Useful to Whom? The Easy-versus-Coverage Boundary Moves with the Learner

Yangze Liu; Xiao-Long Yin; Zhongyi Han

cs.LGSep 22, 2026

Useful to Whom? The Easy-versus-Coverage Boundary Moves with the Learner

Authors: Yangze Liu, Xiao-Long Yin, Zhongyi Han

Organizations: Shandong University · Nanjing University

Abstract

Is the same data equally useful to every learner? The question is whether the value of a training sample belongs to the sample or arises in its interaction with the learner. We test it with a selection experiment. Under a per-class budget, two kinds of samples compete for the slots: easy samples, which a short training run learns first, and coverage samples, which spread over the class in feature space. Easy samples win at small budgets and coverage samples at large ones, and the budget at which the winner flips, the crossover m0, can be measured. We ask whether m0 is set by the data or by the learner. To separate the two, we freeze the selected subsets and change only the learner that trains on them. On low-resolution ImageNet-100, doubling the width of a ResNet-18 moves the crossover from 57 to 85 samples per class on the same subsets. Enlarging the input grid from 32 to 64 pixels at fixed image information moves it from 85 to 57, and a single stride change reproduces or removes this shift. The grid shift shrinks as width grows. Under the native ImageNet-1k protocol, a 4x range of width moves the boundary by at most a few samples per class. On a Vision Transformer, coverage wins at every measured budget, even with easy subsets that work on the convolutional learner. The budget at which one kind of sample stops being the more useful kind therefore belongs to the learner, and the preferred regime of a selection strategy has to be read against the learner that will use the data.

Figures & tables

Figure 1: One instrument, one manipulation. An easy-first set and a coverage set are selected within each class by ResNet-18 ( a ), both index lists are frozen ( b ), only the learner that trains on them changes ( c ), and the crossover $m_{0}$ is read from the gap between the two sets ( d ; schematic curves, measured crossings from Figure 2 A). The grid, stride, and learner-family experiments change something else in c .

Figure 2: The crossover moves with the learner, not with the data. Per-budget gap (easy-first

-

Herding, percentage points) on low-resolution ImageNet-100, mean and

\pm 1

std over 3 seeds. A : the same frozen subsets, selected by ResNet-18 (R18) on the 32@64 cell, trained by R18 and by a

2\times

-wide variant (W2). B : R18 on three input cells; a@b means a px of retained information on a b-px input grid.

Learner	Subset	$m$ =40	55	65	80	100	130
R18	easy-first	27.1	31.6	33.7	36.1	37.6	42.7
R18	Herding	23.3	31.2	35.2	38.5	43.0	48.0
R18	Uniform	19.2	25.1	30.4	33.9	38.3	43.7
W2	easy-first (frozen)	26.0	29.1	31.4	34.5	37.2	41.5
W2	Herding (frozen)	19.9	23.9	28.2	33.9	39.3	43.6
W2	Uniform	16.5	20.0	24.0	29.7	34.6	38.7

Table 1: What the wrong learner’s verdict costs. Test accuracy (%, 3 seeds, std at most 2.5) of the same frozen R18-selected 32@64 subsets trained by R18 and by W2; Uniform is a seed-matched random subset. A learner’s verdict at budget

m

is the strategy with the higher accuracy on it; the cost rows give what one learner loses by following the other’s verdict, computed before rounding.

Lists from	Learner	Feature-map ladder	$m_{0}$
32@32	32@32 (native)	32/16/8/4	84.9
32@32	32@64 (transplant)	64/32/16/8	66.6
32@32	32@32, layer-2 stride 1	32/32/16/8	62.7
32@32	32@32, layer-4 stride 1	32/16/8/8	63.7
32@64	32@64 (native)	64/32/16/8	57.2
32@64	32@32 (transplant)	32/16/8/4	75.6

Table 2: Frozen-list controls on the grid axis. Every row trains on the lists selected in the cell of the first column; only the learner changes. Transplants swap the learner’s input grid; stride controls keep the grid and change one stride. The ladder lists the feature-map side after layers 1–4;

m_{0}

in samples per class.

