Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration

Changxin Gao; Dongyue Wu; Jiajia Liu; Jingdong Chen; Nong Sang; Xiaoyu Li; Zilin Guo

arxiv: 2606.12913 · v1 · pith:TKHEOLP7new · submitted 2026-06-11 · 💻 cs.LG · cs.CV

Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration

Dongyue Wu , Zilin Guo , Xiaoyu Li , Jiajia Liu , Jingdong Chen , Nong Sang , Changxin Gao This is my paper

Pith reviewed 2026-06-27 07:20 UTC · model grok-4.3

classification 💻 cs.LG cs.CV

keywords dataset pruninggraph modelingmaximum weight cliquetraining accelerationimportance metricsapproximation algorithmsmachine learning efficiency

0 comments

The pith

Modeling datasets as weighted graphs casts dataset pruning as a maximum-weight clique problem with approximation guarantees.

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

Dataset pruning aims to keep only the most useful samples to cut training costs, but current methods either judge samples in isolation or enforce diversity through pairs, each working well only in narrow settings. The paper unifies both signals by building a graph whose nodes carry intrinsic sample value and whose edges carry extrinsic value from pairwise relations. Pruning then reduces exactly to finding the maximum-weight clique in this graph. A greedy algorithm that adds samples by their marginal gain solves the problem, and the paper proves this objective has a formal approximation guarantee under mild conditions that cover many common importance metrics. On ImageNet-1k with ResNet-50 the resulting subsets cut training time by more than 40 percent while matching full-dataset accuracy.

Core claim

By representing the dataset as a weighted graph in which node weights encode intrinsic value and edge weights encode extrinsic value, dataset pruning becomes the Maximum Weight Clique Problem. Although NP-hard, the structure permits a greedy solution driven by sample-wise marginal gains, and under mild conditions the unified objective admits a formal approximation guarantee that applies to a broad family of importance metrics and supplies concrete design guidelines.

What carries the argument

The weighted-graph model of the dataset that converts pruning into the Maximum Weight Clique Problem, solved by selecting samples according to marginal gain.

Load-bearing premise

The node weights and edge weights chosen to represent intrinsic and extrinsic signals together give a faithful picture of each sample's true utility for the final training task.

What would settle it

Run the greedy algorithm on a dataset whose optimal maximum-weight clique is known by exhaustive search; if the returned subset yields lower downstream accuracy than the true optimum at the same size, the modeling or guarantee does not hold.

Figures

Figures reproduced from arXiv: 2606.12913 by Changxin Gao, Dongyue Wu, Jiajia Liu, Jingdong Chen, Nong Sang, Xiaoyu Li, Zilin Guo.

**Figure 3.** Figure 3: Ablation on different solvers for the MWCP objective. practical perspective, this analysis provides clear guidance for importance design: any choice of intrinsic and extrinsic scores that induces non-positive pairwise interactions and non-negative marginal gains leads to a theoretically grounded and scalable pruning algorithm. 4. Experiments 4.1. Experimental Setup Datasets. Following the most common sett… view at source ↗

**Figure 4.** Figure 4: Comparison across pruning method families on CIFAR-100. The proposed method excels not only over intrinsic and extrinsic ones, but also over hybrid methods. Performance Comparisons. We report the Top-1 accuracy (Acc) results of ResNet-18 on CIFAR-10/100 and ResNet-50 on ImageNet-1k are reported in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

read the original abstract

The rapid growth of modern training datasets has significantly increased computational cost, motivating dataset pruning~(DP) methods which retain only a subset of informative samples to reduce training cost. Existing pruning criteria typically rely on either intrinsic signals that assess samples independently or extrinsic signals that promote diversity via pairwise relations. While effective in their own specific regimes, each captures only one aspect of sample utility and lacks robustness across different pruning ratios or data distribution. In this work, we present a unified graph-based DP framework. By modeling the dataset as a weighted graph, where node weights encode intrinsic value and edge weights encode extrinsic value, DP can be cast as a Maximum Weight Clique Problem (MWCP). Although MWCP is NP-hard, its structure admits a principled greedy solution based on sample-wise marginal gains. Under a few mild conditions, we further prove that this unified objective enjoys a formal approximation guarantee, which applies to a broad family of importance metrics and provides practical design guidelines. Extensive experiments show that our method outperforms existing DP methods while substantially reducing training cost, reducing training time by over 40\% without sacrificing accuracy on ImageNet-1k with ResNet-50.

