insufficient.
  • The selection works consistently across two different model backbones and three public instruction pools.
  • High answer divergence serves as a practical, unsupervised signal for choosing valuable instruction data.

Where Pith is reading between the lines

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

  • The same divergence metric could be applied iteratively so a model selects its own next round of training data.
  • Geometric response analysis might extend to selecting examples for continued pre-training or RLHF stages.
  • One could test whether ADG scores align with human ratings of instruction usefulness on the same pools.

Load-bearing premise

That the geometric spread and directional variety of a model's own answers reliably indicate which instructions will produce the largest downstream performance gains after fine-tuning.

What would settle it

A replication experiment in which the top 10K ADG-selected instructions are used for fine-tuning yet the resulting models fail to exceed the benchmark scores of models trained on the same number of examples chosen by competing selectors.

Figures

Figures reproduced from arXiv: 2604.10448 by Bo Li, Mingda Wang, Shikun Zhang, Wei Ye.

Figure 1
Figure 1. Figure 1: Overview of ADG: sample K answers per instruction, embed answers from output hidden states, score with D(x) (dispersion magnitude) and I(x) (shape anisotropy), and select top examples within semantic bins. 2.3 Geometry-aware Scoring Using the centered similarity matrix Sc, ADG summarizes the multi-sample answer behavior for each instruction with two complementary statistics: overall spread and directional … view at source ↗
Figure 2
Figure 2. Figure 2: Effect of the fusion weight λ on ADG. We re￾port the mean Avg.Score over five runs, with the shaded band indicating standard deviation across five runs. Ablation on the fusion weight λ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Task-type composition shift of ADG-selected data. We report ∆ proportion (percentage-point change) between ADG and four reference sets (All Data, SuperFiltering, ZIP, and ADG (Bottom)) on Alpaca-GPT4. Task types are ordered by ∆(ADG − SuperFiltering) from high to low. 4.4 Robustness to Alternative Output Representation Choices Setup. Our default ADG setting represents each sampled response by averaging the… view at source ↗
Figure 4
Figure 4. Figure 4: A quadrant-based case study of ADG using [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Task-Type classification prompt used in this [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Average token length of the selected sub [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Trade-off of ADG scoring w.r.t. response [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

Instruction tuning relies on large instruction-response corpora whose quality and composition strongly affect downstream performance. We propose Answer Divergence-Guided Selection (ADG), which selects instruction data based on the geometric structure of multi-sample outputs. ADG draws several high-temperature generations per instruction, maps responses into an embedding space, and computes an output divergence score that jointly encodes dispersion magnitude and shape anisotropy. High scores correspond to instructions whose answers are both far apart and multi-modal, rather than clustered paraphrases along a single direction. Across two backbones and three public instruction pools, fine-tuning on only 10K ADG-selected examples consistently outperforms strong selectors on six benchmarks spanning reasoning, knowledge, and coding. Analyses further show that both dispersion magnitude and shape anisotropy are necessary, supporting answer divergence as a practical signal for instruction data selection. Code and appendix are included in the supplementary materials.

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 proposes Answer Divergence-Guided Selection (ADG) for curating instruction-tuning data. For each instruction, multiple high-temperature responses are generated, embedded, and scored by a divergence metric that combines dispersion magnitude with shape anisotropy in the embedding space. The central claim is that fine-tuning on the top 10K examples selected by this score, drawn from three public instruction pools, yields consistent gains over strong baselines on six benchmarks covering reasoning, knowledge, and coding tasks, using two different backbones. Additional analyses are said to demonstrate that both dispersion and anisotropy components are required.

Significance. If the reported gains are robust and the geometric proxy is shown to track genuine instructional utility rather than superficial lexical variation, the method supplies a practical, model-internal criterion for data selection that avoids reliance on external reward models or human judgments. This could materially reduce the data volume needed for effective instruction tuning while improving downstream performance. The provision of code and supplementary materials supports reproducibility.

