Disentangling Marginal Capacity from Geometry in Optimal-Transport Label Transfer

Ali Khodabandeh Yalabadi; Azim Dehghani Amirabad; Artem Moskalev; Yun-Ching Chen; Mehdi Pirooznia; Scott Oloff; Rui Liao

cs.LGOct 10, 2026

Disentangling Marginal Capacity from Geometry in Optimal-Transport Label Transfer

Authors: Ali Khodabandeh Yalabadi, Azim Dehghani Amirabad, Artem Moskalev, Yun-Ching Chen, Mehdi Pirooznia, Scott Oloff, Rui Liao

Organizations: Johnson & Johnson Innovative Medicine · Independent Researcher

Abstract

Optimal transport (OT) is widely used to align distributions and transfer labels between unpaired source and target data, but source-target composition shifts can cause rare classes to be systematically under-predicted even with high transport confidence. We identify a source of this failure in the transport marginal: under the standard uniform weighting of source points, each class has transport capacity proportional to its source frequency, which can be insufficient to meet its target demand even when separated well in the embedding space. We show that displaced mass is preferentially absorbed by high-capacity classes rather than geometrically similar classes, producing confident errors that are difficult to detect from the transport plan. Downstream read-outs, entropic smoothing, and marginal relaxation provide limited recovery, whereas matching the transport marginal to the target composition substantially improves label transfer. On single-cell data, the oracle composition-matched marginal raises macro-F1 from 0.322 to 0.623, and the best deployable estimator closes 69% of the oracle gap. Correcting the marginal also separates a coverage-dependent component of error from residual error associated with class separability, showing that transport capacity and representation geometry are distinct sources of transfer error.

Figures & tables

Figure 1: Capacity and correction. (a)

c_{4}

is rare in the source yet well separated;

c_{1},c_{2}

overlap. (b) Under the default

\mu=

source frequencies,

c_{4}

is starved and its mass is absorbed by the abundant

c_{1}

. (c) Replacing it with

\mu^{\prime}=\hat{\pi}/n^{\mathrm{s}}

\hat{\pi}

estimating the target composition, restores

c_{4}

’s budget. (d) Correct assignments return; the

c_{1}\!\leftrightarrow\!c_{2}

off-diagonal is unchanged. (e) Recovered mass is the capacity term; the residual tracks separability.

Source marginal	B_Plasma	T_NK	Myeloid	Malignant	Epithelial	Endothelial	Stromal
source frequencies	.65/.63	.95/.19	.30/.53	.64/.55	.36/.53	.05/1.00	.09/.89
uniform per class	.73/.66	.80/.51	.43/.69	.66/.63	.72/ .26	.64/ .29	.60/.73
composition-matched	.78/.68	.75/.71	.61/.62	.61/.78	.45/.48	.46/.72	.69/.72

Table 1: Per-class recall / precision on single-cell data (Jint), natural target composition, 3 seeds. The default marginal produces the capacity signature: a capacity-limited class has low recall but high precision, while the largest class has high recall but low precision.

	single-cell (Jint)	Office-Home
partial $\rho$ (absorbed share, capacity $\mid$ distance)	$\mathbf{+0.566}$	$\mathbf{+0.329}$
partial $\rho$ (absorbed share, distance $\mid$ capacity)	$+0.144$	$-0.206$
$n$ (class, absorber) pairs / units	$198\,/\,27$	$14{,}080\,/\,12$

Table 2: Where displaced mass goes. Partial Spearman correlations of absorbed share with class capacity and embedding distance, each controlling for the other.

intervention	$r_{k}<0.15$	$r_{k}\geq 0.15$
marginal shape (matched to target)	$\mathbf{+0.366}$	$+0.016$
marginal shape (uniform)	$+0.274$	$+0.038$
$\tau=0.01$ (most relaxed)	$\mathbf{+0.208}$	$+0.053$
$\tau=\infty$ (balanced Sinkhorn)	$-0.021$	$-0.013$
$\varepsilon$ ( $3\times$ default)	$\mathbf{+0.000}$	$-0.012$
permuted marginal (control)	$-0.015$	$-0.079$

