Rethinking Time Series Domain Generalization via Structure-Stratified Calibration

Jinyang Li; Shuhao Mei; Xiaoyu Xiao; Shuhang Li; Ruoxi Yun; Jinbo Sun

cs.LGMar 3, 2026

Rethinking Time Series Domain Generalization via Structure-Stratified Calibration

Authors: Jinyang Li, Shuhao Mei, Xiaoyu Xiao, Shuhang Li, Ruoxi Yun, Jinbo Sun

Organizations: Guangzhou Institute of Technology, Xidian University, Xi’an, China.

Abstract

For time series arising from latent dynamical systems, existing cross-domain generalization methods commonly assume that samples are comparably meaningful within a shared representation space. In real-world settings, however, different datasets often originate from structurally heterogeneous families of dynamical systems, leading to fundamentally distinct feature distributions. Under such circumstances, performing global alignment while neglecting structural differences is highly prone to establishing spurious correspondences and inducing negative transfer. From the new perspective of cross-domain structural correspondence failure, we revisit this problem and propose a structurally stratified calibration framework. This approach explicitly distinguishes structurally consistent samples and performs amplitude calibration exclusively within structurally compatible sample clusters, thereby effectively alleviating generalization failures caused by structural incompatibility. Notably, the proposed framework achieves substantial performance improvements through a concise and computationally efficient calibration strategy. Evaluations on 19 public datasets (100.3k samples) demonstrate that SSCF significantly outperforms strong baselines under the zero-shot setting. These results confirm that establishing structural consistency prior to alignment constitutes a more reliable and effective pathway for improving cross-domain generalization of time series governed by latent dynamical systems.

Figures & tables

Figure 1: Overview of structure-consistent domain alignment for time-series domain generalization. (Other) Global alignment ignores structural heterogeneity, causing mismatches between structurally incompatible samples (dashed lines). (Our) We stratify samples by spectral structure and align only within consistent subsets, improving generalization stability.

Figure 2: Overview of the proposed SSCF. Time-series data from the source and target domains are first encoded into shallow feature representations and subsequently stratified in the power spectral feature space to capture coarse-grained spectral patterns. Within each structural stratum, a corresponding reference anchor is constructed. For an arbitrary input sample, SSCF first performs structural matching to identify the most compatible stratum and then conducts amplitude calibration exclusively within that stratum, while explicitly preserving phase information.

Method	LODO	External Target Domains
Method	Avg	ABC	CCSHS	CFS	HMC	ISRUC	Sleep-EDFx	Avg
Baseline	59.76 $\pm$ 0.64	69.26 $\pm$ 1.32	75.60 $\pm$ 0.82	73.33 $\pm$ 0.71	65.08 $\pm$ 2.00	67.76 $\pm$ 1.36	70.55 $\pm$ 1.58	70.26 $\pm$ 1.30
LG-SleepNet	57.45 $\pm$ 0.04	67.82 $\pm$ 0.13	67.68 $\pm$ 0.07	70.05 $\pm$ 0.06	65.18 $\pm$ 0.13	68.83 $\pm$ 0.14	57.14 $\pm$ 0.11	66.12 $\pm$ 0.11
SleepEEGNet	53.22 $\pm$ 0.04	61.08 $\pm$ 0.13	58.11 $\pm$ 0.06	60.92 $\pm$ 0.05	61.97 $\pm$ 0.13	67.72 $\pm$ 0.13	57.07 $\pm$ 0.10	61.15 $\pm$ 0.10
IRM	56.46 $\pm$ 0.63	66.21 $\pm$ 1.53	69.36 $\pm$ 0.83	69.46 $\pm$ 0.73	62.72 $\pm$ 2.06	66.37 $\pm$ 1.45	65.80 $\pm$ 1.72	66.65 $\pm$ 1.39
MMD	62.77 $\pm$ 0.58	70.30 $\pm$ 1.34	76.06 $\pm$ 0.78	74.18 $\pm$ 0.70	66.79 $\pm$ 1.93	69.11 $\pm$ 1.31	70.51 $\pm$ 1.60	71.16 $\pm$ 1.28

Table 1: Overall performance overview (%) for sleep staging under the Leave-One-Domain-Out (LODO) protocol and external target-domain evaluation. The LODO results report the average performance across five source-domain splits, while the external results are evaluated on six unseen target datasets. All results are reported as the mean

\pm

standard deviation over five independent runs. The best results are highlighted in bold.

