Accelerating Benchmarking of Functional Connectivity Modeling via Structure-aware Core-set Selection
Authors: Ling Zhan
Zhen Li
Junjie Huang
Tao Jia
Venue: ICLR 2026 Poster (2026)
Keywords: Functional Connectivity Benchmark
Core-set Selection
Network Modeling
Structure-aware Sampling
Primary area: applications to neuroscience & cognitive science
TL;DR: We frame functional connectivity benchmarking task as a ranking recommendation problem and propose a self-supervised core-set selection framework that achieves up to 23.2% higher ranking stability than baselines at a 10% sampling rate.

Abstract: Benchmarking the hundreds of functional connectivity (FC) modeling methods on large-scale fMRI datasets is critical for reproducible neuroscience. However, the combinatorial explosion of model–data pairings makes exhaustive evaluation computationally prohibitive, preventing such assessments from becoming a routine pre-analysis step. To break this bottleneck, we reframe the challenge of FC benchmarking by selecting a small, representative *core-set* whose sole purpose is to preserve the relative performance ranking of FC operators. 
We formalize this as a ranking-preserving subset selection problem and propose **S**tructure-aware **C**ontrastive **L**earning for **C**ore-set **S**election (**SCLCS**), a self-supervised framework to select these core-sets. **SCLCS** first uses an adaptive Transformer to learn each sample's unique FC structure. It then introduces a novel **S**tructural **P**erturbation **S**core (**SPS**) to quantify the stability of these learned structures during training, identifying samples that represent foundational connectivity archetypes. 
Finally, while **SCLCS** identifies stable samples via a top-$k$ ranking, we further introduce a **density-balanced sampling strategy** as a necessary correction to promote diversity, ensuring the final core-set is both structurally robust and distributionally representative. On the large-scale REST-meta-MDD dataset, **SCLCS** preserves the ground-truth model ranking with just 10% of the data, outperforming state-of-the-art (SOTA) core-set selection methods by up to 23.2% in ranking consistency (nDCG@k). To our knowledge, this is the first work to formalize core-set selection for FC operator benchmarking, thereby making large-scale operators comparisons a feasible and integral part of computational neuroscience. Code is publicly available on: [https://github.com/lzhan94swu/SCLCS](https://github.com/lzhan94swu/SCLCS)

Published as a conference paper at ICLR 2026
ACCELERATING BENCHMARKING OF FUNCTIONAL CONNECTIVITY MODELING VIA STRUCTURE-AWARE CORE-SET SELECTION
Ling Zhan Zhen Li", Junjic Huang', Tao Jia 1.233
"College of Computer and Information Science, Southwest University, Chongqing, China *Chongging Key Laboratory Brain- -nspire Cognitive Computing and Educational Rehabilitation for Children with Special Needs, Chongqing Normal University, China *College of Computer and Information Science, Chongqing Normal University, China (z10327, cs20031z 8email. semail.swu sww. www.edu.....e.ee...........w.... en, {junjiehuang, tjia ) (wwweedd.... edu. cn
ABSTRACT
Benchmarking the hundreds of functional connectivity (FC) modeling methods large-scale fMRI datasets is critical for reproducible neuroscience. However, the combinatorial explosion of model-data pairings makes exhaustive evaluation computationally prohibitive, preventing such assessments from becoming tine pre-analysis step. To break this bottleneck, we reframe the challenge of FC benchmarking by selecting small, representative core-ser whose sole purpose is to preserve the relative performance ranking of FC operators. We formalize this as preeeiiing subset selection problem and propose Structure-ave aware Contrastive Learning for Core-set Selection (SCLCS), a self-supervised framework to select these core-sets. SCLCS first uses an adaptive Transformer learn each sample's 's unique FC structure. It then introduces a novel Structural Perturbation Score (SPS) to quantify the stability of these learned structures during training, identifying samples that represent foundational connectivity archetypes. Finally, while SCLCS identifies stable samples via a top-k ranking, we further introduce bealnce- sampling strategy necessary correction to promote di- versity, ensuring the final core-set is both structurally robust and distributionally representative. On the large-scale REST-meta-MDD dataset, SCLCS preserves the ground-truth model ranking with just 10% of the data, outperforming state-of- the-art (SOTA) core-set selection methods by up 3. in ranking consistency (nDCG@l k). To our knowledge, this is the first work to formalize core-set selection for FC operator benchmarking. thereby making large-scale operators comparisons a feasible and integral part of computational neuroscience. Code is publicly available on httttts://gitttmm com www.m//lhaangaa wtt.c/////aaas4s//SSc.....
INTRODUCTION
Methodological choices can substantially affect scientific reproducibility, as reflected in highly variable outcomes obtained from the same dataset, making systematic benchmarking increasingly important (Kohli et al.) 2024 Qiu et (0244 Marek et al.) 2022). This issue is especially acute in functional connectivity (FC) modeling, where hundreds of candidate statistical pairwise interactions (SPIs) require careful evaluation to ensure reliable conclusions (Liu et al. 2025 Roell et al. 2025). Yet the computational cost of exhaustive evaluation makes it impractical to run as a routine pre- analysis step for data-driven model selection (Ying al. 2024 Zhou et al.) 2021) (see the complexity analysis in Appendix HH). To address this bottleneck, we propose two-stage workflow: we first benchmark all candidate SPIs small, representative core-set identify top performers, and then evaluate the selected SPI(s) on the full dataset for downstream analysis. This workflow hinges on selecting core-set that preserves the relative performance ranking of SPIs.
"Corresponding author.

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Published as a conference paper at ICLR 2026
Pravious: Core-set Selection for Classification
Task: Core-set Selection Benchmarking
FC
Cif Model
SPI-
50 Parting
Coro-sel
Combine
Calculade
Quantification Score
Accuracy
SPI
Core-set
Data Distribution
SPh
sampling
5h Rasterg
Our Method: Structure-aware Contrastive Learning Selection
Seructure Representation MTS
Structure Perturiation Score
Density-based Sampling
X
Attention X
SPS(X)= Σ Ainll
Original
Atlention Head 0
Samar
Care
Attention Head
Train Epoch
SPB
core-set selection. Contrasting with selection for single-model classification (top left), our task is to preserve the performance ranking of SPIs (top right). Our method (bottom) achieves this using a Transformer to learn structures, our novel SPS metric to ensure stability, and density-awand aware strategy to promote diversity.
Figure I: Overview the SCLCS framework for
While core-set selection is well studied, most existing methods target different goal: constructing a small training proxy for a single predictive model (Feldman) 2020: Lee et al. 2024 Hong et al.
2024b). In our setting (Figure [ the core-set must preserve the relative performance ranking across hundreds of candidate SPIs (Liu et al. 2025 Cliff et al.) (003)). This ranking-preservann preservation objective raises three challenges: (1) Formulating selection criterion that targets cross-SPI SPI ranking stability rather than single-model training loss. (2) Defining a principled, structure-aware notion of sample importance based on FC patterns (the targets of SPIs). (3) Reducing the brittleness of score-based top-k selection, which can fail to generalize across sampling ratios and distort rankings.
In this work, we cast core-set selection for FC benchmarking problem. Rather than training a predictive model, we seek subset that preserves the SPI ordering from the full dataset (Figure []. We evaluate on the REST-meta-MDD dataset (Yan et al. 2019 Long et al. 2020), large multi-site resting-state fMRI dataset for MDD, which captures heterogeneity across acquisition sites and a large cohort. We instantiate benchmarking with two tasks, brain fin- gerprinting (Van De Ville et al., (021) and MDD diagnosis (Gallo et al.) 2023), both widely used in FC research (Lu et al., 2024: Otte et al. 2016). For each task, we score each SPI by how well the resulting FC matrices separate within-class from between-class pairs using Spearman's 's rank correla- tion [Sedgwick] 2014), yielding an SPI ranking. Core-set quality measured by nDCG@k (Wang et al. 2013) between
aanking-preserving subset selection
between the SPI rankings induced by the core-set and the full dataset.
We use SPIs as a validation case because benchmarking FC operators has been formalized as a well-defined task in recent work (Liu et al. 2025 Cliff et al. 2023 Honari et al.) 2021). Based this formulation, we propose Structure-aware Contrastive Learning for Core-set Selection (SCLCS).
SCLCS is built around Transformer-based encoder that encodes sample- specific synchronization structure via an adaptively weighted fusion of attention heads. Under the assumptions of Theorem [ we show this encoder has universal approximation capacity for continuous SPI mappings. We then define a Structure Perturbation Score (SPS) to quantify the stability of these structures, and prioritize low-SPS samples to form robust core-set. Because naïve top-A selection can be brittle for certain task structures, SCLCC augments it with density- aware sampling strategy to improve diversity. SCLCS learns in an adentity-superviise contrastive manner, using subject identities to encourage stable "brain fingerprints" /an De Ville et al.) 2021) that SPI-based analyses aim to capture et al., 2025 Luppi et al. (024). This yields aggostic representations suitable for benchmarking. Finally, SCLCS is pre-analysis acceleration tool that makes large-scale benchmarking computationally feasible, rather than a method for the final neuroscientific discovery task.
As shown Figure [
Our theoretical analysis and empirical results on 130 candidate SPIs support our design choices and show consistent improvements over strong baselines. The main contributions are: (1) We formulate
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core-set selection for efficient FC operator (SPI) benchmarking ranking- preservation problem. (2) We propose SCLCS, SCLCS, a structure-aware framework for selecting stable and diverse samples for ranking- based benchmarking. (3) We provide universal approximation result for continuous SPI mappings (Theorem 2 and introduce SPS, a new use of attention dynamics to quantify structural heterogeneity. (4) We show that SCLCC enables reliable benchmarking fraction of the computational cost, making large-scale comparisons practical.
2 RELATED WORK
Benchmarking in Functional Connectivity, Selecting an appropriate SPI (i.e., network modeling method) is a central challenge in modern FC research. Prior studies show that different SPIs can
yield divergent FC topologies and, consequently, different scientific conclusions (Smith et al. 1
2013
Bobadilla-Suarez al. 2020; Mohanty al. 2020 Honari al. 202T Luppi al. 2024).
contributing to long-standing concerns about reproducibility (Collaboration 2015]] Botvinik-
et al.
2020 Marek et al. 20022. Mcanwhile, comprehensive libraries such pyspi(Cliff et al.
which include hundreds of SPIs, highlight the methodological richness of the field and magnify the scale of the selection problem(Liu al., 2025 Roell et al.) 2025). These works motivate systematic benchmarking, but the computational cost of evaluating large SPI suites remains a key practical bottleneck. We address this bottleneck by introducing a core-set selection approach for efficient SPI benchmarking.
2023)
Core-set Selection. Core-set selection is a fundamental problem in machine learning (Guo et al. 2022 Feldman 22000 Ros & Guillaume [211).. Most score-based (Coleman et al. 20200 Feldman & Zhang 2020; Paul al.] 2021; Toneva et al., 2019) and diversity- (Sener & Savarese 2018
Xia et al. (022) methods construct proxy datasets for training single predictive model, which mismatches our aanking-pessevvan
objective over many SPIs. Their criteria are often model- dependent (e.g., EVA (Hong al. 2024bb) and typically assume static i.i.d. inputs, overlooking the temporal dependencies in fMRI time series from which FC structure is derived. Consequently, selected core-sets may not transfer to ranking- based evaluation over large SPI suites (Liu al. 2024; Lee et al. [2024). Training-accelerattoo methods (Hong et al. 2024a Killamsetty et al. 202 I Mirzasoleiman et al. (2020; Wei et al., 2013) share the same single single-model focus and thus do not directly address our setting.
To our knowledge, SCLCS is among the first methods tailored for accelerating benchmarking of FC operators (SPIs) via core-set selection. It uses the stability of learned synchronization structures during training selection criterion, which is particularly natural for neuroimaging. While related to graph structure learning (Li et al. 2023; Zhou et al., 2023 Zong et al., 2024), SCLCS treats learned structure as diagnostic probe rather than an inference output. We therefore do not review general-purpose purpose structure learning in depth.
3 PRELIMINARIES
Benchmarking FC modeling. The goal of FC benchmarking is to produce a principled ranking of statistical pairwise interaction (SPI) operators from a set S. For given fMRI dataset X, where each sample X E is a matrix in RNx each operator S e S maps X to an FC matrix S(X) e N X An evaluation index, I This process induces a ranking over all SPIs in S, which we denote as Rank(S, ('), to guide the selection of a suitable SPI for subsequent analysis.
IR, assigns score each SPI under chosen evaluation protocol.
Core-set Selection for Benchmarking FC Modeling, Computing the full-dataset ranking Rank(S, is often computationally prohibitive. We therefore introduce the task of core-set selection for benchmarking, which seeks to identify a small subset of samples X, C. X where [Xt] < XX] that acts as an efficient proxy. Formally, high-quality core-set is the solution the following optimization problem:
X argmin D(Rank(S, Rank(S,X")) X'c,, |20
where (...)) is a ranking discrepancy metric (c.g., based on nDCG@k) and is the core-set budget. The goal to preserve the full-dataset ranking while using only e samples.
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Directly optimizing this objective is intractable, it requires exhaustively evaluating exponential number subsets, with each evaluation incurring the very computational cost we aim to avoid. We therefore propose practical proxy: selecting structurally representative subset. The core hypothesis that preserving the distribution functional connectivity structures also preserves the SPI ranking. Our SCLCS framework, detailed next, is designed find such subset.
4
METHOD
In this section, we introduce the detailed formulation of the proposed SCLCS. SCLCS consists of four modules: (I) attention-based FC learning, (2) structural perturbation score calculation, (3) structure-aware density-balanced sampling, and (4) contrastive learning.
4.1 ATTENTION-BANT BASED FC LEARNING
To select a rank preeerriee core-set, our framework first requires an encoder that can learn general and expressive representation of each sample's FC structure. The self-attention mechanism within Transformers is a natural candidate for this task, as can model complex inter-regional relation- ships (Vaswani al., 2017). However, naive fusion of multiple attention heads via uniform averaging is insufficient, as it can obscure distinct structural patterns learned by individual heads Theorem (proved App
Theorem 1 (Interference of Averaged Attention). Let (Ar be row-stochastic attention matrices. Assume disjoint structural masks: for each row there exist pairwise-disjoins sets (5) that ji) for all s(a) Let A E An. Then for every row i:
H h== such
supp(a(") U h=1
(1) Sh
and H(al)) min IShSH
11 H(a if (a lh=1 are not all identical.
In particular, H 2 2, naive averaging expands support beyond any single head's mask and inflates entropy, blurring head-specific structure.