Figure 3: One stride change moves the boundary. Frozen 32@32 lists trained by ResNet-18 (top) and by the same network with the stride of layer 4 set to 1 (bottom), which changes only the map entering global average pooling (Table 2 , layer-4 row).

Figure 5: On a ViT, no easy-first phase within the measured range. A : gap curves for ViT-Tiny at patch sizes 8 and 4 with both probes; the dashed curve is ResNet-18 on the same cell. B : accuracy advantage over uniform sampling on ViT-Tiny (patch 8) for the Herding set, the R18-selected easy set, and the ViT’s own easy set; mean and std over 3 seeds.

Figure 6: The ImageNet-1k low-resolution ladder yields orderings and censored bounds, not crossings. Single seed. A : ILSVRC replica, two grids. B : ModelScope replica, three grids. The two replicas build their subsets independently and are compared only within a panel.

		$m_{0}$		Acc. at 64.1
Width	Params	LFrac	EL2N	Easy-first	Herding
$0.5\times$	3.1M	43.8	31.7	38.1	40.5
$1\times$	11.7M	42.5	34.0	42.3	45.0
$2\times$	45.7M	44.4	38.4	44.8	47.7

Table 5: Native ImageNet-1k width sweep on frozen subsets.

m_{0}

per probe, in samples per class; within a probe the three crossings share one sampled bracket, [38.4, 51.2] for LFrac and [25.6, 38.4] for EL2N. Accuracy (%, 3 seeds) at 64.1 samples per class.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Grid	f=.05	f=.10	f=.20	f=.30	f=.50	f=.70	Crossover
32@32	+5.73	+5.92	+2.90	+1.39	+0.85	+1.08	No flip within range
64@64	+3.48	+2.14	+0.85	+0.39	$-$ 0.51	$-$ 0.10	Approx. f=.39, i.e., approx. 193 samples/class
64@128 (upsampled)	+2.81	$-$ 0.69	$-$ 0.78	$-$ 0.49	—	—	Approx. f=.09, i.e., approx. 45 samples/class

Appendix

Table 10

Figure A1: TinyImageNet grid ladder. The x-axis shows the retained fraction

f

per class, and the y-axis shows the LFrac20

-

Herding test-accuracy gap in percentage points. Open markers indicate linear zero crossings between adjacent measured points. The 64@128 condition is upsampled and stops after f=.30, while 32@32 does not flip within the maximum budget.

Probe	$(0.5\times,32)$	$(1\times,32)$	$(2\times,32)$	$(0.5\times,64)$	$(1\times,64)$	$(2\times,64)$
LFrac	Approx. 108; measured, shallow; [100,250)	85; measured; [80,100]	Approx. 95; measured, shallow; [80,110]	64; measured; [55,65]	57; measured; [55,65]	85; measured; [80,90]
EL2N	$\gtrsim 100$ ; shallow crossing, lower bound only	87; measured; the $m=100$ reading is coarse, conservative bracket [87,130)	82; measured; [80,100]	69; measured; [65,80]	54; measured; [40,55]	87; measured; [80,100], decisively confirmed at m130

Appendix

Table 12

m	25	40	55	65	80	100	130	180	250
$(1\times,32@32)$	+5.80 $\pm$ 0.92	+5.96 $\pm$ 0.85	+3.47 $\pm$ 1.29	+1.39 $\pm$ 0.37	+0.43 $\pm$ 2.00	$-$ 1.35 $\pm$ 0.26	$-$ 0.79 $\pm$ 0.89	$-$ 2.39 $\pm$ 0.53	$-$ 2.92 $\pm$ 0.82
$(1\times,32@64)$	+3.75 $\pm$ 1.50	+3.89 $\pm$ 0.46	+0.42 $\pm$ 1.22	$-$ 1.51 $\pm$ 0.63	$-$ 2.35 $\pm$ 0.76	$-$ 5.39 $\pm$ 0.08	$-$ 5.24 $\pm$ 0.75	$-$ 5.94 $\pm$ 0.24	$-$ 5.25 $\pm$ 0.66

Appendix

Table 13

List $\backslash$ Learner	32@32	32@64
32@32 subset	84.9	66.6
32@64 subset	75.6	57.2