Arrhythmia
SD	II, III, IV	I, III, IV	I, II, IV	I, II, III
TD	I	II	III	IV	Avg
Baseline	$59.30\pm 0.21$	$89.33\pm 0.16$	$83.98\pm 0.16$	$60.03\pm 0.25$	$73.16\pm 0.20$
CORAL	$56.55\pm 0.22$	$\mathbf{89.59\pm 0.15}$	$86.73\pm 0.15$	$57.86\pm 0.25$	$72.68\pm 0.19$
MMD	$56.71\pm 0.21$	$73.40\pm 0.26$	$60.45\pm 0.27$	$71.19\pm 0.21$	$65.44\pm 0.24$
IRM	$55.17\pm 0.22$	$89.04\pm 0.16$	$88.92\pm 0.14$	$55.76\pm 0.25$	$72.22\pm 0.19$

Table 2: Performance comparison (Macro-F1 score

\pm

standard deviation) under the Leave-One-Domain-Out protocol. The table is divided into two parts: Arrhythmia (top) and Human Activity Recognition (HAR) (bottom). SD denotes the source domains, and TD denotes the target domain. For each task,

K

is selected solely based on source-domain validation, without access to any target-domain samples. The best results are highlighted in bold.

Alignment Strategy	LODO	External Target Domains
Alignment Strategy	Avg	ABC	CCSHS	CFS	HMC	ISRUC	Sleep-EDFx	Avg
Baseline	59.76 $\pm$ 0.64	69.26 $\pm$ 1.32	75.60 $\pm$ 0.82	73.33 $\pm$ 0.71	65.08 $\pm$ 2.00	67.76 $\pm$ 1.36	70.55 $\pm$ 1.58	70.26 $\pm$ 1.30
Global Alignment	66.40 $\pm$ 0.48	67.94 $\pm$ 1.40	76.65 $\pm$ 0.68	73.63 $\pm$ 0.69	66.94 $\pm$ 1.90	68.72 $\pm$ 1.45	72.81 $\pm$ 1.44	71.12 $\pm$ 1.26
Dataset-based Anchor	63.14 $\pm$ 0.48	72.37 $\pm$ 1.27	78.79 $\pm$ 0.70	75.61 $\pm$ 0.68	69.98 $\pm$ 1.80	72.73 $\pm$ 1.41	74.10 $\pm$ 1.33	73.93 $\pm$ 1.20
Ours (Structural)	69.37 $\pm$ 0.49	71.96 $\pm$ 1.24	81.04 $\pm$ 0.58	77.12 $\pm$ 0.65	72.49 $\pm$ 1.75	74.76 $\pm$ 1.16	73.33 $\pm$ 1.42	75.12 $\pm$ 1.13

Table 3: Ablation study on alignment strategies (Macro-F1). Results are reported under the leave-one-domain-out (LODO) evaluation protocol.

Panel of Figure 3 — Figure 3: Sensitivity analysis of SSCF. Top: effect of structural granularity $K$ . Bottom: impact of anchor matching rank $R$ .