Table 3: Effect of the three OT parameters in Eq. 1 , stratified by capacity. Entries are changes in macro recall relative to the default source marginal on Office-Home.

	single-cell (Jint)				Office-Home
estimate of $\pi$	macro	F1	micro	below	macro	F1	micro	%
source frequencies	$0.433$	$0.322$	$0.393$	$0.030$	$0.392$	$0.359$	$0.437$	n/a
permuted (control)	n/a	n/a	n/a	n/a	$0.333$	$0.284$	$0.360$	n/a
uniform	$0.654$	$0.512$	$0.557$	$0.533$	$0.501$	$0.396$	$0.448$	$6\%$
$k$ NN pre-pass	$0.648$	$0.556$	$0.616$	$0.463$	$0.487$	$0.428$	$0.518$	$48\%$
JCPOT	$0.585$	$0.505$	$0.595$	$0.280$	$0.467$	$0.434$	$0.537$	$\mathbf{59\%}$

Table 4: Label-transfer performance under different source marginals and target-composition estimates. Results are shown for single-cell data (Jint) and Office-Home under the natural target composition.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

	transport	$k$ NN vote
classes resolvable	$65/65$	$64/65$
classes with a finite $r^{\star}$	$36/65$	$47/65$
median $R^{2}$	$0.276$	$0.142$
median $r^{\star}$	$0.142$	$0.108$
median ceiling $a$	$0.657$	$0.606$
fits declined at the $a\leq 1$ bound	$0/36$	$0/47$

Appendix

Table 5: The saturating law fitted on Office-Home, transport read-out against a

k

NN vote. Same protocol as the single-cell fits: per class,

\mathrm{recall}(t)\approx a\,r_{t}/(r^{\star}+r_{t})

, ceiling constrained to

a\leq 1

, and any fit landing within

10^{-3}

of that bound declined. No fit is pinned here (the largest ceiling is

0.9951

), so nothing is declined for that reason. The form does not transfer: the fits are poor, a threshold is undefined for roughly half the classes under transport, the transport-to-vote ratio is close to unity with a range spanning both sides of it, and no class sits at chance. Single-cell fits are not tabulated alongside, because the logged Janesick fits predate the

a\leq 1

convention; Sec. 3.1 rests the single-cell claim on the fit-free resolvability count instead, which no fitting convention can affect.

Figure 2: The failure is in the coupling, and the marginal repairs it. Entropic unbalanced OT couplings between the source (rows) and the target (columns), both sorted by class. Each class is allocated the same number of bins on each axis, so a class holding $0.3\%$ of the source is as legible as one holding half of it, and colour is the share of each target point’s transported mass falling in a given source bin, on one scale shared by both panels and all classes. Left: the source marginal is the source’s own class frequencies. Right: the marginal is rebuilt as $\mu_{j}=\hat{\pi}_{y_{j}}/n^{\mathrm{s}}_{y_{j}}$ from a $k$ NN pre-pass estimate of the target composition, which uses no target labels. Everything else is identical. The horizontal band on the T_NK rows in the left panel is the absorption mechanism of Sec. 3.2 made visible: target points of a starved class are transported to a class that has capacity. Endothelial, the one class below capacity here, is starred and its diagonal block is ringed; uncorrected it sends $46.9\%$ of its mass to T_NK and $3.9\%$ to itself, and corrected it sends $51.3\%$ to itself. Aggregated over the whole target, the T_NK source rows absorb $47.8\%$ of all transported mass before correction and $14.4\%$ after.

