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REVIEW 4 major objections 5 minor 19 references

Measuring Task-Agnostic Training Data Influence Across Language Model Pretraining

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A checkpoint-based, task-agnostic measure of training data influence reveals that the examples most aligned with a model's final parameters shift from literature early in pretraining to STEM later.

desk verdict A clean new task-agnostic influence measure, but the literature-to-STEM crossover is only as solid as the unvalidated SGD decomposition applied to Adam-trained models. read the letter →

arxiv 2608.13515 v1 pith:YPQ4SC7L submitted 2026-08-13 cs.CL

Yuto Nishida , Hirokazu Kiyomaru , Yusuke Oda , Takashi Kodama , Chaoran Liu , Daisuke Kawahara , Yusuke Miyao , Max Müller-Eberstein
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Masaru Isonuma
This is my paper · ORCID
classification cs.CL
keywords trainingdatainfluencelanguagemodelpretrainingtask-agnosticattributioncheckpoint-basedapproximationPythiaPolydomainshifttrajectorymatching
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that training data influence across language model pretraining can be measured without choosing a downstream task: an example's influence is the amount by which its gradient update reduces the squared distance between the current parameters and the final pretrained parameters. The authors derive a checkpoint-based approximation that can be computed post hoc from saved checkpoints, and apply it to 18 configurations of the Pythia and PolyPythia suites, each with 154 checkpoints. They report that the most influential examples are not stable over training: literature-related texts dominate early, while STEM-related texts become more influential in later stages, a crossover that is broadly consistent across model sizes, weight initializations, and data orderings. The value of the proposal, if correct, is a task-agnostic trajectory-level view of pretraining data that complements task-specific influence analyses and speaks to stage-aware data curation.

What carries the argument

The central object is the contribution score $Cont(B_t) = S_t - S_{t+1}$, where $S_t = \|\theta^* - \theta_t\|_2^2$ is the squared distance from the current parameters to the final parameters $\theta^*$. Expanding $S_{t+1}$ turns the score into $2\Delta_t^\top(\theta^* - \theta_t) - \|\Delta_t\|_2^2$, an alignment term between the update and the direction toward the final model minus a squared-norm penalty. Example-level influence is defined by decomposing the update into per-example SGD contributions $\Delta_{t,k}$, and the checkpoint-based approximation replaces step-level states by adjacent saved checkpoints, treating all examples in an interval as if processed at the earlier checkpoint. This machinery lets the score be estimated post hoc from the released 154-checkpoint trajectories without retraining.

What would settle it

Retrain or replay a small Pythia run (e.g., 70M) while storing per-step optimizer states, compute an Adam-faithful per-example attribution by simulating the exact update each example induces through the optimizer, and compare the domain-level rankings with the SGD-based contribution score; if the literature-to-STEM crossover disappears or shifts substantially under the true optimizer, the reported result is an artifact of the decomposition. An intervention that swaps the data schedule—placing STEM data early and literature later—should reverse which domains align with the final parameters if the score tracks causal influence.

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Extended reading notes

Core claim

The central claim is that the set of training examples that most reduce the squared L2 distance to the final model weights undergoes a systematic temporal shift during pretraining: early updates are most aligned with literature-related data, and later updates are most aligned with STEM-related data. The claim is made for the Pythia and PolyPythia model families, and the paper further reports that difficult (high-perplexity) texts contribute disproportionately during the middle stage, that opponent examples—updates that move the model away from the final parameters—become more frequent late in training, and that these dynamics are broadly robust to model scale, seed, weight initialization, and data ordering, with smaller models exhibiting delayed transitions.

Load-bearing premise

The example-level decomposition assumes SGD updates, while the analyzed models were trained with Adam, so the per-example attribution—and therefore the domain crossover—may not reflect the updates that actually moved the model.

