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

Yuyao Wang; Min Yang; Meng Chen; Weiming Huang; Yilong Yin; Yongshun Gong

cs.LGApr 8, 2026

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

Authors: Yuyao Wang, Min Yang, Meng Chen, Weiming Huang, Yilong Yin, Yongshun Gong

Organizations: 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

Abstract

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.

Figures & tables

Method	XA $\to$ BJ						BJ $\to$ XA
	GDP		Population		CO 2		GDP		Population		CO 2
	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE
Non-Alignment	264.30	12.08	981.07	8.56	288.41	6.40	252.91	5.84	946.93	8.53	270.42	8.66
RP	189.84	9.07	684.50	6.55	196.05	4.70	181.08	4.58	670.44	6.46	191.85	6.42
HBP	177.69	8.40	665.46	5.95	188.72	4.18	196.20	3.10	627.46	4.37	176.35	4.25
HSA	201.27	6.83	619.33	4.00	176.40	3.20	188.40	2.11	636.33	5.03	182.91	5.02

Table 1: Single-source transfer results on XA

\leftrightarrow

BJ. Lower is better. Red : best; Blue : runner-up. Gain row reports SCOT ’s relative improvement over the strongest baseline.

Appendix figures & tables31 assets

Supplementary material from the paper’s appendix.

Appendix

City	# Regions	# Trips	Targets
XA	1306	559,729	GDP / Pop / CO 2
CD	1056	384,618	GDP / Pop / CO 2
BJ	1311	78,945	GDP / Pop / CO 2

Appendix

Table 4: Dataset summary.

Figure 9: Illustration of multi-source SCOT .

$\blacktriangleright$ Target: Xi’an (XA)
Direction / Variant	GDP		Population		CO 2
Direction / Variant	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
XA $\to$ XA (w/o Alignment)	155.31 $\pm$ 1.92	3.63 $\pm$ 0.06	467.03 $\pm$ 4.45	2.50 $\pm$ 0.04	130.35 $\pm$ 0.97	2.60 $\pm$ 0.05
XA $\to$ XA (Full SCOT )	156.44 $\pm$ 2.29	3.67 $\pm$ 0.11	467.96 $\pm$ 8.19	2.51 $\pm$ 0.05	130.55 $\pm$ 1.93	2.59 $\pm$ 0.06
$\blacktriangleright$ Target: Beijing (BJ)
BJ $\to$ BJ (w/o Alignment)	95.41 $\pm$ 1.19	2.48 $\pm$ 0.06	531.27 $\pm$ 10.10	2.85 $\pm$ 0.06	154.57 $\pm$ 2.24	2.35 $\pm$ 0.28

Appendix

Table 5: Intra-city prediction with and without alignment (4 seeds, mean

\pm

std). Differences fall within one standard deviation, indicating that alignment does not degrade within-city quality. Lower is better.

Figure 10: Radar-chart matrix for cross-city transfer performance. MAE, MAPE, and Avg (min–max normalized within panel; center = lower error). Smaller polygons indicate better transfer.

Method	XA $\to$ CD						CD $\to$ XA
	GDP		Population		CO 2		GDP		Population		CO 2
	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE
Non-Alignment	323.90	11.49	908.18	4.73	237.73	12.91	232.86	3.74	748.16	5.22	179.25	1.67
RP	191.11	11.64	644.22	3.32	144.87	9.18	194.67	6.57	671.30	6.41	145.51	2.30
HBP	188.61	13.42	660.01	4.26	135.14	11.59	199.79	7.06	697.44	6.93	146.76	2.47
HSA	184.81	11.95	619.72	3.57	137.29	9.92	202.01	7.27	708.80	7.14	147.27	2.54

Appendix

Table 6: Single-source transfer results on XA

\leftrightarrow

CD. Lower is better. Red : best; Blue : runner-up. Gain row reports SCOT ’s relative improvement over the strongest baseline.