Figure 3: The correction acts on class correspondence, not on domain alignment. UMAP of the source together with the target mapped into source space by each row’s transport plan through barycentric projection. The reducer is fit once, on the source alone, and both rows are transformed into that fixed embedding, so the source points are identical in every panel and only the target moves; any difference between rows is therefore attributable to the plan and not to a refit. Top row: source-frequency marginal. Bottom row: composition-matched marginal from the $k$ NN pre-pass. Left column: points coloured by domain, which measures alignment. Right column: points coloured by class, which checks that the biology is preserved. Domain mixing, the fraction of each point’s fifteen nearest neighbours drawn from the other domain on the plotted coordinates, where $0.5$ is perfect interleaving, improves only from $0.346$ to $0.387$ : the two domains were already reasonably interleaved, and alignment is not what the marginal repairs. The class panels show what does change, with the Endothelial population diffuse and largely mislabelled before correction and consolidated after, and below-capacity recall rising from $0.036$ to $0.543$ .

class	$r$	recall before	recall after	diagonal mass
Endothelial (below capacity)	$\mathbf{0.141}$	$0.036$	$\mathbf{0.543}$	$3.9\%\to 51.3\%$
Stromal	$0.320$	$0.094$	$0.619$	$8.7\%\to 55.8\%$
Epithelial	$1.903$	$0.238$	$0.514$	$23.7\%\to 48.6\%$
Malignant	$2.305$	$0.561$	$0.896$	$53.1\%\to 84.9\%$
Myeloid	$3.135$	$0.314$	$0.442$	$32.5\%\to 43.3\%$
B_Plasma	$5.943$	$0.711$	$0.853$	$69.9\%\to 83.9\%$

Appendix

Table 6: Jint fold G1, per class, ordered by coverage ratio. Diagonal mass is the share of a class’s target mass landing on its own source block, read off the plotted matrices of Fig. 2 . Endothelial is the only class below capacity on this fold.

family	read-out	Jint	Janesick rep1	Janesick rep2
hard	argmax	$0.040$	$0.071$	$0.211$
tempered	softmax $T{=}1$	$0.040$	$0.071$	$0.211$
tempered	softmax $T{=}0.05$	$0.040$	$0.071$	$0.211$
soft	soft posterior	$0.040$	$0.071$	$0.211$
propagating	OTP, 1 step	$0.062$	$0.085$	$0.254$
propagating	OTP, 20 steps	$0.063$	$0.086$	$0.259$

Appendix

Table 7: Read-out battery, below-capacity recall under the natural marginal. Every arm except

k

NN consumes the same converged plan. Hard, tempered and soft read-outs are identical to four decimals; propagation buys a little and twenty steps buy nothing over one; the only plan read-outs that help are the two that divide by source class count, which is the marginal correction relocated after the solve.

n=12

(Jint),

2{,}412

(rep1),

1{,}926

(rep2).

dataset	coupling mass	expected recall	argmax recall	extracted
Jint	$0.0041$	$0.041$	$0.040$	$96\%$
Janesick rep1	$0.0190$	$0.077$	$0.071$	$93\%$
Janesick rep2	$0.0160$	$0.183$	$0.211$	$115\%$

Appendix

Table 8: The coupling-mass ceiling, natural marginal. Coupling mass is the share of total transported mass landing on a below-capacity class and expected recall is what a perfect read-out of that plan could achieve; both are read-out-independent properties of the coupling. The last column is what argmax actually extracts as a fraction of that ceiling.

	Janesick	Jint			Janesick
$\tau$	macro	macro	absorption	Endothelial / Stromal	identified $r^{\star}$
$0.01$ (most relaxed)	$\mathbf{0.451}$	$\mathbf{0.586}$	$0.656$	$0.217$ / $0.435$	$6/14$
$0.1$	$0.399$	$0.519$	$0.863$	$0.091$ / $0.222$	$4/14$
$1$ (default)	$0.306$	$0.426$	$0.974$	$0.020$ / $0.058$	$0/14$
$10$	$0.267$	$0.407$	$0.985$	$0.012$ / $0.039$	$0/14$
$\infty$ (balanced)	$0.262$	$0.404$	$\mathbf{0.987}$	$0.012$ / $0.036$	$0/14$