Editorial extensions

If this is right

  • If the crossover is real, pretraining curricula that schedule STEM-heavy data later are given trajectory-level support from the model's own parameter-space geometry, not just from downstream benchmark gains.
  • The contribution score provides a common reference point—the final parameters—so influence rankings can be compared across arbitrary training stages without task labels or validation sets.
  • The rising opponent share late in training implies that a substantial fraction of late updates push against the eventual final model, suggesting that late-stage data selection could improve alignment with the final parameters.
  • Higher-PPL examples matter most in the middle stage, so the trajectory does not follow a simple easy-to-hard curriculum; data difficulty and domain interact with training phase.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the SGD-based decomposition misattributes credit under Adam, the literature-to-STEM crossover could be a property of the approximation rather than of the actual training dynamics; an optimizer-aware attribution on a small run would settle this.
  • Editorial inference: the same score could be computed against intermediate reference checkpoints to ask which examples are most aligned with reaching a specific capability stage, not only the final model.
  • Editorial inference: the measure could transfer to other model families with dense checkpoints and to multimodal pretraining, where domain labels are less clean and task-specific validation sets are even harder to choose.
  • Editorial inference: because the paper's own comparison shows task-specific TracIn scores do not recover the crossover, the measure offers a distinct signal that may be useful for diagnosing phase transitions, such as complementing loss-spike detection in training runs.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a task-agnostic measure of training-data influence for language model pretraining: an example's contribution is the reduction in squared L2 distance to the final parameters caused by its gradient update. The mini-batch version is exact, while the example-level version assumes SGD; both are estimated from public checkpoints using Eq. (4). Applying this to Pythia and PolyPythia runs, the authors report that mean contribution peaks mid-training, opponents (negative-contribution examples) increase late, high-perplexity texts contribute most in the middle stage, and domain composition shifts from literature-related to STEM-related influence across training. They validate the checkpoint approximation on a 70M model, test sensitivity to the reference endpoint, and compare with a task-specific TracIn-style score.

Significance. If the central domain crossover is correct, the paper offers a valuable trajectory-level characterization of pretraining data and a practical demonstration of post-hoc influence analysis without retraining or task labels. The derivation of Cont(B_t) and Cont(x_t^k) is a clean algebraic identity with no fitted parameters, and the use of public checkpoints makes the method easy to apply. The robustness analysis across model scales, initializations, and data orderings is a genuine strength. However, the headline claim currently rests on an unvalidated SGD decomposition for Adam-trained models, and the provided validation is weakest in the early phase where the literature-dominance claim sits. Given the additional reference-endpoint sensitivity, the paper does not yet support its abstract claims at the level claimed.