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Subjects	Fs	EEG Configuration		EOG Configuration
Dataset	Subjects	(Hz)	Raw Channel	Ref	Raw Channel	Ref
SHHS1	5,652	125	EEG	—	EOG(L)	—
P2018	993	200	C3-M2	M2	E1-M2	M2
MROS1	2,872	256	C4	A1	LOC	A2
MROS2	1,007	256	C4	M1	E1	M2
MESA	2,034	256	EEG1	(Pre-ref)	EOG-L	(Pre-ref)

Appendix

Table 4: Detailed Overview of Sleep Staging Datasets and Signal Configuration

Dataset	Subjects	Fs (Hz)	Original Leads	Used Lead
PTB-XL	18,885	500	12 (Standard)	Lead II
CHAPMAN	10,646	500	12 (Standard)	Lead II
INCART	75	257	12 (Standard)	Lead II
MITBIHADB	48	360	2 (MLII, V5)	MLII

Appendix

Table 5: Overview of ECG Arrhythmia Classification Datasets Used in This Study.

Dataset	Subjects	Fs (Hz)	Device Position	Selected Sensors
WISDM	51	20	Waist / Pocket	Accelerometer
UCIHAR	30	50	Waist	Accelerometer
MotionSense	24	50	Pocket	Accelerometer
USCHAD	14	100	Pocket	Accelerometer

Appendix

Table 6: Overview of Human Activity Recognition (HAR) Datasets.

Figure 4: Spectral visualization of structural stratification in the sleep staging task under $K=8$ . Each subfigure corresponds to one structural stratum and shows the normalized power spectral density (PSD) curves of the samples assigned to that stratum, together with their variability ranges. Different strata exhibit clearly distinct spectral profiles in terms of low-frequency energy concentration, dominant frequency bands, and overall spectral decay behavior, while samples within the same stratum demonstrate high spectral consistency.

Rank	Metric	II, III, IV, V	I, III, IV, V	I, II, IV, V	I, II, III, V	I, II, III, IV	AVG
Rank	Metric	I	II	III	IV	V	AVG
1	ACC	$81.18\pm 0.25$	$75.68\pm 0.67$	$86.23\pm 0.24$	$87.70\pm 0.37$	$76.10\pm 0.44$	$\mathbf{81.38\pm 0.39}$
1	MF1	$71.81\pm 0.27$	$71.13\pm 0.67$	$71.16\pm 0.32$	$68.59\pm 0.67$	$63.16\pm 0.50$	$\mathbf{69.37\pm 0.49}$
2	ACC	$77.27\pm 0.30$	$70.40\pm 0.82$	$81.06\pm 0.31$	$85.33\pm 0.43$	$70.09\pm 0.50$	$\mathbf{76.83\pm 0.47}$
2	MF1	$67.75\pm 0.28$	$66.46\pm 0.76$	$65.42\pm 0.32$	$65.99\pm 0.62$	$57.29\pm 0.48$	$\mathbf{64.58\pm 0.49}$
3	ACC	$69.99\pm 0.34$	$66.83\pm 0.86$	$72.21\pm 0.37$	$80.58\pm 0.57$	$62.42\pm 0.58$	$\mathbf{70.41\pm 0.54}$

Appendix

Table 7: Impact of Anchor Matching Quality on Sleep Staging (LODO, Structural Granularity = 8). The “Rank” represents the matching quality measured by the distance to the MAS template, where a lower rank indicates better quality. I–V correspond to SHHS1, P2018, MROS1, MROS2, and MESA, respectively. Each column leaves one domain out as the target domain (TD) and uses the remaining domains as source domains (SD).