Theorem I pertains strictly to the internal attention maps and explains the empirical failure of directly applying the traditional Transformer on core-set selection for benchmarking FC modeling, It motivates to propose an adaptive fusion mechanism that aggregates head-specific attention matrices via learnable weights. This modification is not merely an engineering choice: we prove it endows the architecture with the power of universal approximator for the class of continuous FC operators as formalized in Theorem 2 (proved in Appendix B). This provides a theoretical foundation for its ability to capture the diverse synchronization patterns required for our benchmarking task.
Theorem 2 (Universal Approximation of Continuous Stochastic SPI Let X C R be compact. Let S X + N be continuous, where A N-1xN == (P RNNN P1 1, P 0} denotes the set of row-stochastic matrices. Consider the adaptive multi-head attention family
H
On softmax XWA(W/ )
(x
a QEAH- ->>0, 0,
where mof is applied row-wise. Then for every > 0 there exist H, and parameters {Wo, h w H Jhml and a such that
sup ( <E.
XEX
Our implementation is follows: for each IMRI sample X E NxT, we treat the N ROIs input tokens, where each token has a feature dimension of T. Each attention head independently projects queries and keys using learnable linear maps, parameterized by matrices 8 and wkk
Q2 = X K, Xwk w
w E Dxd h 1, H.
(4)
k
'This statement is for continuous targets on compact domains. If an SPI uses discrete thresholds (hard masks), the guarantee applies to any continuous relaxation (e.g., finite-temperature softmax / sigmoid gates) and then limiting argument is required to justify the hard-threshold limit.
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The attention matrix from head h is computed as:
Qa Vd
A softmax
A E ERNN
Motivated by Theorem 1 uniform head averaging is a structural constraint: OA = 1/H forces every sample to use the same (high-entropy) centroid of head-wise attention patterns. By strict concavity of Shannon entropy, this averaging inflates uncertainty and smears head-specific structure. Learnable fusion weights a relax the constraint, enabling sparse/peaked mixtures (up to single-head selection) to reduce interference while still combining complementary patterns. Thus the operator class strictly expands: by Theorem 2 an adaptive fusion module can approximate continuous FC operator on compact domains.
Thus, we propose a learnable fusion mechanism that aggregates head-specific attention matrices via adaptive weights, formulated as:
" Σ Oh 1, OA 0,
A Σ Or An: with
(6)
where the weight a normalized via softmax. The resulting matrix the operational definition of sample's FC structure, forming the basis for our selection criteria. Importantly, we treat these attention maps as a normalized structural probe-a sample-specine proxy for synchronization structure not attempt to replicate the raw outputs of any particular SPI.
RNNN serves as
4.2 STRUCTURAL PERTURBATION SCORE (SPS)
Having established an encoder that is expressive enough to capture diverse FC structures, the next challenge define criterion for identifying the most fundamental samples for robust benchmark. Our central hypothesis is that samples representing common. foundational connectivity patterns will induce stable structural representations during training, while noisy or atypical samples will cause greater fluctuations. To quantify this phenomenon, we propose the Structural Perturbation Score (SPS), a metric grounded in the principle that perturbation magnitude reflects structural heterogeneity (Proposition I].
perturbation magnitude). Let S(1), ..... S(K) E NxN be distinct prototypes and Dạt = [s 11 (Dui > 0 for + l). Let (Ze)e21 be i.dd with Pr[Ze = s(k)) = 2o. Σx A 1, and define A = 1e - Ze-1117
Proposition 1 (Mixture-
Then
E = Σ AediDii = =
AediDai D
(7)
k.1
ksl
With Dunin mingel D&t and Dmax maxkel Dki.
Dmnu (1-
E S D Dmux 11- Σ x2
<
(8)
In particular. [[Ae] scales with the Gini impurity 1 - Eie dg up constants set by prototype separation. If Dza = D for all l + then
E[Ad] (1 Σ 13
(Proof in Appendix (
Proposition 1 indicates samples that are a purer representation of a single archetype will be more stable (low SPS). The SPS for a sample X E thus defined as the cumulative structural instability across L training epochs:
L SPS(X)
-
Σ
(10)
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(e) (X) denotes the attention-based structure matrix of sample X X' training epoch where A (x)
e E [L,...,L} and || ||e denotes the Frobenius norm. Specifically, A (e) is a proxy for structural (X) representation, not a proposed network model. In this way, SPS captures the structural volatility of the sample-specific synchronization graph during training, not fidelity to any specific SPI. Our rationale is that a robust and reliable benchmark is built upon foundational, structurally stable samples. As supported by Proposition low-SPS samples exhibit less internal structural conflict and thus represent stable archetypes of functional connectivity. Therefore, our primary selection strategy is to rank samples by their SPS and select those with the lowest SPS.
For SPS to be reliable metric, however, we must ensure that it is consistent estimator that does not depend on the arbitrary length of the training process. Lemma] ] (in Appendix (D) provides this theoretical guarantee: Under stable perturbation dynamics, the assumptions of Lemma] | are satisfied. We used extensive grid search to find a configuration that achieves optimal performance on the downstream ranking preservation task detailed in Appendix M Notably, the assumptions of that configuration' 's stationarity and ergodicity in Lemma 1 are empirically supported by our convergence analysis in Appendix K.2 where show that the perturbation dynamics stabilize as the model converges. This standard procedure sufficiently validates the feasibility of SPS.
4.3 STRUCTURE-AWARE DENSITY-BALANCER SAMPLING
While selecting for structurally stable (low-SPS) samples provides robust foundation, naive top-k selection risks creating core-set with low diversity by over-selecting from dense clusters of typical patterns. This lack of diversity can cause the core-set benchmark to diverge from the full-dataset ranking (Theorem 3)
Theorem 3 (Persistent bias of top-k selection). Let X contain two clusters Cp. Gi with proportions To T.. Given x E C₂ (r e {p, q)). let the score s(x) have continuous CDF Fy, and assume scores are independent across samples. Select the k |pN] samples with the smallest scores (p E 10) and write 7, == SS& n C.l/k.
Let T satisfy the mixture- -uuutteequuntile equation
Tt + (T =
(11)
and assume strict separation T:
:: Fp(T) -TT(T) > 0.
(12)
Then
Pr up Fp(T) = -Tp +5,
Pr. Ny F (T)))
Tp > 0. (13)
Rg
Tq 6, =
p
P
Consequently, the representation error As == Tp Tpl + (.g Tgl satisfies A.
Pr. 28 > 0. (See
Appendix E.)
To explicitly balance stability with diversity, we introduce a density-aware sampling scheme, yielding the SCLCCDenee variant. This scheme first ensures robustness by retaining pool of the most stable samples (the bottom 1 - f quantile of SPS scores), then promotes diversity by applying Kernel Density Estimation (KDE) (Weglarezyk) 2018) to up-weight samples from sparser regions within that stable pool. This mitigates redundancy and ensures the core-set captures broader range of structurally distinct subtypes, which crucial for including less common but potentially critical neural patterns often associated with clinical biomarkers.
Specifically, given the set of SPS for all samples in X, we first discard the top 3 quantile of the most unstable samples to form a stable candidate pool X., This is formally defined as:
x= X E X' SPS(X) S Q1-8),
(14)
where Q - is the empirical quantile. On X, we fit a Gaussian KDE to the empirical distribution of (SPS(X): X E X), and define the local density of sample the KDE evaluated at its SPS:
(srs(s)
xXX) (SPS(S))(
(15)

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To promote diversity, weights set inversely proportional to p(X) and normalized over A²:
1 ((X)
x)
w(X)
(16)
p(X) +
Exee w(x)
We then select samples without replacement from X' using weights {w(X)). This yiclds structurally diverse subset that up-weights samples in low-density regions of the SPS distribution within the stable pool. Theoretical guarantees coverage and benchmarking consistency demonstrated in Theorem 4 and Theorem 5 respectively (provided and proved Appendix [F]
and Appendix G respectively). Notably, this scheme is applicable other score-based methods by replacing SPS to different metrics as shown in Appendix
4.4 STRUCTURE-AWARE CONTRASTIVE LEARNING
To learn structural representations, we train the encoder with a structure-aware contrastive objective. Motivated by FC evaluation practices that exploit inter-subject differences (Liu al. [2025] Luppi et al. 2024), we enforce consistency among samples drawn from the same subject within a scan session. This identity-supervised setup encourages the model capture stable, person-specific traits ("brain fingerprints" (Lu et al. 2024)), providing task-agnostic signal for structure- selection.
First, to obtain graph-level embedding for each sample, we compute node-level embeddings Z E Nx by applying the learned attention matrix to the value embeddings and projecting the result through final linear layer. global mean pooling then applied obtain the graph-level embedding z E Rd, which captures the sample's 's global topological semantics and serves as input to our contrastive loss:
exp exp (sim(z, 22)/T) - llg EkEN()) exp sim. Z //T)
Leconrast
Σ (+.))P
(17)
[P]
where sim(..) is cosine similarity, T is a temperature parameter, and the pairs are defined across a batch. Positive pairs (i,j) E P consist of two different temporal segments from the subject, while for a given anchor sample i, the negative sample k E (i) are all other samples in the batch from different subjects. All the trainable parameters are optimized using Adam (Kingma & Ba 2015).
EXPERIMENT
In this section, we present empirical results to validate our proposed framework. We first detail the experimental settings and then present the main quantitative and qualitative results comparing SCLCS to SOTA baselines. Due to space constraints, several important settings and supplemen- tary analyses, including detailed experimental settings for reproduction (Appendix[M) detailed computational cost breakdown (Appendix [H), the effect of supervised information on baselines (Appendix[] the application of our density-awarc sampling to other baselines (Appendix[J). empiri- cal results (Appendix[K) K) for supporting Theorem 2 and the assumptions in Lemma i and additional generalization and robustness analysis (Appendix
5.1
EXPERIMENTAL SETTINGS
Data We validate framework the REST-meta-MDD dataset (Yan al. 2019). large- scale, multi-site resting-state fMRI collection comprising 1,642 subjects from 17 sites. This highly heterogeneous collection rigorous testbed for core-set selection. For efficiency and consistency with prior work, we focus on subset of 904 subjects (Long al., 2020). To capture dynamic patterns, each subject's fMRI record is segmented into overlapping temporal samples via sliding window, yielding 4,520 samples. Demographic statistics are in Table Complete data and preprocessing details are in Appendix M.1
released with a standardized preprocessing pipeline, providing
Baselines Following the experimental setup in Hong et al. (2024b), we extend their comparison with two additions (k-Means and BOSS), evaluating against 9 baselines in total: (1) Random; (2)
k-Means (Hartigan& & Wong 1979); (3) Forgetting score (Toneva al. 2019): y (4) Entropy (Coleman
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Table I: Summary of the used subset of RESST-meta-MIDD.
Site
#Samples
#HC
#MDD
#Male
#Female
Age Range
Education Range (Years)
1.
335
37
30
26
41
19-65
5-21
17
410
41
41
27
55
18-30
9-17
19
245
31
18
19
30
18-51
5-15
20
2395
229
250
157
322
18-65
3-20
21
720
65
79
62
82
18-65
5-15
22
190
20
18
21
17
19-47
8-17
23
225
23
22
18
27
19-54
6-20
Overall
4520
458
446
330
574
18-65
3-21
et al. 2020); (5) EL2N (Paul et al. 2021; (6) AUM (Plciss et al. 2020); (7) CCS (Zheng al.
):23): (8)EVA (Hong et al., (024b); BOSS (Acharya et al. 2024). The latter of them are SOTA methods designed for core-set selection. Detailed introduction summarized in Appendix M.2
Environment Experiments are performed on an 8-GPU (H20) nigh-performance computing cluster provided by the Large-scale Instrument Sharing Platform of Southwest University.
Evaluation Protocol Our goal to select subset that preserves model ranking, not train single predictive model. Therefore, our evaluation deviates from the standard train/test split. The protocol is as follows: (1) Each method selects core-set of a given size from the entire dataset. (2) We then compute the SPI performance ranking on both the full dataset (ground truth) and the selected core-set. (3) The quality of the core-set is measured by the consistency between these two rankings.
Task We use two distinet downstream tasks evaluate SPI discriminability: brain fingerprinting (distinguishing individuals based on subject ID), which probes for fine-grae fine-grained, subject-specific structures, and MDD diagnosis, which relies on cohort-level patterns.
Metrics We use two primary metries. (1) Discriminability Score, metric based on Spearman's rank correlation (Sedgwick 2014) that quantifies the class separability (within- vs. between-clase class) of the resulting FC matrices. (2) Ranking Consistency, the concordance between the full-dataset and (Wang et al. 2013).
core-set SPI rankings using nDCG@5/10) 1/0/20
5.2 QUANTITATIVE RESULTS
We present the primary quantitative results in Table Table Table The evaluation includes SCLCS (using low-SPS top-k selection), SCLCSDense (density-awar selection), and SPSMHA (a variant using naïve attention averaging to empirically test Theorem
Table 2: Performance of different methods on brain fingerprinting ranking task (mean + std) and nDCG@n @k is reported as percentage (x 100).
Method
nDCG@5
aDCG@ 10
nDCG@20
Random
15.17
69.57
66.60
17.97
71.19-m09
66.96
66.98.wm7
21.97
71.33
13.13
k-Means
17.32
65.72 1235
67.29
(114
64.35_mss
peve
22. 11:1
66.78 112s
Forgetting
14.4
54.43 153h
43.36 43.36
15.49
48.57
49.87 1400
20.23 m1:1
55.80
49.70
Entropy
47.40
22.84_15220
59.95
37.73-2544
32.05
58.68-2331
36.05
35.90=18.1
57.72=2154
EI2N
35.56
20.30 20.30
31.03
36.51
33.18
32.70
33.30
35.82-12110
40.06
AUM
65.92
56.68_11.
38.17
60.95..141
62.05
36.83
51.75
59.09
38. 38.341488
CCS
1.90-207
30.53-14115
46.65=2232
2.92-124
29.13
$1.78-22112
16.24+1134
32.56-14115
52.18=2m30
EVA
38.40gu057
62,03
37.80
43.37
55.01
49.56_23328
43.224:522
53.51_1470
65.49-2135
BOSS
42.11_30m1
35.36
29.441mm
40.57
39.15
31.45_v
38.24_2194
38.92
SCLCS
81.21
50.24
72.68 Lains
66.54.1.m
49.45
71.86
57.46
$3.40 18:
70.13
SCLCSuxne
33.73
79.18
$1.344114
35 35844ma
73.45
30.54-11..
41.03
72.96:215
$5.43mm0
SPS
1.324207
12.23
15.624633
2.92-113
13.12.11.3
11.28
1.21
12.13
12.184725
Brain Fingerprinting supervised objective.
