MIRA: Medical Time Series Foundation Model for Real-World Health Data
Authors: Hao Li
Bowen Deng
Chang Xu
ZhiYuan Feng
Viktor Schlegel
Yu-Hao Huang
Yizheng Sun
Jingyuan Sun
Kailai Yang
Yiyao Yu
Jiang Bian
Venue: NeurIPS 2025 poster ()
Keywords: Time Series
Foundation Model
Healthcare
Primary area: machine_learning_for_sciences
TL;DR: A foundation model specifically designed for medical time series forecasting

Abstract: A unified foundation model for medical time series—pretrained on open access and ethically reviewed medical corpora—offers the potential to reduce annotation burdens, minimize model customization, and enable robust transfer across clinical institutions, modalities, and tasks, particularly in data-scarce or privacy-constrained environments.  However, existing time series foundation models struggle to handle medical time series data due to its inherent challenges, including irregular intervals, heterogeneous sampling rates, and frequent missingness. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates a Continuous-Time Rotary Positional Encoding that enables fine-grained modeling of variable time intervals, a frequency-specific mixture-of-experts layer that routes computation across latent frequency regimes to further promote temporal specialization, and a Continuous Dynamics Extrapolation Block based on Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on a large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieving reductions in forecasting errors by an average of 8% and 6% in out-of-distribution and in-distribution scenarios, respectively. We also introduce a comprehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling.

MIRA: Medical Time Series Foundation Model for Real-World Health Data
Hao 1,2 Bowen Deng 1,3 Chang Xu
Zhiyuan Feng
Viktor Schlegel 2,6
Yu-Hao Huang Yizheng Sun 2
Jingyuan Sun
Kailai Yang? 2
Yiyao Yu Jiang Bian
Microsoft Research
University of Manchester 3 Peking University
Nanjing University Imperial Global Singapore, Imperial College London
Tsinghua University
Abstract
A foundation model for medical time series, pretrained ethically approved clinical datasets, can substantially reduce annotation burdens, minimize the need for task-specific tuning, and promote reliable transferability across healthcare institutions, data modalities, and clinical tasks, especially data-scarce or privacy- sensitive environments, However, existing generalist time series foundation models struggle to handle medical time series data due to their inherent challenges, includ- ing irregular intervals, hetcrogeneous sampling rates, and frequent missing values. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates Continuous- Time Rotary Positional Encoding that enables fine seee-griied modeling of variable time intervals, frequency-speciffc mixture-of-exppers layer that routes computation across latent frequency regimes to further promote temporal special- ization, and Continuous Dynamics Extrapolation Block based Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieves reductions in forecasting errors by an average of 8% and 6% in -iitr---istiiittonnn and in-distribution scenarios, respectively, when compared to other pero-shot and fine-tuned baselines. We also introduce a com- prehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling. Our code available at Mi Microsoft/MTRA.
Introduction
Medical time series data, including signals such as electrocardiograms (ECG) [1]. electroenceehalo- grams (EEG) [2], vital signs and laboratory measurements [3], are key to understanding the dynamic physiological states of patients over time [4, 5]. Continuously modeling these patient data trajectories supports clinical forecasting tasks such as predicting organ failure or treatment response [1, 6]. enabling earlier decisions and better patient outcomes [7, 8]. However, effectively utilizing medical time series data practice remains challenging, as patient populations, disease profiles, and clinical protocols can vary widely across regions and institutions [9]. Moreover, such data is often collected in an irregular and asynchronous manner [10, 1 11], further complicating efforts to build generalizable
Work done during research internship at Mierosoft Research. Corresponding author: chanxêmi crosoft. crosofff com.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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ECG
O Fregular
MBP
S
Missing Value
Heterngeneuu sempling frequencias
PH
Time (Hours)
12
18
24
42
Figure I: Medical time series exhibit ① irregular intervals, @ heterogeneooss sampling rates, and frequent missingness driven by clinical workflows.
models. These challenges amplified by regulatory frameworks such GDPR [12, 13), which restrict cross-institutionall data exchange and hinder the development of unified modeling paradigms, often resulting redundant and resource- resource-intensive local optimization efforts. This highlights the need for a foundation model trained on validated medical time series datasets, that is able to learn generalizable patterns from large and varied datasets, reducing the need for extensive data annotation and custom model building, while also helping to share knowledge effectively across different clinical institutions, data types, and medical tasks [14, 15].
However, creating effective medical foundation models for time series is challenging, because clinical data are inherently highly irregular and varied: signals like ECGs recorded millisecond inter- vals [16] are found alongside laboratory tests conducted hours apart [17] (Figure 1). Differences in clinical workflows and equipment limits result in irregular sampling, missing values, and inconsistent temporal dependencies [18, 19]. Furthermore, physiological variables differ widely in their value and frequency ranges, requiring models that can handle these varied scales and types of data. Traditional methods using medical task-specific time-series models [20-25], trained on isolated datasets, often do not generalize well new situations and are difficult scale [26, 27, 10]. Meanwhile recent general- purpose time series foundation models [28-33] show promise, but they usually assume uniform time intervals. Similarly, emerging medical time series foundation models demonstrate cross-dataset generalization but only within narrowly defined domains for example, across EEG datasets for sleep monitoring or across datasets for Alzheimer's diagnosis, and cannot handle continuous-time forecasting irregular sampling [34-37]. These gaps-whert where current models struggle with the complex, irregular, and multi-frequency nature of medical data [28, motivatee our research and raises central question:
How can design scalable and generalizable foundation model that captures the irregularity and multi-freqqency nature of medical time series, while enabling robust transfer across diverse medical tasks?
To address this central question, introduce MIRA MEDICAL FOUNDATION MODEL FOR IRREGULARITY ADAPTATION. MIRA is specifically designed to address the challenges of medical time series: First, propose Continuous-Time Rotary Positional Encoding (CT-RoPE), which extends the standard RoPE [39] to handle time values using learnable frequency adjustments, allowing MIRA accurately model the varying frequency intervals of irregularly sampled data. Second, to further improve its ability to adapt to different time features in medical signals, MIRA uses a frequency-specific mixture-of-experts (MoE) layer that learns to route frequency-relatee information through specialized components. Finally, MIRA integrates a Continuous Dynamics Extrapolation Block, using Neural Ordinary Differential Equations (Neural ODEs) [40]. This feature allows the model to predict patient health paths at any future time point, moving beyond the limits of fixed observation grids. MIRA pretrained on a large curated collection of medical time series. comprised of over 454 billion time points from publicly available datasets. These datasets cover readings from intensive care units (ICUs), operating rooms, pediatric critical care, and long-term sleep and mental health monitoring. All data undergo preprocessing that standardizes time alignment, normalizes sampling frequencies, and maintains clinical realism. MIRA A outperforms other time series foundation models with similar number of activated parameters across various real-woril

