CAMOS: Coupled Oscillatory State-Space Model for Multimodal Clinical Time-Series

Maxx Richard Rahman; Mostafa Hammouda; Wolfgang Maass

stat.MLSep 30, 2026

CAMOS: Coupled Oscillatory State-Space Model for Multimodal Clinical Time-Series

Authors: Maxx Richard Rahman, Mostafa Hammouda, Wolfgang Maass

Organizations: Saarland University and German Research Center for Artificial Intelligence (DFKI) Saarbrücken, Germany · Saarland University Saarbrücken, Germany

Abstract

Longitudinal clinical cohorts are multimodal, irregularly sampled and pervasively incomplete: in ADNI, positron emission tomography and cerebrospinal fluid assays are absent from roughly half of all visits. Linear state-space models handle irregular sampling gracefully but treat a missing modality by masking the input, leaving the transition operator untouched. We prove that this is a representational limitation: the latent state of any linear state-space layer whose transition operator does not depend on the availability pattern is an additive function of the availability indicators, so no such layer can represent an interaction between two modalities being jointly present or jointly absent. We propose CAMOS, which gives each modality a bank of second-order oscillators coupled through a matrix that sits inside the differential equation and is gated by availability, so the transition operator itself becomes a function of which measurements were taken. Coupling invalidates the analysis of uncoupled oscillatory models, and we restore it: a per-channel Gershgorin budget makes the effective stiffness positive definite uniformly over all $2^M$ availability patterns and all gaps, an energy argument charges amplification to availability transitions rather than sequence length, and a channel factorization preserves exact associative parallel scans. On ADNI, CAMOS outperforms uncoupled oscillatory state-space models and clinical fusion models on same-visit staging, landmark prediction and longitudinal forecasting, and under zero-shot transfer to OASIS-3 it is the only model that avoids collapse to the majority class.

Figures & tables

Figure 1: CAMOS architecture consists of static and longitudinal multimodal patient data through availability-gated coupled oscillators, irregular-time dynamics, and cross-modal attention.

ADNI
Models	Accuracy $\uparrow$	Macro F1 $\uparrow$	Macro Prec. $\uparrow$	Macro Recall $\uparrow$	Macro Spec. $\uparrow$
LinOSS-IM	$0.6593_{\pm 0.0041}$	$0.6815_{\pm 0.0039}$	$0.6804_{\pm 0.0045}$	$0.6864_{\pm 0.0037}$	$0.8147_{\pm 0.0021}$
LinOSS-IMEX	$0.7206_{\pm 0.0058}$	$0.7234_{\pm 0.0061}$	$0.7394_{\pm 0.0055}$	$0.7424_{\pm 0.0059}$	$0.8513_{\pm 0.0030}$
MedFuse	$0.6648_{\pm 0.0072}$	$0.6697_{\pm 0.0076}$	$0.6564_{\pm 0.0069}$	$0.7139_{\pm 0.0070}$	$0.8284_{\pm 0.0034}$
DrFuse	$0.7322_{\pm 0.0049}$	$0.7354_{\pm 0.0046}$	$0.7488_{\pm 0.0044}$	$0.7683_{\pm 0.0042}$	$0.8599_{\pm 0.0024}$
CAMOS	$\textbf{0.7824}^{\dagger}_{\pm\textbf{0.0016}}$	$\textbf{0.7790}^{\dagger}_{\pm\textbf{0.0018}}$	$\textbf{0.7970}^{\dagger}_{\pm\textbf{0.0022}}$	$\textbf{0.7786}^{\dagger}_{\pm\textbf{0.0025}}$	$\textbf{0.8836}^{\dagger}_{\pm\textbf{0.0013}}$

Table 1: Same-visit CN/MCI/AD staging on ADNI and OASIS-3. † denotes that CAMOS is significantly better than the best baseline (

p<0.01

, two-sided Welch’s

t

-test).