Method	BJ $\to$ CD						CD $\to$ BJ
	GDP		Population		CO 2		GDP		Population		CO 2
	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE
Non-Alignment	191.36	5.31	889.37	3.97	192.64	15.77	163.93	7.04	805.78	5.07	192.96	1.98
RP	158.57	8.71	726.42	5.39	175.21	14.49	150.56	6.63	697.53	6.64	156.97	2.03
HBP	155.05	8.30	698.75	4.80	172.65	13.22	166.30	7.29	715.27	6.84	154.77	1.79
HSA	147.74	6.87	667.95	4.20	160.10	11.55	148.87	6.59	648.28	5.75	166.55	2.64

Appendix

Table 7: Single-source transfer results on BJ

\leftrightarrow

CD. Lower is better. Red : best; Blue : runner-up. Gain row reports SCOT ’s relative improvement over the strongest baseline.

Method	GDP		Population		CO 2
Method	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
Non-Alignment	276.33 $\pm$ 10.63	9.46 $\pm$ 1.98	958.52 $\pm$ 31.66	5.99 $\pm$ 1.82	278.25 $\pm$ 9.95	5.39 $\pm$ 0.75
RP	192.05 $\pm$ 26.62	6.65 $\pm$ 1.48	676.21 $\pm$ 28.24	4.00 $\pm$ 0.66	194.70 $\pm$ 11.88	3.71 $\pm$ 0.22
HBP	186.21 $\pm$ 10.14	8.17 $\pm$ 0.88	664.15 $\pm$ 24.83	4.68 $\pm$ 0.89	188.14 $\pm$ 5.39	3.99 $\pm$ 0.20
HSA	179.96 $\pm$ 17.62	7.30 $\pm$ 1.00	631.69 $\pm$ 27.93	4.64 $\pm$ 1.19	180.21 $\pm$ 8.29	3.57 $\pm$ 0.64
MMD	162.63 $\pm$ 16.27	5.93 $\pm$ 0.90	596.60 $\pm$ 21.41	3.63 $\pm$ 0.66	169.99 $\pm$ 7.14	2.91 $\pm$ 0.46

Appendix

Table 8: XA

\to

BJ results averaged over 4 random seeds (mean

\pm

std). Lower is better. Red : best; Blue : runner-up. Gain row reports SCOT ’s relative improvement over the strongest baseline.

Method	GDP		Population		CO 2
Method	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
Non-Alignment	220.31 $\pm$ 22.10	7.91 $\pm$ 1.43	975.83 $\pm$ 65.55	9.63 $\pm$ 1.27	276.84 $\pm$ 18.56	9.70 $\pm$ 1.14
RP	175.21 $\pm$ 4.15	4.60 $\pm$ 0.53	671.08 $\pm$ 11.95	6.37 $\pm$ 0.22	191.56 $\pm$ 3.33	6.30 $\pm$ 0.24
HBP	180.60 $\pm$ 13.16	2.97 $\pm$ 0.82	629.09 $\pm$ 5.07	4.95 $\pm$ 0.39	179.17 $\pm$ 2.76	4.91 $\pm$ 0.45
HSA	176.42 $\pm$ 10.52	3.66 $\pm$ 1.35	649.08 $\pm$ 16.82	5.66 $\pm$ 0.62	185.72 $\pm$ 4.29	5.62 $\pm$ 0.57
MMD	180.71 $\pm$ 5.39	2.25 $\pm$ 0.22	500.12 $\pm$ 27.35	1.93 $\pm$ 0.09	141.24 $\pm$ 4.96	1.91 $\pm$ 0.08

Appendix

Table 9: BJ

\to

XA results averaged over 4 random seeds (mean

\pm

std). Lower is better. Red : best; Blue : runner-up. Gain row reports SCOT ’s relative improvement over the strongest baseline.

Method	GDP		Population		CO 2
Method	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
RP	187.13	13.31	630.44	3.62	167.76	14.05
HBP	176.35	11.11	631.26	3.69	125.97	9.96
HSA	180.71	8.18	651.06	3.41	159.86	11.79
MMD	163.82	5.07	639.32	3.93	145.74	10.83
Adv	183.26	12.43	687.72	4.73	156.37	12.92

Appendix

Table 10: Multi-source transfer results (Target: CD). Lower is better. Red : best; Blue : runner-up. Gain row reports SCOT ’s relative improvement over the strongest baseline.

