Flattening the Connectome Spectrum: A Spectral Filter for FC Induces a Pretraining Target for fMRI Encoders

Giovanni Marraffini; Victoria Shevchenko; Carlo Alberto Barbano; Demian Wassermann

cs.AISep 29, 2026

Flattening the Connectome Spectrum: A Spectral Filter for FC Induces a Pretraining Target for fMRI Encoders

Authors: Giovanni Marraffini, Victoria Shevchenko, Carlo Alberto Barbano, Demian Wassermann

Organizations: UNITO · MIND

Abstract

Self-supervised pretraining reshaped prediction in language and vision, and brain foundation models (BFMs) inherited its promise. Representations learned from large unlabelled corpora should capture individual functional dynamics and generalise across cohorts. However, kernel ridge regression (KRR) fitted on functional connectivity (FC) matrices still predicts individual phenotypes more accurately than any BFM we tested. In this paper, we show that KRR is weighted by the eigenvalues of the FC which are miscalibrated for phenotype prediction. We apply an efficient spectral filter to recalibrate the eigenvalues of each subject's FC matrix, enabling the model to exploit more inter-individual variance. Across the 5 datasets, 11 parcellations and 6 prediction targets we tested, we match or exceed the KRR baseline. Based on this finding, we then pretrain a small encoder model on about 4,000 hours of fMRI from 162 open datasets, whereby we align the pairwise similarities between the embeddings of recording snippets with those between the recalibrated connectomes. Our model performs on par with the best of the 6 published BFMs we tested while having an order of magnitude fewer parameters. Our encoder performs better than FC on short scans and in smaller cohorts, especially in fingerprinting. We release the pretrained model weights, the code and the pretraining data, preprocessed and parcellated.

Figures & tables

Figure 1: (a) The eigenvalue spectrum of the FCs from HCP-YA ( Van Essen et al., 2013 ) by rank, averaged over the

955

subjects, before (

\alpha=1

, red) and after raising the eigenvalues to

\alpha^{*}

(blue). The transform is concave with a fixed point at

\lambda=1

, so eigenvalues are pushed onto an increasingly compact support around 1, with their order preserved. (b) The distribution of eigenvalues pooled over the same

955

subjects, from

\alpha=1

(red, raw FC) down to

\alpha=0.05

; the one at

\alpha^{*}

is blue. Each is the histogram of

\log_{10}\lambda^{\alpha}

; lowering

\alpha

pulls the distribution toward

\lambda=1

from both sides (Appendix C ).

Figure 2: The recalibrated connectome $\mathbf{\Sigma}^{\alpha}$ of one HCP-YA subject at Schaefer-400 for $\alpha=0$ , $0.1$ , $\alpha^{*}$ , $0.6$ and $1$ , each scaled by its largest eigenvalue so that one colour scale serves the row; $\alpha=1$ is raw FC and $\alpha=0$ the identity.

Figure 3: The kernel-alignment objective. Each timepoint of the window becomes one token through a linear projection, and a prepended [CLS] token carries the loss. The teacher is the $\mathrm{FC}^{\alpha^{*}}$ of the entire recording, vectorised, centred and scaled to unit norm. Every recording of a batch of $B$ goes through both lanes, and the $B$ embeddings and the $B$ teacher vectors each define a $B\times B$ kernel, $[\mathbf{K}_{s}]_{ij}=\mathbf{e}_{i}^{\top}\mathbf{e}_{j}$ and $[\mathbf{K}_{t}]_{ij}=\mathbf{z}_{i}^{\top}\mathbf{z}_{j}$ , and the loss is one minus their centred alignment (Equation 5 ).