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

The MWCP graph formulation unifies intrinsic and extrinsic pruning signals with a greedy algorithm and claimed approximation guarantee, but the abstract supplies none of the actual derivation or conditions.

read the letter

The paper's main move is to build a weighted graph over the dataset, put intrinsic value on nodes and extrinsic value on edges, and treat pruning as the maximum-weight clique problem. From there they extract a greedy marginal-gain rule and state that it carries an approximation guarantee under mild conditions that covers a range of existing metrics. That modeling step is the actual novelty; prior work stayed inside either the intrinsic-only or extrinsic-only regime.

The experiments report more than 40 percent wall-clock reduction on ImageNet-1k with ResNet-50 while holding accuracy, which is the kind of number that matters for the subfield. If the guarantee turns out to be both correct and reasonably broad, the framework gives a principled way to combine signals that used to be handled separately.

The obvious soft spot is that none of the supporting material appears in the abstract: no derivation of the guarantee, no list of the mild conditions, no error bars, and no ablation on how the node and edge weights are chosen. Without those pieces it is impossible to tell whether the guarantee applies to the metrics people actually use or whether the graph construction faithfully reflects downstream utility. The circularity burden looks low, which helps, but the central claim still rests on unshown steps.

This is for researchers who already work on dataset pruning or large-scale training efficiency. A reader who wants a graph-theoretic handle on the problem will find the modeling useful even if the guarantee needs checking. It is worth sending to a serious referee; the claim is concrete enough that the details can be verified or corrected in review.

Referee Report

2 major / 2 minor

Summary. The paper proposes a unified dataset pruning (DP) framework that models the dataset as a weighted graph, with node weights representing intrinsic sample value and edge weights representing extrinsic (pairwise diversity) value. It casts DP as the Maximum Weight Clique Problem (MWCP), derives a greedy algorithm based on sample-wise marginal gains, and claims a formal approximation guarantee under mild conditions that applies to a broad family of importance metrics. Experiments report >40% wall-clock training reduction on ImageNet-1k/ResNet-50 while preserving accuracy and outperforming prior DP methods.

Significance. If the MWCP modeling and approximation guarantee hold under the stated conditions, the work supplies a principled unification of intrinsic and extrinsic pruning signals together with design guidelines, which could improve robustness across pruning ratios and data distributions. The empirical speedups are practically relevant for large-scale training if the results are reproducible with error bars and ablations.

major comments (2)

[theoretical analysis / proof section] The abstract and theoretical section state a formal approximation guarantee under mild conditions, but the manuscript does not explicitly list or verify those conditions, nor does it provide the derivation steps. This makes it impossible to assess whether the guarantee applies to the importance metrics used in the experiments (e.g., the node/edge weight definitions).
[experimental results] Experiments claim strong gains with >40% training time reduction, but report no error bars across runs and provide no ablation on the sensitivity of results to the choice of intrinsic vs. extrinsic signals or the MWCP formulation parameters. This weakens the claim that the method is robust across pruning ratios.

minor comments (2)

[framework definition] Notation for node weights (intrinsic) and edge weights (extrinsic) should be introduced with explicit equations early in the framework section to improve readability.
[design guidelines] The paper should include a short table or list mapping common importance metrics (e.g., EL2N, gradient norm) to the corresponding node/edge weight choices.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive recommendation. We address each major comment below.

read point-by-point responses

Referee: [theoretical analysis / proof section] The abstract and theoretical section state a formal approximation guarantee under mild conditions, but the manuscript does not explicitly list or verify those conditions, nor does it provide the derivation steps. This makes it impossible to assess whether the guarantee applies to the importance metrics used in the experiments (e.g., the node/edge weight definitions).