Appendix

Table 9: The

\tau

sweep on both datasets. Identified

r^{\star}

is the number of the fourteen Janesick classes yielding a fit that is not declined; at the default

\tau

and tighter, every fit is declined with its ceiling pinned and the note that the curve does not saturate within the observed window.

domain	marginal	$\tau{=}0.01$	$0.1$	$1$	$10$	$\infty$	span	$z$
Office-Home	default	$\mathbf{0.450}$	$0.359$	$0.217$	$0.193$	$0.190$	$\mathbf{0.260}$	$11.8$
	deployable	$\mathbf{0.477}$	$0.451$	$0.431$	$0.426$	$0.426$	$0.051$	$1.8$
	oracle	$0.528$	$\mathbf{0.542}$	$0.541$	$0.538$	$0.537$	$0.014$	$0.5$
single-cell	default	$\mathbf{0.408}$	$0.203$	$0.057$	$0.044$	$0.042$	$\mathbf{0.366}$	$8.7$
	deployable	$0.547$	$0.542$	$0.552$	$\mathbf{0.555}$	$0.555$	$0.013$	$0.2$
	oracle	$0.549$	$0.572$	$0.634$	$0.643$	$\mathbf{0.644}$	$0.096$	$1.3$

Appendix

Table 10: Marginal

\times

\tau

, below-capacity macro-F1. Deployable is JCPOT on Office-Home and the

k

NN pre-pass on single-cell data, each the leading estimator in its own panel; oracle uses the true composition and is an upper bound rather than a method. Span is best minus worst within the row, with its

z

. On a wrong marginal

\tau

is a large lever; on a corrected one no setting is distinguishable from any other. Office-Home is

4

domain pairs

\times

3

seeds and single-cell is

3

folds

\times

3

seeds, both complete. A further arm at

\tau=0.001

leaves every conclusion unchanged (App. E ).

$\varepsilon$	degenerate	below-cap. recall	macro	sel.	conf. correct	conf. wrong
$0.01\times$	yes	$0.000$	$0.143$	$1.00$	—	—
$0.03\times$	yes	$\mathbf{0.132}$	$0.312$	$1.15$	—	—
$0.1\times$	no	$0.027$	$0.441$	$2.94$	$0.974$	$0.874$
$0.3\times$	no	$0.027$	$\mathbf{0.442}$	$2.89$	—	—
$1\times$	no	$0.024$	$0.438$	$3.28$	$0.927$	$0.744$
$3\times$	no	$0.002$	$0.408$	$5.15$	$0.817$	$0.554$

Appendix

Table 11: The

\varepsilon

sweep, as a multiple of the calibrated default. No setting has both meaningful below-capacity recall and a detector clearing the pre-registered bar. The two smallest values produce a numerically degenerate plan. Sel. is the selectivity of the best output-side detector; conf. are mean confidences on correct covered points and on wrong below-capacity points. Six scorable units: one fold has no below-capacity class, so the detector suite is undefined there and it contributes no rows. The bar is cleared on at most three of six units at any

\varepsilon

, never all six.

prior for $\pi$	removable $\sim\log r$	removable $\sim$ sep	residual $\sim$ sep	residual $\sim\log r$
oracle (published)	$\mathbf{-0.813}$	$+0.135$	$\mathbf{-0.338}$	$+0.034$
uniform	$-0.573$	$+0.316$	$-0.502$	$-0.157$
$k$ NN pre-pass	$-0.517$	$+0.263$	$-0.374$	$\mathbf{-0.435}$
JCPOT	$-0.516$	$+0.188$	$-0.313$	$-0.287$
BBSE	$-0.541$	$+0.282$	$-0.422$	$-0.296$
RLLS	$-0.538$	$+0.289$	$-0.429$	$-0.305$

Appendix

Table 12: The decomposition under seven priors, Office-Home,

n=780

. Cells are partial Spearman

\rho

with the other predictor controlled. Removable stays coverage-governed and residual stays separability-governed on every arm, while the near-zero cells at the oracle become non-zero under every estimate.