Joint OLS: $y\sim\mathcal{L}_{\mathrm{Con}}+\mathcal{L}_{\mathrm{OT}}$		Partial correlation with $\mathcal{L}_{\mathrm{Con}}$
		(controlling for $\mathcal{L}_{\mathrm{OT}}$ )
Std. coef. on $\mathcal{L}_{\mathrm{Con}}$	Adj. $R^{2}$	Pearson $r$	Spearman $\rho$	$p$ -value
0.77	0.94	0.95	0.93	$<\!0.001$

Appendix

Table 11: Empirical verification of Proposition 3.1 . The standardized coefficient on

\mathcal{L}_{\mathrm{Con}}

remains strongly positive after controlling for

\mathcal{L}_{\mathrm{OT}}

, and partial Pearson/Spearman correlations both exceed

0.93

with

p<0.001

Figure 11: OT coupling diagnostics. Histograms of column entropy $H(P_{:,j})$ , row entropy $H(P_{i,:})$ , and column marginals $c_{j}=\sum_{i}P_{ij}$ (here shown for a representative epoch).

Figure 12: Ablation study on cross-city transfer performance. We report MAE (top row) and MAPE (bottom row) for GDP, population, and CO 2 prediction across six transfer directions (BJ $\rightarrow$ XA, XA $\rightarrow$ BJ, XA $\rightarrow$ CD, CD $\rightarrow$ XA, BJ $\rightarrow$ CD, CD $\rightarrow$ BJ).

$\blacktriangleright$ Target: Xi’an (XA)
Target / Variant	GDP		Population		CO 2
Target / Variant	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
Ours (Hub)	154.49 $\pm$ 2.10	2.12 $\pm$ 0.31	467.54 $\pm$ 17.42	2.23 $\pm$ 0.25	133.58 $\pm$ 4.64	1.51 $\pm$ 0.18
No Hub (Pairwise)	157.45 $\pm$ 3.31	2.52 $\pm$ 0.48	511.37 $\pm$ 23.34	2.98 $\pm$ 0.64	135.56 $\pm$ 6.90	1.71 $\pm$ 0.35
$\blacktriangleright$ Target: Chengdu (CD)
Ours (Hub)	143.91 $\pm$ 6.84	4.54 $\pm$ 0.49	565.65 $\pm$ 14.55	2.38 $\pm$ 0.09	102.20 $\pm$ 11.20	5.92 $\pm$ 0.67

Appendix

Table 12: Multi-source ablation: shared-prototype Hub vs. pairwise OT with global gating ( No Hub ), across three targets (mean

\pm

std over 4 seeds). Red : better in each pair. Lower is better.

Prior Variant	GDP		Population		CO 2
Prior Variant	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
Uniform (no target)	186.33 $\pm$ 3.93	3.42 $\pm$ 0.14	575.81 $\pm$ 17.09	3.27 $\pm$ 0.33	156.56 $\pm$ 10.13	1.85 $\pm$ 0.18
Frozen (fixed)	181.47 $\pm$ 3.16	4.79 $\pm$ 0.19	553.05 $\pm$ 8.68	3.81 $\pm$ 0.10	148.89 $\pm$ 0.67	2.83 $\pm$ 0.02
Adaptive (Ours)	154.49 $\pm$ 2.10	2.12 $\pm$ 0.31	467.54 $\pm$ 17.42	2.23 $\pm$ 0.25	133.58 $\pm$ 4.64	1.51 $\pm$ 0.18
$\Delta$ vs. Uniform	+17.1%	+38.0%	+18.8%	+31.8%	+14.7%	+18.4%

Appendix

Table 13: Ablation on the target-induced prototype marginal

\mathbf{b}

(XA as target, 4 seeds, mean

\pm

std). The adaptive prior wins on every metric. Lower is better.

Figure 13: Entropy of prototype marginal $b_{t}$ over training. The uniform prior stays at $\log K$ ; the adaptive prior decreases steadily, indicating progressive prototype specialization guided by target semantics.

Panel of Figure 14 — Figure 14: Comparison of balanced and unbalanced OT in the hub (CD,BJ $\rightarrow$ XA, $\tau_{b}=0.5$ ).