This task rewards subject-specific patterns, which aligns with our identity-
As shown in Table 2 SCLCC achieves stronger performance with lower
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variance at sampling ratios 0.1 and 0.5, suggesting that selecting structurally stable samples via low-SPS top-k ranking is effective. In contrast, SPSMHA performs poorly, consistent with Theorem [ At the moderate ratio 0.3, SCLCS degrades, whereas SCLCSpeme performs best. This pattern supports Theorem 3 when stability ranking alone is insufficient, explicitly promoting structural diversity provides corrective signal.
Table 3: Performance of different methods on MDD diagnosis ranking task (mean + std) and nDCG@K is reported as pereentage (x 100).
Method
nDCG@s
nDCG@ 10
nDCG@ 20
0.1
0.5
0.1
0.3
0.5
0.3
Random
49.58
23,77
31,76
25.8 23.8 60.50.11.0
77.95.ma7
67.04
82.71 82.71 30.30
k-Means
51.322m145
32.45=3344
37.33
30.1821245
40.47:143:
43.75
28.62 28.62.23433
37.87=1477
79.8 79.83
Forgetting
28.70
41.60=2006
61.424431
40.56-22005
50.27=32.31
66.7244m
44.37
57.02_23339
75.70+755
Entropy
29.00.45.00
31.84_
57.48
29.17=4121
40.75
63,23
30.30
45.85_4500
70.79_18.0
EIZN
30.93 10.93
$1.70 1011
18.85
36.05 1:14
58.54
12.96
41.04
64.68 77675
78.85 11.56
AUM
36.07=12.55
42,68-44116
35. 35.4921437
39. 39.17=1453
44,41
58, 18.1441154
44.94=11.a
48 48.44-42.48
64.36=1440
15.95
59.92_
74.73 in
59.25gim66
67.01
75.41
68.
68.98
71662-1115
18.77
EVA
31.80
66.81
70.07 Laars
36.11
72.61 1ams
76.26
48.39
75.34 75.34
81.73 1561
BOSS
42.44
57.52.20011
79.57.1668
50.64225112
64.86:2146
84.70.1407
58. 22.222
71.36=1894
88 48.95
SCLCS
48, 382000
70.27-23.37
64, 18:25.
50.59
73.86 73.8621558
66.15
61. 12
76. 76.89
68. 68.43211522
SCI.CSpese
57.29
74.62-18.0
81887
64.34_1607
77.52=
86.25.122
69.8421471
82.70-1104
89.45
SPS
19.13
26.82_ 16.11
27.45
20.13
22.75gu131
23.19
17.85_ 11003
20.73 11.90
MDD Diagnosis This cohort-level task requires broader structural coverage than fingerprinting. As achieves superior performance with lower variance across sampling
shown in Table ratios and evaluation depths, highlighting the benefit of density-aware sampling for capturing diverse patterns in group-comparison benchmarking. In this setting, the standard SCLCCS (top-k) less effective, suggesting that the best sampling strategy depends on the task's structural demands. Finally, simpler heuristics such as k-Means and class-mmbllance-prort criteria such as Entropy (Figure perform less competitively, reinforcing the need for structure-awact selection.
The behavior of the Random bascline suggests that ranking preservirr selection differs from tradi- tional single-model core-set objectives, and that methods designed for the latter may not transfer well. The non-monotonic trend (30% < 10%) observed for SCLCS and SCLCCDeese is consistent with The- orem 3, indicating that na've score-based top-k sampling can be brittle: it may over-represent dense clusters of typical patterns while missing rarer but important structures. This motivates SCLCSDense. which mitigates this failure mode via density-aware sampling.
Table 4: Empirical validation of Theorem 2. Our modified Transformer approximates a diverse set of SPIs. The model demonstrates effective fitting and generalization.
SPI Operator
Train (Start)
Train (End)
MSR
SPI Operator
Train (Start)
MSE (Knd)
Test
joc.
0.0K05
0,0534
ply multisper motn
0.0588
phase multitgee mean
0,0295
0.0264
0.0265
cohmag mulitpprr_maae mat
0.5721
0,0055
0,0057
pi multinger mean
0.0239
0.0221
0.0222
to. kemel
0.8513
0.0181
0,013
0,0237
0.0211
0.0222
bary, www__uudddannmaa
1.9840
0.1164
0L1153
pei wonelet mus
6,0059
3,5833
3,5789
sme gussinn
0.9223
0.0155
0.1 S8
yee. mulittperr maan macn
0.2082
0.1391
0.1382
je. kemel
7.5831
0.1021
0L1025
gwinu
6,6630
1,8087
1.8124
ce kernel
0.9243
0.0141
0.0144
koh, muhtinper mean
0.0797
0.0206
0.0206
loss consriint
0.2608
0.0020
0.0020
To empirically test the approximation capacity implied by Theorem 2 we train our modified Transformer to approximate the FC matrices produced by 16 representative SPI operators selected from the taxonomy of Cliff et al. (2023). For each target SPI, we train a separate model on fMRI time series by minimizing the mean squared error (MSE) to the SPI-generated FC matrices. Table shows low final test MSE across all 16 targets, indicating that the model can closely approximate a diverse set of SPIs. Approximation fidelity varies by SPI, but the overall trend supports Theorem 2
Empirical Validation of Theorem 2
Together, Theorem 2 and Table suggest that the architecture is expressive enough to serve as a structural probe for fMRI time series. Small approximation errors (c.g.. imperfect emulation of discrete statistical tests) need not invalidate our stability signal: SPS aims to distinguish structurally stable samples (low SPS) from unstable ones (high SPS), rather than maximize approximation
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fidelity. Quantifying how approximation error propagates ranking preservation is an important direction for future work. Full details and convergence curves are provided in Appendix
Balance (Sample/Subjeal Coverage)
M H Balance (MDDHC Cass Ba ance. Log Scale)
Sample Itale
Sumpe Tadl
0.1
05
0.3
Mean M-H Balence (leg
B.GL
Aandton
Forpeting
Entropy
E5A
Bcon
BLCLSpomm
$1.00
Atnston
kddean
Fopeding
Enthap
cCB
Boan
Mathod
Method
Figure 2: Sample coverage balance on subjects and MDD/HC of baselines.
Sample Coverage Balance Analysis Beyond performance, we assess the reliability and repre- sentativeness of selection by analyzing sample coverage balance (Figure 2 We introduce two metrics: S-I Balance (selected samples per subject, lower indicates broader subject coverage) and M-H Balance (MDD-to-HC ratio; deviation from indicates class imbalance). As shown in Figure 2 SCLCS and SCLCSpense maintain balanced coverage with low variance on both metrics, whereas several baselines unstable. Entropy particularly sensitive class-label effects, selecting almost exclusively MDD subjects at low ratios. This produces a skewed, unrepresentative core-set and can make downstream benchmarking mislcading, highlighting the risk of naïve score-based selection.
5.3 QUALITATIVE RESULTS: VISUALIZING SPS DYNAMICS
To provide an intuitive check of the SPS metric, we visualize the evolution of the learned attention map (xx over the early training epochs e. While the results in Appendix K indicate that attention maps typically stabilize after
epochs, F that the stabilization dynamics vary across samples: a low-SPS sample (top row) rapidly converges to stable structural pattern, whereas high-SPS sample (bottom row) exhibits sustained fluctuations. These observations suggest that SPS reflects stable, sample-specific property rather than transient optimization noise, supporting its use identifying foundational samples for benchmarking.
Epoch
Epoch 10
Epoch 20
Epoch 30
Epoch 40
Epoch 50
Epoch 60
Epoch 70
1.25
Min
0.50
0.00
-0.50
Figure The evolution of the learned attention map A across training epochs.
CONCLUSION
In this work, we address the computational bottleneck of large-scale FC operator (SPI) benchmarking by casting core-set selection as preeerigpressrvattionn task. Our key technical contributions are: (1) A modified Transformer architecture with universal approximation guarantee for continuous SPI mappings under our assumptions. (2) The SPS metric to identify structurally stable samples. (3) The SCLCS framework, which outperforms 9 baselines in ranking-preservaaiee preservation evaluation. By accelerating FC benchmarking, SCLCS makes large-scale, pre-analysis SPI comparisons practical and supports more reproducible computational neuroscience.
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ACKNOWLEDGEMENTS
This work is supported by Natural Science Foundation of China (No. 62402398, No. 72374173), the Fundamental Research Funds for the Central Universities (No. SWU-XDJH202303, No. SWU- KR24025), the Technological Innovation and Application Development Project of Chongging (No. SSTB202STIAD-KPX0000
University Innovation Research Group of Chongqing (No. CXQT21005), China Scholarship Council (CSC) program (No. 202406990056) and Chongqing Graduate Research Innovation Project (CYB240088). The experiments are supported by the High Performance Computing clusters and the Large-Scale Instrument Sharing Platform (H20 GPU Server) at Southwest University.
REPRODUCIBILITY STATEMENT
To ensure our research is fully reproducible, have made our code, data sources, and experimental details available as follows:
Code: The complete source code for our SCLCS framework and all experiments is publicly available on httpps://giithub.comm/// clt.l//ann..coa 94sw////wwCWWC
Dataset and Preprocessing: REST-met-MDD Yan et al. 2019) dataset is publicly ac-
cessible /ttts:://ftri..oottttt REST meta MDD Our detailed data preprocessing
pipeline is described in Appendix M.
External Libraries: Our analysis relies on the pyspi library (Cliff et al. 2023) which is publicly available at https:: /iihtub.... com/ Dww.micsAnddeeusse...oeeeeaaaaee al alSystema emss/ pyspi The specific criteria used to select SPIs for our benchmark are detailed in Ap- pendix
Experimental Settings: A summary of the experimental setup is presented in Section 5.1 with comprehensive breakdown of all parameters and configurations available in Ap- pendix M
Complete proofs for all theorems, propositions, and lemmas presented in this paper can found Appendix G
Theoretical Proofs:
ETHICS STATEMENT
Our work provides framework for evaluating and selecting computational models used in neu- roimaging analysis, which can be applied to clinical tasks such as discase diagnosis. Therefore, it is important consider the potential societal impacts of the models ultimately chosen via benchmarking process. A potential negative impact could arise if a core-set, while efficient, is not perfectly representative of the full dataset's 's diversity, leading to the selection of model that biased or performs suboptimally on underrepresented demographic or clinical groups. To mitigate this, we emphasize that our framework is tool for pre-clinical scientific validation. Any model selected using our approach for real-world medical scenarios must undergo its own rigorous, independent clinical validation, and the final diagnostic decision must always remain with a qualified physician.
REFERENCES
Abhinab Acharya, Dayou Yu, Qi Yu, and Xumin Liu. Balancing feature similarity and label variability for optimal size-aware one-shot subset selection. In Forty-first International Conference Machine Learning, 2024.
Elena A Allen, Eswar Damaraju. Sergey M Plis, Erik B Erhardt, Tom Eichele, and Vince D Calhoun. Tracking whole-brain connectivity dynamics in the resting state. Cerebral cortex, 24(3):663 666.. 2014.
George D Birkhoff. Proof of the ergodic theorem. Proceedings of the National Academy of Sciences, 17(12):656-66) 1931.
11

---

Published as a conference paper at ICLR 2026
Sebastian Bobadilla- Christiane Ahlheim, Abhinav Mehrotra, Aristeidis Panos, and Bradley C Love. Measures of neural similarity. Computational brain & behavior, 3(4):369- -3813333,,, 2020.
Rotem Botvinik-Nezer, Felix Holzmeister, Colin F Camerer, Anna Dreber, Juergen Huber, Magnus Johannesson, Michael Kirchler, Roni Iwanir, Jeanette A Mumford, Alison Adcock, et al. Variability in the analysis of single neuroimaging dataset by many teams. Nature, 582(7810);
84-88, 2020.
Oliver M Cliff, Annie G Bryant, Joseph T Lizier, Naotsugu Tsuchiya, and Ben D Fulcher. Unifying pairwise interactions in complex dynamics. Nature Computational Science, 3(10):883889) -93388 2023.
Cody Coleman, Christopher Yeh, Stephen Mussmann, Baharan Mirzasoleiman, Peter Bailis, Percy Liang. Jure Leskovec, and Matei Zaharia. Selection via proxy: Efficient data selection for deep learning. In International Conference on Learning Representations, 2020.
Open Science Collaboration. Estimating the reproducibility of psychological science. Science, 349
(6251) (aac4)6, 2015.
Nico UF Dosenbach, Binyam Nardos, Alexander L Cohen, Damien A Fair, Jonathan D Power, Jessica Church, Steven M Nelson, Gagan Wig, Alecia C Vogel, Christina Lessov-Schlaggar, et al. Prediction of individual brain maturity using fmri. Science, 329 2010.
Dan Feldman. Core-sets: Updated survey, Sampling techniques for supervised or unsupervised tasks, pp. 23-44, 2020.
Vitaly Feldman and Chiyuan Zhang. What neural networks memorize and why: Discovering the long tail via influence estimation. Advances in Neural Information Processing Systems, 33:2881-2891,, 2020.
Selene Gallo, Ahmed El- Gazzazz Paul Zhutovsky, Rajat M Thomas, Nooshin Javaheripour, Meng Li, Lucie Bartova, Deepti Bathula, Udo Dannlowski, Christopher Davey, et al. Functional connectivity signatures major depressive disorder: machine learning analysis of two multicenter neuroimaging studies. Molecular Psychiatry, 28(7):3013-3022 2023.
Chengeheng Guo, Bo Zhao, and Yanbing Bai. Deepcore: comprehensive library for coreset selec- tion in deep learning. In International Conference on Database and Expert Systems Applications, pp. 181-195. Springer, 2022.
John A Hartigan and Manchek A Wong. Algorithm as 136: A k-means clustering algorithm. Journal of the royal statistical society. series e (applied statistics). 2801):100-108, 1979.
Hamed Honari, Ann S Choe, and Martin A Lindquist. Evaluating phase synchronization methods in fmri: A comparison study and new approaches. Neurolmage, 228: 128:11778 11704,, 2021.
Feng Hong, Yueming Lyu, Jiangchao Yao. Ya Zhang, Ivor Tsang, and Yanfeng Wang. Diversified batch selection for training acceleration. In ICML, 2024a.
Yuxin Hong, Xiao Zhang, Xin Zhang, and Joey Tianyi Zhou. Evolution-awar variance (eva) coreset selection for medical image classification. In Proceedings of the 32nd ACM International Conference on Multimedia, pp. 301-310, 2024b.
Jerry Yao-Chich Hu, Hude Liu, Hong- Yu Chen, Weimin Wu, and Han Liu. Universal approximation with softmax attention. arXiv preprint arXiv:2504. 15956, 2025.
Krishnateja Killamsetty, Sivasubramanian Durga, Ganesh Ramakrishnan, Abir De, and Rishabh Tyer. Grad-match: Gradient matching based data subset selection for efficient deep model training. In International Conference on Machine Learning, pp. 5464-5474. PMLR, 2021.
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. ICLR, 2015.