Rank	Metric	II, III, IV, V	I, III, IV, V	I, II, IV, V	I, II, III, V	I, II, III, IV	AVG
Rank	Metric	I	II	III	IV	V	AVG
1	ACC	$79.68\pm 0.27$	$77.02\pm 0.64$	$86.46\pm 0.22$	$87.11\pm 0.39$	$75.98\pm 0.46$	$\mathbf{81.25\pm 0.40}$
1	MF1	$70.32\pm 0.29$	$72.99\pm 0.60$	$73.62\pm 0.29$	$68.71\pm 0.63$	$62.85\pm 0.49$	$\mathbf{69.70\pm 0.46}$
2	ACC	$79.41\pm 0.28$	$75.15\pm 1.85$	$80.92\pm 0.31$	$84.74\pm 0.41$	$69.79\pm 0.51$	$\mathbf{78.00\pm 0.67}$
2	MF1	$70.05\pm 0.30$	$66.24\pm 2.01$	$67.66\pm 0.34$	$62.80\pm 0.53$	$56.78\pm 0.52$	$\mathbf{64.71\pm 0.74}$
3	ACC	$78.60\pm 0.28$	$71.32\pm 2.09$	$70.93\pm 0.40$	$82.51\pm 0.45$	$64.66\pm 0.57$	$\mathbf{73.60\pm 0.76}$

Appendix

Table 8: Impact of Anchor Matching Quality on Sleep Staging (LODO, Structural Granularity = 5). The “Rank” represents the matching quality measured by the distance to the MAS template, where a lower rank indicates better quality. I–V correspond to SHHS1, P2018, MROS1, MROS2, and MESA, respectively. Each column leaves one domain out as the target domain (TD) and uses the remaining domains as source domains (SD).

Rank	Metric	II, III, IV	I, III, IV	I, II, IV	I, II, III	AVG
Rank	Metric	I	II	III	IV	AVG
1	ACC	$98.48\pm 0.09$	$92.04\pm 0.27$	$86.54\pm 0.23$	$99.21\pm 0.04$	$\mathbf{94.07\pm 0.16}$
1	MF1	$98.59\pm 0.08$	$90.41\pm 0.34$	$89.14\pm 0.20$	$99.56\pm 0.02$	$\mathbf{94.43\pm 0.16}$
2	ACC	$98.73\pm 0.05$	$90.73\pm 0.26$	$85.04\pm 0.15$	$99.13\pm 0.05$	$\mathbf{93.41\pm 0.13}$
2	MF1	$98.82\pm 0.05$	$88.71\pm 0.27$	$87.82\pm 0.16$	$99.52\pm 0.02$	$\mathbf{93.72\pm 0.13}$
3	ACC	$99.12\pm 0.08$	$79.20\pm 0.50$	$80.96\pm 0.25$	$98.98\pm 0.04$	$\mathbf{89.57\pm 0.22}$

Appendix

Table 9: Impact of Anchor Matching Quality on HAR (LODO, Structural Granularity = 8). The “Rank” represents the matching quality measured by the distance to the MAS template, where a lower rank indicates better quality. I–IV correspond to MotionSense, UCIHAR, USCHAD, and WISDM, respectively. Each column leaves one domain out as the target domain (TD) and uses the remaining domains as source domains (SD).

Rank	Metric	ABC	CCSHS	CFS	HMC	ISRUC	Sleep-EDFx	AVG
1	ACC	$76.88\pm 1.45$	$88.43\pm 0.50$	$86.92\pm 0.55$	$77.48\pm 1.87$	$79.04\pm 1.32$	$81.73\pm 1.25$	$\mathbf{81.75\pm 1.16}$
1	MF1	$71.96\pm 1.24$	$81.04\pm 0.58$	$77.12\pm 0.65$	$72.49\pm 1.75$	$74.76\pm 1.16$	$73.33\pm 1.42$	$\mathbf{75.12\pm 1.13}$
2	ACC	$70.46\pm 1.72$	$88.34\pm 0.49$	$86.95\pm 0.56$	$75.93\pm 1.86$	$77.89\pm 1.40$	$76.93\pm 1.64$	$\mathbf{79.42\pm 1.28}$
2	MF1	$64.27\pm 1.67$	$79.60\pm 0.60$	$75.59\pm 0.66$	$69.52\pm 1.71$	$71.95\pm 1.33$	$67.25\pm 1.77$	$\mathbf{71.36\pm 1.29}$
3	ACC	$61.93\pm 2.06$	$83.43\pm 0.66$	$82.60\pm 0.72$	$69.70\pm 1.92$	$73.24\pm 1.81$	$70.12\pm 2.11$	$\mathbf{73.50\pm 1.55}$
3	MF1	$55.85\pm 1.72$	$71.38\pm 0.78$	$68.89\pm 0.75$	$62.39\pm 1.66$	$66.02\pm 1.55$	$59.97\pm 2.03$	$\mathbf{64.08\pm 1.42}$

