Accelerating Benchmarking of Functional Connectivity Modeling via Structure-aware Core-set Selection

AI summary

Overview

Research area: Machine learning for neuroimaging — specifically core-set selection and benchmarking of functional connectivity (FC) modeling methods, applied to resting-state fMRI (arXiv:2602.05667v1 [cs.LG], 05 Feb 2026, by Ling Zhan, Zhen Li, Junjie Huang, and Tao Jia).

Technical level: Advanced — the paper combines Transformer attention theory, ranking-preserving subset selection, contrastive learning, and empirical evaluation over 130 statistical pairwise interaction (SPI) operators.

Scope: The paper formalizes and solves the problem of selecting a small, representative subset of fMRI samples whose sole purpose is to preserve the relative performance ranking of FC operators, so that large-scale benchmarking becomes computationally feasible.

What This Paper Is About

Benchmarking the hundreds of candidate functional connectivity (FC) modeling methods — called statistical pairwise interactions (SPIs) — against large-scale fMRI datasets requires evaluating every model–data pairing, and this combinatorial explosion makes exhaustive evaluation computationally prohibitive. The authors reframe the task: instead of finding a core-set that trains one predictive model well, they search for a small subset of subjects that preserves the relative ranking of FC operators that would be obtained on the full dataset. The goal is to turn large-scale operator comparison into a routine, affordable pre-analysis step rather than an impractical one-off effort.

Key Contributions

1. The paper formulates core-set selection for efficient FC operator (SPI) benchmarking as a ranking-preservation problem, rather than the single-model training-proxy objective targeted by most prior core-set work.
2. It proposes SCLCS (Structure-aware Contrastive Learning for Core-set Selection), a self-supervised framework that selects structurally stable and distributionally diverse samples for ranking-based benchmarking, with a density-aware variant called SCLCS Dense.
3. It provides a universal approximation result for continuous SPI mappings (Theorem 2) for an adaptively weighted multi-head attention family, and introduces the Structural Perturbation Score (SPS), a new use of attention dynamics during training to quantify structural heterogeneity in samples.
4. It demonstrates that SCLCS enables reliable benchmarking at a fraction of the computational cost, with code publicly available at https://github.com/lzhan94swu/SCLCS.

Main Findings

• Ranking preserved with 10% of the data: 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 core-set selection methods by up to 23.2% in ranking consistency (nDCG@k).

• Brain fingerprinting results (nDCG@k reported as percentage, ×100): Under the paper's evaluation, SCLCS achieved nDCG@5 of 81.21 ± 2.86 and nDCG@10 of 66.54 ± 1.10 at a sampling ratio of 0.1; at 0.5 it achieved nDCG@5 of 72.68 ± 20.83 and nDCG@20 of 70.13 ± 1.57. The authors note SCLCS is stronger with lower variance at sampling ratios 0.1 and 0.5.

• Diversity correction at moderate sampling ratios: At the moderate ratio of 0.3, SCLCS degrades while SCLCS Dense performs best (nDCG@5 of 79.18 ± 6.29, nDCG@10 of 73.45 ± 1.42, nDCG@20 of 72.96 ± 3.35). The authors interpret this as support for Theorem 3: when stability ranking alone is insufficient, explicitly promoting structural diversity provides a corrective signal.

• Naïve attention averaging fails: The SPS MHA variant, which uses plain multi-head attention averaging, performs poorly — for example nDCG@5 of 1.32 ± 2.07, nDCG@10 of 2.92 ± 1.13, and nDCG@20 of 1.21 ± 1.04 at ratio 0.1 — consistent with Theorem 1 on interference of averaged attention.

• Theoretical guarantees: Theorem 1 shows that naïve averaging of row-stochastic attention matrices expands support beyond any single head's mask and inflates entropy; Theorem 2 establishes universal approximation of continuous stochastic SPIs by the adaptive fusion family; Theorem 3 proves a persistent positive bias of top-k selection when clusters separate; Theorem 4 and Theorem 5 (Appendices F and G) provide coverage and benchmarking-consistency guarantees for the density-balanced scheme; Proposition 1 links expected perturbation magnitude to the Gini impurity of the underlying prototype mixture.

• MDD diagnosis results (partial in the available text): Table 3 reports the MDD diagnosis ranking task but is truncated in the provided content; the SCLCS rows for that table are not visible in the supplied text. Visible baseline entries include EVA (nDCG@5 of 66.81 ± 9.12 at ratio 0.3) and BOSS (nDCG@5 of 79.57 ± 16.62 at ratio 0.5), with the table cut off mid-entry at BOSS nDCG@10 at ratio 0.5.

• Dataset scope: Evaluation uses REST-meta-MDD, a multi-site resting-state fMRI collection of 1,642 subjects from 17 sites; the study focuses on a subset of 904 subjects, and sliding-window segmentation yields 4,520 samples across 7 sites (site-level counts of 335, 410, 245, 2395, 720, 190, and 225 samples; overall 458 HC, 446 MDD, 330 male, 574 female; age range 18–65; education range 3–21 years).