HCP-YA, resting state
parcellation	FC ( $\alpha{=}1$ )	$\mathrm{FC}^{\alpha^{*}}$	$\Delta$
Schaefer-100	$0.505\pm 0.088$	$0.575\pm 0.081^{*}$	$+0.070$
Schaefer-400	$0.543\pm 0.083$	$\mathbf{0.627\pm 0.080}^{*}$	$+0.084$
AOMIC-ID1000, movie watching
Schaefer-100	$0.310\pm 0.091$	$0.409\pm 0.083^{*}$	$+0.099$
Schaefer-400	$0.348\pm 0.084$	$\mathbf{0.432\pm 0.081}^{*}$	$+0.084$

Table 1:

\mathrm{FC}^{\alpha^{*}}

against raw FC on the same folds, correlation-kernel KRR. Pearson

r

, mean

\pm

std over folds;

\Delta

is the paired difference and ∗ marks

p_{\mathrm{NB}}<0.05

(Appendix G ).

modes	raw $\lambda$ ( $\alpha{=}1$ )	$\lambda^{\alpha^{*}}$
top-1	$0.321\pm 0.110$	$0.321\pm 0.110$
top-20	$0.544\pm 0.079$	$0.610\pm 0.079$
top-40	$0.542\pm 0.079$	$0.606\pm 0.082$
all 400	$0.542\pm 0.079$	$0.624\pm 0.077$

Table 2: Cognitive composite from the top-

k

eigenvectors of each subject’s FC, with raw eigenvalues and with eigenvalues raised to

\alpha^{*}

. Mean

\pm

std over folds (Appendix F ).

Figure 4: Learning curves on HCP-YA Schaefer-400 for

\mathrm{FC}^{\alpha^{*}}

and raw FC. (a) Against the number of training subjects, at the full scan. (b) Against the duration of the first contiguous minutes of each scan, with all

939

subjects that have complete runs. Bands are the standard deviation across folds; protocol details in Appendix B .

reads the full scan
		input		HCP-YA			CoRR
encoder	params	parcels	scan	composite	sex	age	fingerprint
$\mathrm{FC}^{\alpha^{*}}$ (ours)	79.8k	Sch-400	57.6m	$\mathbf{0.642\pm.078}$ ∗	$\mathbf{0.99\pm.00}$ ∗	$\mathbf{0.63\pm.04}$	$\mathbf{0.895\pm.009}$ ∗
FC	79.8k	Sch-400	57.6m	$0.559\pm.083$	$0.97\pm.01$	$0.62\pm.03$	$0.762\pm.010$
F-BERT-8M (ours)	8.1M	Sch-450	57.6m	$\mathbf{0.502\pm.083}$ ∗	$\mathbf{0.96\pm.02}$	$\mathbf{0.61\pm.03}$	$\mathbf{0.841\pm.009}$ ∗
F-BERT-1M (ours)	0.85M	Sch-450	57.6m	$\underline{0.488\pm.090}$ ∗	$0.94\pm.02$	$\underline{0.61\pm.04}$	$\underline{0.670\pm.012}$ ∗

Table 3: Frozen linear-kernel probe (Section 3.1 ): HCP-YA cognitive composite (Pearson

r

), sex and age (AUC), and CoRR test–retest fingerprint accuracy, mean

\pm

std over folds. Within each group the best value per column is bold and, among the foundation models, the second best is underlined; ∗ marks a paired difference with

p<0.05

(Table 9 ), against FC at the same scan length for

\mathrm{FC}^{\alpha^{*}}

and against the best published model of the group for our encoders. params : encoder weights, or the probe’s ridge weights for the FC rows. Parcellations and windows are those each model was released for (Appendix I ); § Brain-Semantoks covers the recording as

16

evenly spaced

200

s crops whose embeddings are averaged to match the protocol of its released probe.

Figure 5: Two targets of Table 3 : (a) HCP-YA cognitive composite and (b) CoRR identification accuracy, where chance is

1/391

. Error bars are the std over folds in (a) and a subject bootstrap in (b). Blue is FC-derived, orange is ours, grey is published.

	subjects
min	$100$	$150$	$250$	$350$	$700$	all
1.2	$+0.17\pm 0.44$	$+0.15\pm 0.35$	$+0.10\pm 0.25$	$+0.12\pm 0.23$	$+0.09\pm 0.14$ ∗	$+0.09\pm 0.11$ ∗
2.4	$+0.21\pm 0.39$	$+0.18\pm 0.34$	$+0.13\pm 0.20$ ∗	$+0.15\pm 0.20$ ∗	$+0.08\pm 0.11$ ∗	$+0.06\pm 0.09$ ∗
4.8	$+0.22\pm 0.37$ ∗	$+0.19\pm 0.32$ ∗	$+0.12\pm 0.22$	$+0.09\pm 0.17$	$+0.03\pm 0.09$	$+0.03\pm 0.08$
9.6	$+0.22\pm 0.38$ ∗	$+0.15\pm 0.29$	$+0.09\pm 0.19$	$+0.06\pm 0.16$	$+0.00\pm 0.08$	$-0.00\pm 0.07$
19.2	$+0.14\pm 0.40$	$+0.09\pm 0.25$	$+0.06\pm 0.17$	$+0.02\pm 0.14$	$-0.01\pm 0.08$	$-0.02\pm 0.06$