	ADNI		OASIS-3
Models	AUROC $\uparrow$	AUPRC $\uparrow$	AUROC $\uparrow$	AUPRC $\uparrow$
LinOSS-IM	$0.9223_{\pm 0.0031}$	$0.7102_{\pm 0.0087}$	$0.9533_{\pm 0.0024}$	$0.3588_{\pm 0.0142}$
LinOSS-IMEX	$0.9307_{\pm 0.0027}$	$0.7389_{\pm 0.0074}$	$0.9560_{\pm 0.0029}$	$0.4185_{\pm 0.0163}$
MedFuse	$0.9134_{\pm 0.0045}$	$0.6900_{\pm 0.0102}$	$0.8467_{\pm 0.0058}$	$0.2594_{\pm 0.0121}$
DrFuse	$0.9386_{\pm 0.0022}$	$0.7689_{\pm 0.0069}$	$0.8787_{\pm 0.0047}$	$0.3183_{\pm 0.0135}$
CAMOS	$\textbf{0.9611}^{\dagger}_{\pm\textbf{0.0014}}$	$\textbf{0.8687}^{\dagger}_{\pm\textbf{0.0041}}$	$\textbf{0.9600}^{*}_{\pm\textbf{0.0018}}$	$\textbf{0.7894}^{\dagger}_{\pm\textbf{0.0093}}$

Table 2: 3-year MCI-AD landmark prediction on ADNI and OASIS-3. CAMOS is significantly better than the best baseline at

{}^{\dagger}p<0.01

{}^{*}p<0.05

(two-sided Welch’s

t

-test).

Panel of Figure 2 — Figure 2: Next-visit ( $h=1$ ) forecasting on ADNI (left) and OASIS (right) per modality.

Panel of Figure 3 — Figure 3: Relative improvement of CAMOS over the best baseline on each of the reported metrics.

	Staging	Landmark Prediction		Longitudinal Forecasting
Variants	Macro F1 $\uparrow$	AUROC $\uparrow$	AUPRC $\uparrow$	Sparse MAE $\downarrow$	Dense MAE $\downarrow$
w/o coupling ( $C\equiv 0$ )	$0.7561_{\pm 0.0034}$	$0.9530_{\pm 0.0021}$	$0.8193_{\pm 0.0068}$	$0.5491_{\pm 0.0057}$	$0.4354_{\pm 0.0032}$
w coupling ungated ( $g_{kj}^{n}\equiv 1$ )	$0.7694_{\pm 0.0029}$	$0.9478_{\pm 0.0026}$	$0.7916_{\pm 0.0081}$	$0.5668_{\pm 0.0063}$	$0.4487_{\pm 0.0038}$
w asymmetric gate ( $g_{kj}^{n}=a_{j}^{n}$ )	$0.7532_{\pm 0.0041}$	$0.9562_{\pm 0.0019}$	$0.8384_{\pm 0.0059}$	$0.5315_{\pm 0.0049}$	$0.4176_{\pm 0.0027}$
w IMEX discretization	$0.6530_{\pm 0.0062}$	$0.9546_{\pm 0.0024}$	$0.8063_{\pm 0.0074}$	$0.7127_{\pm 0.0089}$	$0.5057_{\pm 0.0046}$
CAMOS	$\textbf{0.7790}_{\pm\textbf{0.0018}}$	$\textbf{0.9611}_{\pm\textbf{0.0014}}$	$\textbf{0.8687}_{\pm\textbf{0.0041}}$	$\textbf{0.5097}_{\pm\textbf{0.0036}}$	$\textbf{0.4029}_{\pm\textbf{0.0022}}$

Table 3: Ablation study evaluating the contribution of coupling, gating, and discretisation choices.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning	Symbol	Meaning
$M$	number of modalities ( $M=4$ )	$d$	oscillators per modality
$N$	visits for a subject	$m=Md$	total latent width
$h$	shared projection width	$L$	number of GCO blocks
$p_{k}$	raw dimension of modality $k$	$p_{s}$	static covariate dimension
$t_{n}$	time of visit $n$ (years)	$\Delta t_{n}$	$t_{n}-t_{n-1}>0$
$u_{k}^{n}\in\mathbb{R}^{p_{k}}$	raw features	$\tilde{u}_{k}^{n}\in\mathbb{R}^{h}$	projected

Appendix

Table 7

Panel of Figure 4 — Figure 4: Input gating versus transition gating. In (a) the indicators multiply the forcing only, so the state unrolls into a sum of per-modality, per-visit contributions and every mixed availability difference vanishes. In (b) the gate enters the homogeneous part, so the state is a product of availability-dependent operators and contains genuine interactions among availability indicators.

Group	Setting	Value
Architecture	GCO blocks $L$	grid $\{2,4,6\}$
	oscillators per modality $d$	grid $\{32,64,128\}$
	projection width $h$	grid $\{32,64,128\}$
	attention heads $H$	$4$
	dropout	$0.1$
	static encoder	$2$ -layer MLP, width $2m$ , GELU

Appendix

Table 4: Complete CAMOS configuration.