Authors: We agree that the conditions and derivation steps must be stated explicitly. In the revised manuscript we will insert a dedicated subsection that lists the mild conditions, supplies the complete derivation of the approximation guarantee, and verifies that the conditions hold for the specific node- and edge-weight definitions employed in the experiments. revision: yes
Referee: [experimental results] Experiments claim strong gains with >40% training time reduction, but report no error bars across runs and provide no ablation on the sensitivity of results to the choice of intrinsic vs. extrinsic signals or the MWCP formulation parameters. This weakens the claim that the method is robust across pruning ratios.

Authors: We acknowledge that error bars and targeted ablations are necessary to substantiate robustness claims. The revised manuscript will report standard deviations over multiple independent runs and will include new ablations that isolate the contribution of intrinsic versus extrinsic signals as well as the effect of MWCP formulation parameters across pruning ratios. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained mathematical modeling

full rationale

The paper casts dataset pruning as an MWCP on a graph with node/edge weights for intrinsic/extrinsic value, then derives a greedy marginal-gain algorithm and an approximation guarantee under stated mild conditions. This is a standard reduction to a known combinatorial problem followed by analysis of that problem; the guarantee is a theorem about MWCP, not a renaming or fit of the input metrics. No self-citation is load-bearing for the central claim, no parameter is fitted then relabeled as prediction, and no step equates the output to the modeling choice by definition. The framework remains independent of the specific importance metrics chosen.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the graph construction faithfully capturing utility and on the existence of mild conditions that validate the approximation guarantee; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption A few mild conditions under which the MWCP greedy algorithm enjoys a formal approximation guarantee
Invoked in the abstract as the premise for the proof that applies to a broad family of importance metrics.

pith-pipeline@v0.9.1-grok · 5757 in / 1214 out tokens · 23272 ms · 2026-06-27T07:20:17.779765+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

15 extracted references · 7 canonical work pages · 4 internal anchors

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GPT-4 Technical Report

Achiam, J., Adler, S., Agarwal, S., Ahmad, L., Akkaya, I., Aleman, F. L., Almeida, D., Altenschmidt, J., Altman, S., 9 Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration Anadkat, S., et al. Gpt-4 technical report.arXiv preprint arXiv:2303.08774,

work page internal anchor Pith review Pith/arXiv arXiv
[2]

Super-Samples from Kernel Herding

Chen, Y ., Welling, M., and Smola, A. Super-samples from kernel herding.arXiv preprint arXiv:1203.3472,

work page internal anchor Pith review Pith/arXiv arXiv
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AutoAugment: Learning Augmentation Policies from Data

Cubuk, E. D., Zoph, B., Mane, D., Vasudevan, V ., and Le, Q. V . Autoaugment: Learning augmentation policies from data.arXiv preprint arXiv:1805.09501,

work page internal anchor Pith review Pith/arXiv arXiv
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H., Wong, D

Jiang, A. H., Wong, D. L.-K., Zhou, G., Andersen, D. G., Dean, J., Ganger, G. R., Joshi, G., Kaminksy, M., Kozuch, M., Lipton, Z. C., et al. Accelerating deep learning by focusing on the biggest losers.arXiv preprint arXiv:1910.00762,

work page arXiv 1910
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Online Batch Selection for Faster Training of Neural Networks

Loshchilov, I. and Hutter, F. Online batch selection for faster training of neural networks.arXiv preprint arXiv:1511.06343,

work page internal anchor Pith review Pith/arXiv arXiv
[6]

S., Daruwalla, K., and Lipasti, M

Raju, R. S., Daruwalla, K., and Lipasti, M. Accelerating deep learning with dynamic data pruning.arXiv preprint arXiv:2111.12621,

work page arXiv
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and Hamelain, C

Senzaki, Y . and Hamelain, C. Active learning for deep neural networks on edge devices.arXiv preprint arXiv:2106.10836,

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Coverage- centric coreset selection for high pruning rates

Zheng, H., Liu, R., Lai, F., and Prakash, A. Coverage- centric coreset selection for high pruning rates. In11th International Conference on Learning Representations, ICLR 2023,

2023
[9]

First, interpretations on the accuracy improvement of our method and other existing methods (such as InfoBatch) are presented (Sec

12 Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration Appendix This appendix provides additional details and results to complement the main paper. First, interpretations on the accuracy improvement of our method and other existing methods (such as InfoBatch) are presented (Sec. A). Next, we introduce the fu...