Table 4: Gain of F-BERT-1M over raw FC on the cognitive composite by scan length (rows) and number of subjects (columns), mean

\pm

std of the paired per-fold difference under the probe of Table 3 ; ∗ means one-sided

p_{\mathrm{NB}}<0.05

in favour of the encoder. Green is a gain, red a loss.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: The scaled eigenvectors

\lambda_{i}\mathbf{v}_{i}

(left) and

\lambda_{i}^{\alpha^{*}}\mathbf{v}_{i}

(right) of the mean HCP-YA Schaefer-400 spectrum in a random three-dimensional projection, both drawn at one scale, set so the shaded sphere of radius

\lambda_{20}^{\alpha}

is the same size in each. In raw FC a few modes extend far beyond the sphere and the remaining modes are shorter than a small fraction of its radius; after the transform no mode exceeds four sphere radii.

Figure 7: The geodesic and heat-kernel interpretations on the

955

HCP-YA Schaefer-400 spectra. (a) Eigenvalues of the mean spectrum along the geodesic

\mathbf{\Sigma}^{\alpha}

, straight lines in

\log\lambda

from

1

\alpha=0

\lambda_{i}

\alpha=1

. (b) Log-Euclidean distance of

\mathbf{\Sigma}^{\alpha}

from the identity and from the raw matrix, as fractions of

d(\mathbf{I},\mathbf{\Sigma})

; both are linear in

\alpha

. (c) Participation ratio

Z(t)^{2}/Z(2t)

and first-to-twentieth eigenvalue ratio

(\lambda_{1}/\lambda_{20})^{t}

against diffusion time, means over subjects. The dotted line is

\alpha^{*}

in every panel.

Figure 8: Two of the criteria of Section 3.3 on HCP-YA at Schaefer-400, from the same eigendecompositions and folds. (a) Cognitive composite under the correlation-kernel KRR, mean over the

200

folds with the standard deviation across folds as the bar. (b) Centred kernel-target alignment with the cognitive composite inside training folds, mean and standard deviation over the

200

folds; the dashed vertical line is its continuous optimum

\alpha_{\mathrm{A}}=0.387

. In each panel the dashed curve is a variance-weighted quadratic fit over

\alpha\in[0.10,0.75]

with its peak marked, and the dotted vertical line is

\alpha^{*}

transform	$r$
$\mathrm{FC}^{\alpha^{*}}$	$\mathbf{0.628\pm 0.077}$
log-Euclidean	$0.586\pm 0.085^{*}$
tangent space, harmonic reference	$0.578\pm 0.083^{*}$
raw FC	$0.545\pm 0.083^{*}$
partial correlation	$0.389\pm 0.100^{*}$

Appendix

Table 5:

\mathrm{FC}^{\alpha^{*}}

against raw FC and three standard transformations. HCP-YA Schaefer-400, cognitive composite, correlation-kernel KRR,

10\times 10

family-aware CV, mean

\pm

std over the

100

folds. ∗ marks a row significantly below

\mathrm{FC}^{\alpha^{*}}

on shared folds,

p_{\mathrm{NB}}<0.05

under the corrected resampled

t

-test ( Nadeau & Bengio, 2003 ) .

transform	$r$	transform	$r$
$\mathrm{FC}^{0.25}$	$0.622\pm 0.079$	Fisher $z$ of the edges	$0.555\pm 0.082$
$\mathrm{FC}^{0.5}$ (matrix square root)	$0.619\pm 0.077$	degree normalisation	$0.554\pm 0.084$
$\mathrm{FC}^{0.75}$	$0.589\pm 0.080$	raw FC ( $\alpha{=}1$ )	$0.545\pm 0.083$
log-Euclidean ( $\alpha\to 0$ )	$0.586\pm 0.085$	PCA, $300$ components	$0.539\pm 0.086$
tangent, harmonic reference	$0.578\pm 0.083$	factor analysis / ICA	$0.510\pm 0.081$ / $0.503\pm 0.084$
tangent, corpus reference	$0.578\pm 0.086$	Cholesky / log-Cholesky	$0.503\pm 0.090$ / $0.502\pm 0.094$