Appendix

Table 10: Impact of Anchor Matching Quality on Sleep Staging (Independent Test Sets, Structural Granularity = 8). Performance (mean

\pm

std). The “Rank” indicates the distance to the MAS template (lower is better). The last column (AVG) reports the average performance across all datasets.

Rank	Metric	ABC	CCSHS	CFS	HMC	ISRUC	Sleep-EDFx	AVG
1	ACC	$77.35\pm 1.48$	$86.63\pm 0.63$	$85.63\pm 0.62$	$76.99\pm 1.86$	$78.31\pm 1.35$	$81.57\pm 1.24$	$\mathbf{81.08\pm 1.20}$
1	MF1	$72.26\pm 1.20$	$79.01\pm 0.69$	$75.49\pm 0.71$	$71.95\pm 1.74$	$74.00\pm 1.19$	$73.10\pm 1.39$	$\mathbf{74.30\pm 1.15}$
2	ACC	$71.14\pm 1.64$	$87.12\pm 0.53$	$86.07\pm 0.59$	$75.62\pm 1.81$	$77.99\pm 1.27$	$76.90\pm 1.64$	$\mathbf{79.14\pm 1.25}$
2	MF1	$64.75\pm 1.48$	$77.67\pm 0.62$	$74.08\pm 0.70$	$69.41\pm 1.57$	$72.16\pm 1.16$	$66.88\pm 1.79$	$\mathbf{70.83\pm 1.22}$
3	ACC	$67.02\pm 1.93$	$85.42\pm 0.53$	$84.81\pm 0.60$	$72.42\pm 1.82$	$75.62\pm 1.40$	$73.67\pm 1.85$	$\mathbf{76.49\pm 1.36}$
3	MF1	$59.88\pm 1.61$	$73.34\pm 0.64$	$70.62\pm 0.67$	$65.27\pm 1.54$	$68.46\pm 1.26$	$62.60\pm 1.84$	$\mathbf{66.70\pm 1.26}$

Appendix

Table 11: Impact of Anchor Matching Quality on Sleep Staging (Independent Test Sets, Structural Granularity = 5). Performance (mean

\pm

std). The “Rank” indicates the distance to the MAS template (lower is better). The last column (AVG) reports the average performance across all datasets.

Granularity	Metric	II, III, IV, V	I, III, IV, V	I, II, IV, V	I, II, III, V	I, II, III, IV	AVG
Granularity	Metric	I	II	III	IV	V	AVG
1	ACC	$79.76\pm 0.26$	$71.68\pm 0.82$	$85.36\pm 0.23$	$84.67\pm 0.43$	$80.36\pm 0.38$	$\mathbf{80.37\pm 0.42}$
1	MF1	$69.20\pm 0.27$	$63.64\pm 0.74$	$70.41\pm 0.34$	$62.65\pm 0.59$	$66.08\pm 0.48$	$\mathbf{66.40\pm 0.48}$
2	ACC	$82.72\pm 0.23$	$68.89\pm 0.76$	$86.29\pm 0.22$	$86.56\pm 0.43$	$78.72\pm 0.40$	$\mathbf{80.64\pm 0.41}$
2	MF1	$72.48\pm 0.26$	$58.47\pm 0.79$	$73.99\pm 0.30$	$66.60\pm 0.73$	$64.00\pm 0.47$	$\mathbf{67.11\pm 0.51}$
3	ACC	$80.77\pm 0.24$	$72.98\pm 0.71$	$81.92\pm 0.33$	$85.17\pm 0.41$	$79.95\pm 0.44$	$\mathbf{80.16\pm 0.43}$

Appendix

Table 12: Sensitivity to Structural Granularity on Sleep Staging (LODO). Performance comparison with Structural Granularity varying from 1 to 8. I–V correspond to SHHS1, P2018, MROS1, MROS2, and MESA, respectively. Each column leaves one domain out as the target domain (TD) and uses the remaining domains as source domains (SD).