OT Variant	GDP		Population		CO 2
OT Variant	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
Unbalanced OT ( $\rho=0.3$ )	212.96 $\pm$ 27.46	7.22 $\pm$ 1.16	721.83 $\pm$ 95.63	4.80 $\pm$ 0.69	174.77 $\pm$ 41.48	3.17 $\pm$ 1.29
Unbalanced OT ( $\rho=1$ )	173.59 $\pm$ 13.68	4.16 $\pm$ 1.54	563.30 $\pm$ 33.74	3.49 $\pm$ 1.09	149.69 $\pm$ 9.89	1.90 $\pm$ 0.48
Unbalanced OT ( $\rho=3$ )	165.98 $\pm$ 11.66	2.06 $\pm$ 0.90	530.68 $\pm$ 13.40	2.27 $\pm$ 0.47	147.91 $\pm$ 8.99	1.81 $\pm$ 0.14
Balanced OT (Ours)	154.49 $\pm$ 2.10	2.12 $\pm$ 0.31	467.54 $\pm$ 17.42	2.23 $\pm$ 0.25	133.58 $\pm$ 4.64	1.51 $\pm$ 0.18

Appendix

Table 14: Balanced vs. unbalanced OT on BJ

\to

XA (4 seeds, mean

\pm

std). Balanced OT achieves the best mean and lowest variance on every metric, while unbalanced OT requires careful tuning of

\rho

to approach competitive accuracy. Red : best per column. Lower is better.

$\blacktriangleright$ Direction: BJ $\to$ XA
Variant	GDP		Population		CO 2
Variant	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
One-sided (Ours)	160.21 $\pm$ 3.53	1.87 $\pm$ 0.18	450.14 $\pm$ 2.81	1.73 $\pm$ 0.12	127.79 $\pm$ 1.08	1.78 $\pm$ 0.10
Two-sided	160.92 $\pm$ 2.94	1.65 $\pm$ 0.20	503.85 $\pm$ 14.49	2.51 $\pm$ 0.35	143.18 $\pm$ 2.82	2.47 $\pm$ 0.30
$\blacktriangleright$ Direction: XA $\to$ BJ
One-sided (Ours)	120.25 $\pm$ 7.30	3.59 $\pm$ 0.48	527.04 $\pm$ 6.38	2.17 $\pm$ 0.23	149.20 $\pm$ 1.58	1.80 $\pm$ 0.17

Appendix

Table 15: One-sided vs. two-sided cycle reconstruction across four transfer directions (4 seeds, mean

\pm

std). The one-sided design wins on 22 of 24 metrics , with the largest degradation under two-sided occurring on Population and CO 2 . Red : better in each pair. Lower is better.

OT variant in SCOT	XA $\to$ BJ						BJ $\to$ XA
	GDP		Pop		CO 2		GDP		Pop		CO 2
	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE
Balanced (Ours)	115.33	3.17	528.50	2.13	149.42	1.79	154.92	1.60	452.67	1.58	128.74	1.63
Partial (frac $=0.7$ )	137.18	4.54	556.49	3.11	156.70	2.34	172.49	2.01	462.15	1.56	131.25	1.60
Sinkhorn divergence	141.78	3.90	562.76	2.23	160.57	2.06	167.83	2.62	476.30	2.54	136.74	2.50
Unbalanced (KL marginal)	145.04	5.77	627.52	5.15	177.08	3.67	172.09	2.42	487.21	2.62	139.69	2.52

Appendix

Table 16: OT variant comparison on XA

\leftrightarrow

BJ. Balanced entropic OT (our default) achieves the best results on

11

12

metrics; on the single exception (Pop MAPE in BJ

\,\to\,

XA), Partial OT is essentially tied. The variants are ranked by overall performance: Balanced

>

Partial

>

Sinkhorn divergence

>

Unbalanced —a pattern aligned with the strictness of the marginal constraints. Red : best per cell. Lower is better.

Cost variant in SCOT	XA $\to$ BJ						BJ $\to$ XA
	GDP		Pop		CO 2		GDP		Pop		CO 2
	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE	MAE	MAPE
$\ell_{2}$ on embeddings (Ours)	115.33	3.17	528.50	2.13	149.42	1.79	154.92	1.60	452.67	1.58	128.74	1.63
Graph-aware ( $\alpha=0.7$ )	152.93	5.73	588.56	3.74	168.17	2.96	166.51	2.43	458.53	2.27	131.21	2.24
Mobility-profile ( $\alpha=0.5$ )	175.20	7.49	598.49	4.58	176.77	3.67	172.54	2.15	468.85	1.93	132.97	1.88
Gromov-Wasserstein	177.10	6.62	607.10	3.54	174.19	3.03	167.70	2.53	501.56	2.57	142.65	2.65

Appendix

Table 17: Cost formulation comparison on XA

\,\leftrightarrow\,

BJ.