Appendix

Table 6: Transforms of the HCP-YA Schaefer-400 FC matrix, cognitive composite, correlation-kernel KRR,

10\times 10

family-aware CV, mean

\pm

std over folds. Power-Euclidean rows and the log-Euclidean map are per-subject; tangent maps use a group reference (harmonic mean or corpus mean); the remaining rows are covariance estimators, edge normalisations and subspace reductions.

HCP-YA, resting state, $N{=}955$
parcellation	FC ( $\alpha{=}1$ )	$\mathrm{FC}^{\alpha^{*}}$	$\Delta$	$p_{\mathrm{NB}}$
Schaefer-100	$0.505\pm 0.088$	$0.575\pm 0.081$	$+0.070$	$1{\times}10^{-6}$
Schaefer-200	$0.519\pm 0.080$	$0.595\pm 0.078$	$+0.076$	$2{\times}10^{-8}$
Schaefer-300	$0.527\pm 0.084$	$0.618\pm 0.077$	$+0.090$	$2{\times}10^{-10}$
Schaefer-400	$0.543\pm 0.083$	$\mathbf{0.627\pm 0.080}$	$+0.084$	$2{\times}10^{-9}$
Schaefer-400 + Tian-S3	$0.519\pm 0.083$	$0.574\pm 0.083$	$+0.055$	$5{\times}10^{-5}$

Appendix

Table 7: Table 1 at every parcellation. Pearson

r

, mean

\pm

std over the

200

fold-level values of a

20\times 10

replicated CV.

\Delta

is the paired gain on shared folds and

p_{\mathrm{NB}}

its corrected resampled

t

-test ( Nadeau & Bengio, 2003 ) . Sixteen HCP-YA recordings are shorter than the rest; the same table restricted to the

939

subjects with four complete runs is Appendix H .

parcellation	FC ( $\alpha{=}1$ )	$\mathrm{FC}^{\alpha^{*}}$	$\Delta$	$p_{\mathrm{NB}}$
HCP-YA, resting state, $N{=}939$
Schaefer-100	$0.494\pm 0.086$	$0.567\pm 0.083$	$+0.073$	$3{\times}10^{-7}$
Schaefer-200	$0.509\pm 0.086$	$0.588\pm 0.080$	$+0.079$	$2{\times}10^{-7}$
Schaefer-300	$0.522\pm 0.088$	$0.614\pm 0.079$	$+0.092$	$6{\times}10^{-9}$
Schaefer-400	$0.540\pm 0.085$	$\mathbf{0.624\pm 0.080}$	$+0.083$	$3{\times}10^{-8}$

Appendix

Table 8: Table 1 restricted to the

939

HCP-YA subjects whose four runs are all complete. AOMIC is unchanged and omitted.

encoder	pooled $r$ (Table 3 )	per-fold $r$
$\mathrm{FC}^{\alpha^{*}}$	$0.642$	$0.629\pm 0.078$
FC	$0.559$	$0.550\pm 0.083$
F-BERT-8M	$0.502$	$0.520\pm 0.083$
F-BERT-1M	$0.488$	$0.491\pm 0.090$
Brain-Semantoks	$0.441$	$0.437\pm 0.095$
BrainMass	$0.423$	$0.433\pm 0.094$

Appendix

Table 9: Paired tests behind Table 3 , HCP-YA cognitive composite. Table 3 reports the correlation of the pooled out-of-fold predictions, averaged over the

20

repetitions; a paired test needs one value per fold, so it uses the

200

per-fold correlations of the same runs, whose mean is given next to the pooled value (top). Bottom: for each pair and target, the difference of per-fold means and its corrected resampled

t

-test

p_{\mathrm{NB}}

( Nadeau & Bengio, 2003 ) , over

200

folds for the composite and

100

(

10\times 10

) for sex and age; for the CoRR fingerprint, the difference in identification accuracy over the