Dataset	Role	$M$	$p$	Subjects	Visits	Mean visits/subj.	Max visits/subj.	Missing (%)
ADNI	train / val / test	4	19	2749	7432	2.7	15	32.5
OASIS-3	zero-shot	3	19	1377	8522	6.2	20	28

Appendix

Table 5: Cohort statistics.

M

: number of modalities;

p=\sum_{k}p_{k}

: total raw feature dimension; missing rate: percentage of modality-visit pairs unobserved.

ADNI
Models	Accuracy $\uparrow$	Macro F1 $\uparrow$	Macro Prec. $\uparrow$	Macro Recall $\uparrow$	Macro Spec. $\uparrow$
LinOSS-IM	$0.6593_{\pm 0.0041}$	$0.6815_{\pm 0.0039}$	$0.6804_{\pm 0.0045}$	$0.6864_{\pm 0.0037}$	$0.8147_{\pm 0.0021}$
LinOSS-IMEX	$0.7206_{\pm 0.0058}$	$0.7234_{\pm 0.0061}$	$0.7394_{\pm 0.0055}$	$0.7424_{\pm 0.0059}$	$0.8513_{\pm 0.0030}$
D-LinOSS	$0.6820_{\pm 0.0324}$	$0.6882_{\pm 0.0271}$	$0.6912_{\pm 0.0294}$	$0.6975_{\pm 0.0281}$	$0.8392_{\pm 0.0152}$
S5	$0.6562_{\pm 0.0226}$	$0.6696_{\pm 0.0196}$	$0.6731_{\pm 0.0207}$	$0.6804_{\pm 0.0196}$	$0.8215_{\pm 0.0118}$
Mamba	$0.7187_{\pm 0.0203}$	$0.7304_{\pm 0.0163}$	$0.7386_{\pm 0.0174}$	$0.7412_{\pm 0.0169}$	$0.8561_{\pm 0.0097}$

Appendix

Table 6: Same-visit CN/MCI/AD staging on ADNI (in-distribution) and OASIS-3 (zero-shot).

Panel of Figure 5 — Figure 5: ROC and PR curves for 3-year MCI-to-AD landmark prediction on ADNI (left) and OASIS-3 (right).

	ADNI		OASIS-3
Models	AUROC $\uparrow$	AUPRC $\uparrow$	AUROC $\uparrow$	AUPRC $\uparrow$
LinOSS-IM	$0.9223_{\pm 0.0031}$	$0.7102_{\pm 0.0087}$	$0.9533_{\pm 0.0024}$	$0.3588_{\pm 0.0142}$
LinOSS-IMEX	$0.9307_{\pm 0.0027}$	$0.7389_{\pm 0.0074}$	$0.9560_{\pm 0.0029}$	$0.4185_{\pm 0.0163}$
D-LinOSS	$0.9142_{\pm 0.0187}$	$0.7022_{\pm 0.0721}$	$0.8236_{\pm 0.0412}$	$0.1134_{\pm 0.0481}$
S5	$0.9087_{\pm 0.0163}$	$0.6925_{\pm 0.06201}$	$0.9412_{\pm 0.0265}$	$0.5982_{\pm 0.1889}$
Mamba	$0.8795_{\pm 0.0204}$	$0.6187_{\pm 0.0686}$	$0.8418_{\pm 0.0537}$	$0.1260_{\pm 0.1104}$

Appendix

Table 7: 3-year MCI-to-AD conversion on ADNI (in-distribution) and OASIS-3 (zero-shot).

	Cognition $\downarrow$		CSF $\downarrow$		Genetics $\downarrow$		Imaging $\downarrow$
Model	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
LinOSS-IM	0.4471	0.7704	0.7715	1.0832	0.8270	0.9662	0.4468	0.8457
LinOSS-IMEX	0.4343	0.7526	0.7676	1.0795	0.8183	0.9607	0.5567	0.8053
D-LinOSS	0.5579	0.8736	0.7651	1.0724	0.7802	0.9731	0.6017	0.8612
S5	0.4973	0.8012	0.7591	1.0689	0.5147	0.9712	0.5945	0.8547
Mamba	0.4932	0.7894	0.7056	1.0180	0.5964	0.9480	0.5646	0.8273

Appendix

Table 8: Next-visit (

h=1

) forecasting on ADNI per modality.