Ravin Kohli, Matthias Feurer, Katharina Eggensperger. Bernd Bischl, and Frank Hutter. Towards quantifying the effect datasets for benchmarking: look at tabular machine learning. In JCLR Workshop, volume 2, pp. 6, 2024.
12

---

Published as a conference paper at ICLR 2026
Hojun Lee, Suyoung Kim, Junhoo Lee, Jaeyoung Yoo, and Nojun Kwak. Coreset selection for object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 7682-7691, 2024.
Zhixun Li, Liang Wang, Xin Sun, Yifan Luo. Yanqiao Zhu, Dingshuo Chen, Yingtao Luo, Xiangxin Zhou, Qiang Liu, Shu Wu, et al. Gslb: The graph structure learning benchmark. Advances in Neural Information Processing Systems, 36:30306-30318 2023.
Shizhan Liu, Zhengkai Jiang, Yuxi Li, Jinlong Peng, Yabiao Wang, and Weiyao Lin. Density matters: improved core-set for active domain adaptive segmentation. Proceedings of the AAAI Conference Artificial Intelligence, volume 38, pp. 13999 14009, 2024.
Zhen-Qi Liu, Andrea Luppi, Justine Y Hansen, Ye Ella Tian, Andrew Zalesky, BT Thomas Yeo, Ben Fulcher, and Bratislav Misic. Benchmarking methods for mapping functional connectivity in the brain. Nature Methods, pp. 1-10, 2025.
Yicheng Long, Hengyi Cao, Chaogan Yan, Xiao Chen, Le Li, Francisco Xavier Castellanos, Tongjian Bai, Qijing Bo, Guanmao Chen, Ningxuan Chen, et al. Altered resting-state dynamic func- tional brain networks in major depressive disorder: Findings from the rest-meta-mdd consortium. Neurolmage:
Clinical, 26: 102163, 2020.
Jiay Lu, Tianyi Yan, Lan Yang, Xi Zhang, Jiaxin Li, Dandan Li, Jie Xiang, and Bin Wang. Brain fingerprinting and cognitive behavior predicting using functional connectome of high inter-subject variability. Neurolmage, 100651, 2024.
Andrea Luppi, Helena M Gellersen, Zhen-G Qi Liu, Alexander RD Peattie, Anne E Manktelow, Ram Adapa, Adrian M Owen, Lorina Naci, David K Menon, Stavros Dimitriadis, et al. Systematic evaluation of fmri data-procsssing pipelines for consistent functional connectomics. Nature Communications, 15(1):4745, 2024.
Scott Marek, Brenden
Finnegan J Calabro, David F Montez, Benjamin P Kay, Alexander Hatoum, Meghan Rose Donohue, William Foran, Ryland L Miller, Timothy J Hendrickson, et al. Reproducible brain-wide association studies require thousands of individuals. Nature, 603(7902):654-666)) 2022.
Baharan Mirzasoleiman, Jeff Bilmes, and Jure Leskovee. Coresets for data-efficient training of machine learning models. In International Conference on Machine Learning, pp. 6950-6960.
PMLR, 2020.
Rosaleena Mohanty, William A Sethares, Veena Nair, and Vivek Prabhakaran. Rethinking measures of functional connectivity via feature extraction. Scientific reports, 10(1):1298, 2020.
Christian Otte, Stefan M Gold, Brenda W Penninx, Carmine M Pariante, Amit Etkin, Maurizio Fava, David C Mohr, and Alan Schatzberg. Major depressive disorder. Nature reviews Disease primers, 2(1):1-20, 2016.
Mansheej Paul, Surya Ganguli, and Gintare Karolina Dziugaite. Deep learning on data diet: Finding important examples early training. Advances neural information processing systems, 34: 20596-20607, 2021.
Geoff Pleiss, Tianyi Zhang, Ethan Elenberg, and Kilian Q Weinberger. Identifying mislabeled data using the area under the margin ranking. Advances in Neural Information Processing Systems, 33: 17044-17056, 2020.
Maria Giulia Preti, Thomas AW Bolton, and Dimitri Van De Ville. The dynamic functional connec- tome: State-of-the-art and perspectives. Neuroimage, 160:41-54, 2017.
Xiangfei Qiu, Jilin Hu. Lekui Zhou, Xingjian Wu, Junyang Du, Buang Zhang, Chenjuan Guo, Aoying Zhou, Christian Jensen, Zhenli Sheng, and Bin Yang. Tib: Towards comprehensive and fair benchmarking of time series forecasting methods. In Proc. VLDB Endow, pp. 2363-2377, 2024.
13

---

Published as a conference paper at ICLR 2026
Lukas Roell, Stephan Wunderlich, David Roell, Florian Raabe, Elias Wagner, Zhuanghua Shi, Andrea Schmitt, Peter Falkai, Sophia Stoecklein, and Daniel Keeser. How to measure functional connec- tivity using resting-state fmri? comprchensive empirical exploration of different connectivity metrics. Neurolmage, pp. 121195, 2025.
F Ros and S Guillaume. Core-sets: Updated survey. Sampling Techniques for Supervised or Unsupervised Tasks, pp. 23, 2019.
Philip Sedgwick. Spearman's 's rank correlation coefficient. Bmj, 349, 2014.
Ozan Sener and Silvio Savarese. Active learning for convolutional neural networks: A core-set approach. In International Conference on Learning Representations, 2018.
Stephen M Smith, Karla L Miller, Gholamreza KhorsiKio Matthew Webster, Christian F Beckmann, Thomas E Nichols, Joseph D Ramsey, and Mark W Woolrich. Network modelling methods for fmri. Neuroimage, 54(2))875-811, 2011.
Stephen M Smith, Diego Vidaurre, Christian F Beckmann, Matthew F Glasser, Mark Jenkinson, Karla L Miller, Thomas Nichols, Emma Robinson, Gholamreza
Mark W Woolrich, et al. Functional connectomics from resting-state fmri. Trends in cognitive sciences, 17 (12):666-68) 6826666662..6 2013.
Mariya Toneva, Alessandro Sordoni, Remi Tachet des Combes, Adam Trischler, Yoshua Bengio, and Geoffrey Gordon. An empirical study example forgetting during deep neural network learning. arXiv preprint arXiv: (eX2.0:8122055599 2018.
Mariya Toneva, Alessandro Sordoni, Remi Tachet des Combes, Adam Trischler, Yoshua Bengio, and Geoffrey J. Gordon. An empirical study of example forgetting during deep neural network learning. International Conference on Learning Representations, 2019.
Dimitri Van De Ville, Younes Farouj, Maria Giulia Preti, Raphaël Liégeois, and Enrico Amico. When makes you unique: Temporality of the human brain fingerprint. Science advances, 7(42):eabj0751, 2021.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention all you need. Advances in neural information processing systems, 30, 2017.
Yining Wang, Liwei Wang, Yuanzhi Li, Di He, and Tie-Yan Liu. A theoretical analysis of ndeg type ranking measures. In Conference on learning theory, pp. 25-54. PMLR, 2013.
Stanistaw Weglarezyk. Kernel density estimation and its application. In ITM web of conferences, volume 23, pp. 00037. EDP Sciences, 2018
Kai Wei, Rishabh Iyer, and Jeff Bilmes. Submodularity in data subset selection and active learning. In International conference on machine learning, pp. 1954-1963, PMLR, 2015.
Xiaobo Xia, Jiale Liu, Jun Yu, Xu Shen, Bo Han, and Tongliang Liu. Moderate coreset: A universal method of data selection for real-woril data-efficient deep learning. In The Eleventh International Conference on Learning Representations, 2022.
Chao-Gan Yan, Xiao Chen, Le Li, Francisco Xavier Castellanos, Jiag-Jian Bai, Qi-Jing Bo, Jun Cao, Guan-Mao Chen, Ning-Xuan Chen, Wei Chen, et Reduced default mode network functional connectivity in patients with recurrent major depressive disorder. Proceedings of the National Academy of Sciences, 116(18)99078-908) 2019.
Jiahao Ying, Yixin Cao, Yushi Bai, Qianru Sun, Bo Wang, Wei Tang, Zhaojun Ding, Yizhe Yang, Xuanjing Huang, and Shuicheng Yan. Automating dataset updates towards reliable and timely evaluation of large language models. Advances in Neural Information Processing Systems, 37: 17106-17132, 2024.
Haizhong Zheng, Rui Liu, Fan Lai, and Atul Prakash. Coverage-centric coreset selection for high pruning rates. arXiv preprint arXiv:2210. 15809, 2022.
14

---

Published as a conference paper at ICLR 2026
Haizhong Zheng, Rui Liu, Fan Lai, and Atul Prakash. Coverage-centric centric coreset selection for high pruning rates. In The Eleventh International Conference on Learning Representations, 2023.
S Kevin Zhou, Hayit Greenspan, Christos Davatzikos, James S Duncan, Bram Van Ginneken, Anant Madabhushi, Jerry L Prince, Daniel Rueckert, and Ronald M Summers. review of deep learning in medical imaging: Imaging traits, technology trends, case studies with progress highlights, and futture promises. Proceedings of the IEEE, 109(5):820-88 2021.
Zhiyao Zhou, Sheng Zhou, Bochao Mao, Xuanyi Zhou, Jiawei Chen, Qiaoyu Tan, Daochen Zha, Yan Feng, Chun Chen, and Can Wang. Opengsl: A comprehensive benchmark for graph structure learning. Advances in Neural Information Processing Systems, 36: 66:17904-1799 2023.
Yongcheng Zong, Qiankun Zuo, Michael Kwok-Po Ng, Baiying Lei, and Shuqiang Wang. A new brain network construction paradigm for brain disorder via diffusion- based graph contrastive learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024. 2024.
A PROOF OF THEOREM
1H Theorem (Interference of Averaged Attention, full version). Let {Am be collection of row stochastid attention matrices with As E NNN, For every row index E {l...., NN assume there exist sets $ C (I....,,N] NN that are pairwise disjoint, meaning $ n ( = Ø for all h + hi, and such that
Jn( 0 for all j S
Define the uniform average A == H Σn An. Then for every row i:
1
(a) Support expansion. supp(a (+)) = U S/a0 If 2 2, then for every h, supp(a!!) g
sl
(b) Entropy inflation. With H(p) == Ej= log
H
H(a()) (
Z
1
H(a
(0)
H(a))) IshS
min
H
H and strict inequality holds whenever the vectors {a Th=1 are not all identical. In particular, under the disjoint mask assumption, strict inequality holds for every i whenever H 2 2.
Proof. Fix a row index and write ==
(8) ab.
A N-1 By definition,
1 H
p = (
Σ (p))s-
Pho
Pj
H
(a) Support expansion. All entries are nonnegative, so Py if and only if there exists a head with (Px); > 0. Under the masking assumption, (Px), > 0 implies j E s( Conversely, since each Pa is probability vector supported on s(i) every j E s with nonzero mass in head contributes positive term py. Therefore,
H U h=1
supp U supp(pa)
S
s(()) we have supp(pk) * Ø and supp(pı) ((()) so supp(p) equals the union of the head supports and is contained in the union of the masks. If, as in the theorem statement, the intended structural supports are exactly the mask sets
Moreover, because Pa is row stochastic and supported inside
Fach is probability distribution produced by softmax: (x(i,) and ΣS" An(i,)
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(that is, the mask defines which indices can receive positive mass), then supp(pa) S/ and hence supp(p) - U ((() When H 2 and the sets {S), (((()) Th=1 are pairwise disjoint, the union strictly
contains each S so supp(p) g s for every
(b) Entropy inflation. The Shannon entropy H is strictly concave on the probability simplex. By Jensen's inequality,
H(P) 2
1
Σ H(Pa)
2
min H(Pa), 1ShSH
H
A=1
and the first inequality is strict unless P1 = РH- Under the disjoint mask assumption with H 2 2, the vectors cannot all be identical: pt P for some h + h', then their supports coincide
and are nonempty, so s/() n ((()) # Ø, contradicting disjointness. Hence p Prr are not all identical, so H(()) H
1 Σ M(Ps) and therefore H(p) > min, H(px).
Together, (a) and (b) show that uniform averaging introduces additional nonzero entries and increases entropy, which blurs head specific structural patterns.
B PROOF OF THEOREM 2
Proof. We use an existing attention-oni only universal approximation result as the main engine and then specialize it to row-stochastic matrix-valued targets.
Step (Reduce sequence-to-seqqeene approximation). View X RNXT as length-N sequence with token dimension T. Likewise, view S(X) E RN as length-N sequence of row vectors in RN, Since X' is compact and is continuous, this continuous sereenceet--equeene map compact domain.
Step 2 (Attention-only universality on compact sets). Recent results show that (softmax- Jattention-only architectures with linear projections are universal approximators for continuous sequence-to-sequene maps on compact domains (Hu et al. 2025). In particular, attention modules can simulate piecewise-linear bases and hence achieve uniform approximation without requiring feed-forward sublayers. We invoke such a theorem.
Step 3 (Constrain the output to be row-stochastic). Our target operator satisfies S(X) A N-1x for all X. The model family equation is also row-stochastic by construction: each head output is row-stochastic (row-wise softmax), and the convex mixture with a E A preserves row-stochasticity. Therefore the approximating attention-only construction can be chosen to lie entirely inside A N-1xN
Step (Uniform approximation Frobenius norm). The cited attention-only universality
provides uniform approximation in a sup norm over the compact domain. Since || || S | the same parameter choice yields
sup XEx
Ax( S(X) <E
after tightening constants.
This completes the proof.
C PROOF PROPOSITION
Proof. Because Ze and Ze-1 are i.i.d.,
K
K
E[A
Σ
Pr = S(k) Ze-1 Ze-1= 500 $
1m
K
K
Dedr
1=1
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which gives the first equality in equation 7 Since D&A- and DRI Diks
AcDiDa = Σ
AADiDRa k<l
k=
proving the second equality in equation
For the bounds equation 8 note that for all l 1, Dunn S DDa S D Dmax hence
2imin
Σ
Ande S 2
AxA S 2D max
AEd
k<l
hel
kil
Finally,
Σ A6
A
2 =
k<l
which is the Gini impurity of }
This yields equation
g
If Du D for all & + I, then equation
becomes
E A. 2D Σ Axd1 100001(111 1
establishing equation
D LEMMA I AND PROOF
Lemma (Consistency of SPS). Let {A (2) be the sequence of attention- bassed structure
(e)
matrices for a fixed sample X generated by a stochastic optimization algorithm. Assume the sequence of differences
( = A
(x) 1|
(18)
(X)
Then the empirical SPS forms a stationary and ergodic process with finite mean (XX E(A,(X)), estimator
SP)
-L Σ Ax
(19)
converges almost surely (X) as oo: SP)
0² (2(X) a.s.