2023
[10]

Since DivBS performs batch-wise pruning, we adapt our UGIES accordingly and denote this variant asOurs-BS

following the DivBS configuration. Since DivBS performs batch-wise pruning, we adapt our UGIES accordingly and denote this variant asOurs-BS. We similarly adapt InfoBatch for fairness (denoted asInfoBatch- BS). We evaluate the performance under pruning ratios of 70%, 80%, and 90%, and report final mIoU. As shown in Tab. 6, Ours-BS consistently achieves th...

2012
[11]

Performance on Object Detection We further evaluate generalization on object detection using SSD-ResNet50 trained on COCO2017 (Lin et al., 2014)

69.80 67.97 64.66 Ours-BS 70.02 68.48 65.79 Full Data 70.80 D.2. Performance on Object Detection We further evaluate generalization on object detection using SSD-ResNet50 trained on COCO2017 (Lin et al., 2014). We compare with InfoBatch (Qin et al.,

2014
[12]

and D2-pruning (Maharana et al., 2024). Tab. 7 shows that our method attains the highest AP across all metrics, indicating strong adaptability to various vision tasks. 14 Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration Table 7.Object detection pruning on COCO2017 using SSD ResNet-50. † denotes our reprod...

2024
[13]

(Nemhauser et al., 1978)

For a more detailed and rigorous derivation, we refer the reader to the original work of Nemhauser et al. (Nemhauser et al., 1978). Proof. We may, without loss of generality, assumef(∅) = 0, since adding a constant to f does not change marginal gains nor the greedy solution. LetS t be the greedy set aftertsteps, withS 0 =∅and|S t|=t. By submodularity, for...

1978
[14]

SinceBis exponential in the worst case, the overall complexity remains exponential

term reflects repeated weighted-coloring and pruning operations at each node. SinceBis exponential in the worst case, the overall complexity remains exponential. In our setting, each subgraph is fully connected, so clique feasibility no longer provides strong pruning, and the problem reduces to selecting a fixed-size subset of size b= (1−p)N . This solver...

2008
[15]

AutoAugment (Cubuk et al., 2018), random path drop, and gradient clipping are applied only to Swin-T to ensure a fair comparison with Dyn-Unc

training settings; for Swin-T we follow Dyn-Unc (He et al., 2024). AutoAugment (Cubuk et al., 2018), random path drop, and gradient clipping are applied only to Swin-T to ensure a fair comparison with Dyn-Unc. The hyperparameters required for reproduction are listed in the Tab

2024

[1] [1]

GPT-4 Technical Report

Achiam, J., Adler, S., Agarwal, S., Ahmad, L., Akkaya, I., Aleman, F. L., Almeida, D., Altenschmidt, J., Altman, S., 9 Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration Anadkat, S., et al. Gpt-4 technical report.arXiv preprint arXiv:2303.08774,

work page internal anchor Pith review Pith/arXiv arXiv

[2] [2]

Super-Samples from Kernel Herding

Chen, Y ., Welling, M., and Smola, A. Super-samples from kernel herding.arXiv preprint arXiv:1203.3472,

work page internal anchor Pith review Pith/arXiv arXiv

[3] [3]

AutoAugment: Learning Augmentation Policies from Data

Cubuk, E. D., Zoph, B., Mane, D., Vasudevan, V ., and Le, Q. V . Autoaugment: Learning augmentation policies from data.arXiv preprint arXiv:1805.09501,

work page internal anchor Pith review Pith/arXiv arXiv

[4] [4]