Figure 4: Dose-response under a deployable class prior. Coverage deciles as in Fig. 8 , with the oracle marginal, the best deployable estimator and uniform balancing overlaid. The shape, the sign change and the cost at high coverage survive; the amplitude at the starved end and the break-even coverage do not.

$\alpha$	macro-F1	below F1	absorption	macro-F1	below F1	absorption
	single-cell (Jint)			Office-Home
$0.0$	$0.322$	$0.062$	$0.971$	$0.349$	$0.211$	$0.846$
$0.1$	$0.383$	$0.232$	$0.852$	$0.386$	$0.298$	$0.754$
$0.2$	$0.429$	$0.338$	$0.763$	$0.413$	$0.368$	$0.669$
$0.3$	$0.466$	$0.418$	$0.685$	$0.434$	$0.413$	$0.599$
$0.4$	$0.498$	$0.476$	$0.620$	$0.453$	$0.452$	$0.534$

Appendix

Table 13: Performance along the path from the source composition to the target. Single-cell is

3

folds

\times

3

seeds and Office-Home is

4

domain pairs

\times

3

seeds. Rows are the eight values of

\alpha

measured on both domains. Absorption falls monotonically throughout, so the mechanism tracks the marginal rather than the metric.

Figure 5: Office-Home. Performance along the interpolation path, plotted against

\alpha

(left) and against the divergence remaining to the target composition (right), with the divergence axis reversed so both panels read from the default marginal to the oracle. Bands are standard errors over

12

units. Circles mark where each estimator of Sec. 4.3 sits: its horizontal position is the divergence of its own estimate from the target, and its vertical position is its measured below-capacity macro-F1. The two transport-native estimators land on the curve, so for them the divergence alone predicts what the correction will deliver.

Figure 6: Single-cell. As Fig. 5 . The horizontal axis of the right panel spans roughly twice the range, because the single-cell composition shift is about twice as large in divergence. The

k

NN pre-pass is the best estimator on both axes at once: it achieves the lowest divergence to the target composition and the highest below-capacity macro-F1 of any arm.

domain	estimate of $\pi$	divergence	path equivalent	below-capacity F1
Office-Home	JCPOT	$0.252$	$0.264$	$0.426$
	$k$ NN pre-pass	$0.257$	$0.258$	$0.407$
	RLLS	$0.273$	$0.234$	$0.437$
	MLLS	$0.351$	$0.236$	$0.460$
	uniform	$0.423$	$0.071$	$0.465$
single-cell	$k$ NN pre-pass	$\mathbf{0.585}$	$0.408$	$\mathbf{0.583}$

Appendix

Table 14: Where each estimator of Sec. 4.3 falls relative to the path. Divergence is the mean

\mathrm{KL}

from the estimate to the target composition, and path equivalent is the

\alpha

at which the interpolation reaches the same divergence. Estimators whose divergence exceeds the endpoint separation lie off the swept range and are omitted.

solver	macro	Endothelial	absorption	detector (side)	median sel. / pass
$k$ NN vote (reference)	$0.638$	$0.295$	$0.541$	plan confidence (out)	$2.43$ / $6/27$
UOT $+$ centering	$0.426$	$0.020$	$0.974$	split conformal (out)	$2.38$ / $1/27$
moscot	$0.424$	$0.014$	$0.981$	reject-sink OT (out)	$1.51$ / $0/27$
UOT, no centering	$0.320$	$0.009$	$0.994$	transport entropy (out)	$0.42$ / $0/27$
				coverage rule (source)	$24.50^{\ast}$ / $3/27$

Appendix

Table 15: Solver invariance and output-side detectors, single-cell (Jint). Left: four independent entropic-OT implementations on identical embeddings, points, labels, folds and seeds, with a

k

NN vote on the same embedding for reference. Absorption is the fraction of a starved class’s target mass received by a single other class. Fixed-per-class target composition, so this is a within-run contrast across solvers rather than a cross-design comparison; the corrected natural-composition comparison is Table 17 . Right: detectors for below-capacity points,

9

folds

\times

3

seeds, against a bar fixed in advance of selectivity at least

3\times

at coverage at least

90\%

; suite verdict

0/5

, with

10/135

unit evaluations passing. ∗ over the units where it fires.