Proof. Because (X.(X) is assumed stationary and ergodic with finite first moment, Birkhoff's pointwise ergodic theorem (Birkhoff 1931) applies:
Σ (X) (X) = (X().
(20)
L
But the left-hand side precisely SPS). Hence the estimator strongly consistent.
E PROOF OF THEOREM 3
i= and let 8(k) the k-th order statistic. Equivalently, Sy (x; 8; S } up to tie-breaking on null event (because the score distributions are continuous).
Proof. Write the scores as [
Step 1: Identify the population selection threshold. Let satisfy equation 11 Intuitively, 7 is the
population score threshold whose expected accepted fraction p:
N
Σ
1ss < = =xFF((T) + ny FT) p.
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Step 2: The empirical threshold concentrates.
Define the empirical accepted fraction at threshold
N E 1(s st).
(t = N 2=1
Because scores are independent across samples and each indicator is bounded, a standard concen- tration argument (e.g., Hoeffding) yields that (t( concentrates uniformly compact intervals around its mean G(t) ;= TpLp (t) ( TT ( (f). Since Fp, Fg are continuous and G is strictly increasing (under mild regularity), it follows that the empirical quantile ((k) converges in probability T:
Pr
(k)
T.
(21)
N
Step 3: Selected cluster counts converge to their expectations. of selected points from cluster Cp is
Conditional on s(k), the number
S n C
E
1(((x) S $(a))-
xEC,
Given $(k), the indicators in the sum are i.i.d. Bernoulli with parameter ()((())), so by the law of large numbers (and Slutsky using equation 21).
S& nal
Ps F2(T).
(22)
np
Similarly,
S& ng Pr Pa(T).
(23)
ng
Step 4: Convert to selected proportions and compute the bias. Divide equation 22 by k/N
(Sa) SSk Cplll
SS n CpI/N
(np/N) (1Sx n Cpp/mp) Pr, FpFp(T)
k/N
k/N
Using equation
we compute
Tp (T()
Tp Tp (b(()) P) = 7p (p((T - Fp(T)) -p
- Ne Fg
Tp T (F,(t)-F((T))
P
Under equation 12 this equals 5 = Np 7 > 0, establishing the first limit in equation
13 The
p
statement for 7, (Sk) follows since (Sx) = (Sa), and then A = (Sa) xp
28
0.
F THEOREM 4 AND PROOF
Theorem 4 (s-coverage of density density-reweighted sampling). Fix 0 < 8 < 1 and >> 0. Let Xe be the candidate pool with = |& and let S C & be the subset of size m. returned by the proposed sampling procedure. Let N₂ the E-covering number of X, under d(A, A') || A'llF. Under Assumption if
nXPmax + +T) m
Pmin + (log No log(1/6))
(24)
then S is E-cover of X. with probability at least 1 5. 5.
Define the cencture-represeenttii space (M, d) with metric d(A, A') = - - For = > 0 let N₂ be the covering number of X, M. That is, the smallest number closed d-balls of radius needed to cover all subjects in X
Assumption 1. After the 8-filter step, define the KDE-induced density x(X) == psrs (SSS(SSS))) (X))
where psps is Gaussian KDE fit (SPS(X) X &c). Assume the estimator is bounded on the candidate pool: Punin & p(X)= S Pmax < 0o for every X E &
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Assumption 1 is mild because Gaussian KDE with finite bandwidth produces bounded, strictly positive estimate on any finite sample.
Proof. Define the (normalized) sampling weight for X E X as
(X) Ezex, p(2)+7
x(X)+
(25)
weight bounded below by + Am and Σz p(Z)+
By Assumption for all X,
n
Hence every point has
1/mmax + +T) Pmin +
w X
Wmin-
(26)
(/mmnn + 7) (Pmmax + +T)
Let {B..... BN. be collection of closed d-balls of radius covering Xe. Since Xe C X each By contains at least one candidate point. Therefore its total sampling mass satisfies W,
ExeByrut w(X)= 2 Wmin.
Consider sequential sampling without replacement where at each draw we sample from the remaining points proportionally to their weights (renormalized), If we have not yet sampled from Bj, then removing points outside B, can only increase the renormalized mass of By; thus, at every draw the conditional probability of selecting a point outside B, is at most 1 W I
Wmin- Therefore
Pr(B, ns e0 (1 Wmin) " S exp(p= m.)
(27)
Choose that win m) < 8/N i.e.
Wmin (log Ng log(1/6)). A union bound over
the Ng balls yields Pr[Ej B, n Ø S 5. Hence with probability at least 1 8, every ball contains at least one sampled point, so S is an E-cover of X,.
G THEOREM
5 AND PROOF
Theorem 5 (Expectation discrepancy under e-coverage). Let (M, d) be the structure-vepresentttio space with ((A,A)) ||A-A'l A'|lr and representation map X (X) M. Let P be a probability distribution supported on X. Assume & C X is an 8-cover of X in M: for every E X there exists X E X with d(A (X) A (x)) S.
Let X + & be any (measurable) selection satisfying d(A (((())) S E for all X, and define the push-forwant measure P, := P -- X. Then for any function f X - IR that is L-Lipschitz w.r.. d,
EX [xx(([(()) EX [[()] Le.
(28)
Proof. Because f is L-Lipschitz w.r.t. d, for every X E X,
[(X) f(x(())) < T. (x) A (x(x)) < L..
Taking expectation under P and using Jensen/triangle incquality,
[x-r([(X)) Ex-r([(T(X))) < F - & Le.
Finally, by definition of the push- push-forward measure Pr.
Ex=p[f(T(X)) Ex=P,[f(X)
Combining completes the proof.
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Computation Time Distribution of SPS
Total SPI Methods: 266
10a
10P
51000, 207 methods
10
#100: 180 methods
Time
10a
elc: 130 methode
10-1
10
5P5
Figure AI: Time consumption of different SPIs on a single sample.
Table A1: SPIs included in pyspi (bolded ones are used in this paper).
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vpll maltiper marn deel fatte ft
wall mattoper, mam, Inateee Brandd
vpil caaaaeee mare mnttd Dins
expll maltiger del 250---25 fusoddd
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H COMPUTATIONAL COMPLEXITY ANALYSIS
H.1 COMPUTATIONAL. COMPLEXITY AND SELECTION OF SPIS
We compute all Statistical Pairwise Interactions (SPIs) using the open-source Python library pyspi (Cliff et al., (023), which provides a unified implementation of 284 diverse measures. To ensure numerical stability, we exclude 18 SPIs that produced invalid matrix entries (NaN values), resulting in final of |S| 266 methods for our benchmark.
For single multivariate time series (MTS) sample X E R where N is the number of regions of interest (ROIs) and T' is the number of time points, the time complexity of a typical SPI compu- tation scales as O(N2L), L). where L reflects the method-specific internal dependency length. When considering the entire benchmarking task over a dataset and the full suite of SPIs S, the overall computational complexity lower bound becomes O(1-) [S] L).
To quantify this theoretical burden in practical terms, we benchmarked each of the 266 SPIs on representative sample (size 33 240). Using a 128 vCPU cluster as concrete example, the resulting time distribution is shown in Figure AT Based on these timings, we can estimate the total cost for our full dataset of | 4520 samples. The time to process
sample with all 266 SPIs is approximately 18, 950 CPU-seconds (summing estimates from different time bins: 14 methods x 1000s 45 100s 27 x 10s 180 x 1s). Extrapolating to the full dataset, the total computational cost is a staggering 4520 x 18, 950 z 8.57 x 10 CPU-seconds, equivalent to over 990 CPU-days (= 7.7 CPU-days environments, this enormous consumption of resources makes a full benchmark practically infeasible and time-prohibitive.
128 vCPU). Even with access to massively parallelized cluster
This severe computational bottleneck motivates our core research question: how can we drastically reduce the number of samples while preserving robust and reliable evaluation of the SPIs? This challenge naturally leads to our investigation of core-set selection for IMRI-based SPI benchmarking. As calculated, on a 10% core-set the load reduces to the same 128-vCPU cluster, this would take: 99 CPU-days/ 128 cores = 0.77 days (or = 18.5 hours). To validate our approach, we necessarily performed this exhaustive computation to establish a ground-truth ranking. However, for the purpose of evaluating core-set quality in our experiments, we restrict our analysis tractable subset of SPIs that take less than one second per sample, enabling rapid yet informative evaluation. The full list of 284 SPIs is summarized in Table Al with those used for our core-set evaluation highlighted in bold.
CPU-days (10% of the full cost). On
H.2 COMPUTATIONAL COST OF SELECTION METHODS
To complete our analysis of efficiency, we provide an empirical comparison of the computational cost for SCLCS and the baseline methods. Table Table|A2 details the practical time consumption required for each method. The 'Time per Epoch' reflects the average wall-clock time to complete a single training epoch. The 'Score Calculation Time' is the specific, one memtime overhead for computing the final selection metric after the training phase is complete.
Table A2: Computational cost for core-set selection methods.
Method
Time per Epoch (s) Score Calculation Time (s)
Forgetting 1.8708
0.0000
Entropy
1.9851
2.1588
EL2N
2.5309
0,3420
AUM
2,8389
0.0957
CCS
2,8389
11.9414
EVA
2,5964
0.6479
BOSS
2.0952
61.5406
SCLCSDense 6.9296
249.8204
As the results indicate, all core-set selection methods incur modest, one-time computational cost. This up-front investment is negligible when contrasted with the over 990 CPU-days required for full
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downstream benchmark (as detailed in Appendix H It is worth noting that the score calculation for SCLCS Dense, which computes the SPS metric by measuring differences between attention matrices across epochs, represents fixed, post-training overhead. While this step appears slower than other methods' scoring, is a one-time process that is highly parallelizable. These findings confirm that investing small computational budget in core-set selection is practical and efficient solution. This validates our proposed paradigm for tackling the intractable problem of large-scale model benchmarking.
1 INFLUENCE OF LABELS ON BASELINES
In the main paper, we report results of baseline methods trained using labels aligned with the evaluation objective. However, proposed SCLCS framework uniformly adopts subject identity as the supervisory signal, which raises the question of training-evaluatio label misalignment. To provide more comprehensive analysis, this section further investigates the influence of such misalignment on baselines.
1.1 USING MDD LABEL FOR BRAIN FINGERPRINTING RANKING
Table A3: Comparison of brain fingerprinting ranking with subject and with MDD labels (mean + std). Arrows indicate change under MDD supervision.
Method
Label
aDCG@s
0.3
0.5
0.1
aDCG
0.
0.5
0.1
nDXGGer20
0,3
0.5
Forgeting
Subject
14A12
14.4
14.43
43.36_141
43.36_.135
18.49
15,4
48.57 -
20.23 =
49.87
20.23gnm
55.80_471:
35.80
Entropy
MDD
Subject
24.38-2126.
47.40ga10
36.60
22
68.74
59.95 s
29345-2534
45.86
22.05
58.27 -23mn
33.17
36.05 m1
46.55
35.90
59.05
E12N
MDD
Subject
35.56
4.51
19.27
20. 50
44.09 c
31.05
14.67
2355
22.51
35. 18
47.17 200e
12.20-2051
14.60
33. 11.30,33 55
15.8220330
48.5
40.06 2200
AUM
Subject
MDD
42 42.32__e3l
65 mm
72.58
56 56.68.1111
48.75-00mf
38.17
36.06_
60 20
63.74g
62.05
53.60
26.83
1457
51 45
53,85 15.14
59.09 39
58, 24.34
1.90
30.53:14:5
46.65
2,92
29.13
51.76:2412
1622
32.562143
52.18-
MDD
11:25-n.s7
41.014245:
12.98 12u7
44.33
38.11
18.45 13355
33.65 46.20
Suhject
38,40
62.03
37,80
43.37
49.56.2321
43.22
53.51
65 65.4
EVA
MDD
11.99-mmm
30.57,344.
42.34.-2.0
50.85 ma3)
31,90
41.31
28.07
BOSS
MDD
Subject
22.90_2201
15.96 2255
51.70gmaal
42.11am4m
40,08
35.36
51.87203 22.92
29.4
40.57
39.62-001
39 15
51.71amml n9
31.45
38.24
40 40.14
38.92
We first evaluate the performance of bascline methods trained with MDD diagnosis labels for core-set selection in the brain fingerprinting ranking task, using the results from subject-identity supervision (as reported in the main paper) as reference. This alternative labeling scheme aligns with the intended design of most baseline algorithms, which aim to select core-sets based on the target task labels (i.e., MDD vs. HC diagnosis labels from the REST-meta-MDD dataset).
As shown in Table A3 this supervision shift generally leads to performance degradation across most methods, suggesting a potential mismatch between the binary nature of MDD labels and the requirements of brain fingerprinting, which involves a one-vs-all subject-level identification task. Specifically, training with MDD labels provides weaker sample-level supervision due to reduced class granularity, potentially limiting the diversity captured during core-set selection. Consequently, the selected samples may fail to adequately support the subject-wise discriminative capacity of SPIs.
Nevertheless, certain methods such as AUM and BOSS exhibit improved ranking stability at higher sampling ratios. This may be attributed their scoring strategies, which explicitly account for sample diversity or informativeness. Under this paradigm, incorporating diagnosis- labels introduces an additional semantic dimension that enhances the selection process, enabling these methods to better preserve the representational structure of the full dataset.
I.2 USING SUBJECT LABEL FOR MDD RANKING
As a complementary analysis, we also evaluate the performance of baselines trained with subject identity labels for core-set selection in the MDD diagnosis ranking task. This setting closely aligns with our proposed SCLCS framework and allows us to investigate whether individual-leww supervision provides a stronger basis for core-set construction.
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Table A4: Comparison of MDD diagnosis ranking with MDD labels and with subject identities - std). Arrows indicate change under subject supervision.
abcGss
#D
Mothod
Label
0.5
0.1
0.3
0.5
0.1
Forgetting
MDD
Subject
24.64-200el
28.70
41,50
28.522mas m
61. =1
40.56:220
46.33
50.27732.
88.57
66.
22.22
90.9 20 21,60 12.35
64.37
57,02a3133
75.70
MDD
29.00:45.0
21.84
57.48220:
29.17.433-
40.75
63.25
30
30.30
45.85
70.79 21u00
Ensropy
Subject
17.0
16.09
66
58, 58.70.w367
52.25
15.19_1537
15536
81
E12N
MDD
66.75-21as11
30.93
42.90
51,70,3a:4
68.85
ml
71 71,38_22221
36.05 43144
58.54
50,92
26.67
12.96,157
56.72
78.65 78.65.u43
MDD
36002/n w
42.68.45
39.17
g8.14
14
48.44.0010
14.36_114
Subject
41. 7
12.722251351
53.6243.44
58.66221351
67.17
23.62
65.26
70.07.4471
CCS
MDD
Subject
47.81 1
a5.95
25.25
59:9213338
56.95
14.75
46.4611
49425
32.40
6240
62.59
75.41 11.