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benchmarks, achieving reductions in forecasting errors by an average of 8% and 6% in out-of- distribution and in-distribution scenarios, respectively.
To summarize, this paper makes the following contributions: First, we propose MIRA, a new foundation model specially designed for medical time series forecasting. MIRA directly tackles the challenges of irregular sampling and varied temporal dynamics within a single, well-structured system. Second, we curate, preprocess and release an extensive and diverse corpus of medical time series, containing over 454 billion observations, to be used for model pre-training. This collection, built from multiple public datasets, is curated cover diverse types of medical time series. We select data sources and control their proportions to reflect real-world variability, ensuring correct time alignment, consistent types, and high quality. Third, we establish a comprehensive benchmark suite that covers a wide range of clinical forecasting tasks. This suite allows for consistent evaluation of MIRA and future models, encouraging further research and development into robust and generalizable medical time series models.
2 Related Work
Medical Time Series Models. Machine learning has enabled significant progress in healthcare
time series analysis, supporting a wide range of tasks, including dynamic forecasting [21, 22, 41, 42], survival analysis [43, 44), clustering and phenotyping [45-47], screening and monitoring
[23, 48, 49], early diagnosis [24, 25, 50), pharmacology [51]. treatment effect estimation [52, 53, 42), epidemiological and pandemic influenza surveillance [54], and hospital resource allocation [20, 55]. Despite this progress, most existing methods are narrowly designed for specific tasks or datasets, limiting their adaptability to diverse clinical scenarios [56]. Recently, foundation models for medical time series have emerged, showing promising cross cross-dataset generalization [34, 37, 35J. However, these models focus primarily on classification tasks and are not designed to handle continuous-time forecasting or irregular temporal patterns common in real-world clinical data.
Generalist Time Series Foundation Models. Recent foundation models have shown strong zero- shot forecasting without task-specific tuning [57-61]. Chronos [33] first adapted T5 [62] by dis- cretizing time series intervals as text tokens. More recent models-Moiine [28]. Sundial [32], and TimesFM [30]-improve support for variable dimensions and frequencies. Time-MoR [29] and Moirai-MoF [31] further improve specialization with sparse experts. However, these models largely require regularly sampled data, limiting their use on irregular clinical data. See Appendix A for more information.
Irregular Time Series Models. Modeling irregular time series has attracted increasing attention, particularly for applications requiring continuous-time reasoning. Early works such as Neural ODEs [40, 63] and State Space Models (6S 65] have demonstrated the ability to capture continuous dynamics by parameterizing the evolution of latent states over time. Another line of research focuses on adapting deep neural architectures, such as RNNs [66-68] and Transformers [19, 69-71], irregular settings. While these models have shown success in tasks like interpolation and classification, their effectiveness for long-term forecasting remains underexplored.
3 Methodology
In this section, we discuss the architecture of MIRA. We first formalize the irregular medical time series forecasting task (Section 3.1). We then introduce the model architecture (Section 3.2). Finally, we present the pretraining corpus and training strategy (Section 3.3).
3.1 Irregular Medical Time Series Forecasting
Let each time series instance be represented as paired sequences of timestamps and observations: {(t,, x; where t; E R+ are strictly increasing (fz < tx) and x; real values or missing entries. Our model is designed to handle two prevalent irregular patterns: (1) Regular-grid missing values. Observations occur at equidistant timestamps 4; = i but with live- missing values: some timestamps may have missing measurements. Formally, there exists a subset M C 1...., N such that the corresponding observations x; are missing (i.e., J; = NaN) for all E M, while the timestamps remain fully observed. (2) Irregular sampling. Timestamps
[NaN) contains