Appendix

Table 14

m	25	40	55	65	80	100	130	180	250
$(0.5\times,64@64)$	+4.88 $\pm$ 1.28	+2.84 $\pm$ 1.66	+0.26 $\pm$ 1.39	$-$ 0.96 $\pm$ 1.14	$-$ 2.71 $\pm$ 1.19	$-$ 4.41 $\pm$ 1.58	$-$ 5.23 $\pm$ 0.24	$-$ 5.95 $\pm$ 1.45	$-$ 6.12 $\pm$ 1.13
$(2\times,64@64)$	+5.88 $\pm$ 1.44	+3.64 $\pm$ 0.18	+0.70 $\pm$ 2.59	$-$ 1.01 $\pm$ 1.11	$-$ 2.89 $\pm$ 1.42	$-$ 7.43 $\pm$ 2.28	$-$ 4.52 $\pm$ 2.32	$-$ 7.40 $\pm$ 1.47	$-$ 7.03 $\pm$ 1.78

Appendix

Table 15

Control	Grid	Ladder (layers 1–4)	Lists	$m_{0}$ [bracket]	Native cell	Transplant, same lists
Forward: layer-2 stride 1	32	32/32/16/8	32@32	62.7 [55,65]	84.9 (32@32)	66.6 (32@64 learner)
Reverse: stem stride 2	64	32/16/8/4	32@64	89.8 [80,100]	57.2 (32@64)	75.6 (32@32 learner)
Rung: layer-4 stride 1	32	32/16/8/8	32@32	63.7 [55,65]	84.9 (32@32)	66.6 (32@64 learner)

Appendix

Table 16

Learner	Probe	m=25 gap	m=250 gap	$m_{0}$ status
ViT-Tiny P8	LFrac	$-$ 0.63	$-$ 2.66	$<$ 25, left-censored
ViT-Tiny P8	EL2N	$-$ 1.54	$-$ 2.51	$<$ 25, left-censored
ViT-Tiny P4	LFrac	$-$ 1.23	$-$ 2.77	$<$ 25, left-censored
ViT-Tiny P4	EL2N	$-$ 0.98	$-$ 3.79	$<$ 25, left-censored

Appendix

Table 17

m	25	40	55	65	80	100	130	180	250
P8 LFrac $-$ Herding	$-$ 0.63	$-$ 1.35	$-$ 1.17	$-$ 1.75	$-$ 2.54	$-$ 2.61	$-$ 1.26	$-$ 2.55	$-$ 2.66
P4 LFrac $-$ Herding	$-$ 1.23	$-$ 1.35	$-$ 1.41	$-$ 2.03	$-$ 1.83	$-$ 2.11	$-$ 2.29	$-$ 2.43	$-$ 2.77

Appendix

Table 18

Figure C1: Complete LFrac gap sequences for ViT. All nine measured points for both P8 and P4 lie below zero, so both can only be reported as

m_{0}<25

. Local rebounds in the curves do not change the censoring verdict.

m	R18 easy set $\to$ ViT	Uniform $\to$ ViT	ViT easy set $\to$ ViT	Herding $\to$ ViT	R18 easy $-$ Uniform
25	10.4 $\pm$ 0.1	10.2 $\pm$ 0.1	10.9 $\pm$ 0.3	11.5 $\pm$ 0.8	+0.1
65	15.4 $\pm$ 0.3	14.5 $\pm$ 0.5	15.1 $\pm$ 0.3	16.9 $\pm$ 0.4	+0.9
100	18.4 $\pm$ 0.7	18.0 $\pm$ 0.4	18.0 $\pm$ 0.3	20.6 $\pm$ 1.0	+0.4
180	23.8 $\pm$ 0.3	23.3 $\pm$ 0.2	23.6 $\pm$ 0.5	26.2 $\pm$ 0.7	+0.5

Appendix

Table 20

m	20	30	40	50	65	80	100	130	180	250
32@32 LFrac $-$ Herding	+6.65	+7.94	+9.34	+9.50	+9.88	+10.56	+10.34	+8.10	+7.69	+6.90
32@64 LFrac $-$ Herding	+6.19	+8.59	+9.33	+8.45	+7.98	+8.91	+7.06	+4.93	+3.54	+2.85