62.04
68 1557
41.36
71,6242:15
69.
78.77
69.14
EVA
MDD
Subject
21.25 21.25_11.4.
51,80
67.32
66.812911
15.63
70.07
16
72.61
79.06
76 26
48 2
10.82
75. 75.34_.
83.18.izal
81.73as
MDD
42.44-003
57.52
79,57g11
50642251
34.20gmm 64.8
71.36
5895
Subject
39.60_37ae-
67.40
79.51amal
45.30,m125)
08.4721335
86213345f
54.29
77.59mme
87.29
Compared to the MDD-supervised setting, we observe that a greater number of methods benefit from improved ranking stability under subject identity supervision. For instance, Entropy. AUM, and E12N exhibit consistent performance gains at higher sampling ratios (e.g., AUM improves from 58.14% 67.17% in nDCG@ 10@0.5, and Entropy from 63.23% to 75. 15%.. This trend suggests that supervision aligned with subject-level heterogeneity may better preserve fine-grained information necessary for identifying high-quality representative samples.
Despite these improvements, clear performance gap remains between all baselines and our method, as shown in Tableß] This highlights the non-trivial advantage of SCLCS, where structural perturba- tion scoring and density-awart sampling jointly enforce both informativeness and diversity in selected subsets.
Interestingly, AUM shows consistent gains across nearly all metrics, suggesting that its original scoring, formulated under task-specific supervision, may underestimate structural variation among samples. Subject-based based training appears compensate for this limitation by injecting more diverse contrastive signals during scoring, revealing a potential direction for enhancing its robustness.
Entropy also achieves performance gains across the board, with improvements high 11.6% in nDCG@ 20 (from 70.79% to 81.40%). However, as shown in Figure 2 Entropy consistently selects highly imbalanced subsets regardless of supervision label, often dominated by small number of subjects. This structural bias undermines its utility for benchmarking core-set methods, as it fails to preserve representative distribution of the dataset. Thus, despite the numerical improvements. Entropy remains unsuitable for core-set-basee SPI evaluation.
These findings reinforce the need to consider both label alignment and structural diversity in core-set selection. Subject-level supervision offers promising direction, but our method's explicit modeling of structure-aware consistency and coverage remains critical for reliable benchmarking.
J INFLUENCE OF THE PROPOSED DENSITY-BALANCER SAMPLING ON BASELINES
As stated in Section SCLCS framework, but also generalizable to other score- score-based core-set selection methods. To evalu- ate its applicability beyond our method, we visualize comparative results on the Brain Fingerprinting and MDD Diagnosis tasks in Figure A2 and Figure A3 respectively. We exclude CCS and BOSS from this analysis due to their use of task-specific sampling designs.
4.3 our proposed density-based sampling strategy is not only central to the
On the Brain Fingerprinting task, density-based sampling frequently alters SPI ranking performance across baselines. For example, E12N underperforms in multiple metrics when density is applied (e.g.. nDCG@5 at ratio 0.1 drops from 400 to 20), while EVA shows inconsistent trends across sampling ratios. This instability may be attributed to the fact that, when supervised with subject identity, ccore-based methods tend to prioritize samples that support lubject-level diversity. Replacing this priority with a density- based criterion may inadvertently distort the structural balance of the selected subset.
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Rank Comparison on Brain Fingerprinting using Rank/Density-bbaeed Sampling Strategles
Panki based
DensitySasse Sased
nDCGgS
nDCG@10
nDCo@20
9-
100
A2M
Rerpntung
A2M
600
Entropy
Herpettig
600
Rerpettnd
Figure A2: Rank comparison on brain fingerprinting using minkddessty-basee sampling strategies.
Conversely. in the MDD Diagnosis setting, density-based sampling consistently improves perfor- mance. Baselines such as EVA and Entropy show marked gains in ranking stability, with EVA's nDCG@ 10 increasing from 70 to ~99 at sampling ratio 0.5. This contrast suggests that when supervision involves fewer discrete classes (e.g., binary labels), the density structure becomes easier to estimate and more semantically aligned with the downstream evaluation objective.
interesting deviation is observed the Forgetting method. high sampling ratios in both tasks, its performance noticeably declines under bensity-based sampling. This may stem from Forgetting's underlying assumption: that low-confidence samples correspond to noisy or uninformative data, which does not hold well for fMRI. Due to the complex nature of brain dynamics, such samples may actually be densely clustered and structurally meaningful. Consequently, density- sampling could overemphasize regions marked by high forgetting scores, thereby degrading ranking consistency.
In summary, density- bease sampling demonstrates strong compatibility with several baseline strate- gies, highlighting its potential general purpose augmentation. However, the interaction between density criteria and different scoring heuristics can be nontrivial, and may lead to unintended trade- offs in performance. These results underscore the importance of further empirical studies to better understand the conditions determining whether density-based selection benefits or interferes with score-driven core-set construction.
curppoe-
K EMPIRICAL. RESULTS FOR THEOREMS
K.1 CONVERGENCE OF UNIVERSAL APPROXIMATION
To empirically validate the universal approximation capability of our modified Transformer architecture, posited in Theorem 2 we designed and conducted direct fitting experiment. The theorem states that our model architecture is, in principle, capable of approximating any continuous Statistical Pairwise Interaction (SPI) operator.
Experimental Setup
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Rank Comparison MDD using Rank/Density-based Sampling Strategles
Park bated
Denatty based
nDCG@g
nDCo@10
nDCG@20
02
102
62
Perpeting
Forgeting
Figure A3: Rank comparison on MDD diagnosis using rank/density- based sampling strategies.
orth
phuse mi E.Eaaerrr mews 2o frite Iraood-25 28 mimm toper, mean Bel, (iin- fraedd 25 up muu thtpeer meen f-11 Pmin- fmix-0-25
That M52
241 Mavdltt 15 max BDC mult laper meat fel min-222
1och mutthaper mazn 1-2 9ma--0
MI2 1000
posssion
Figure A4: Training and validation MSE loss convergence curves for the SPT operators used the empirical validation of Theorem 2.
The core objective of this experiment was to train instances of our model to directly mimic the Functional Connectivity (FC) matrices produced by specific SPI operators. We trained separate
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model instance for each operator in diverse set of 16 representative SPIs. The experimental setup was as follows:
The imput for each model was fMRI time series sample X RVXT consistent with the primary data used in our paper.
Input:
Target: For each model, the learning target was the "ground-truth" FC matrix As E RN*N, computed for that specific fMRI sample using the corresponding SPI operator.
Loss Function: We optimized the model parameters by directly minimizing the Mean Squared Error (MSE) between the model's 's output adjacency matrix A and the target matrix As. Specifically, we use MSE((A + A /2, (As s + /22 to ensure the symmetry of the adjacencies.
Training and Validation: We partitioned the dataset into training, validation, and testing sets with 10%%/% split. During training, employed early stopping (patience= 10) based on the validation set performance to ensure the model learned a generalizable trans- formation rather than merely overfitting the training data.
Results and Analysis Figure A4 displays the convergence curves from the training process for all 16 SPI operators. Each subplot in the figure represents independent model instance, with the x-axis denoting the training epoch and the y-axis representing the MSE Loss. The blue line indicates the MSE on the training set, while the orange line represents the MSE on the validation set.
As the plots clearly demonstrate, our model architecture exhibits a strong capacity to fit all 16 SPIs, regardless of their diverse underlying computational principles. Key observations include:
1. Successful Convergence: In all experiments, both the training and validation MSE decrease rapidly from high initial value and eventually converge to stable, low level. This indicates that the optimization process was successful and that the model effectively learned the mapping from the fMRI time series to the target FC matrix.
2. Good Generalization: The validation loss curves closely track the training loss curves without significant divergence. This confirms that the models did not overfit and that the learned approximations generalize well to unseen data.
These convergence curves, combined with the low final test MSE values reported in Table of the main text, provide strong empirical support for Theorem 2 The results collectively confirm that proposed modified Transformer architecture possesses the practical expressive power required to represent the diverse functional forms inherent our benchmarking task.
K.2 STATIONARY AND CONVERGENCE ANALYSIS
Perturbation Trends
Training Loss
4.
25
4.5
25-
26-
03-
Epoch
Epoch
Figure A5: Convergence dynamics of SCLCS. (Left) Perturbation trends show that the mean SPS stabilizes relatively early in training. (Right) The training loss converges more gradually over 1000 epochs. The different x-axes used to visualize the distinct convergence timescales of each metric.
As demonstrated in Lemma I the reliability of the Structural Perturbation Score (SPS) relies on the assumption that the per-epoch difference (X)
||A (e)
A (c-1) is stationary and ergodic.
(x)
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Table A5: Performance comparison: brain fingerprinting MDD diagnosis
Method
Bruin Fingerprinting
Diagnosis nDCG 10
nDCG@s
nDCG@10
nDCG@
20
nDCG@5
nDCG@
Ratio
0.1
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
0.1
0.3
0.5
SECTION
Slow-Only SPIs
Random
0,883 0.863 0.805 0.903
0.898
0.835
0.921
0.923
0.863
0.946
0.998
0.997
0.962
0.998
0.998
0.975
0.999
0.998
Forgetting
0.591 0.441 0.837 0.614 0,478 0.871
0.642
0.514
0.8%8
0.781
0.946
0.997
0.839 0.965 0.998 0.886 0.977 0.999
Entropy
0,544 0.963 0.907 0.615 0,970
0.977
0.683
0.975
0.982
0.604
0.636
0.941
0.619 0.640
0.959 0.628 0.652 0.973
EI2N
0.887 0.852 0.928 0.912 0,884 0.945
0.928
0.909
0.958
0.967
0.897 0.994 0.976 0.930 0.996 0.983 0.957 0.997
AUM
0,835 0,983 0.808 0.866 0,984
0.848
0.905
0.983
0.881
0.934
0.849
0.933
0.953
0.890
0.955 0.963 0.923 0.971
CCS
0.785
0.859
0.840
0,999
0.923
0.999
EVA
0,628 0,906 0.650 0.663
0,923
0.707
0.701
0.935
0.761
0.795
0.997 0.999
0.848
0.998 0.999 0,895 0.999 0.999
BOSS
0.385 0.956
0.444
0,951 0.656
0.521
0.945
0.710
0.636 0.968 0.992 0.760
0.976 0.995 0.843
0.995
SCLCS
0,879 0.94] 0.999 0.907
0,955
0.999
0.932
0.961
0.999
0.874
0.983
0.997
0.916
0.989
0.998 0.945
0.993 0.999
SCLCSpene
0.903 0.962 0.943 0.922 0,967
0.956
0.935
0.969
0.964
0.954
0.999
0.999
0.969
0.999
0.999
0.979
0.999
0.999
SECTION B: Mixture SPIs
Random
0,280 0.680 0.646
0.389 0.689
0.715
0.392
0.765
0.722
00.504
0.242
0.718
0.601
0.263
0.779
0.633
0.306
0.828
Forgetting
0,323 0.464 0.711 0.421 0.485
0.742
0.465
0.497
0.749
0.255
0.415
0.634
0,380
0.502
0.670
0.432
0.563 0.758
Entropy
0.442 0.660 0.663 0.485 0.656
0.678
0.551
0,668
0.684
0.289
0.327 0,565
0.291
0.414
0.621
0.307
0.467 0.702
E12N
0,485 0.441 0.531 0,552 0.515 0.570
0.564
0.570 0.623
0,310
0.522
0.656
0,360
0.576
0.705
0,416
0.646
0.761
AUM
0.491 0.680 0.870 0.565 0.737 0.882
0.604
0.767
0.877
0.361 0.415 0.536
0.403
0.435
0.585
0.452
0.478 0.640
CCS
0,228 0.480 0.495 0.345 0.478 0.507
0.352
0.576
0.549
0.469
0.599 0.747
0.519
0.670
0.754
0.628
0.699 0.790
EVA
0.193 0.527 0.601 0.362 0.597 0.622
0.396
0.274
0.353
0.755
0.440
0.616 0.812
BOSS
0,438 0,592 0.505 0.433
0.662
0.531
0.428
0.687
0.561
0.373
0.620
0.796
0.435
0.620
0.859
0.519
0.721 0.879
SCLCS
0.790
0.795
0.823
0.755
0.279
0.303
0.368
SCLCSpese
0.442 0.758
0.812
0.552
0.751
0.827
0.576
0.750
0.827
0.447
0.449
0.716
0.522
0.533
0.706
0.621
0.594 0.752
Since our training does not incorporate iosiiaatioo-aaaeee early stopping, we use model convergence as an implicit criterion for termination. To empirically support this, Figure A5 visualizes the convergence trends of structural perturbation and training loss.
Notably, these two metrics converge on different effective timescales. The left panel shows that the mean SPS (blue curve), which reflects the stability of the learned connectivity structures, reaches stable plateau relatively early (around epoch 500). The initial spike in perturbation reflects an expected "burn-in" phase before the model learns stable representations. In contrast, the right panel shows that the training loss continues to decrease more gradually over the full 1000 epochs as the model makes finer adjustments to the embedding space to fully optimize the contrastive objective.
The clear convergence of both metrics, despite their different timescales, provides strong empirical validation for the assumptions in Lemma This confirms that SPS is a stable and consistent measure of structural influence, and the overall loss convergence supports the robustness of our end-to-end training pipeline for core-set selection.
L GENERALIZATION AND ROBUSTNESS ANALYSIS
This section provides experiment results to address the concerns regarding site-level generalization and SPI subset bias to prove the impact of the proposed task.
L. EXTENSION ON SPI PROPERTIES
We create two new benchmark sets: (1) A "Slower-Only" set containing 50 SPIs with >> Is compute time (up to 10s), and (2) A "Mixture" set combining these 50 slow SPIs with our original 130 fast SPIs (Total 180). Results are reported in Table A5
The findings are two-fold:
Surprisingly, the ranking task becomes "easier." Even the Random baseline performs robustly (e.g., nDCG@5 5 > 0.9 on the MDD task). This suggests that for this specific subset of slower methods, performance is less sensitive to specific data selection.
On "Slow-Only":
On "Mixture" (Full Benchmark): However, when combining fast and slow SPIs, SCLCS re-emerges as the clear winner. On the Brain Fingerprinting task (10% ratio), SCLCS achieves nDCG@5 of 0.79, whereas Random collapses to 0.28.
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It proves that simple heuristics (like Random) are brittle and fail in realistic, heterogeneous bench- marking scenarios (the "Mixture" case). SCLCS is necessary because robustly handles the full spectrum of SPI behaviors, effectively weighting the up-performing methods that researchers care about most. More importantly, it suggests that different properties of the candidate models may affect the difficulty of the proposed problem. Exploring such effect promising future direction.