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CD Extrapolation
Neural ODE Solver
xN
Oulpul Hidden
IN-1
Mixture-of Expert
W+1
Time
Add Norm
Router
0,00
Causal Attention
K-2
CT-RoPE
(x)
(C 0K
Input Hidden
Norm
QueryKKey
Position Encoded Query/Key
① Takes irregular medical time series and timestamps as input, applying CT-RoPE for continuous temporal encoding. A Sparse Temporal coature-of-Experre layer routes tokens to specialized experts based on frequency. @ A Continuous Dynamics Ex- trapolation Block evolves latent states toward arbitrary target timestamps for flexible time-aware forecasting.
Figure 2: Architecture of MIRA.
I follow non-uniform intervals with A4; = 4++1 - 4 varying for different i. All observations at existing timestamps are present (r; IR), but the temporal spacing is irregular. Adhering the chamnel-independent setting [60], we formulate the problem in a uni-variate time series manner [28]. Given history {2,, t=) the forecasting task requires predicting future values at known target timestamps }
&L+LL+ = fa 4 ( E ER"
where (t))/=21 may follow either regularity pattern.
3.2 Model Overview
We present MIRA, a decoder-only architecture for universal irregular medical time series forecasting. As illustrated in Figure 2, MIRA consists of three key components: (1) Mistinuous-Time Rotary Positional Encoding, (2) a Sparse Temporal Mixture-of -oxtere-f--Experts Module, and (3) a Continuous Dynamies Extrapolation Block. Together, they enable scalable, frequency-adaptiv modeling of non-uniform clinical sequences.
3.2.1 Continuous-Tin Rotary Positional Encoding
Standard RoPE [39] assumes discrete and uniformly spaced token indices, which limits its applicabil- ity to clinical time series with real-valued and irregular timestamps. To address this, we propose Continuous Time Rotary Positional Encoding (CT-RoPE) that generalizes RoPE to operate directly on continuous-time inputs. Let 2 20 denote the timestamp of token in an irregularly sampled sequence, and let d be the model dimensionality, assumed to even. Specifically, we discretize continuous timestamps 2 ( into rotation angles without assuming fixed intervals, enabling the model to handle irregular sampling (more detail can be found at Appendix B). The angular frequencies {w:) d/2-1
defined as: W; 10000-2if3 24/d, The resulting dimeddependent rotation angle is given by:
( w;
(2)
Given an input embedding TRd, we partition into d/2 two-dimensional sub-vectors (122, x24+1), and apply planar rotation using the computed angle (t):

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T22 2 2244
cos (t(
sin 0,(t) cos (1(()
22
sin (i(
12i+1
CT-RoPE with Attention. The design of the rotary position encoding naturally supports relative position modeling. Specifically, the inner product between rotated query and key vectors depends only the difference between their timestamps. This can be by expanding the attention score:
(gm: kin) TT (Re(tt)) (l w Zn.
Since each (t) is rotation matrices constructed from trigonometric functions the timestamp- derived angles, their product is itself a rotation matrix dependent only the time difference:
(Re)) T (e().) = Re((n -m):
This implies that the positional interaction between two tokens is solely function of their relative timestamp offset (n 15-m) m)) In CT-RoPE, this property generalizes real-valued timestamps, enabling the attention mechanism to capture continuous-time relational structure while retaining the efficiency and structure of standard dot-product attention. line with Chowdhery et [72], we remove biases except in QKV projections to enhance extrapolation. More detail can be found in Appendix C.
3.2.2 Frequency-Speciffe
ceeture-off-xperte Block
Medical time series often exhibit dynamics across multiple temporal frequencies, ranging from smooth long-term trends to rapid, short-term variations. To effectively capture such heterogeneity while maintaining computational efficiency, we adopt a sparse Mixture-of-Expert. (MoE) architecture to replace the standard feedforward sub-layer in each Transformer block. In practice, each token is routed to subset of K experts selected from a shared pool of N lightweight feedforward networks. These experts are parameterized independently and are intended specialize in distinct temporal or semantic structures. Additionally, shared expert is universally applied to all tokens, serving as global residual pathway. Given the token representation ūi E R D at layer 1, the output of the MoE block is calculated as:
N
MoE (u.) 9N+11 FFNN+1 (u.) + Σ 9.. FFN, (u)),
(6)
where F-N,(-) denotes the i-th expert network, x+1+)) the shared expert, and Je, IN+1, i the corresponding routing weights. The non-shared expert weights Ji,r are obtained via a softmax gating mechanism followed by top-K K selection:
exp ((W)) ub)
8i.t:
if 81, E [opK([s;.)) K)
81,
N Σラ exp (WW) Tu))
Dt.t
otherwise,
where W R are the trainable gating vectors. The shared expert weight 9N+1,1 is computed independently using a sigmoid gate:
9N+1.1 - (W u
(8)
where ((-) denotes the element-wist wise sigmoid function and W vector.
N+1 D is the shared expert gating
5