782

shared scans and an exact McNemar test on the discordant scans. Bold: first encoder significantly ahead (

p<0.05

), the rule that places the asterisks of Table 3 .

reads the full scan
	input			AOMIC-ID1000			ABIDE-I
encoder	params	parcels	scan	cognition	sex	age	autism
$\mathrm{FC}^{\alpha^{*}}$ (ours)	79.8k	Sch-400	full	$\mathbf{0.430\pm.087}$ ∗	$\mathbf{0.97\pm.02}$ ∗	$\mathbf{0.55\pm.04}$	$\mathbf{0.778\pm.083}$
FC	79.8k	Sch-400	full	$0.368\pm.095$	$0.90\pm.03$	$0.53\pm.04$	$0.751\pm.092$
F-BERT-8M (ours)	8.1M	Sch-450	full	$\mathbf{0.364\pm.087}$	$\mathbf{0.92\pm.03}$ ∗	$0.52\pm.04$	$0.671\pm.014$
F-BERT-1M (ours)	0.85M	Sch-450	full	$\underline{0.325\pm.092}$	$0.88\pm.03$	$\underline{0.53\pm.04}$	$\underline{0.707\pm.047}$

Appendix

Table 10: The frozen probe of Table 3 on AOMIC-ID1000 (movie watching,

n{=}874

10.6

min; cognition is Pearson

r

against the Intelligence Structure Test composite, sex and age are AUC, subject-level CV) and ABIDE-I (autism diagnosis, AUC, site-grouped CV on the all-model intersection,

n{=}158

), with the groups, input columns, bold, underline and asterisk rules of Table 3 (paired tests in Table 12 ). “full” is the whole recording of each cohort; the window rows read the first minutes stated. § As in Table 3 .

encoder	params	parcels	scan	ADHD
reads the full scan
$\mathrm{FC}^{\alpha^{*}}$ (ours)	79.8k	Sch-400	full	$\mathbf{0.565\pm.007}$ ∗
FC	79.8k	Sch-400	full	$0.560\pm.009$
F-BERT-8M (ours)	8.1M	Sch-450	full	$0.504\pm.004$
F-BERT-1M (ours)	0.85M	Sch-450	full	$\underline{0.523\pm.020}$
Brain-Semantoks	63M	Sch-457	full §	$\mathbf{0.557\pm.002}$

Appendix

Table 11: ADHD-200 diagnosis (AUC) under the frozen probe of Table 3 ,

n{=}298

over two acquisition sites, site-grouped CV; groups, bold, underline and asterisk rules as in Table 10 (paired tests in Table 12 ). BrainMass, BrainHarmonix and both BrainLM models are absent because their inputs cover only one of the two sites, so no site-grouped fold can be formed.

encoder	pooled $r$ (Table 10 )	per-fold $r$
$\mathrm{FC}^{\alpha^{*}}$	$0.430$	$0.422\pm 0.087$
FC	$0.368$	$0.366\pm 0.095$
F-BERT-8M	$0.364$	$0.366\pm 0.087$
F-BERT-1M	$0.325$	$0.329\pm 0.092$
Brain-Semantoks	$0.279$	$0.281\pm 0.094$
BrainMass	$0.303$	$0.303\pm 0.105$

Appendix

Table 12: Paired tests behind Table 10 , AOMIC-ID1000 cognition (

n{=}874

), as in Table 9 : pooled

r

of the table against the mean of the

200

per-fold correlations (top), and per pair and target the difference of per-fold means with its corrected resampled

t

-test (bottom):

200

folds for AOMIC cognition,

100

for AOMIC sex and age,

30

site-grouped folds for ABIDE-I (

10

repetitions of

4

site folds, those whose held-out site has one class skipped; test fraction

1/4

in the correction) and

20

for ADHD-200 (

10

repetitions over

2

sites, test fraction

1

). Bold: first encoder significantly ahead (

p<0.05

), the rule that places the asterisks of Table 10 ; n/r where one encoder cannot be scored on ADHD-200 (see Table 11 ).