Appendix

Table 21

m	20	40	65	80	100
32@32 LFrac $-$ Herding	+6.44	+9.32	+10.66	+9.99	+10.14
32@64 LFrac $-$ Herding	+5.82	+9.56	+7.09	+7.43	+5.88

Appendix

Table 22

m	32@32 gap	32@64 gap	32@128 gap
20	+6.44	+5.82	+5.84
40	+9.32	+9.56	+7.10
65	+10.66	+7.09	+5.75
100	+10.14	+5.88	+2.28

Appendix

Table D1: Shared budgets across the three ImageNet-1k input grids. Single-seed results; m is the absolute number of samples per class, and gaps are in percentage points.

32@128, m	LFrac acc.	Herding acc.	Uniform acc.	gap
100	25.99	23.71	18.95	+2.28
130	29.12	26.14	22.21	+2.98
180	32.03	29.30	26.99	+2.73

Appendix

Table D2: Tail readings for ImageNet-1k 32@128. Single-seed results; m is the absolute number of samples per class, test accuracy is in %, and gaps are in percentage points.

samples/class	12.8	25.6	38.4	51.2	64.1	76.9	89.7	102.5
W05( $0.5\times$ )	+5.80	+3.19	+0.91	$-$ 1.28	$-$ 2.35	—	—	—
W1( $1\times$ )	—	—	+0.48	$-$ 1.04	$-$ 2.71	—	—	—
W2( $2\times$ )	—	+4.22	+1.08	$-$ 1.23	$-$ 2.82	$-$ 3.74	$-$ 4.49	$-$ 4.91

Appendix

Table 25

Figure D1: Native ImageNet-1k: per-budget gap at three widths on the same frozen subsets , for LFrac ( A ) and EL2N ( B ). The gray band is the sampled budget bracket shared by the three crossings, not a confidence interval.

samples/class	12.8	25.6	38.4	51.2	64.1
W05( $0.5\times$ )	+2.69	+0.66	$-$ 0.72	$-$ 1.85	$-$ 2.24
W1( $1\times$ )	+2.88	+1.10	$-$ 0.58	$-$ 1.37	$-$ 2.21
W2( $2\times$ )	—	+2.27	$-$ 0.01	$-$ 1.07	$-$ 1.67

Appendix

Table 27

Setting / probe	Width contrast	Shift	95% interval	Unresolved
IN-100 32@64 / LFrac	$1\times\to 2\times$	27.7	[22.4, 35.8]	0
IN-1k native / LFrac	$0.5\times\to 1\times$	$-1.2$	[ $-3.0$ , $-0.8$ ]	1
	$1\times\to 2\times$	1.9	[ $-0.3$ , 4.0]	1
	$0.5\times\to 2\times$	0.7	[ $-1.4$ , 2.5]	0
IN-1k native / EL2N	$0.5\times\to 1\times$	2.3	[1.4, 2.4]	0
	$1\times\to 2\times$	4.4	[3.8, 6.6]	0

Appendix

Table D3: Width-induced shifts in

m_{0}

, in samples/class. Positive means a rightward shift. “Unresolved” counts bootstrap draws without two observed crossings, out of 27.

Evidence	Setting	Seeds	$m_{0}$ / verdict	Status
IN-100 input grid	32@32/32@64/64@64, R18, $3\times 3$ -stem	3 (paired)	85 / 57 / 53	measured
Frozen-list	32@64 cell, R18 subsets $\to$ W2	3	57 $\to$ 85	measured
Grid transplant ( $2\times 2$ )	32@32 $\rightleftarrows$ 32@64 both directions, both arms’ subsets frozen	3	learner main effect 18.3/18.4, list 9.3/9.4	measured (control)
Capacity $\times$ grid (LFrac)	$\{0.5\times,1\times,2\times\}\times\{32,64\}$	3	grid 32: $\sim 108$ (shallow)/85/ $\sim 95$ (shallow); grid 64: 64/57/85	measured
Capacity $\times$ grid (EL2N)	same as above	3	grid 32: $\geq 100$ /87/82; grid 64: 69/54/87	5 cells measured, 1 cell shallow-crossing lower bound
64@64 width sweep (LFrac)	$\{0.5\times,1\times,2\times\}$ at 64@64	3 (paired)	57.1/53/59.1, spread about 6	measured (shallow crossings at both ends, brackets overlap)