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3.2.3 Continuous Dynamics Extrapolation Block
Auto-regressive transformer architectures, which generate predictions in stepwise manner under causal masking, cannot incorporate the timestamp of the target token during inference, as is not available until after generation. To address this limitation and enable extrapolation to arbitrary timestamps, we introduce Neural ODE-based [40] extrapolation module that evolves the latent state from the current token's s timestamp to the target prediction token timestamp, allowing time-aware forecasting at unseen or irregular time points.
Given h(tN) E Id (the state at time fn) and the next target timestamp +N+1. the Neural ODE module extrapolates hy to h(tx+1). We define the temporal evolution of the hidden state h(s) over the interval E [EN, [N+1] as:
dh(s) f(s - LN, h(s) ds
h(tx) hN, for E (tN,tN+1)
where f IR20 x Dmodet - Dmodel is the dynamics function, parameterized by a neural network (e.g., MLP) with parameters OODE- takes the relative time As = iN and the current state h(s)) as input. The state at the target time t is obtained by integrating the ODE dynamics:
/ AN+1
h((N+1)= =(t=))
h(NN)
f(s LN h();; (ODE)ds
(10)
This integral is computed numerically using an ODE solver (i.e. the Dormand-Prince (RK45) method). Let the result of this numerical integration be denoted h'y41 h(tx+1). More detail is in Appendix D.
Implementation with Adaptive ODE Solvers We numerically approximate the solution to Equa- tion 10 using adaptive step-size ODE solvers. Appropriate absolute and relative error tolerances (e.g., 10 10-6) are set manage the trade-off between accuracy and computational cost.
3.3 Model Training
Medical Pretraining Dataset. To support generalizable and clinically relevant time series modeling. we curate large pretraining corpus spanning over 454 billion time points from various real-world healthcare settings. The dataset collection includes signals from ICUs a nd operating rooms, pediatric critical care, long-term sleep and mental health monitoring, and population-level epidemiological surveillance. All data are drawn from publicly available clinical datasets, including MIMIC-II [73], MIMIC-IV [74], PTB-XL [75], Sleep-EDF [76], and the WAVES Pediatric Waveform Database [77]. To enable the model to acquire general knowledge, we resumed training from the Time-MoE checkpoint. A full summary of included datasets and the pre-processing applied is provided in Appendix E.
Loss Function. Training large-scale medical time series models requires balancing predictive accuracy, numerical stability, and sparse expert utilization. To ensure robustness against outliers and noisy measurements common in clinical data, we employ the Huber loss Luuber over autoregressive multi-horizon predictions:
[ 2)2 8 (|xr 21
if x - # < 5, 1)) otherwise,
Luuber (ar (I,
(11)
where 5 threshold controlling the transition between I.2 and L1 loss regimes. To avoid expert collapse in the sparse MoE layer, we introduce load balancing loss Lax that promotes uniform usage of experts. Let fa the fraction of tokens assigned to expert i, and ri the average routing probability:
Laux N -i= firi,
(12)
where /1 = KT Ef= T(Experti selected at 1) and r; routing score.
$. T = 17
17 Si, with 81, being the softmax

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Table 1: A high-level summary of MIRA model configurations.
Layers
Experts
K
duudel
da
dexpert
Activated Params
Total Params
M MIRAsmal
8
2
288
1152
144
30 M
73 M
R.Aasee
2
384
1536
192
50
114
MTRAtarge
12
2
768
3072
384
200 M
455 M
Model Configurations. We adopt similar model configuration strategy following Time-MoF [29] by providing three model variants of increasing scale: M MTRAsmalis with approximately 73 million parameters; M MTRAbases with approximately 114 million parameters; MTRAtarga with approximately 455 million parameters:Al models are trained on max eight NVIDIA 80G 1/A100 GPUs, using micro batch size of 128, and maximum sequence length of 512. For model configurations and training details, refer to Appendix F.
Experiments
In this section, we present the empirical evaluation of MIRA. We begin by outlining the experimental setup (Section 1).. We then evaluate MIRA on zero-shot forecasting benchmarks under both out-of-distribution (Section 4.2) and in-distribution (Section 4.3) settings. Additionally, we analyze the model's s scaling behavior across varying model and dataset sizes, and evaluate its robustness to different levels of data irregularity (Section 4.4). Finally, conduct ablation studies to examine what contributes to MIRA's 's performance (Section 4.5).
4.1 Experiment Setup
Downstream Datasets. We evaluate MIRA on diverse suite of real-world clinical and public health datasets, spanning multi-modal physiological signal analysis, critical care monitoring, ambulatory bio- signal tracking, epidemiological surveillance, and healthcare resource utilization. To systematically study temporal robustness, we group datasets into two categories: (1) inherently irregular datasets, which exhibit irregular sampling and natural missing values due to clinical or observational workflows. This are CinC 2012 [78]. Furthermore, we use (2) originally regular datasets, i.e.,ITT-IHH [79], Johns Hopkins COVID-19 Dataset [80] ,CDC Influenza Hospitalizations Admissions (CDC-IHA) ! Heart Rate [81] and illness [82], for which we simulate irregularity by randomly masking 30% of time points. The full list of datasets and statistics is provided in Appendix G.
Baselines. We compare MIRA against 13 state-of-the-art forecasting models, which we catego-
rize into three groups: (i) zero-shot foundation models, including Time-MoE [29] 2, Moirai [28], Moirai-MoE [31], Moment [83], TimeGPT [84], Timer [85], Lag-Llama [86], TimesFM [30], and
Chronos [33], which require inputs to be interpolated for evaluation; and (ii) full-shot forecasting
models, including ContiFormer [19], T-PatchGNN [87], Neural-CDE [88], and ODE-RNN [66].
which are specialized for irregularly sampled time series and require task-specific training. (iii) Continue pre-trained zero-shot foundation models on medical corpora, including Time-MoE [29], Moirai [28] and Chronos [33] which performance best on zero-shot evaluation. Implementation details for all baselines are provided in Appendix H.
Evaluation Metrics. We measure the Root Mean Squared Error (RMSE) and the Mean Absolute Error (MAB) as the evaluation metrics. Detailed definitions are provided in Appendix
4.2 Performance on Out-of-distribution Forecasting
Objective. We evaluated seven unseen benchmarks excluded from pre-training corpora. For com- parison, we fine-tuned the full-shot forecasting models the training split of each benchmark, while the zero-shot foundation models were evaluated directly without any task-specific training or fine-tuning. To validate the effectiveness of our model architecture, we additionally pre-trained existing foundation models on the same medical corpus. Notably, CINC 20/2 was excluded from this evaluation for foundation models, as applying regular-grid interpolation at the finest resolution results in over 98% time steps being interpolated, leading to poor performance for all baselines.
hhtps://www.cde www.f/u-frrecastin//aaaaa-aaaeee wwwp/vvree///weeeeeee week.
We excluded Time-Mot Ultra and Sundial from baselines they open-sourced the moment.
7