\ell_{2}

\ell_{2}

-normalized embeddings ( SCOT ’s default) achieves the best result on all

12

metrics. Red : best per cell. Lower is better.

Panel of Figure 15 — Figure 15: Sensitivity to $\tau$ on XA $\to$ BJ. (a) U-shape with sweet spot $\tau\in[0.1,0.5]$ . (b) Geometry mirrors metrics: extreme $\tau$ yields weak interleaving or over-smoothing; $\tau=0.1$ aligns cleanly without collapsing clusters.

Panel of Figure 16 — Figure 16: Sensitivity to $\eta$ on XA $\to$ BJ. (a) Best in $\eta\in[0.1,0.5]$ ; large $\eta$ degrades sharply. (b) $\eta=0$ under-aligns; $\eta=0.5$ aligns cleanly; $\eta=5$ over-mixes the two cities.

Figure 17: t-SNE under varying $\lambda_{\mathrm{align}}$ on XA $\to$ BJ. The recommended setting $\lambda_{\mathrm{align}}=1$ (middle) produces coherent interleaving with preserved clusters; extreme values outside the recommended range $[0.1,1]$ , namely $0.05$ (left) and $3$ (right), bracket the boundary behavior. Blue $\circ$ : source; orange $\triangle$ : target.

Figure 18: Sensitivity to hub size

K

on CD,BJ

\to

XA (multi-source). MAE / MAPE for GDP, population, and CO 2 . Performance is stable across

K\in[4,32]

;

K=2

underfits and

K\!\geq\!64

over-resolves the hub space.

Panel of Figure 19 — Figure 19: Sensitivity to $\tau_{b}$ on multi-source CD,BJ $\to$ XA. (a) Performance plateau across $\tau_{b}\in[0.3,0.8]$ . (b) Normalized entropy $H(p)/\log K$ and effective prototype count $\exp(H(p))$ on XA: hub usage stabilizes at $\sim 4$ effective prototypes within the same range, providing direct mechanistic evidence for the metric plateau.

Variant	Time	Memory
Single-source SCOT	$O(Tn_{s}n_{t})$	$O(n_{s}n_{t})$
Multi-source, naive pairwise OT	$O(TMn^{2})$	$O(Mn^{2})$
Multi-source SCOT (hub)	$\boldsymbol{O(T(M\!+\!1)nK)}$	$\boldsymbol{O((M\!+\!1)nK)}$
Speedup over pairwise	$\sim n/K$	$\sim n/K$

Appendix

Table 18: Complexity of SCOT ’s alignment module.

n

: city size;

T

: Sinkhorn iterations;

M

: number of sources;

K

: hub size.

$\blacktriangleright$ Target: Beijing (BJ)
Target / Variant	GDP		Population		CO 2
Target / Variant	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$
Best single-source (oracle)	118.48	3.41	580.95	2.74	148.50	1.54
Multi-source (Ours)	104.16	2.57	525.10	1.87	143.53	1.46
$\blacktriangleright$ Target: Xi’an (XA)
Best single-source (oracle)	154.92	1.60	452.67	1.58	128.74	1.63

Appendix

Table 19: Single-source vs. multi-source SCOT across three target cities. The single-source baseline uses the best source per target–task (an oracle assumption). Multi-source SCOT wins on 8 of 9 combinations; the Xi’an GDP case is mechanistically explained by elevated source conflict (Table 20 ) and operationally addressed by the conflict-aware variant. Red : best per cell pair. Lower is better.

Target	$\mathcal{L}_{\mathrm{OT}}$			$\mathcal{L}_{\mathrm{Con}}$			Transport mass
Target	S1	S2	$\Delta$	S1	S2	$\Delta$	S1	S2	$\Delta$
Beijing (BJ)	0.558	0.557	0.001	0.999	0.987	0.012	0.431	0.447	0.016
Chengdu (CD)	0.435	0.403	0.032	1.075	0.839	0.237	0.489	0.515	0.026
Xi’an (XA)	0.470	0.420	0.050	1.080	0.660	0.420	0.480	0.580	0.100

Appendix

Table 20: Near-convergence hub diagnostics for each source–target pair.