	Imaging $\downarrow$		Cognition $\downarrow$		Genetics $\downarrow$
Model	MAE	RMSE	MAE	RMSE	MAE	RMSE
LinOSS-IM	0.7748	0.9968	0.6719	0.9356	0.7993	1.0398
LinOSS-IMEX	0.7745	0.9966	0.6712	0.9352	0.8011	1.0408
D-LinOSS	0.7721	0.9937	0.6789	0.9387	0.7904	1.0341
S5	0.8116	1.0342	0.6916	0.9512	0.7840	1.0296
Mamba	0.7866	1.0081	0.6867	0.9458	0.7711	1.0213

Appendix

Table 9: Next-visit (

h=1

) forecasting on OASIS-3 per modality.

	Staging	Landmark Prediction		Longitudinal Forecasting
Variants	Macro F1 $\uparrow$	AUROC $\uparrow$	AUPRC $\uparrow$	Img. MAE $\downarrow$	Clin. MAE $\downarrow$	Gen. MAE $\downarrow$
w/o coupling ( $C\equiv 0$ )	$0.5422_{\pm 0.0285}$	$0.9678_{\pm 0.0203}$	$0.7677_{\pm 0.0802}$	$0.7647_{\pm 0.0197}$	$0.3947_{\pm 0.0097}$	$0.3214_{\pm 0.0056}$
w coupling ungated ( $g_{kj}^{n}\equiv 1$ )	$0.5341_{\pm 0.0339}$	$0.9602_{\pm 0.0350}$	$0.7324_{\pm 0.0991}$	$0.7798_{\pm 0.0201}$	$0.4075_{\pm 0.0116}$	$0.3392_{\pm 0.0076}$
w asymmetric gate ( $g_{kj}^{n}=a_{j}^{n}$ )	$0.5493_{\pm 0.0341}$	$0.9661_{\pm 0.0361}$	$0.7586_{\pm 0.1121}$	$0.7702_{\pm 0.0201}$	$0.3989_{\pm 0.0116}$	$0.3298_{\pm 0.0076}$
w IMEX discretization	$0.4880_{\pm 0.0425}$	$0.9535_{\pm 0.0308}$	$0.7069_{\pm 0.1782}$	$0.8173_{\pm 0.0255}$	$0.6110_{\pm 0.0265}$	$0.7032_{\pm 0.0131}$
CAMOS	$\textbf{0.5573}_{\pm\textbf{0.0260}}$	$\textbf{0.9707}_{\pm\textbf{0.0210}}$	$\textbf{0.7777}_{\pm\textbf{0.0626}}$	$\textbf{0.7614}_{\pm\textbf{0.0190}}$	$\textbf{0.3913}_{\pm\textbf{0.0111}}$	$\textbf{0.3210}_{\pm\textbf{0.0045}}$

Appendix

Table 10: Ablation study evaluating the contribution of coupling, gating, and discretisation choices on OASIS-3.

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Jun 6, 2026, cs.LGJ/K move · Enter open · S save

LongMoE: Longitudinal Multimodal Learning via Trajectory-Aware Mixture-of-Experts

Maxx Richard Rahman, Prakhar Kumar, Wolfgang Maass

German Research Centre for Artificial Intelligence (DFKI) Saarbrücken, Germany

Multimodal Clinical Data Missing Modalities Multimodal Learning Trajectory-Aware Hidden-State Analyses

Open paper AskPDF arXiv

Multimodal clinical learning is increasingly important for integrating diverse patient data, including imaging, text, and personalised health records. However, it faces two fundamental challenges: i) modality missingness, where arbitrary subsets of modalities are unavailable at a given patient visit, ii) longitudinal dynamics, where the diagnostic significance of an observation depends on the patient's evolving disease trajectory over time. Existing methods address these challenges in isolation: missing-modality frameworks treat each visit as an independent static snapshot and discard temporal context, while longitudinal models often assume complete modality availability and degrade under systematic modality incompleteness. We propose LongMoE (Longitudinal Mixture-of-Experts), the unified framework to jointly address both challenges. LongMoE combines a context-aware imputation module with an attentional tokenization module that captures frequency-domain temporal patterns across irregular visit sequences, a trajectory-aware encoder for modeling disease progression, and context-conditioned Sparse MoE routing for patient-specific expert selection. Experiments on ADNI, OASIS-3, and MIMIC-IV show that LongMoE improves robustness under missing or weak contemporaneous modalities and remains competitive in full-modality settings, establishing a strong foundation for longitudinally-aware multimodal clinical learning.

Abstract

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