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Table 2: Zero-shot forecasting performance on -uttrf-diittibutionn datasets that are regularly sampled but contain missing values. Reported values are averaged across all prediction lengths. Lower RMSE and MAE indicate better predictions. Red: the best; Blue: the second best compared to zero-shot baselines; Underline: the best performance compared to full-shot baselines.
Zero-shol Ours
Fall-shot Time Series Models
Models
MIRA. RMSE
MiRAuuse
MIRAurge
Contiformer
T-PatchGNN
ODE-RNN RMSE
Nearal-CDE
TimesFM
Metrics
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
MAE
RMSE
MAE
Cine (10))
7.136
6.981
6.702
6.734
6.221
6.115
5.967
5,085
0,247
6.246
6.907
0.005
7,496
7,407
R 7
1.768
1.5.1
1.753
1.11
1.322
1,510
0.793
1.665
0.167
10395
'0765
12587
"TIM"
MIT-BIIt
0.293
0.198
0.199
0.141
0.173
0.130
0.453
0.354
0.705
0.627
0.882
0.023
0.212
0.196
0.335
0.111
CDC-IHA
5.976
5.729
5.211
4.103
10.068
4.408
JH COVID-19
0.407
0.335
0.504
0.349
0.478
0.336
0.323
0.297
0.350
0.291
0.424
0.331
0.545
0.503
2,320
0,322
ILI
1.294
1.077
1,218
1.024
1.154
1.041
0.391
0.224
0.186
D 0.143
0410
0.264
0.423
0.314
2,034
1.393
1 Cound
0
4
3
0
0
0
0
0
0
Zeco-shot Foundation Mudels Pre-triined on General-domain Curpora
Baseline
Lag-Llama RMSE
TImeGPT RMSE
Timer
Moment.cout
Moments..
Moments.rge
Motral-MoE.nn.
Molral-MoE...
MAE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Heart Rate (10-1)
1.761
1.188
2,258
1.915
1.901
1.704
2.966
1,852
2.938
1.835
2.917
1.735
1.962
1.600
2.181
1,652
MIT-BIH
6:217
0.169
0:251
0.185
0.255
0.213
0.417
0.229
0.416
0.228
0,413
0.224
0.206
0.167
0.208
0.167
CICC-IA (103)
6.631
6.654
4.857
17,808
5.307
5.260
7.630
5.802
JH COVID-19 (10))
8.696
1.432
1.879
1,580
2.447
2.328
3.077
0.563
3.087
0.554
3.064
0.549
1.452
0.725
19.301
3.190
ILI 1 Count
1,780
1 1,305
2.011
1.077
1.882
1.492
1.570
1,066
1,566
1.044
1.566
1.052
2.001
1,678
1.983
1,664
0
0
0
0
0
0
Zero-shot Foundation Models Pre trained General- domain Corpora
Baseline
Moiral.mait RMSE
Moiralsaee
Mobralirgs
Time-MoEecss
Time-MoEEarxe
Chronos.muti
Chronos
Chronos
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Heart Rate (10-1)
2.350
1.965
2.156
1.767
2.098
1.664
0.850
0.650
0.833
0.639
1.357
0.587
1.189
0.459
1.218
0.506
MIT-BIH
0.343
0.249
0.421
0.302
0.393
0.189
0.171
0.135
0,172
0.135
0.353
0.147
0.361
0.149
0,350
0.137
CICC-HA (10))
6.835
7.328
5.302
6.311
4.748
6.312
4.716
502
4.421
16.825
4.438
4.517
JH COVID
1.917
0.805
0.991
0.474
0.402
0.586
0.402
0.512
0.371
4.825
1,031
3.835
0.551
3.478
0.521
ILI 1 Count
1.996
1.671
1.871
1.561
1.808
1.499
1,288
0.961
1,368
1.015
2,054
1.400
1.940
1,308
1.870
1.252
0
0
0
0
0
0
0
0
Zero-hoot Foundation Models Continue Pre-trained Medical Corpora
Baseline
Moirni.mail
Moirai
Moiral
Time-MoFacs
Time-MoF,,rr Morze
Chronos,mait
Chronos
Chronotrage
RMSE
RMSE
MAE
RMSE MAE
RMSE MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Heart Rate (10")
2.047
1.685
1.907
1.536
1.601
1.263
0.648
0.324
0.603
0.488
1,340
0.565
0.965
0.488
0.902
0.458
MIT-BIII
0,239
0.201
0.274
0.190
0.219
0.186
0,201
0.155
0.185
0.143
0,311
0.137
0.320
0.139
0.300
0.127
CDC--HA (10P)
6.690
6,304
5,376
6.095
5.114
6.327
4.008
6,259
4.006
14.502
4.321
14.825
4.338
14,986
4.417
COVIIDDI1
0.579
0.448
0.619
0.478
0.337
0.509
0.353
0.517
0.362
4.225
0.947
3.328
0.409
ILI
1.528
1. 288
1.435
1.191
1.501
1.229
1.188
0.915
1,201
0.527
1.705
1.127
1.639
1.081
1.547
1.028
1 Count
10
0
0
0
0
0
0
0
Results. Detailed results of duitri-disti performance are reported in Table 2. First, MIRA consistently achieves state-of-the-an performance, outperforming all general-domain foundation models and specialized time series baselines. Specifically, MIRA MIRAtorge achieves the best results on all datasets, improving RMSE by over 8% on average compared to the strongest baselines, confirming the advantage of scaling and medical pretraining. This advantage is particularly pronounced on clinical benchmarks such as MIT-BIH and CDC-IHA, where MIR achieves both the lowest RMSE and MAE. Second, domain-specifie pretrnaining proves essential. All model variants continue pretrained on medical This demonstrates the benefit of leveraging medical-spectie -seicii--pecifie temporal structures and distributions during pretraining. Interestingly, even smaller MIRA models surpass larger general-domain models, suggesting that data relevance performance close to or even exceeding fine-tuned full-shot models in several cases. For instance, M MIRAgagge outperform than full-shot baseline on MIT-BIH and slight lower in CDC-IHA.
cotoora-conssstettt outperform models trained on general time series data.
more critical than model size alone. Third, MIRA achieves
4.3 Performance on In-distribution Forecasting
Objective. We evaluated in-distribution performance by holding out portion of the pre-training datasets as test sets, ensuring no data leakage. All models were tested in zero-shot settings.
Results. As shown in Table 3, MIRA consistently achieves highly competitive zero-shot performance across all five pre-training datasets. Compared to baselines such as Moirai, Time-MoE, and Chronos, MIRA A demonstrates lower RMSE and MAE on most datasets, particularly excelling on PTB-XL, MIMIC-III, and MIMIC-IV. This advantage holds across all model scales, indicating stable scalability and generalization. In contrast, baselines show larger variance or degradation challenging datasets
8