\Delta

is the inter-source gap (absolute difference); larger

\Delta

flags structural source imbalance detectable without target labels .

Method	Population MAE $\,\downarrow$
Method	BJ $\to$ NYC	CD $\to$ NYC	XA $\to$ NYC
Non-Alignment	468.84	502.65	531.28
RP	382.72	421.94	472.61
HBP	294.10	317.57	386.93
HSA	354.46	389.83	418.72
MMD	331.55	372.64	356.38

Appendix

Table 21: Cross-country transfer with NYC (Population MAE; lower is better). SCOT wins on all six directions, with larger gains for transfer to NYC (

21.0

–

31.8\%

) than from NYC (

5.4

–

9.7\%

). Red : best; Blue : runner-up.

Method	BJ+CD+XA $\to$ NYC
Non-Alignment	487.36
RP	426.58
HBP	339.84
HSA	356.27
MMD	327.45
Adv	462.91

Appendix

Table 22: Multi-source transfer to NYC with

M\!=\!3

sources (BJ, CD, XA). Population MAE; lower is better. SCOT -Hub wins over both the strongest baseline (

+21.0\%

) and the best single-source variant of SCOT (

+3.9\%

), confirming that the hub design scales effectively beyond

M\!=\!2

. Red : best.

Variant	Population MAE $\,\downarrow$
Variant	Target: BJ	Target: XA
Best single-source SCOT	528.50	452.67
SCOT -Hub ( $M\!=\!2$ , Chinese sources)	525.10	446.13
SCOT -Hub ( $M\!=\!3$ , +NYC)	514.76	438.14
$\Delta$ vs. best single-source	+2.6%	+3.2%
$\Delta$ vs. $M\!=\!2$ Hub	+2.0%	+1.8%

Appendix

Table 23: Multi-source scaling: SCOT -Hub at

M\!=\!3

(adding NYC as a third source) vs.

M\!=\!2

(Chinese sources only). Population MAE; lower is better. Adding a heterogeneous source (NYC) further improves performance, demonstrating that the hub absorbs additional sources without dilution. Red : best per target.

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Oct 10, 2026

Disentangling Marginal Capacity from Geometry in Optimal-Transport Label Transfer

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.

Ali Khodabandeh Yalabadi, Azim Dehghani Amirabad, Artem Moskalev +4

Johnson & Johnson Innovative Medicine · Independent Researcher

Optimal Transport Label Shift Class-Imbalanced Learning

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Feb 17, 2026

UrbanVerse: Learning Urban Region Representation Across Cities and Tasks

Recent advances in urban region representation learning have enabled a wide range of applications in urban analytics, yet existing methods remain limited in their capabilities to generalize across cities and analytic tasks. We aim to generalize urban representation learning beyond city- and task-specific settings, towards a foundation-style model for urban analytics. To this end, we propose UrbanVerse, a model for cross-city urban representation learning and cross-task urban analytics. For cross-city generalization, UrbanVerse focuses on features local to the target regions and structural features of the nearby regions rather than the entire city. We model regions as nodes on a graph, which enables a random walk-based procedure to form "sequences of regions" that reflect both local and neighborhood structural features for urban region representation learning. For cross-task generalization, we propose a cross-task learning module named HCondDiffCT. This module integrates region-conditioned prior knowledge and task-conditioned semantics into the diffusion process to jointly model multiple downstream urban prediction tasks. HCondDiffCT is generic. It can also be integrated with existing urban representation learning models to enhance their downstream task effectiveness. Experiments on real-world datasets show that UrbanVerse consistently outperforms state-of-the-art methods across six tasks under cross-city settings, achieving up to 35.89% improvements in prediction accuracy.

Fengze Sun, Egemen Tanin, Shanika Karunasekera +3

School of Computing and Information System, University of Melbourne, Melbourne, Australia · School of Computer Science and Engineering, University of New South Wales, Sydney, Australia

Urban Representation Learning Geospatial Representation Learning Spatial Generalization Multi-Task Learning Graph Representation Learning

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Abstract

Transfer Learning

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Domain Transfer Becomes Identifiable via a Single Alignment

Disentangling Marginal Capacity from Geometry in Optimal-Transport Label Transfer

UrbanVerse: Learning Urban Region Representation Across Cities and Tasks