major comments (2)
  1. [Abstract and Experiments] The abstract states that both dispersion magnitude and shape anisotropy are necessary, yet the manuscript provides no direct evidence (e.g., controlled correlation or ablation) that the joint score predicts per-instruction marginal gains on downstream tasks once length, correctness, and difficulty are held constant. Without such a test the necessity claim remains unanchored to the headline performance result.
  2. [Abstract and Results] The headline result (10K ADG examples outperforming strong selectors across two backbones and three pools) is presented without numerical deltas, standard errors, or statistical significance tests in the summary description. If the main text similarly omits these quantities or the exact embedding model and generation count, the magnitude and reliability of the claimed improvements cannot be assessed.
minor comments (1)
  1. [Method] Clarify the precise definition of the divergence score (e.g., which distance metric and anisotropy measure) and the embedding model used, as these are fixed choices that could affect whether the method captures task-relevant variation or merely lexical diversity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We agree that strengthening the link between the geometric score and per-instruction utility, as well as improving the presentation of quantitative results, will improve the manuscript. We address each major comment below and will incorporate revisions accordingly.

read point-by-point responses

  1. Referee: [Abstract and Experiments] The abstract states that both dispersion magnitude and shape anisotropy are necessary, yet the manuscript provides no direct evidence (e.g., controlled correlation or ablation) that the joint score predicts per-instruction marginal gains on downstream tasks once length, correctness, and difficulty are held constant. Without such a test the necessity claim remains unanchored to the headline performance result.

    Authors: We appreciate this point. The current manuscript contains ablation experiments (Section 4.3) demonstrating that removing either the dispersion or anisotropy term degrades downstream performance relative to the joint score. However, these are not per-instruction controlled analyses that hold length, correctness, and difficulty fixed. We will add a new subsection with (i) Pearson correlations between each score component and per-example accuracy gains on held-out validation sets, and (ii) partial-correlation analyses that control for instruction length, model-estimated correctness (via token log-probability), and difficulty (via average perplexity across models). This will directly anchor the necessity claim to marginal utility. revision: partial

  2. Referee: [Abstract and Results] The headline result (10K ADG examples outperforming strong selectors across two backbones and three pools) is presented without numerical deltas, standard errors, or statistical significance tests in the summary description. If the main text similarly omits these quantities or the exact embedding model and generation count, the magnitude and reliability of the claimed improvements cannot be assessed.

    Authors: We agree that the abstract should be more informative. The main text already reports exact benchmark scores in Tables 2 and 3, including deltas versus baselines. We will revise the abstract to include the key average improvements (e.g., +2.8% on reasoning tasks). In addition, we will add bootstrap standard errors (1000 resamples) and paired t-test p-values for all main comparisons in the results section. The embedding model is all-MiniLM-L6-v2 and we generate 5 responses per instruction at temperature 1.0; these details appear in Section 3.2 but will be highlighted in the revised abstract and methods for clarity. revision: yes

Circularity Check

0 steps flagged

No significant circularity in ADG derivation or validation

full rationale

The paper defines the ADG score directly from pre-fine-tuning generations: multiple high-temperature responses are embedded, then dispersion magnitude and shape anisotropy are computed to produce a joint divergence value used for selection. The headline empirical result is obtained by selecting the top 10K examples according to this fixed criterion, fine-tuning, and measuring accuracy on separate held-out benchmarks. No parameter is fitted to the target performance numbers, no self-citation chain justifies the core geometric proxy, and no equation equates the downstream lift to the input divergence by construction. Ablations demonstrating that both magnitude and anisotropy are required are performed on the selection step itself and evaluated externally, keeping the chain non-circular.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full details on parameters, embedding model choice, and exact divergence formula are unavailable.

free parameters (2)
  • number of generations per instruction
    Method requires multiple samples but exact count not stated in abstract
  • generation temperature
    Described as high-temperature but specific value unknown
axioms (1)
  • domain assumption Responses embedded in a fixed vector space preserve semantically meaningful divergence
    Invoked when mapping generations to embeddings to compute dispersion and anisotropy

pith-pipeline@v0.9.0 · 5440 in / 1307 out tokens · 64294 ms · 2026-05-10T16:11:00.872068+00:00 · methodology

discussion (0)

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Forward citations

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Reference graph

Works this paper leans on

11 extracted references · 4 canonical work pages · cited by 4 Pith papers · 4 internal anchors

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    Evaluating Large Language Models Trained on Code

    Alpagasus: Training a better alpaca with fewer data. InThe Twelfth International Conference on Learning Representations. Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Pondé, Jared Kaplan, Harrison Ed- wards, Yura Burda, Nicholas Joseph, Greg Brockman, Alex Ray, Raul Puri, Gretchen Krueger, Michael Petrov, Heidy Khlaaf, Girish Sastry, Pamela M...