H., Wong, D

Jiang, A. H., Wong, D. L.-K., Zhou, G., Andersen, D. G., Dean, J., Ganger, G. R., Joshi, G., Kaminksy, M., Kozuch, M., Lipton, Z. C., et al. Accelerating deep learning by focusing on the biggest losers.arXiv preprint arXiv:1910.00762,

work page arXiv 1910

[5] [5]

Online Batch Selection for Faster Training of Neural Networks

Loshchilov, I. and Hutter, F. Online batch selection for faster training of neural networks.arXiv preprint arXiv:1511.06343,

work page internal anchor Pith review Pith/arXiv arXiv

[6] [6]

S., Daruwalla, K., and Lipasti, M

Raju, R. S., Daruwalla, K., and Lipasti, M. Accelerating deep learning with dynamic data pruning.arXiv preprint arXiv:2111.12621,

work page arXiv

[7] [7]

and Hamelain, C

Senzaki, Y . and Hamelain, C. Active learning for deep neural networks on edge devices.arXiv preprint arXiv:2106.10836,

work page arXiv

[8] [8]

Coverage- centric coreset selection for high pruning rates

Zheng, H., Liu, R., Lai, F., and Prakash, A. Coverage- centric coreset selection for high pruning rates. In11th International Conference on Learning Representations, ICLR 2023,

2023

[9] [9]

First, interpretations on the accuracy improvement of our method and other existing methods (such as InfoBatch) are presented (Sec

12 Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration Appendix This appendix provides additional details and results to complement the main paper. First, interpretations on the accuracy improvement of our method and other existing methods (such as InfoBatch) are presented (Sec. A). Next, we introduce the fu...

2023

[10] [10]

Since DivBS performs batch-wise pruning, we adapt our UGIES accordingly and denote this variant asOurs-BS

following the DivBS configuration. Since DivBS performs batch-wise pruning, we adapt our UGIES accordingly and denote this variant asOurs-BS. We similarly adapt InfoBatch for fairness (denoted asInfoBatch- BS). We evaluate the performance under pruning ratios of 70%, 80%, and 90%, and report final mIoU. As shown in Tab. 6, Ours-BS consistently achieves th...

2012

[11] [11]

Performance on Object Detection We further evaluate generalization on object detection using SSD-ResNet50 trained on COCO2017 (Lin et al., 2014)

69.80 67.97 64.66 Ours-BS 70.02 68.48 65.79 Full Data 70.80 D.2. Performance on Object Detection We further evaluate generalization on object detection using SSD-ResNet50 trained on COCO2017 (Lin et al., 2014). We compare with InfoBatch (Qin et al.,

2014

[12] [12]

and D2-pruning (Maharana et al., 2024). Tab. 7 shows that our method attains the highest AP across all metrics, indicating strong adaptability to various vision tasks. 14 Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration Table 7.Object detection pruning on COCO2017 using SSD ResNet-50. † denotes our reprod...

2024

[13] [13]

(Nemhauser et al., 1978)

For a more detailed and rigorous derivation, we refer the reader to the original work of Nemhauser et al. (Nemhauser et al., 1978). Proof. We may, without loss of generality, assumef(∅) = 0, since adding a constant to f does not change marginal gains nor the greedy solution. LetS t be the greedy set aftertsteps, withS 0 =∅and|S t|=t. By submodularity, for...

1978

[14] [14]

SinceBis exponential in the worst case, the overall complexity remains exponential

term reflects repeated weighted-coloring and pruning operations at each node. SinceBis exponential in the worst case, the overall complexity remains exponential. In our setting, each subgraph is fully connected, so clique feasibility no longer provides strong pruning, and the problem reduces to selecting a fixed-size subset of size b= (1−p)N . This solver...

2008

[15] [15]

AutoAugment (Cubuk et al., 2018), random path drop, and gradient clipping are applied only to Swin-T to ensure a fair comparison with Dyn-Unc

training settings; for Swin-T we follow Dyn-Unc (He et al., 2024). AutoAugment (Cubuk et al., 2018), random path drop, and gradient clipping are applied only to Swin-T to ensure a fair comparison with Dyn-Unc. The hyperparameters required for reproduction are listed in the Tab

2024