---

Table Zero-shot forecasting performance on in-distribution datasets that are regularly sampled but contain missing values. Reported values are averaged across all prediction lengths. Lower RMSE and MAE indicate better predictions. Red: the best; Blue: the second best.
Model
Ours
Baselic
MIRA....
MHRAAu.
MIRAAary
Moirsh..al
Mairai....
Meirais...
Time--aeEss.
Tine-Ma....
Chrent...l
Chrosso Chreptl
FIB-AL
11:227
11:121
11377
0.271
11:115
01311
113003
(1228
11:531
11:201
MIMILSI
11128
14300
01.03
0.383
0.226
01372
0.300
013113
06353
11.04
11301
MIMICAVV
11111
1110L
03382
0.3441
01863
01310)
IUSDI
Count
Siaptti (1IF)
0.390
11382
01.35
0.363
0.227
012223
01301
01.113
013553
11350
01110
11080
14322
0.314)
11:01
1100
MIMIC-111 2111
0.080
0.881
MIMIC-IV
0.011
0.003
0.883
0.258
0.291
0.143
0.064
0
0.354
0.142
0.34
WAVES
0.125
01112
0.106
0.157
0.361
0.155
0.124
0.16
0.310
0.118
0.117
Count
with missing values. These results validate the robustness of MIRA's architecture in handling imperfect medical time series data without requiring task-specific adaptation.
4.4 Model Scaling and Data Behavior.
Table 4: Zero-shot forecasting performance on different missing rates. Reported values are averaged across all prediction lengths. Lower RMSE and MAE indicate better predictions. Red: the best; Blue: the second best.
Micsing Rate
10%
20%
30%
40%
50%
60%
70%
80%
90%
I Count
Metries (1IP)
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE.
RMSE
MAE
RMSE
MAA.
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
Medical Setting Genvril Settin Opn
MIRA.mot
5.15
2.52
3.24
2.55
3.41
3.05
3.54
3.20
3.67
3.34
3,30
3.47
3.53
3.61
4.07
3.75
4.22
3.30
0
MIRAsser
2.98
2.08
3.11
2.81
3.25
2.94
3.38
31.07
3.53
3.20
3.64
5.33
3.75
3.38
3.55
3.63
3.10
3.71
0
MIRAusg
2:85
2.36
2.00
2.63
3.08
2.75
3:21
2.50
3:35
3.01
3.40
5:
3.63
3.31
3.99
3.86
3.90
3.51
8
Time-MaFaun
5.55
2.76
3.16
2.92
3.32
3.05
3:45
3.18
3.58
3.51
5.71
5.43
3.85
3.57
3.99
3.71
3.15
3.90
0
Time-MaFaraa
5:50
2:51
3.53
3.04
3:17
5.17
3:50
3.20
3.75
3.41
5:86
5.54
3.00
3.67
1.15
5.81
4.28
3.90
0
Mairsiara
4.50
4.18
5.30
1.64
5.68
4.65
0.00
0.83
6.00
5.06
8.18
5.02
6.5L
5.09
6.51
5.24
6.71
5.50
0
Mairsisus
4.88
4.15
4.00
4.30
5.20
4.25
5.64
4.58
5.76
4.63
5,80
8.60
6.03
4.97
5.95
4.78
6.00
4.57
01
Moirsiscat!
4.01
4.22
5.04
4.20
6.12
4.95
6.201
4.08
6.64
5.49
6.47
6.38
6.50
5.00
6.66
5.20
6.866
0.71
11
Chronokurge
4.71
4.10
4.85
4.22
5.02
4.31
5.31
4.72
5.66
4.70
5.82
6.01
5.97
5.10
6.15
5.32
6,43
5,40
11
Chronosacae
5,02
4.40
5.21
4.51
5.45
4.08
5.62
4.8%
5.85
4.95
B.02
5.12
6.21
5.51
5.40
5.49
6.57
5.52
0)
Chroaos-no!!
5.32
4.71
5.40
4,82
5.65
4.95
5,51
5.00
6.01
5.20
6.21
5,32
6.40
5.49
6.58
5.61
6,33
5,72
Time Moki
2.55
2.70
3.06
0.83
235
3:35
3.007
3.35
3.22
35.35
3.39
355
3.65
3,04
-3.77
3""
Time- Molaare
5.55
2.78
3.18
2.91
3.32
3.04
3.45
3.17
3.58
3.30
3.11
3.43
3.85
3.57
3.90
3.71
3.15
3.50
0
Mairalans
4.41
5.26
4.00
3.30
5.35
1.41
5.69
3.76
5.03
1.80
6.90
0.23
4.98
6:45
5.29
0.60
5.30
0
Mairsl
4.55
4.78
1.56
5.49
0.40
5.78
1.64
5.00
6.51
1.97
5.92
4.75
5.50
0.71
0
Moirsi s
5.02
5.30
5.55
1.95
5.99
5.34
5:11
5.55
0
Chremesirgg
4.30
4.58
1.51
6.73
4.91
6.02
Chrssoos
4.61
4.83
1.70
6.01
Cli Chromok.cw!!!
4.53
5.02
4.43
5.02
5.58
4.70
4.91
5.30
6.82
6.71 5.51
Objective. We investigate the robustness of the MIRA by comparing performance with baselines under varying missing datarates on the WHO FluNet dataset which is not used in pre-training.
Data Behavior Result. Table 4 summarizes the zero-shot forecasting performance under varying missing rates, ranging from 10% to 90%. MIRA consistently outperforms all baselines across all missing rates, with MiRaieg achieving the lowest RMSE and MAE in nearly every setting. Notably, MIRAtarge maintains strong performance even as the missing rate increases, showing minimal performance degradation compared to other models. This demonstrates its robustness to severe information loss. While Time- - M -oEaaagee performs competitively at lower missing rates, its performance drops more quickly as missingness increases.
4.5 Ablation Analysis
Table 5: Ablation studies. (Left) Evaluated with different model components. (Right) Analysis per-
formance and inference speed across different top, setups. Lower values indicate better performance.
Component
RMSE
MAE
Top, Setup
RMSE
MAE
Speed (s/iter)
MIRAbase
0.154
0.118
w/ (Top.)
0.160
0.121
0.097
w/ [Topa]
0.154
0.118
0.101
w/o CT-RoPE
0.158
0.125
w/ (Topa)
0.154
0.117
0.112
MoE Block
0.157
0.122
w/ [Tope)
0.156
0.120
0.124
w/o CT- Extrapolation Block
0.162
0.128
w/ (Tops)
0.159
0.122
0.127