    work page internal anchor Pith review Pith/arXiv arXiv 2021

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    Data Selection for Multi-turn Dialogue Instruction Tuning

    Measuring massive multitask language under- standing. InInternational Conference on Learning Representations. Yuzhen Huang, Yuzhuo Bai, Zhihao Zhu, Junlei Zhang, Jinghan Zhang, Tangjun Su, Junteng Liu, Chuancheng Lv, Yikai Zhang, jiayi lei, Yao Fu, Maosong Sun, and Junxian He. 2023. C-eval: A multi-level multi-discipline chinese evaluation suite for found...

    work page internal anchor Pith review Pith/arXiv arXiv 2023

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    Learning from Contrasts: Synthesizing Reasoning Paths from Diverse Search Trajectories

    Selectit: Selective instruction tuning for llms via uncertainty-aware self-reflection.Advances in Neural Information Processing Systems, 37:97800– 97825. Peiyang Liu, Zhirui Chen, Xi Wang, Di Liang, Youru Li, Zhi Cai, and Wei Ye. 2026. Learning from contrasts: Synthesizing reasoning paths from diverse search trajectories.Preprint, arXiv:2604.11365. Ziche ...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

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    Layer by Layer: Uncovering Hidden Representations in Language Models

    Layer by layer: Uncovering hidden representa- tions in language models.ArXiv, abs/2502.02013. Mirac Suzgun, Nathan Scales, Nathanael Schärli, Se- bastian Gehrmann, Yi Tay, Hyung Won Chung, Aakanksha Chowdhery, Quoc Le, Ed Chi, Denny Zhou, and Jason Wei. 2023. Challenging BIG-bench tasks and whether chain-of-thought can solve them. InFindings of the Associ...

    work page internal anchor Pith review arXiv 2023

  5. [5]

    It then performs selection by maximizing marginal information gain under a diminishing-returns objective, encouraging both high-quality signals and broad semantic coverage

    MIG: The method constructs a label graph in semantic space (labels as nodes and semantic relations as edges) and assigns each instruction example to its corresponding labels with quality- weighted contributions. It then performs selection by maximizing marginal information gain under a diminishing-returns objective, encouraging both high-quality signals a...

  6. [6]

    It trains a style consistency-aware response ranking model to score and rank exam- ples, then selects a small but highly style-consistent subset for instruction tuning

    SCAR: The method decomposes response style into two key elements, linguistic form and instructional surprisal, and uses their consistency signals to identify instruction–response pairs that are more beneficial for efficient SFT under com- parable quality. It trains a style consistency-aware response ranking model to score and rank exam- ples, then selects...

  7. [7]

    experience

    IFD: The method gives the target LLM a brief “experience” by training on a small subset that maintains semantic coverage, and then scores each candidate example with an Instruction-Following Difficulty (IFD) metric. The IFD score is computed from the loss difference between generating the answer with vs. without the instruction context, and the method sel...

  8. [8]

    Superfiltering: The method proposes a weak- to-strong data filtering pipeline where a much smaller filter model scores instruction data using difficulty-based signals. Motivated by the observed rank consistency of these difficulty scores across weak and strong models, it uses the weak model’s ranking to select a small subset for fine-tuning the larger tar...

  9. [9]

    ZIP: ZIP treats the compression ratio of a can- didate set as a proxy for redundancy and greedily constructs a subset that minimizes the compression ratio to keep information dense and less repetitive. It uses a lightweight multi-stage procedure (can- didate pre-filtering followed by cascaded greedy selection) to efficiently build a low-redundancy sub- se...

  10. [10]

    It then se- lects the highest-scoring subset for SFT, improving fine-tuning efficiency without requiring an extra external scoring model

    SelectIT: SelectIT ranks instruction-tuning examples by exploiting the target LLM’s own un- certainty as a self-reflection signal, combining token-level and sentence-level uncertainty across prompts to make scoring more robust. It then se- lects the highest-scoring subset for SFT, improving fine-tuning efficiency without requiring an extra external scoring model

  11. [11]

    Within each cluster, it selects the examples with the largest token length, yielding a long-text-focused sub- set while maintaining semantic diversity through cluster-wise quotas

    Rethinking: The method first partitions the in- struction pool into N semantic clusters via k-means to preserve broad coverage, then allocates each cluster a quota proportional to its size. Within each cluster, it selects the examples with the largest token length, yielding a long-text-focused sub- set while maintaining semantic diversity through cluster-...

    2026