Table A6: Site balance core-set (L1 distance, lower better)
Method
L1 Distance @ 0.1 ratio
L1 Distance @ 0.3 ratio
Distance
0.5 ratio
Sample Level
Subject Level
Sample Level
Subject Level
Sample Level
Subject Level
Forgetting
0.239
0.243
0.184
0.107
0.126
0.048
Entropy
0.186
0.139
0.149
0.112
0.146
0.157
B12N
0.303
0.350
0.260
0,220
0.235
0.195
AUM
0.157
0,143
0.094
0,181
0.057
0.176
CCS
0.202
0.183
0.143
0.175
0.103
0.148
EVA
0.111
0,101
0.047
0,017
0.024
0.081
BOSS
0.737
0.362
0.457
0.107
0.248
0.022
SCLCS
0.127
0,146
0.096
0,039
0.068
0.011
SCLCS
0.195
0.146
0.112
0.054
0.071
0.017
L.2 EXTENSION ON DATA PROPERTIES
We further explore the relationship between 'site ID' and the core-sets selected by all the baseline methods and the proposed SCLCS (which is blind to site). Performances are quantified by calculating the LI Distance between the site distribution of the original dataset and the site distribution of the selected core-set. The samples of each subject are same on the original dataset but vary on the core-set. Thus we provide two levels of result based on sample and subject, respectively. Results are reported in Table A6]
SCLCS demonstrates robustness site imbalance. For example, at 30% sampling ratio, SCLCS achieves an L1 distance of x 0.096, ranking second only to the variance-based method EVA ( 0.047). Crucially, SCLCS significantly outperforms other baselines like Entropy (0. (0.149), which tend to be more biased towards specific sites. This is an interesting finding. It necessitates exploring methods to balance different data properties and the performance on the proposed ranking preservation task, which is beyond the scope of our current paper.
L.3 ROBUSTNESS WINDOW SIZE
We re-process the entire dataset using a different sliding window configuration (Window Size 50 TRs, Stride 45 TRs), which differs significantly from the setting used in the main paper (Window Size 70, Stride 35). We then re-calculated all 130 SPIs and re-evaluated the ranking consistency of SCLCS against all baselines on both downstream tasks.
The results, detailed in Table A7
empirically demonstrate that SCLCS maintains its superior performance and ranking stability regardless of the window size, confirming that our method captures intrinsic structural patterns rather than artifacts of specific preprocessing parameters.
On MDD diagnosis task, even with shorter window lengths (which can introduce more noise). SCLCS and SCLCSDenss consistently outperform all baselines. Notably, at the challenging 0. sampling ratio, SCI.CS achieves an nDCG@5 of 0.661, which significantly higher than the strongest baselines like AUM (0.452) and CCS (0.464). This confirms that our density-aware selection strategy is highly robust to variations in temporal segmentation.
On brain fingerprinting task, SCLCS continues to show state-of-the-ar performance, particularly at the 0.1 ratio with an nDCG@5 of 0.475, far exceeding Random (0.206). While baselines like E12N show high variance (performing well 0.3 but dropping significantly at 0.5), SCLCS and SCLCS exhibit a more stable performance trajectory as the sampling ratio increases (e.g.. SCLCS improves from 0l475 to 0.673).
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Table A7: Robustness of different methods to window size
Method
Robustness on MDD Diagnosis Task
Robustness on Brain Fingerpriating Task
#DCG@
aDCG@10
nDCG@/20
nDCG@5
aDCG@
aDCG@#2)
Ratio
0.1
0.1
Random
0,213 0.498 0.802
0.413
0.611
0.843
0.558
0.707
0.886
00.206
0.285
0.282
0.234
0.386
0.353
0.270
0.443 0.376
Fregetting
0.234 0.190 0.637
0.336
0.287
0.689
0.469
0.376 0.745
0.252 0.478
0.417
0.287
0.525
0.461
0.324
0.556
0.500
Entropy
0.258 0.467 0.566
0.293
0,506
0.633
0.360
0.533
0.717
0.227
0.474 0.576
0.243
0.526
0.582
0,347
0.544
0.591
EIZN
0.174 0.007
0.253
0.344
0.372
0.366
0.374
AUM
0.452 0.631 0.701 0.490
0.725
0.784
0,528
0.797
0.852
01.291 0.690 0.399
0.324
0.684
0.483 0.332
0.728 0.522
CCS
0.464 0.596
0.554
0.682
0.794
0.625
0.757
00.240
0.502
0.282
0.560
0.306 0.566
EVA
0.347 0.422 0.513 0,456
0,496
0.597
0.500
0,580
0.663
0.430 0.456 0,444
0.417
0,510
0.476
0.474
0.517 0.488
BOSS
0,281 0.369 0.833 0,380
0.430
0.867
0.468
0.493
0.899
0.062 0.364 0.669
0.110
0.379 0.747
0.151
0.416 0.752
SCLCS
0.621
0.834 0.708
0.662
0.818
0.766
0.735
0.849
0.826
0.475
0.569
0.673
0.491
0.569
0.750
0.495
0.593 0.762
SCICCSase
0.661 0.732 0.836
0.718
0.781
0.885
0.778
0.826
0.917
0.440
0.593
0.712
0.459
0.617
0.707
0.496
0.657
0.705
These empirical results directly demonstrate that SCLCS is not sensitive to the choice of window size and can reliably select high-quality core-sets across different pipeline configurations. We believe this evidence strongly supports the practical reliability of SCLCS in diverse experimental settings.
M REPRODUCIBILITY INFORMATION
M.1 DATA PREPROCESSING
We use a subset of 904 subjects (458 MDD, 446 controls) from the REST-meta-MDD consortium, selected via two-stage filtering process. First, we adopt the quality-cottrolled cohort defined in Yan itt al. (2019), which retains 1, 642 subjects across 17 sites. Second, we intersect this cohort with the 9-site subset used in Long et al. (2020), chosen for consistent acquisition parameters (3T scanners, 240 time points, TR 2000 ms). This yields a final sample from 7 sites with harmonized imaging protocols.
The analysis focuses on 33 regions of interest (ROIs) associated with the default mode network (DMN), as defined in the Dosenbach- 160 atlas (Dosenbach et al.. 2010). ROI-level time series were obtained directly from the preprocessed data released by WEST-meta-MDD. We use the version with global signal regression (GSR) applied, consistent with prior findings (Yan et al. 2001)).
Our decision to focus on the DMN-33 ROI was principled decision based on scientific control, reproducibility, and computational feasibility:
Scientific Control:
To validate the proposed new 'ranking preservation' task, our first priority was to isolate variables. Our primary goal is to define the "Ranking Preservation" problem and prove that peructure-basedd approach is a feasible path. Introducing multiple atlases or pipelines would change our scenario from Benchmark (SPIs) to a different, combinatorially explosive scenario of Benchmark (SPIs atlases/pipelines), which is valuable, promising but separate scientific task.
Reproducibility: This scientific control principle is reinforced by the dataset itself. To en- sure the highest standard of reproducibility, we used the official, standardized pre-processed data from the REST-meta-MDD consortium. This setting ensures the results are not affected by personally defined preprocessing pipelines.
The Computational Infeasibility: Finally. even if we were use an official atlas like AAL-90 (N 90), an average complexity of each SPI would increase compute time by Rs 9x (from N = 33).
Each subject is represented by multivariate time series of T x R, where T is the number of time points and A = 33. To standardize downstream sampling, we truncate all time series to 210 time points. We apply sliding window of length 70 TRs with a step of 35 TRs, yielding five overlapping temporal segments per subject. This configuration is consistent with prior dynamic connectivity studies (Allen et al. 2014 Preti et al.] 2017: Long al. 2020), and provides a balance between temporal resolution and estimation reliabiiity. These segments serve as dynamic samples for our core-set selection framework, alongside statie networks built from each subject's full time series.
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Table A8: Acquisition details of the selected REST-meta-MDD sites. All data collected using
3T scanners and have consistent TR (2, 000 ms). Minor variation exists in number of time points.
Site ID
Institution
MDD
HC
Scamner
TR (ms)
TE (ms)
Timepoluts
Zhongda Hospital, Southeast University
37
30
Siemens Verio 3T GE Signa
2000
25.0
240
First Affilatedd Hospital Chongqing Modical University
2000
40.0
240
Anhui Medical University
GB Siemens Tim Trio 3T
2000
22.5
Southwest University
229
250
2000
30.0
242
21
Beijing Anding Hospital, Cupital Medical Uni-
65
79
Stemens Tim Trio 3T
2000
30.0
240
versity
Second Xiangya Hospital, Central South Uni-
20
18
Philips Gyrescan Achiova 3.0T
2000
30.0
250
versity
China Hospital, Sichuan University
Philips
Across the selected sites in the REST-meta-MDD consortium, the number of retained time points after preprocessing slightly varies due to site- site-specific acquisition protocols. While most sites provided 230 time points, others contributed data with 232 or 240 time points. These variations are result of both initial protocol settings and preprocessing procedures (e.g.. discarding initial scans to ensure magnetization equilibrium). summary of time point lengths by site is given in Table A9
Table A9: Post-preprocessing time point lengths across selected sites.
Site ID
Institution
Timepoints (after preprocessing)
15
Zhongda Hospital, Southeast University
230
17
First Affiliated Hospital of Chongqing Medical University
230
19
Anhui Medical University
230
20
Southwest University
232
21
Beijing Anding Hospital, Capital Medical Uni- versity
230
22
Second Xiangya Hospital, Central South Uni-
240
versity
23
West China Hospital, Sichuan University
230
To ensure consistency in downstream dynamic sampling, all time series were uniformly truncated to the first 210 time points. This guarantees consistent sampling space across all subjects regardless of site-specific acquisition length.
We then applied sliding window with a fixed length of 70 TRs and a step size of 35 TRs. This configuration yields exactly five overlapping segments per subject, each representing a snapshot of short-term functional dynamics. These segments serve as candidate samples for evaluating structural stability and selecting representative subjects in our core-set selection framework.
We used 33 regions of interest (ROIs) associated with the default mode network (DMN), selected from the Dosenbach- 160 atlas (Dosenbach et al.) 2010) following the specification provided by Yan et al. (2019) These ROIs were identified using public scripts available at /ttpt::/tttttttt Chaogan Wawn/apperrrriieaepppppp tee htt//mmateer/ee Yan 2019 PNAS/Dos (60 and used con- sistently in REST-meta-MDD-rrlated studies.
com/
M.2 BASELINE INTRODUCTION AND PARAMETER SETTINGS
Baseline Introduction
Random: Uniformly samples instances without considering model behavior or data statis- ties.
k-Means Harttgann & Wong 1979| An unsupervised clustering algorithm that partitions data into clusters based on feature similarity, with the core-set formed by selecting samples closest to the cluster centroids.
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Table A10: List of 33 DMN-related ROIs selected from the Dosenbach- atlas.
ROI Index
ROI Type
Yeo Network (Label)
1
vmPFC
7 (DMN)
4
mPFC
(DMN)
5
aPFC
7 (DMN)
6
vmPFC
(DMN)
7
vmPFC
7 (DMN)
11
vmPFC
(DMN)
13
vmPFC
(DMN)
ACC
(DMN)
15
vIPFC
(DMN)
17
sup frontal
(DMN)
20
sup frontal
(DMN)
25
vFC inf temporal
(DMN)
63
(DMN)
72
inf temporal
7 (DMN)
73
post cingulate
(DMN)
85
precuneus post cingulate
7 (DMN)
90
(DMN)
91
inf temporal
7 (DMN)
93
post cingulate
(DMN)
94
precuneus
7 (DMN)
100
sup temporal angular gyrus
(DMN)
102
(DMN)
104
IPL
(DMN)
105
precuneus
(DMN)
108
post cingulate
(DMN)
111
post cingulate
(DMN)
112
precuneus
7 (DMN)
115
post cingulate
(DMN)
117
angular gyrus
7 (DMN)
124
angular gyrus
(DMN)
132
precuneus
(DMN)
134
IPS occipital
(DMN)
137
(DMN)
Forgetting (Toneaa et al. 2018): Ranks samples by the number of times they transition from correct to incorrect predictions during training.
Entropy (Coleman et al.
2020 Scores samples using the entropy of model output proba- bilities to reflect prediction uncertainty.
Area Under the Margin (AUM) (Pleiss et al.
2020): Computes the average margin between the true class probability and the highest conntruc probability across epochs.
2021): Measures the L2 norm between model predictions and true labels over early training epachs as proxy for example difficulty.
Example-Level L2 Norm (EL2N) Pauul et al.
Stratifies samples by importance scores (e.g., AUM) and performs balanced sampling across strata to preserve distributional coverage.
Coverage- Centric Selection (CCS) (Zheng et al. 2022):
Evolution-aware Variance (EVA) (Hong et al. 2024b): Aggregates prediction error vari- ances within early and late training windows capture evolving sample dynamics.
Balanced One-shot Subset Selection (BOSS) (Acharya al. 2024) Greedily selects subset by maximizing Beta-weighter objective over feature similarity, label variability, and difficulty-based scores.
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Parameter Settings All baseline methods are evaluated using unified training setup. The classifi- cation model is a compact residual network designed for multivariate time series inputs. It consists of stem convolution followed by three residual blocks with output channels of 32, 64, and 128, respectively. A global average pooling layer and a fully connected classifier complete the architecture. This design balances expressiveness and efficiency for medium-scale time series classification.
The model is trained for 200 epochs using the Adam optimizer with a learning rate of 0.01, weight decay of le-4, and batch size of 256. All methods, including full-data training and subset-based training, use identical configurations.
Per-sample importance scores derived from training dynamics and used evaluate a range of sampling strategies. For EVA, we compute the variance of the prediction error vector within two non-overlapping windows: epochs 100-109 and 190-199, following the original protocol.
Hyper parameters of SCLCS are optimized using grid searching in the flowing spaces:
1. Dimension of Transformer: [4, 8. 32, 64, 128, 256].
2. Head Number: [2, 4, 8, 16, 32, 64).
3. Epochs for calculating SPS: [50, 100, 150, 200].
M.3 ENVIRONMENT
Experiments are performed on an 8-GPU (H20) high-performance computing cluster provided by the Large-sces scage Instrument Sharing Platform of Southwest University.
N
LIMITATIONS
While this work establishes a new paradigm for efficient FC benchmarking, we identify several exciting avenues for future investigation that build upon our findings:
Deepening the SPS-SPI Connection: Our results demonstrate a strong empirical link between low SPS (structural stability) and effective core-set selection. However, the precise theoretical mechanism connecting the training dynamics of our encoder to the performance ranking of diverse, external SPI models warrants deeper investigation. Future work could explore this link to build a more formal bridge between learnable latent structures and statistical model behavior.