---

Objective. We further perform an ablation study by removing key components of MIRA, to quantify their contribution, and the impact of the number of experts on performance.
Component Ablation Results. As shown the left-hand side of Table 5, removing CT--RoPE (w/o CT-RoPE) leads to a performance drop, confirming the importance of continuous-time positional encoding. Similarly, eliminating the Mixture-of-Fi -fxprrssss block (w/o MoE Block) slightly degrades performance, showing the value of expert specialization. The largest degradation is observed when disabling the CT-Extrapolation Block, with RMSE and MAE increasing by 5 and 8%, respectively, highlighting its role in improving extrapolation. These results showcase the complementary benefits of all three components in achieving robust performance.
Expert Activation Analysis.
We further examine the trade-off between predictive performance and inference efficiency by varying the number of activated experts (topg), as shown in the right-hand side of Table 5. Activating two experts (top2) achieves the best balance, reaching the low- est RMSE of 0.154 with an inference speed of O. 101 s/iter. Increasing to four experts provides no mean- ingful improvement in performance but increases in- ference time to 0.112 s/iter. Further increasing to six eight experts leads to slower inference with di- minishing returns. Conversely, using a single expert (top1) sacrifices accuracy (0.160) for only a marginal speed gain. These findings indicate that using two experts offers an optimal trade-off between efficiency and accuracy for scalable deployment.
Figure 3: Gating scores for experts across dif- ferent layers in the three different frequency datasets.
Activation Visualization.
We further visualize expert activation patterns on three datasets with distinct temporal resolutions: MIT-BIH (high-frequency, Hz-level). CDC-IHA (weekly). and COVID-19 (daily). As shown in Figure 3, low-frequency datasets such as Covid19 dataset tend to activate different set of experts compared to the figuefryy MIT-BIH dataset.
5 Discussion & Conclusion
We introduce MIRA, a foundation model designed for medical time series forecasting under irregular conditions. By integrating CT-RoPE, SpeeiSppeal MOE module, and Continuous Dynamics Extrapolation, MIRA demonstrates strong generalization capabilities across diverse medical datasets. This work highlights the potential of scalable and temporally adaptive solutions real-world medical challenges.
Limitation. This work is based publicly available, de-identified medical datasets. While these resources offer broad coverage and ensure reproducibility, they may not fully reflect the complexities of real-world clinical deployment. In addition, although these datasets are anonymized, residual privacy risks may still exist; however, addressing such risks lies beyond the scope of this work.
Acknowledgments and Disclosure of Funding
We thank Microsoft Research for providing the computational resources that made this work possible. We are also grateful to the anonymous reviewers for their insightful comments and constructive suggestions, which significantly improved the quality of this paper. Viktor Schlegel is part of the IN-CYPHER programme and is supported by the National Research Foundation, Prime Minister's ' Office, Singapore, under its Campus for Research Excellence and Technological Enterprise (CRE- ATE) programme. We acknowledge the support from the UMRI IDR Placement 2025 Pioneering project "Foundational Jingyuan Sun), and The European High Performance Computing Joint Undertaking (EuroHPC JU) with project CHPCC-DEV-2022006-000 (PI: Dr. Jingyuan Sun) and project EEPCC-BEN-2025805-000 (PI: Dr. Jingyuan Sun).
Models for Brain Computer Interfaces and Neuro- Control" (PI: Dr.
10