major comments (4)
  1. [§3.2, Eq. (3), footnote 1, Appendix A] The example-level decomposition assumes standard SGD with per-example updates Δ_{t,k} = −η_t ∇ℓ(x;θ_t), so the per-example contributions sum to the true mini-batch update only for plain SGD. Pythia and PolyPythia are trained with Adam (footnote 1; §A), where per-example effects on the actual update are mediated by optimizer states and by other examples in the batch. The mini-batch influence Cont(B_t) in Eq. (2) is exact and optimizer-agnostic, but the domain-level rankings in §4.4 are computed from the SGD-based Eq. (3)/(4). The validation in §5.1 compares Eq. (4) only with Eq. (3); both quantities share the same SGD assumption, so the validation does not test whether the decomposition identifies the examples that actually drive an Adam-trained model. Because the abstract's literature-to-STEM crossover is derived from these rankings, this gap is load-bearing. A concrete fix would be to rerun the validation with Adam and compare per-example attribution against an Adam-aware decomposition, or at minimum to show that the domain-level crossover is preserved when Eq. (3) is replaced by an Adam-corrected score.
  2. [§5.1, Table 1] The checkpoint approximation has Pearson r=0.622 and Spearman r=0.592 in the early interval (1k→2k), versus 0.808/0.811 mid and 0.950/0.947 late. The paper's claim that literature-related data are most strongly aligned 'early in training' rests precisely on the early interval, where the approximation is weakest. The paper should report, for the early interval, whether the top- and bottom-5% domain compositions from the approximate scores agree with those from the exact scores, or at least report the correlation restricted to the top and bottom ranks. Without this, the early-stage domain claim may be driven by approximation error rather than by true contribution.
  3. [§5.2, Table 3] The contribution rankings are highly dependent on the reference endpoint: using the 70k checkpoint gives Spearman −0.174 with the final-reference scores and top-5% overlap 0.316; using 120k gives 0.566 and 0.680. Since the final checkpoint is itself a choice, the paper needs to show that the domain-level crossover (literature early, STEM late) is not an artifact of that choice. The current analysis reports only aggregate rank correlations and set overlaps; it does not report whether the top/bottom domain composition still exhibits the crossover when alternative near-final endpoints are used. Please provide the domain-composition analogue of Table 3, or explicitly state the range of reference endpoints for which the crossover persists.
  4. [§4.4, Figure 4, §B.3] The evidence for the 'literature-related data are more strongly aligned early' part of the claim is indirect. Figure 4(a) shows that STEM domains are overrepresented among bottom-5% contributors early and that Books & Literature become more common among bottom-5% later; Figure 4(b) shows that the STEM share among top-5% increases late. Neither panel directly shows literature as a top-5% contributor early. The abstract's claim should either be backed by explicit early top-5% domain shares for Books & Literature or softened to 'literature is less likely to be among bottom contributors early.' This matters because the top-5% patterns in Figure 8 are also less uniform across model sizes than the bottom-5% patterns.
minor comments (5)
  1. [Figures 4, 7–12] The x-axis labels in the domain-composition figures appear as encoded strings such as '/aj17' and '/aj19/aj17' rather than training-step labels; this rendering issue must be fixed before publication.
  2. [Figure 2(a)] The learning-rate curve is plotted on a secondary axis but the figure has no legend; please specify which curve corresponds to the right-hand axis.
  3. [§4.3] Min–max normalization within each checkpoint interval removes scale information, so the 'share of normalized contribution' is not directly comparable across intervals; state this explicitly when interpreting the PPL-bin shares.
  4. [§5.3] The abstract says the crossover is 'broadly consistent across model configurations,' but the top-5% cross-scale results in Appendix B.3 show no single directional pattern shared across all six models; consider tightening the wording to reflect the bottom-5% and domain-pair specific evidence.
  5. [§5.4] The TracIn-style comparison reports no confidence intervals or seed variation; the conclusion that this score 'does not consistently recover' the crossover would be strengthened by quantifying variability across the sampled examples and validation subsets.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the contribution measure is parameter-free and applied to externally released checkpoints; the only shared-author citation is minor and not load-bearing.

full rationale

The derivation is a self-contained algebraic identity rather than a fitted or self-referential chain. Cont(B_t) is defined as S_t - S_{t+1}, the exact reduction in squared distance to the final parameters, and Eq. (3) is the exact per-example decomposition of that mini-batch quantity under the explicitly stated SGD assumption, summing to Cont(B_t) by construction. No constants are fitted to the data and no held-out quantity is predicted from a fitted parameter, so the literature-to-STEM crossover is a computed property of the measure, not a consequence of tuning. The endpoint dependence is disclosed and explicitly examined in Section 5.2, where near-final reference checkpoints give nearly identical rankings, so the self-reference is a tested design choice rather than a hidden circular step. The checkpoint approximation in Eq. (4) is validated in Section 5.1 against the exact SGD-defined quantity; the fact that both share the SGD assumption is a robustness or correctness concern, not circularity, because the validation still tests the checkpoint approximation and the paper does not claim the approximation validates the optimizer assumption. The only shared-author citation is to PolyPythia (van der Wal et al., 2025) for public model checkpoints and for the initial/critical learning-phase framing; these are externally released artifacts and are not used to force the central result, so any self-citation is minor and non-load-bearing. No circular steps were identified.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The method is parameter-free apart from the reference endpoint; the key unproven inputs are the SGD decomposition for Adam-trained models and the checkpoint approximation, both explicitly acknowledged in the paper. No new physical or ontological entities are introduced.