Granularity	Metric	II, III, IV	I, III, IV	I, II, IV	I, II, III	AVG
Granularity	Metric	I	II	III	IV	AVG
1	ACC	$61.62\pm 0.18$	$80.99\pm 0.24$	$80.92\pm 0.22$	$65.92\pm 0.22$	$\mathbf{72.36\pm 0.22}$
1	MF1	$69.56\pm 0.17$	$89.51\pm 0.16$	$89.28\pm 0.14$	$76.70\pm 0.18$	$\mathbf{81.26\pm 0.16}$
2	ACC	$54.84\pm 0.19$	$76.37\pm 0.27$	$81.58\pm 0.21$	$52.18\pm 0.24$	$\mathbf{66.24\pm 0.23}$
2	MF1	$58.94\pm 0.21$	$83.02\pm 0.22$	$88.78\pm 0.14$	$61.95\pm 0.24$	$\mathbf{73.17\pm 0.20}$
4	ACC	$55.16\pm 0.18$	$78.12\pm 0.26$	$77.37\pm 0.23$	$53.47\pm 0.23$	$\mathbf{66.03\pm 0.23}$

Appendix

Table 13: Sensitivity to Structural Granularity on Arrhythmia Detection (LODO). Performance comparison with Structural Granularity varying from 1 to 16. I–IV correspond to PTB-XL, MITBIHADB, INCART, and CHAPMAN, respectively. Each column leaves one domain out as the target domain (TD) and uses the remaining domains as source domains (SD).

Granularity	Metric	II, III, IV	I, III, IV	I, II, IV	I, II, III	AVG
Granularity	Metric	I	II	III	IV	AVG
1	ACC	$99.34\pm 0.06$	$83.91\pm 0.36$	$86.57\pm 0.23$	$98.15\pm 0.07$	$\mathbf{91.99\pm 0.18}$
1	MF1	$99.39\pm 0.05$	$78.48\pm 0.52$	$89.16\pm 0.20$	$98.99\pm 0.04$	$\mathbf{91.51\pm 0.20}$
2	ACC	$99.21\pm 0.06$	$88.68\pm 0.32$	$87.48\pm 0.23$	$98.28\pm 0.06$	$\mathbf{93.41\pm 0.17}$
2	MF1	$99.27\pm 0.06$	$85.75\pm 0.42$	$89.95\pm 0.20$	$99.05\pm 0.04$	$\mathbf{93.51\pm 0.18}$
3	ACC	$98.77\pm 0.08$	$89.82\pm 0.30$	$87.42\pm 0.23$	$98.06\pm 0.07$	$\mathbf{93.52\pm 0.17}$

Appendix

Table 14: Sensitivity to Structural Granularity on HAR (LODO). Performance comparison with Structural Granularity varying from 1 to 8. I–IV correspond to MotionSense, UCIHAR, USCHAD, and WISDM, respectively. Each column leaves one domain out as the target domain (TD) and uses the remaining domains as source domains (SD).