Developing an Adaptive Sampling Strategy: Our experiments show that the optimal choice between simple low-SPS ranking (SCLCS) and density- aware sampling (SCLCS Dense) is uusk-dependent A key next step is to develop heuristics or a meta- meta-lcarning framework to automatically select the optimal sampling strategy based dataset characteristics (e.g.. class structure, sample heterogeneity). removing the need for manual selection.
While our evaluation on the large-scale, het- erogeneous REST-meta-MDD dataset provides a strong test robustness, the framework's 's generalizability should be further validated. A full study of supervision (site-ID, multi-task, and more) and how SPI properties modulate task difficulty is a valuable future direction. The relationship between the RP problem and data properties is another major extension to our work. Future studies should also apply SCLCS to fMRI datasets from different clinical populations (e.g., Alzheimer's disease, ADHD), other imaging modalities, even entirely different domains of multivariate time-series analysis to establish the full scope of its applicability.
Broader Generalization and Application:
More Heterogeneous Scenarios: Simply pulling resting- state and task- Misk scans together into the contrastive loss would be problematic, the functional state changes. This poses a more complex heterogeneous data fusion challenge. Exploring model benchmarking problem on heterogeneous scan types is valuable future direction.
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THE USE OF LARGE LANGUAGE MODELS (LLMS)
In the preparation of this manuseript, we utilize Large Language Models (LLMs) in a supportive capacity. Specifically, their use is confined the following areas:
Writing and Editing: LLMs are employed to enhance the clarity, grammar, and style of the text, ensuring the manuscript's readability.
Assistance with Theorem Proofs: LLMs serves an assistive tool to verify the logical
consistency and correctness of individual steps within our mathematical derivations and proofs.
The scientific ideas, the structure of the proofs, the experimental design, and all final conclusions presented in this paper are conceived and developed entirely by the authors.
33


Reviews:
[{"review_id": "AGTuUdSAFI", "reviewer": "Reviewer_83WM", "summary": "This paper introduces an idea for performing core-set (small, representative subset of data that preserves some performance metric) selection for functional connectivity model benchmarking in neuroimaging. The core-set selection is based on statistical pairwise interaction type measures and preserving ranking among methods that use SPIs for modeling functional connectivity. They introduce a technique called SCLCS (Structure-aware Contrastive Learning for Core-set Selection)—a self-supervised Transformer framework that learns sample-specific FC structure representations, defines a score (structural perturbation score) to measure structural stability and use a density-based sampling technique to ensure the resulting core-set is both robust and diverse. \n\nThe authors show experimental results on the REST-meta-MDD dataset, where their method achieves up to 23% higher ranking consistency than other coreset selection methods with a fraction (10%) of the data.", "questions": "Are SPIs still widely used for prediction in fMRI?\n\nTheorem 1 assumes row-stochasticity of matrices, but can it be directly applied to the real valued symmetric matrices arising from SPIs? \n\nIs model ranking a valid goal?\n\nCan the authors comment on the adaptability of the method to deep learning models?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "While the concept of core-set selection is not new, to my knowledge, this is the first work that is undertaking this problem for ranking functional connectivity performance. This is the main strength of the paper. \n\nThe issue of core-set selection has been mostly ignored in neuroimaging, mainly because the datasets are generally small. However, as the number of datasets are growing in size, the number of algorithms are also getting contributed and tested, the problem of benchmarking is suddenly becoming important. Thus the overall concept that the paper proposes does make a contribution in the right direction\n\nThe overall theoretical framework of ranking preservation, the SCLCS, as well as the adapted transformer architecture is sound and is a novel contribution for this application.", "weaknesses": "The main weakness in the paper is that the ranking is based on Statistical Pairwise Interactions (SPIs). Although the authors test 130 SPIs, these are functional connectivity estimators and not end to end predictive machine learning models. SPIs are generally used in classical fMRI analyses and not widely used in modern ML based approaches including deep learning. \n\nIn modern data-driven models (graph neural nets, attention-based architectures), the functional network connectivity structure is learned jointly with metric optimization, and thus make SPI type analysis unnecessary. \n\nSince the method is mainly based on SPIs,  it has limited adaptability to non-SPI workflows/benchmarks. The model ranking objective assumes each model produces a connectivity matrix via a pairwise operator. Further, the structure-aware feature extraction is built around this notion of symmetric, subject-level matrices. Finally the evaluation metric nDCG makes sense only if multiple SPIs are given as input for comparison. The benchmarking and core-set selection strategy therefore applies directly to workflows that explicitly compute connectivity features before classification. \nThus the method may not generalize to deep learning models trained end-to-end on fMRI data, graph-neural network type approaches that infer connectivity structure and optimize it internally before prediction as well as other fMRI prediction algorithms, where the internal structure is not amenable for SPI comparison. \nThe experimental evaluation is only done on a single dataset and only two downstream tasks to evaluate SPI discriminability: brain fingerprinting (distinguishing individuals based on subject ID), which probes for fine-grained, subject-specific structures, and MDD diagnosis, which relies on cohort-level patterns.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "mAEr1536mo", "reviewer": "Reviewer_7LHN", "summary": "The paper tackles the prohibitive cost of benchmarking functional connectivity (FC) “signal processing indices” (SPIs) by reframing core-set selection as a **ranking-preservation** problem rather than single-model accuracy. It proposes **SCLCS**, a structure-aware, self-supervised framework that (i) encodes sample-wise FC structure with a modified Transformer, (ii) scores sample stability via a **Structural Perturbation Score (SPS)** over training epochs, and (iii) augments selection with **density-balanced sampling** to avoid top-k brittleness. On REST-meta-MDD (904 subjects; DMN 33 ROIs; 4,520 temporal segments), SCLCS preserves SPI rankings substantially better than nine strong baselines and maintains balanced subject/class coverage, while being orders-of-magnitude cheaper than full benchmarks.", "questions": "1. **Parcellation & preprocessing robustness.**  \n  How do core-set ranking nDCG@k and coverage metrics change under alternative parcellations (e.g., Schaefer-200) and without GSR? Please include sensitivity to window length/stride (70/35 TRs vs. others). \n2. **SPI subset bias.**  \n  Can you report results where the full-set ranking includes a stratified sample of *slow* SPIs (e.g., iterative/graphical models) to test transfer beyond <1s/sample operators? Even a small but representative slow-SPI slice would help. \n3. **Supervision choice.**  \n  Beyond subject identity, have you tried *site-ID* or *multi-task* (subject + site + MDD/HC) supervision when computing SPS? Does supervision alter SPS distributions and downstream ranking stability? \n4. **Site-aware analysis.**  \n  Please provide site-conditioned ranking preservation (per-site nDCG@k) and site-aware coverage (selected samples per site) or a leave-site-out core-set test to assess generalization under dataset shift.\n5. **Universality scope.**  \n  What is the formal class of SPIs covered by the universality claim? For statistical-test SPIs (e.g., Johansen cointegration), how does approximation error affect ranking, and can you bound nDCG degradation as a function of operator approximation error? \n6. **Compute benefits in practice.**  \n  Could you report wall-clock benchmarks (e.g., 10%/20% core-set vs. 100% full benchmark) on a standard 32–128 vCPU cluster to quantify realized speedups?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- **Well-motivated objective and metricization.**  \n  Focusing on cross-model *ranking* (not accuracy) matches the real need in SPI selection; nDCG@k is a sensible measure. \n- **Principled structure-aware selection.**  \n  SPS is theoretically grounded (mixture-driven perturbation; stationarity/ergodicity) and operationally tied to the encoder’s attention dynamics; density-balanced sampling addresses the known failure mode of top-k. \n- **Comprehensive empirical study and practicality.**  \n  The study spans two downstream tasks, nine baselines, coverage/fairness diagnostics, and compute analysis showing that a small one-time selection cost can replace ~990 CPU-days of exhaustive SPI evaluation.", "weaknesses": "1. **External validity limited by parcellation and preprocessing choices.**  \n  Experiments are confined to 33 DMN ROIs (Dosenbach-160) with global signal regression; it remains unclear whether conclusions (e.g., SPS behavior, density effects, ranking stability) hold for whole-brain parcellations (e.g., Schaefer, AAL), alternative TRs, or non-GSR pipelines.\n2. **Ground-truth ranking restricted to *fast* SPIs.**  \n  To keep evaluation tractable, the “full-set” ranking is computed on a subset of SPIs (<1s/sample). This could bias findings toward operators with particular computational/statistical properties; evidence of transfer to slower/iterative SPIs is limited.\n3. **Surrogate discriminability and stability assumptions.**  \n  Ranking relies on a discriminability score derived from Spearman correlations; SPS assumes stationarity/ergodicity and measures attention perturbations. Although supported by analyses, sensitivity to the discriminability proxy and to encoder hyperparameters (heads, depth, temperature) is not fully characterized.\n4. **Self-supervision via subject identity may conflate fingerprinting with diagnosis.**  \n  Positive pairs are temporal segments from the same subject. While this is apt for fingerprinting, its alignment with clinical separability (MDD vs. HC) is indirect; the paper partially explores label influence, but a principled study of supervision choices (subject vs. site vs. phenotype) is missing. \n5. **Site effects and dataset shift under-analyzed.**  \n  Coverage balance (subject/class) is reported, but explicit *site-aware* balance and ranking stability across sites (or leave-site-out coresets) are not provided; this is critical for multi-site rs-fMRI. \n6. **Theory–practice gap for universality claim.**  \n  The “universal approximator for SPIs” is empirically checked on 16 operators; many SPIs (e.g., cointegration tests) are statistical procedures with thresholds/optimization loops. Clarification is needed on the operator class for which approximation guarantees are intended and how approximation error propagates to ranking.\n7. **End-to-end wall-clock benefits not fully quantified.**  \n  The paper convincingly contrasts selection cost vs. exhaustive benchmarking (~990 CPU-days), but does not report actual *end-to-end* benchmarking speedups (e.g., core-set size vs. hours on a realistic cluster), which would clarify practical impact.\n\n## Minor\n- Fig. 1 caption/text: \"**Construstive** Learning\" → \"**Contrastive** Learning.\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "6D43HxkWZI", "reviewer": "Reviewer_sSb7", "summary": "This paper proposes SCLCS, a core-set selection method for comparing various functional connectivity operators based on statistical pairwise interactions (SPIs) fairly and efficiently. By leveraging the convergence stability of attention matrices, structure perturbation score (SPS), SCLCS evaluates each sample’s structural representativeness and uses this to select the representative core-set for ranking different SPIs.", "questions": "### Major\n- Please provide robustness analysis results across different-sized windows for the sliding-window approach, and see if the method is robust across the window size.\n- Please provide results on the effect of different pre-processing pipelines, at least the selection of different atlases, for the rebuttal.\n- Please provide an interpretation of the ranking result across different SPIs. Would there be a recommended SPI for constructing the connectivity matrix? If so, why would that SPI be representative in terms of neuroscientific literature?\n\n\n### Minor\n- Notational precision can be further revised. (e.g., inconsistent use of $X$ and $\\mathbf{X}$)", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Raises an unaddressed, important research question in the field of neuroimage analysis (efficient comparison between different SPIs)\n- Theoretical rigor is well aligned with the research motivation.", "weaknesses": "- Ultimately, the work could provide further insight to the neuroscience community if SCLCS could be used to derive experimental suggestions on which SPIs are suggested to be representative for constructing the functional connectivity matrices. The experiments had a limited scope on validating that the efficiency and robustness of the core-set selection of SCLCS.\n- Connectivity patterns constructed from different SPIs can be significantly susceptible to different pre/post-processing of the BOLD timeseries. Stability across different BOLD pre/post-processing could have been addressed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "skPBnQXRx3", "reviewer": "Reviewer_JU9n", "summary": "The authors propose a core-set selection framework to more effectively benchmark many SPI measures on large fMRI datasets. This method first selects a small but representative subset of subjects, and then use it to rank the SPI methods. The goal is not to maximize the accuracy of any single model, but to preserve the relative ranking between SPI methods in terms of downstream task performance.", "questions": "1. The authers mentioned that different papers can draw contradictory scientific conclusions from the same SPI. What makes you believe that you can build a unified SPI based on such agreement? \n\n2. In several settings, the “random” selection baseline performs surprisingly well, sometimes close to or even better than more carefully designed selection strategies. This is especially noticeable at certain sampling rates. How should we interpret this? Is random performing well because the dataset is already large and diverse, so almost any 30–50% subset is representative? Or is it because some SPIs are relatively insensitive to which subjects are chosen? Also, why do we sometimes see that an intermediate sampling rate (e.g., 30%) looks worse than 10% or 50%? Is there a theoretical or empirical explanation for these non-monotonic patterns?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The motivation is clear and convincing. If we can preserve the ranking of SPIs using only a small subset, then SPI selection for a known downstream task becomes easier and faster.\n\n2. The paper provides a well-defined evaluation objective. Instead of reporting absolute accuracy only, the authors explicitly measure how well the core-set preserves the global ordering of SPIs.", "weaknesses": "1. The paper claims to promote “diversity” in the core-set, but it is not fully clear which notion of diversity is being optimized. Is it diversity in learned functional structure, or in subject identity, or something else? Could this diversity sampling still cluster subjects along other confounders (for example age, site, motion level), in a way that systematically benefits certain SPIs? The authors should analyze whether the selected core-sets are imbalanced along basic covariates, and whether such imbalance correlates with SPI rankings.\n\n2. This work treats the learned attention matrix $A(X)$ as if it reflects some functional relationship between brain regions and is presented as if it were neurobiologically meaningful, but this is not yet justified. Good performance on fingerprinting or diagnosis does not prove that $A(X)$ corresponds to a biologically valid network. in principle it could simply be a discriminative mathematical signature with no stable neurophysiological interpretation. The paper would be much stronger if it (a) explained the neuroscientific meaning the authors believe $A(X)$ captures, and (b) showed visualizations or qualitative analysis of what patterns are considered “stable” for different tasks (e.g., MDD vs. CN). \n\n3. SPS is defined from training dynamics, i.e., how stable a subject’s learned structure is across epochs. However, SPS may depend on optimizer choice, learning rate schedule, or even small architectural changes in the encoder. The paper should include these sensitivity analysis. Without this, it is hard to know whether SPS is an intrinsic property of the data/subject, or just an artifact of one specific training run.\n\n4. All experiments are built around one clinical setting (MDD). This raises several questions:   \nWould the method still work in a setting where each subject has multiple different scan types (e.g., resting-state fMRI and task fMRI)? If you try to pull all scans from the same subject together in the contrastive loss, does the approach still identify “stable structure,” or does it break because the functional state changes?   \nWhat happens in datasets where each subject only has a single scan (no multiple time segments for contrastive learning)? Is the method still applicable, or does it fundamentally rely on repeated measures per subject?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)