free parameters (1)
  • Reference endpoint theta* (choice of final checkpoint) = Final checkpoint at step 143k for Pythia-1.4B; corresponding final checkpoints for other runs
    The influence measure is defined relative to theta*; Section 5.2 shows rankings flip when earlier references such as step 30k are used (Spearman -0.55), so this hand-chosen reference is consequential.
assumptions (5)
  • domain assumption The final parameters theta* of a pretraining run are a meaningful reference point for measuring training data influence.
    The whole influence measure is defined as reduction in squared distance to theta* (Eq. 1); the paper does not justify why the final parameters represent general capability.
  • ad hoc to paper Per-example updates are modeled as SGD steps Delta_t,k = -eta_t grad_l(x; theta_t) even though the models are trained with Adam.
    Footnote 1 explicitly states the SGD assumption; all example-level and domain analyses use this decomposition.
  • domain assumption Within each checkpoint interval, theta_t is approximated by theta_c and the total update is approximated by theta_c' - theta_c for every example in the interval.
    Equation (4); validated only on three intervals of Pythia-70M, with early-interval correlations around 0.62.
  • domain assumption The NeMo Curator domain classifier assigns correct semantic domains to training examples.
    Domain-level results in Sections 4.4 and 5.4 depend on this classifier, with no manual verification reported.
  • domain assumption The Pile subsets filtered against the Pythia training stream provide valid held-out validation sets for the TracIn comparison.
    Used in Section 5.4; exact-match filtering may leave near-duplicates that could inflate alignment, though this only affects the secondary comparison.

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Cite this review

Pith. "Pith review of Measuring Task-Agnostic Training Data Influence Across Language Model Pretraining." pith.science (2026). https://pith.science/paper/YPQ4SC7L

@misc{pith2026260813515,
  author       = {Pith},
  title        = {Pith review of: Measuring Task-Agnostic Training Data Influence Across Language Model Pretraining},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YPQ4SC7L}},
  note         = {Machine review of arXiv:2608.13515}
}
read the original abstract

Measuring training data influence consistently across language model pretraining is challenging. It is difficult to select downstream tasks or validation sets representative of a model's general capabilities, and reliance on task performance at intermediate checkpoints complicates comparisons across training. We propose a measure of training data influence that does not require selecting a downstream task or validation set as the attribution target. Specifically, we define an example's influence by how much its gradient update reduces the squared distance to the final parameters of a given pretraining run, and estimate this quantity from intermediate checkpoints without retraining. Applying the method to 18 configurations from the Pythia and PolyPythia suites, we find systematic temporal changes in influential data. Early in training, literature-related data are more strongly aligned with the trajectory toward the final parameters, whereas STEM data become more strongly aligned in later stages. This qualitative crossover is broadly consistent across model configurations. Our results provide a tractable trajectory-level view of how influential data change throughout pretraining, complementing influence analyses defined with respect to specific downstream tasks or validation sets.

Figures

Figures reproduced from arXiv: 2608.13515 by the authors.

Figure 1
Figure 1. Overview of our task-agnostic, training data contribution measure: Top contribu [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Training dynamics of the contribution distribution on Pythia-1.4B-Deduped. All [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Relationship between text PPL and contribution for Pythia-1.4B-Deduped. Each [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Domain composition of examples with extreme contribution values on Pythia [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Training dynamics of the contribution distribution across the six Pythia-Deduped [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Relationship between text PPL and contribution across the six Pythia-Deduped [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Domain composition of the bottom 5% of contribution examples across the six [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: Domain composition of the top 5% of contribution examples across the six Pythia [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: Domain composition of the bottom 5% of contribution examples across standard [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Domain composition of the top 5% of contribution examples across standard [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Domain composition of extreme-contribution examples for PolyPythia-160M [PITH_FULL_IMAGE:figures/full_fig_p022_11.png]
Figure 12
Figure 12. Figure 12: Domain composition of extreme-contribution examples for PolyPythia-160M [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: Domain composition of training examples with extreme TracIn-style scores. Each [PITH_FULL_IMAGE:figures/full_fig_p024_13.png]

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