Figure 9: The KL objective of Equation 6 . The same student and teacher as Figure 3 ; each recording’s row of similarities is turned into a distribution over the other recordings in the batch by a temperature-scaled softmax on both sides, and the two distributions are matched with a KL divergence.

objective	$B=128$	$B=256$	$B=1024$
KL (Eq. 6 )	$0.461\pm 0.091$	$0.442\pm 0.088$	$0.413\pm 0.095$
CKA (Eq. 5 )	$0.490\pm 0.090$	not run	$\mathbf{0.510\pm 0.086}$

Appendix

Table 13: Objective against batch size,

1

M encoder, HCP-YA cognitive composite, windowed protocol (

144

s windows averaged per subject, linear-kernel ridge,

20\times 10

family-aware CV), best checkpoint of each run.

objective	protocol	$1$ M ( $128$ d, $4$ L)	$8$ M ( $384$ d, $8$ L)
CKA	windowed	$0.510\pm 0.086$	$0.541\pm 0.083$
KL	windowed	$0.461\pm 0.091$	$0.486\pm 0.088$
CKA	one sequence	$0.488\pm 0.090$	$0.502\pm 0.083$
KL	one sequence	$0.453\pm 0.089$	$0.426\pm 0.105$

Appendix

Table 14: Scaling, HCP-YA cognitive composite. Windowed protocol as in Table 13 , and the whole recording read as one sequence as in Table 3 .

Figure 10: Cognitive composite on HCP-YA, linear-kernel ridge probe of Table 3 , pooled out-of-fold

r

. (a) Against the number of subjects in a random subsample, full scan,

10

-fold family-aware CV within the subsample; points are the mean over

20

subsamples and bands their standard deviation. (b) Against the duration read from the start of each recording,

20\times 10

family-aware CV; bands are the standard deviation over the

200

folds. The encoder points at

2.4

and

57.6

min are the cells of Table 3 . FC is at Schaefer-400 at every duration, whereas its

2.4

min row in Table 3 is at Sch-450, the encoders’ input; subjects shorter than a duration are dropped from it (

939

remain at

57.6

min). Brain-Semantoks reads at

\mathrm{TR}=2

s and is shown at its own durations.

	subjects
min	$100$	$150$	$250$	$350$	$500$	$700$	all
1.2	$+0.17\pm 0.44$	$+0.15\pm 0.35$	$+0.10\pm 0.25$	$+0.12\pm 0.23$	$+0.09\pm 0.18$	$+0.09\pm 0.14$ ∗	$+0.09\pm 0.11$ ∗
2.4	$+0.21\pm 0.39$	$+0.18\pm 0.34$	$+0.13\pm 0.20$ ∗	$+0.15\pm 0.20$ ∗	$+0.09\pm 0.14$ ∗	$+0.08\pm 0.11$ ∗	$+0.06\pm 0.09$ ∗
4.8	$+0.22\pm 0.37$ ∗	$+0.19\pm 0.32$ ∗	$+0.12\pm 0.22$	$+0.09\pm 0.17$	$+0.05\pm 0.12$	$+0.03\pm 0.09$	$+0.03\pm 0.08$
9.6	$+0.22\pm 0.38$ ∗	$+0.15\pm 0.29$	$+0.09\pm 0.19$	$+0.06\pm 0.16$	$+0.02\pm 0.11$	$+0.00\pm 0.08$	$-0.00\pm 0.07$
19.2	$+0.14\pm 0.40$	$+0.09\pm 0.25$	$+0.06\pm 0.17$	$+0.02\pm 0.14$	$+0.01\pm 0.11$	$-0.01\pm 0.08$	$-0.02\pm 0.06$

Appendix

Table 15: Gain of F-BERT-1M over raw FC on the cognitive composite by scan length (rows) and number of subjects (columns), HCP-YA Sch-450: mean

\pm

std of the paired per-fold difference under the probe of Table 3 ; ∗ one-sided

p_{\mathrm{NB}}<0.05

in favour of the encoder. Green is a gain, red a loss. F-BERT-8M in Table 16 , surfaces in Figure 11 .