Appendix

Table E1: Evidence summary and measurement status. “Measured” requires a positive-to-negative flip between adjacent budgets; “censored” reports only the boundary of the measured range; control experiments report only performance relations. a@b denotes a px of retained information on a b-px input grid (§3.2), and R18/W2 denote ResNet-18 at

1\times/2\times

width. Corroborating evidence such as TinyImageNet does not enter the load-bearing summary. The full-scale grid axis and capacity axis are listed separately, to avoid splicing different stem families onto one numerical axis.

Experiment group	Datasets	Result files
Input-grid ladder, native cells (32@32 / 32@64 / 64@64)	ImageNet-100	171
Grid-ladder corroboration	TinyImageNet	34
Capacity $\times$ grid map ( $0.5\times$ / $1\times$ / $2\times$ , incl. 64@64 wings)	ImageNet-100	378
Cross-selector and cross-grid transplants	ImageNet-100	165
Stride controls (layer-2, layer-4, and stem)	ImageNet-100	171
Inductive bias (ViT-Tiny P8/P4)	ImageNet-100	221

Appendix

Table 30

Training Data Selection

Training data selection studies how to choose, filter, weight, or schedule examples to improve learning while reducing data and compute costs.

See all 184 papers

Are Coreset Selection Methods Worth Their Cost?
Sep 19, 2026Yangze Liu, Zhongyi HanBenchmark Design Training Data Selection
Shandong University
A Coreset Selection Framework with Ensemble Aggregation for Image Classification
Jul 10, 2026Pedro Rocha Dantas, Lucas Pascotti ValemTraining Data Selection Coreset Selection
Institute of Mathematics and Computer Science (ICMC) University of S˜ao Paulo (USP) S˜ao Carlos – SP – Brazil
GLOBE: Trajectory-Aligned Gradient Matching with Structured SparseOptimization for Coreset Selection
Aug 3, 2026Hetian Liu, Jin Cui, Mengcheng Shi +4Training Data Selection Coreset Selection
State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, and Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University · School of Software Engineering, Xi’an Jiaotong University · School of Computer Science and Technology, Xi’an Jiaotong University

Sep 19, 2026J/K move · Enter open · S save

Are Coreset Selection Methods Worth Their Cost?

Yangze Liu, Zhongyi Han

Shandong University

Benchmark Design Training Data Selection Coreset Selection

Open paper AskPDF arXiv

Coreset selection picks a representative subset of the labeled training set to make training cheaper. However, it is usually evaluated by downstream accuracy at a fixed subset size, ignoring both the time spent selecting the subset and the training recipe behind each reported number. We introduce an end-to-end benchmark that standardizes downstream training and charges selection and training to the same auditable wall-clock budget, spanning 4 datasets from CIFAR-10 to ImageNet-1K, 11 selectors, 5 fractions, and 3 seeds, with over 1,500 released runs. Repeated-sampling work has shown that budget-aware evaluation already favors random strategies. Our two budget studies test whether that verdict survives when every selector is granted its most favorable operating point. Across eight wall-clock budget anchors on each of CIFAR-10 and Tiny ImageNet, no anchor is won by a sophisticated selector: every winner is class-balanced random sampling, repeated random sampling, or full-data training. In fixed-budget duels on ImageNet-1K, training on all data for fewer epochs beats every selection strategy we probe while also costing the least. A per-dataset cost audit shows that selection cost is dominated at every scale by a fixed full-dataset scan, so it cannot be amortized away by selecting a smaller fraction, and its absolute size does not extrapolate from one dataset to another. We further quantify when selection does pay back through subset reuse, and document 9 correctness fixes to a widely used codebase, one of which shifts a standard Herding baseline by nearly 6 points. Selection time is not free preprocessing, and an evaluation that ignores it measures the wrong quantity.

Abstract

Training Data Selection

Explore similar work

Are Coreset Selection Methods Worth Their Cost?

A Coreset Selection Framework with Ensemble Aggregation for Image Classification

GLOBE: Trajectory-Aligned Gradient Matching with Structured SparseOptimization for Coreset Selection