Granularity	Metric	ABC	CCSHS	CFS	HMC	ISRUC	Sleep-EDFx	AVG
1	ACC	$75.17\pm 1.58$	$85.96\pm 0.53$	$85.82\pm 0.53$	$73.39\pm 2.00$	$74.79\pm 1.55$	$82.13\pm 1.27$	$\mathbf{79.54\pm 1.24}$
1	MF1	$67.94\pm 1.40$	$76.65\pm 0.68$	$73.63\pm 0.69$	$66.94\pm 1.90$	$68.72\pm 1.45$	$72.81\pm 1.44$	$\mathbf{71.12\pm 1.26}$
2	ACC	$76.07\pm 1.57$	$85.77\pm 0.55$	$85.79\pm 0.55$	$72.18\pm 1.97$	$73.76\pm 1.61$	$82.70\pm 1.19$	$\mathbf{79.38\pm 1.24}$
2	MF1	$68.91\pm 1.41$	$77.15\pm 0.65$	$74.50\pm 0.69$	$65.88\pm 1.94$	$67.66\pm 1.58$	$73.37\pm 1.37$	$\mathbf{71.25\pm 1.27}$
3	ACC	$76.67\pm 1.54$	$86.74\pm 0.58$	$86.07\pm 0.59$	$76.24\pm 1.94$	$77.95\pm 1.37$	$77.95\pm 1.37$	$\mathbf{80.27\pm 1.23}$
3	MF1	$71.46\pm 1.23$	$78.88\pm 0.65$	$75.64\pm 0.68$	$71.61\pm 1.74$	$73.38\pm 1.25$	$73.38\pm 1.25$	$\mathbf{74.06\pm 1.13}$

Appendix

Table 15: Sensitivity to Structural Granularity on Sleep Staging (Independent Test Sets). Performance comparison (mean

\pm

std) with Structural Granularity varying from 1 to 8. The last column (AVG) reports the average performance across all six independent datasets.

Method	LODO	External Target Domains
Method	Avg	ABC	CCSHS	CFS	HMC	ISRUC	Sleep-EDFx	Avg
Baseline	73.49 $\pm$ 0.57	76.57 $\pm$ 1.63	84.83 $\pm$ 0.70	84.72 $\pm$ 0.62	71.61 $\pm$ 2.12	74.57 $\pm$ 1.53	80.52 $\pm$ 1.35	78.80 $\pm$ 1.33
LG-SleepNet	67.80 $\pm$ 0.03	73.32 $\pm$ 0.12	79.44 $\pm$ 0.05	81.00 $\pm$ 0.04	70.92 $\pm$ 0.13	73.89 $\pm$ 0.13	62.21 $\pm$ 0.10	73.46 $\pm$ 0.10
SleepEEGNet	59.59 $\pm$ 0.03	61.49 $\pm$ 0.13	63.33 $\pm$ 0.06	67.45 $\pm$ 0.05	62.86 $\pm$ 0.13	68.46 $\pm$ 0.14	58.41 $\pm$ 0.10	63.67 $\pm$ 0.10
IRM	70.94 $\pm$ 0.60	73.90 $\pm$ 1.80	81.73 $\pm$ 0.75	82.91 $\pm$ 0.64	70.32 $\pm$ 2.17	73.81 $\pm$ 1.67	76.81 $\pm$ 1.53	76.58 $\pm$ 1.43
MMD	74.97 $\pm$ 0.47	76.81 $\pm$ 1.64	85.28 $\pm$ 0.67	85.16 $\pm$ 0.60	72.77 $\pm$ 2.10	75.37 $\pm$ 1.49	80.16 $\pm$ 1.37	79.26 $\pm$ 1.31

Appendix

Table 16: Sleep staging performance (Accuracy) under leave-one-domain-out (LODO) evaluation and external target domain testing. LODO explains average performance across five source-domain splits. External results are evaluated on six unseen target datasets. All values are reported as mean

\pm

std over five runs.