Figure 7: The double dissociation. What the composition-matched marginal removes (top) and what survives it (bottom), against coverage (left) and class separability (right), on Office-Home. The two null panels are shown deliberately: what is removed is explained by coverage and not by separability, and what survives is explained by separability and not by coverage. Points are class-observations ( $4$ domain pairs $\times$ $3$ seeds), the line is a binned mean with standard error, and the band at residual $=1.0$ is classes the correction leaves at zero recall. The panels are interpretable only because the predictors were orthogonalized by construction; in the single-cell data they are confounded at $\rho=-0.618$ .

Figure 8: Dose-response of the correction. Change in macro recall from the composition-matched marginal against coverage, binned. Monotone on both domains, crossing zero and turning negative on the best-covered classes. The single-cell panel has

21

class-observations in

5

bins against Office-Home’s

780

10

and is a companion rather than an equally powered replication, and the

x

-ranges differ, so the two crossing points are not comparable thresholds.

	foundation	PCA	cut	$n$	shape	$\tau$	$\varepsilon$
confident errors	$33/33$	$33/33$	$r<0.05$	$56$	$0.472$	$0.243$	$0.006$
absorber = nearest	$0/33$	$0/33$	$r<0.10$	$136$	$0.419$	$0.234$	$0.014$
absorber = largest	$30/33$	$33/33$	$r<0.15$	$235$	$0.366$	$0.208$	$0.013$
confidence ratio	$0.874$	$0.906$	$r<0.30$	$389$	$0.296$	$0.176$	$0.015$
macro recall	$0.445$	$0.495$
detector suite	$0/5$	$0/5$

Appendix

Table 16: Left: backbone invariance,

9

folds

\times

3

seeds each on a

40{,}000

-point source, fixed-per-class target, so a within-run contrast. Counts differ slightly from Sec. 3.2 because that run uses natural composition and this one does not. Right: the below-capacity knob ordering of Table 3 at four cut points, as

\Delta

macro recall against the default marginal.

read-out	macro	macro-F1	micro	below capacity
transport, default	$0.433$	$0.322$	$0.393$	$0.030$
$k$ NN vote, uncorrected	$0.627$	$0.553$	$0.625$	$0.351$
linear probe, uncorrected	$0.268$	$0.212$	$0.215$	$0.014$
$k$ NN, prior-corrected	$\mathbf{0.654}$	$0.571$	$0.640$	$0.430$
$k$ NN, composition-matched	$0.635$	$0.577$	$0.652$	$0.414$
linear probe, corrected	$0.452$	$0.391$	$0.377$	$0.278$

Appendix

Table 17: Matched corrections, single-cell (Jint),

3

folds

\times

3

seeds, natural composition. Composition-matched arms, transport and vote alike, use the true target composition and are therefore matched oracles; prior-corrected arms divide by the source class prior and use no target information, so they are matched to each other at a lower information level. The oracle-to-oracle comparison is transport

0.546

against vote

0.414

below capacity, where below is the below-capacity stratum, three (fold, class) cells averaged over seeds.

read-out	macro	macro-F1	micro	below capacity
transport, default	$0.388$	$0.356$	$0.440$	$0.136$
$k$ NN vote, uncorrected	$0.367$	$0.327$	$0.506$	$0.154$
linear probe, uncorrected	$0.199$	$0.136$	$0.313$	$0.004$
$k$ NN, prior-corrected	$0.553$	$0.483$	$0.580$	$0.526$
$k$ NN, composition-matched	$0.460$	$0.461$	$\mathbf{0.644}$	$\mathbf{0.566}$
linear probe, class-balanced	$\mathbf{0.590}$	$\mathbf{0.533}$	$0.641$	$0.542$