• Baseline comparison: Evaluation covers 9 baselines: Random, k-Means, Forgetting score, Entropy, EL2N, AUM, CCS, EVA, and BOSS — the latter 7 of which are state-of-the-art core-set selection methods.

Methodology in Plain English

The authors treat each fMRI record as a set of brain-region tokens and use a Transformer to learn a sample-specific synchronization structure, represented by an attention matrix over regions. They show mathematically that simply averaging the attention heads blurs distinct structural patterns, so they instead learn adaptive weights that combine heads — and prove this adaptive version can approximate any continuous FC operator mapping on compact domains. During training, they track how much each sample's learned structure changes from one epoch to the next; this fluctuation is the Structural Perturbation Score (SPS). The intuition is that samples representing common, foundational connectivity patterns stay stable, while atypical or noisy samples fluctuate. The primary selection rule is to rank samples by SPS and take the lowest scores.

Because top-k selection by a single score can over-select from dense clusters and distort the ranking of operators (shown in Theorem 3), the authors add a density-aware correction: they first discard the most unstable samples (the top β quantile of SPS), then fit a Gaussian kernel density estimate on the SPS values of the remaining pool and weight samples inversely to their local density, sampling without replacement. The encoder is trained with an identity-supervised contrastive objective — two temporal segments from the same subject form positive pairs, and samples from other subjects in the batch form negatives — which encourages stable, person-specific "brain fingerprints" without depending on a downstream task label. For evaluation, each SPI is scored by how well its FC matrices separate within-class from between-class pairs using Spearman's rank correlation, producing an SPI ranking. Core-set quality is the nDCG@5/10/20 agreement between the core-set ranking and the full-dataset ranking. The authors also state that SCLCS is a pre-analysis acceleration tool making large-scale benchmarking feasible, not a method for the final neuroscientific discovery task.

Why This Matters

Impact on research: The work makes large-scale operator comparisons a feasible and integral part of computational neuroscience, addressing a reproducibility problem in which different SPIs yield divergent FC topologies and different scientific conclusions. Prior comprehensive libraries such as pyspi contain hundreds of SPIs, which magnifies the scale of the selection problem; this paper offers a principled way to shrink the evaluation without losing the ordering that matters. The evaluation was performed on an 8-GPU (H20) high-performance computing cluster provided by the Large-scale Instrument Sharing Platform of Southwest University.

Real-world applications (as grounded in the paper's setting):

• Rapid pre-analysis model selection in FC pipelines, where a researcher first benchmarks candidate SPIs on a small core-set and then evaluates the selected SPI(s) on the full dataset.
• Multi-site fMRI studies, where the authors note heterogeneity across acquisition sites; REST-meta-MDD spans 17 sites.
• Clinical research into major depressive disorder, one of the two downstream tasks used alongside brain fingerprinting.
• Brain fingerprinting research that relies on distinguishing individuals by subject ID from fine-grained, subject-specific structure.

Industry relevance: Lowering the computational cost of exhaustive model–data pairings matters to neuroimaging software and tooling ecosystems (the paper cites pyspi as a comprehensive SPI library), to clinical-trial and biobank-scale neuroimaging analysis, and to HPC and cloud providers whose costs scale with the number of model–data evaluations.

Future Directions

• Extending to other score-based selectors: The authors note the density-balanced scheme is applicable to other score-based methods by replacing SPS with a different metric (Appendix J), which opens the question of how far the density correction generalizes.
• Broadening beyond SPIs as the validation case: The paper frames SPIs as one well-defined instantiation of FC operator benchmarking; whether the approach transfers to other FC operator families is left open.
• Standing theoretical assumptions: Theorem 2's guarantee is for continuous targets on compact domains, and the authors note that SPIs using discrete thresholds require either a continuous relaxation (e.g., finite-temperature softmax or sigmoid gates) or a limiting argument to justify the hard-threshold limit.
• Robustness of SPS estimation: The theoretical reliability of SPS depends on stationarity and ergodicity assumptions (Lemma 1), which the authors support empirically with a convergence analysis in Appendix K.2; sensitivity of the score under other training regimes remains a question the appendices address rather than the main text.

Target Audience

This paper is best suited to machine learning and neuroimaging researchers working on core-set selection, data-efficient benchmarking, or functional connectivity methodology; to computational neuroscientists who need to compare large suites of connectivity operators under practical compute budgets; and to practitioners building reproducible fMRI analysis pipelines. The theoretical content (universal approximation, persistent-bias results) will particularly interest readers with a machine learning theory background, while the density-aware sampling procedure and public code make the empirical portion accessible to applied researchers who want to reproduce or adapt the framework.

Authors’ 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 Structure-aware Contrastive Learning for Core-set Selection (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 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 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