Arrhythmia
SD	II, III, IV	I, III, IV	I, II, IV	I, II, III
TD	I	II	III	IV	Avg
Baseline	$56.77\pm 0.18$	$83.06\pm 0.23$	$74.71\pm 0.23$	$49.95\pm 0.24$	$66.12\pm 0.22$
CORAL	$55.55\pm 0.18$	$\mathbf{83.26\pm 0.23}$	$78.62\pm 0.22$	$48.65\pm 0.23$	$66.52\pm 0.22$
MMD	$53.85\pm 0.18$	$63.17\pm 0.30$	$49.86\pm 0.27$	$59.80\pm 0.23$	$56.67\pm 0.25$
IRM	$54.62\pm 0.19$	$82.77\pm 0.23$	$\mathbf{81.59\pm 0.21}$	$46.66\pm 0.23$	$66.41\pm 0.22$

Appendix

Table 17: Performance comparison (Accuracy

\pm

Std). The table is organized into two panels: Arrhythmia (top) and HAR (bottom). SD: Source Domains, TD: Target Domain. The best results are highlighted in bold.

Method	Metric	II, III, IV, V	I, III, IV, V	I, II, IV, V	I, II, III, V	I, II, III, IV	AVG
Method	Metric	I	II	III	IV	V	AVG
Baseline	ACC	$76.58\pm 0.31$	$69.34\pm 0.76$	$85.04\pm 0.25$	$82.21\pm 0.73$	$54.26\pm 0.80$	$73.49\pm 0.57$
Baseline	MF1	$66.40\pm 0.33$	$59.44\pm 0.74$	$69.09\pm 0.36$	$65.90\pm 0.79$	$37.98\pm 1.00$	$59.76\pm 0.64$
LG-SleepNet	ACC	$71.79\pm 0.02$	$43.21\pm 0.05$	$79.56\pm 0.02$	$82.02\pm 0.03$	$62.41\pm 0.03$	$67.80\pm 0.03$
LG-SleepNet	MF1	$61.48\pm 0.02$	$41.91\pm 0.05$	$68.48\pm 0.03$	$65.04\pm 0.06$	$50.34\pm 0.04$	$57.45\pm 0.04$
SleepEEGNet	ACC	$63.68\pm 0.02$	$60.63\pm 0.05$	$71.42\pm 0.02$	$67.30\pm 0.04$	$34.90\pm 0.03$	$59.59\pm 0.03$

Appendix

Table 18: Performance Comparison of Different Methods on Sleep Staging (LODO). I–V correspond to SHHS1, P2018, MROS1, MROS2, and MESA, respectively. Each column leaves one domain out as the target domain (TD) and uses the remaining domains as source domains (SD). ACC and Macro-F1 (MF1) are reported as mean

\pm

std.

Domain Generalization

Domain generalization develops models that perform reliably in new environments without training on target-domain data.

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STEP: Scientific Time-Series Encoder Pretraining via Cross-Domain Distillation

Chen Zhang, Liwei Liu, Jun Tao, Xiaoyu Yang+5

Shanghai Aritificial Intelligence Laboratory · Tsinghua University · Harbin Institute of Technology+2

Time Series Representation Learning Time-Series Foundation Models Cross-Domain Transfer Learning

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Scientific time series are central to scientific AI but are typically sparse, highly heterogeneous, and limited in scale, making unified representation learning particularly challenging. Meanwhile, foundation models pretrained on relevant time series domains such as audio, general time series, and brain signals contain rich knowledge, but their applicability to scientific signals remains underexplored. In this paper, we investigate the transferability and complementarity of foundation models from relevant time series domains, and study how to effectively leverage them to build a unified encoder for scientific time series. We first systematically evaluate relevant foundation models, showing the effectiveness of knowledge transfer to scientific tasks and their complementary strengths. Based on this observation, we propose STEP, a Scientific Time Series Encoder Pretraining framework via cross domain distillation. STEP introduces adaptive patching to handle extreme-length sequences and a statistics compensation scheme to accommodate diverse numerical scales. It further leverages cross-domain distillation to integrate knowledge from multiple foundation models into a unified encoder. By combining complementary representations across different domains, STEP learns general-purpose and transferable features tailored for scientific signals. Experiments on seven scientific time series tasks demonstrate that STEP provides both an effective structure and an effective pretraining paradigm, taking a STEP toward scientific time series representation learning.

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Domain Generalization

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