Appendix

Table 18: Matched corrections on Office-Home,

4

domain pairs

\times

3

seeds, deep-starvation configuration. Below is the below-capacity stratum,

n=235

class-observations.

	replicate 1		replicate 2
estimate of $\pi$	macro	micro	macro	micro
source frequencies	$0.141$	$0.224$	$0.334$	$0.477$
uniform	$\mathbf{0.206}$	$0.149$	$\mathbf{0.591}$	$0.346$
$k$ NN pre-pass	$0.180$	$0.167$	$0.479$	$0.437$
JCPOT	$0.179$	$0.157$	$0.461$	$0.389$
BBSE	$0.161$	$\mathbf{0.316}$	$0.346$	$0.436$

Appendix

Table 19: Janesick under natural target composition, macro / micro recall by marginal, two replicates

\times

3

seeds.

Optimal Transport

Optimal transport compares and transforms probability distributions by finding low-cost ways to move mass between them.

See all 287 papers

SCOT: Multi-Source Cross-City Transfer with Optimal-Transport Soft-Correspondence Objective
Apr 8, 2026Yuyao Wang, Min Yang, Meng Chen +3Transfer Learning Multi-Source Domain Adaptation
Department of Mathematics and Statistics, Boston University, Boston, MA, USA · School of Software, Shandong University, Jinan, China · School of Geography, University of Leeds, Leeds, UK
Simultaneous Neural Optimal Transport
Sep 29, 2026Milena Gazdieva, Kirill Sokolov, Jiawei Chen +2All-in-One Image Restoration Optimal Transport
Applied AI Institute AXXX Moscow, Russia · Lomonosov Moscow State University Moscow, Russia · MIRIAI Moscow, Russia
Dynamic Neural Optimal Transport for Subset Alignment
Oct 16, 2026Austin J. Brockmeier, Bilal RiazOptimal Transport
Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, 19711 · Department of Computer and Information Sciences, University of Delaware, Newark, DE, 19711

Apr 8, 2026J/K move · Enter open · S save

SCOT: Multi-Source Cross-City Transfer with Optimal-Transport Soft-Correspondence Objective

Yuyao Wang, Min Yang, Meng Chen, Weiming Huang+2

Department of Mathematics and Statistics, Boston University, Boston, MA, USA · School of Software, Shandong University, Jinan, China · School of Geography, University of Leeds, Leeds, UK

Transfer Learning Multi-Source Domain Adaptation Geospatial Representation Learning Optimal Transport

Open paper AskPDF arXiv

Cross-city transfer improves prediction in label-scarce cities by leveraging labeled data from other cities, but it becomes challenging when cities adopt incompatible partitions and no ground-truth region correspondences exist. Existing approaches either rely on heuristic region matching, which is often sensitive to anchor choices, or perform distribution-level alignment that leaves correspondences implicit and can be unstable under strong heterogeneity. We propose SCOT, a cross-city representation learning framework that learns explicit soft correspondences between unequal region sets via Sinkhorn-based entropic optimal transport. SCOT further sharpens transferable structure with an OT-weighted contrastive objective and stabilizes optimization through a cycle-style reconstruction regularizer. For multi-source transfer, SCOT aligns each source and the target to a shared prototype hub using balanced entropic transport guided by a target-induced prototype prior. Across real-world cities and tasks, SCOT consistently improves transfer accuracy and robustness, while the learned transport couplings and hub assignments provide interpretable diagnostics of alignment quality.

Abstract

Optimal Transport

Explore similar work

SCOT: Multi-Source Cross-City Transfer with Optimal-Transport Soft-Correspondence Objective

Simultaneous Neural Optimal Transport

Dynamic Neural Optimal Transport for Subset Alignment