arxiv: 2605.11312 · v1 · submitted 2026-05-11 · 💻 cs.AI

Recognition: no theorem link

Constraint-Data-Value-Maximization: Utilizing Data Attribution for Effective Data Pruning in Low-Data Environments

Danilo Brajovic , David A. Kreplin , Marco F. Huber

Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:35 UTC · model grok-4.3

classification 💻 cs.AI

keywords data pruningdata attributionShapley valuesconstrained optimizationinfluence maximizationlow-data regimesmodel performance

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The pith

Constraint-Data-Value-Maximization selects a small training subset by maximizing total influence while capping any single point's contribution to individual test examples.

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

The paper demonstrates that standard data attribution scores such as Shapley values do not guide optimal choices when most training examples must be discarded. It therefore reformulates the pruning decision as a constrained optimization problem that maximizes the sum of selected attribution scores subject to limits on how much any one training point can affect any given test point. This produces retained subsets that support stronger model performance than direct ranking by attribution value. A reader would care because many applications must operate with only a tiny fraction of available labeled data due to cost, privacy, or storage limits.

Core claim

Existing data value estimates are not optimally suited for pruning low-value data when only a limited amount remains. By casting pruning as a constrained optimization that maximizes total influence and penalizes excessive per-test contributions, the CDVM approach selects subsets that preserve downstream model utility even at very low retention rates.

What carries the argument

Constraint-Data-Value-Maximization (CDVM), the formulation that turns data pruning into a constrained optimization maximizing aggregate attribution scores while bounding per-test-point influence contributions.

If this is right

Models retain higher test accuracy when trained on the CDVM-chosen subset rather than a top-k attribution subset at the same small retention rate.
The procedure works with any underlying data attribution method without altering how the scores themselves are obtained.
Runtime stays competitive with standard attribution-based pruning on existing evaluation suites.
The performance benefit holds across varying model types and datasets in the reported experiments.

Where Pith is reading between the lines

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

The same constrained selection logic could be adapted to decide which historical examples to retain in continual learning settings.
Tuning the per-test contribution penalty might expose how much redundancy is present in common training collections.
One could check whether CDVM subsets also improve model robustness under distribution shift compared with standard pruning.

Load-bearing premise

Attribution scores computed on the full dataset remain reliable guides to each example's value once most other examples have been removed.

What would settle it

If models trained on CDVM-selected subsets show no consistent accuracy advantage over models trained on subsets chosen by ranking attribution scores, when both are tested at the same low retention fractions on repeated benchmark runs, the central advantage claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.11312 by Danilo Brajovic, David A. Kreplin, Marco F. Huber.

**Figure 1.** Figure 1: (a) Baseline synthetic dataset comprising 8 points from 4 clusters. (b) Illustrates the changed decision boundary after removing an [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: All plots show test accuracy as a function of the fraction of training data removed. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Accuracy on 30%, 25%, 20%, 15%, 10%, and 5% of remaining training data for six datasets in the OpenDataVal benchmark [Jiang [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: (a) Runtime vs. normalized performance for all benchmarked methods, aggregated over six datasets and six pruning levels. (b) CDVM performance as a function of how often each sample is seen during training for sampling probability p (cyan) and number of models trained T (blue). (c) Distribution of the selected slack threshold κ across datasets and retention fractions. (d) Average overlap coefficient |A∩B| m… view at source ↗

**Figure 5.** Figure 5: CDVM performance for different sampling probabilities [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

**Figure 6.** Figure 6: Effect of model-count and slack constraint on CDVM’s runtime and accuracy. For each dataset, we compare CDVM using 3,000, [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 7.** Figure 7: Selection frequency spectrum of training instances, sorted by total majority-selected fraction (highest at top). Each bar is divided at [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

**Figure 8.** Figure 8: (a) Test accuracy for different sparsity cut-offs in the attribution matrix, expressed as the percentage of entries retained by not setting them to zero. (b) Runtime (in seconds) for solving the CDVM optimization on each corresponding sparse matrix. (c) CDVM test performance compared against a random-pruning baseline. So far, we have evaluated CDVM on the OpenDataVal benchmark by subsampling each split to … view at source ↗

**Figure 9.** Figure 9: Synthetic clustered dataset. The training set consists of eight points from four Gaussian clusters with centers [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗

**Figure 10.** Figure 10: Effect of removing an entire cluster. The removed cluster is grey. [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗

**Figure 11.** Figure 11: Leave-one-out (LOO) on the dataset from Figure 9. All clusters except the last contain more than one point; therefore, the decision [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗

**Figure 12.** Figure 12: Shapley data valuation scores for the synthetic dataset. The black line represents the decision boundary of an MLP trained on [PITH_FULL_IMAGE:figures/full_fig_p025_12.png] view at source ↗

read the original abstract

Attributing model behavior to training data is an evolving research field. A common benchmark is data removal, which involves eliminating data instances with either low or high values, then assessing a model's performance trained on the modified dataset. Many existing studies leverage Shapley-based data values for this task. In this paper, we demonstrate that these data values are not optimally suited for pruning low-value data when only a limited amount of data remains. To address this limitation, we introduce the Constraint-Data-Value-Maximization (CDVM) approach, which effectively utilizes data attributions for pruning in low-data scenarios. By casting pruning as a constrained optimization that both maximizes total influence and penalizes excessive per-test contributions, CDVM delivers robust performance when only a small fraction of the data is retained. On the OpenDataVal benchmark, CDVM shows strong performance and competitive runtime.

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.

Desk Editor's Note private letter to a colleague

CDVM adds a per-test contribution constraint to attribution-based pruning and gets better low-retention results on OpenDataVal than plain Shapley pruning.

read the letter

The paper's main contribution is a constrained optimization that maximizes aggregate data value while limiting how much any single test point can draw from one training example. This directly targets the concentration problem that appears when standard Shapley pruning is applied with very small retained sets. The formulation is stated clearly in the full text and does not collapse into prior heuristics. Experiments on OpenDataVal show consistent gains over baselines in the low-retention regime and keep runtime competitive, which is the practical evidence that matters here. The authors acknowledge the dependence on pre-computed attributions and test the end-to-end pipeline, so the central claim is not circular. One soft spot is that the method still inherits whatever noise or bias exists in the initial attribution scores; the paper does not include extensive sensitivity checks on noisy attributions, but this is a minor rather than load-bearing issue given the benchmark results. The work is aimed at researchers who already use data valuation for pruning or selection and want a drop-in improvement for data-scarce settings. It is not a broad theoretical advance, but the idea is cleanly executed and the empirical support is present. I would send it to peer review.

Referee Report

0 major / 1 minor

Summary. The paper claims that Shapley-based data attribution scores are suboptimal for pruning low-value data in low-retention regimes. It introduces Constraint-Data-Value-Maximization (CDVM), which formulates pruning as a constrained optimization problem that maximizes aggregate data influence while penalizing excessive per-test-point contributions. On the OpenDataVal benchmark, CDVM achieves strong performance gains over baselines with competitive runtime when only a small fraction of data is retained.

Significance. If the results hold, the work is significant for data-efficient machine learning and attribution methods. It provides a principled constrained-optimization lens on pruning that directly addresses limitations of direct thresholding on attribution scores in low-data settings. Strengths include the explicit CDVM formulation (constrained maximization of total value with per-test penalties), consistent empirical gains in the low-retention regime on a standard benchmark, competitive runtime, and transparent reliance on pre-computed attributions that is empirically tested.

minor comments (1)

Abstract: The summary of the method would be clearer if it briefly stated the form of the constraint (e.g., the per-test contribution penalty) rather than only describing its effect.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The referee summary correctly identifies the core contribution of CDVM as a constrained optimization formulation that maximizes aggregate data influence while penalizing excessive per-test-point contributions, along with its empirical advantages in low-retention regimes on the OpenDataVal benchmark.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces CDVM as a constrained optimization applied to pre-existing data attribution scores (e.g., Shapley values) for pruning, without deriving or re-fitting those attributions within the method itself. No equations, self-citations, or ansatzes are shown that reduce the optimization outcome or performance claims to tautological restatements of inputs. The approach is explicitly built on external attribution techniques, with empirical results on the OpenDataVal benchmark providing independent validation. This constitutes a standard, non-circular extension of prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are described. The method relies on pre-existing data attribution scores and standard constrained optimization without introducing new postulated entities.

pith-pipeline@v0.9.0 · 5450 in / 1108 out tokens · 43397 ms · 2026-05-13T01:35:34.622990+00:00 · methodology

discussion (0)

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