	subjects
min	$100$	$150$	$250$	$350$	$500$	$700$	all
1.2	$+0.18\pm 0.41$	$+0.12\pm 0.36$	$+0.09\pm 0.24$	$+0.12\pm 0.21$ ∗	$+0.10\pm 0.17$ ∗	$+0.12\pm 0.14$ ∗	$+0.12\pm 0.10$ ∗
2.4	$+0.21\pm 0.39$	$+0.15\pm 0.33$	$+0.10\pm 0.20$	$+0.12\pm 0.18$ ∗	$+0.06\pm 0.14$	$+0.07\pm 0.11$ ∗	$+0.05\pm 0.08$ ∗
4.8	$+0.20\pm 0.38$	$+0.18\pm 0.30$ ∗	$+0.10\pm 0.20$	$+0.07\pm 0.17$	$+0.04\pm 0.13$	$+0.04\pm 0.09$	$+0.03\pm 0.06$
9.6	$+0.20\pm 0.37$	$+0.13\pm 0.29$	$+0.06\pm 0.18$	$+0.05\pm 0.16$	$+0.01\pm 0.11$	$+0.00\pm 0.08$	$+0.00\pm 0.06$
19.2	$+0.11\pm 0.38$	$+0.11\pm 0.24$	$+0.05\pm 0.17$	$+0.02\pm 0.14$	$-0.00\pm 0.10$	$-0.01\pm 0.08$	$-0.01\pm 0.06$

Appendix

Table 16: As Table 15 , for F-BERT-8M minus raw FC.

F-BERT-1M minus FC
	subjects
min	$100$	$150$	$200$	$250$	$300$	all
0.7	$-0.17\pm 0.04$	$-0.16\pm 0.03$	$-0.15\pm 0.02$	$-0.14\pm 0.02$	$-0.15\pm 0.01$	$-0.14\pm 0.00$
1.3	$-0.08\pm 0.04$	$-0.09\pm 0.03$	$-0.09\pm 0.01$	$-0.09\pm 0.02$	$-0.10\pm 0.02$	$-0.10\pm 0.00$
2	$-0.06\pm 0.05$	$-0.07\pm 0.04$	$-0.07\pm 0.02$	$-0.07\pm 0.02$	$-0.08\pm 0.01$	$-0.09\pm 0.00$
2.7	$-0.06\pm 0.04$	$-0.06\pm 0.04$	$-0.07\pm 0.03$	$-0.07\pm 0.02$	$-0.07\pm 0.01$	$-0.08\pm 0.00$

Appendix

Table 17: Gain of each encoder over raw FC in CoRR identification accuracy by scan length (rows) and number of subjects (columns), Sch-450: mean

\pm

std of the difference over

20

random subject subsets shared by both; ∗ one-sided paired

t

-test

p<0.05

in favour of the encoder. Scans shorter than the row’s length are dropped, so the

6

-minute row has

262

subjects; – where the column exceeds them.

Figure 11: Cognitive composite (pooled out-of-fold

r

, probe of Table 3 ) over scan length and number of subjects, HCP-YA Sch-450, shown as the higher of raw FC and the encoder at each cell, coloured by which one is ahead; Tables 15 and 16 give the paired differences.

parcellation	FC ( $\alpha{=}1$ )	$\mathrm{FC}^{\alpha^{*}}$	$\Delta$	$p_{\mathrm{NB}}$	folds won
Schaefer-400	$0.302\pm 0.085$	$0.373\pm 0.085$	$+0.071$	$8{\times}10^{-5}$	181/200
Schaefer-500	$0.309\pm 0.081$	$0.390\pm 0.080$	$+0.081$	$4{\times}10^{-6}$	191/200
Schaefer-600	$0.314\pm 0.082$	$0.405\pm 0.081$	$+0.091$	$1{\times}10^{-7}$	197/200
Schaefer-800	$0.312\pm 0.083$	$0.404\pm 0.082$	$+0.092$	$3{\times}10^{-8}$	197/200
Schaefer-1000	$0.312\pm 0.085$	$0.401\pm 0.085$	$+0.089$	$2{\times}10^{-8}$	197/200
A424	$0.287\pm 0.086$	$0.378\pm 0.084$	$+0.092$	$1{\times}10^{-6}$	191/200

Appendix

Table 18: FC

{}^{\alpha^{*}}

against FC on AOMIC-ID1000 under a single re-parcellation pipeline (

n{=}879

subjects with the composite under that pipeline), correlation-kernel KRR,

20\times 10

subject-level CV, mean

\pm

std over the

200

folds.

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