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A Further Related Work
In this section, we delve deeper into the related work on (medical) time series foundation models. Current research efforts in universal forecasting with time series foundation models can be broadly classified into four categories, as summarized in Table 6:
(i) Encoder-only models. Moirai is trained on the LOTSA dataset comprising 27B time points, with model sizes up 311M parameters [28]. MOMENT, based the T5 architecture, is pretrained on the Time-series Pile dataset containing approximately IB time points, reaching up to 385M parameters [83].
(ii) Encoder-decoder models, exemplified by Chronos [33], which tokenizes time series data via scaling and quantization, training on both public and synthetic dftasess,offers pre-trained models at multiple scales, with the largest containing up to 710M parameters.
(iii) Decoder-only models. TimesFM is trained on a corpus of 100B time points, with model sizes up to 500M parameters [30]. Lag-Llama focuses on univariate probabilistic forecasting. utilizing decoder-only Transformer architecture with up to 200M parameters [86]. Timer is generative pre-trained Transformer model designed for large-scale time series modeling, with base version containing 84M parameters and pre-trained on 260B time points [85].
(iv) Hiixtur-oof-xpertt architectures. Recent models adopt sparse Mfxture-of-Expeeee (MoE) architectures to enhance scalability and efficiency. Time-MoE [29] scales to 2.4B parameters with only few experts activated per input, while Moirai-MoE [31] achieves token-level specialization without frequency heuristics, improving adaptability and inference cost.
Table 6: Comparison between time series models.
MIRA
Sundial
Time-MoE Moirai-MoE:
Moirai (2024)
TimesFM Moment Chronos
Timer (2024)
Lag-Llama TimeGPT (2023)
Method
(Ours)
(2025)
(2024)
(2024)
(2024)
(2024)
(2024)
(2023)
Architocture
Decoder
Decoder
Decoder
Decoder
Eaceder
Decoder Encoder EneDee Decoder
Decoder
EneDee
(Max) Model Size
455M
444M
1.18
311M
385M
710M
200M
Unknown
Inpur Token
Point
Patch
Point
Patch
Patch
Parch
Patch
Point
Patch
Point
Patch
Dataset Scale
454B
1TB
309B
27B
27B/231B*
100B
1.13B
84B
29B
0.36B
100B
Longth
512
5000
5000
512
512
Unknown
FFN
Sparse
Dense
Sparse
Sparse
Dense
Donse
Donse
Donse
Dense
Dense
Dense
Depend on the way of calculation according to the original paper.
B Time Normalization
MIRA operates in continuous time and relies on rotary positional encoding adapted to irregular timestamps (CT-RoPE). To ensure stable phase computation and consistent temporal scaling across training and autoregressive inference, we apply a deterministic min-max normalization to each full timestamp sequence.
Given a strictly increasing timestamp sequence
= [1 (11,l2,...,44
(13)
compute
Jani min fi
1max max Li
(14)
and rescale every timestamp into a canonical range that aligns with the sequence length:
t tmin
Imin + (T 1).
(15)
Lmax
where, (T - corresponds to the maximum index of sequence length T, ensuring that the normalized time domain matches the index range used in standard rotary encodings, while preserving the original temporal spacing continuous form. The small constant prevents numerical instability when the timestamp range is narrow [89, 90].
24

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C Mathematical Analysis of CT-RoPE
C.1 Theoretical Properties
Linear Angle Scaling,
For any timestamp t 0, the rotation angles grow linearly with time:
(,(() w3
(16)
where w, 10000 2:/d are fixed angular frequencies.
Proof. Directly from Equation (1) in the main text. The linear formulation preserves temporal causality while maintaining bounded rotation magnitudes through exponentially decaying frequencies:
Wi exp (-26 In 10000)
2i (-a
(17)
ensuring higher dimensions receive progressively smaller rotations.
Relative Position Encoding. temporal difference:
The inner product between rotated vectors depends only on their
(Re(tig, (t(()) (g, Re(ti t4)k).
(18)
Proof. Using properties of orthogonal rotation matrices:
d/2-1 1
cos(wu(t) - t:))
sin(wa 44)
(t,):) Re(t)) = θ
(19)
sin(wa(ts - -t)
cos(wn (t; - ti))
==
= Relts ti),
(20)
where we assume 1j 2 4: otherwise, Relli - 44) = Re(ll - 4:) due to cos(-0) = =cos(0) and sin( sin(
C.2 Rotation Matrix Construction.
For an even- even-dimensional model (d even), define the block-diagonal rotation operator:
d/2-1
[oos(wit) sin(wat)
sin(wit) cos(w,t)
Re(t)= = + 0
(21)
Key properties include:
Norm Preservation: [1) = ||0||, Vr Rd.
Temporal Monotonicity:
l2 0,((1) < 01(22).
Differentiability: aRa(t) exists for all t > 0.
C.3 Attention Mechanism Extension
The scaled dot-product attention becomes:
(Ress Q) [)) V vd
Attention(Q, K, V) softmax
(22)
where lo and (x are query/key timestamps respectively. This maintains:
Temporal Locality: limac-o Re.t4a Re. O(At)
Causality: For tq tk. relative rotations prevent information leakage
Efficiency: Requires only ((d) extra computation standard attention
25

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Algorithm Neural ODE State Transition
Require:
Hidden state h(tx), timestamps NN 1N+1
Ensure: Evolved state f((t+11)
1: Configure ODE solver tolerances: rtol + 10 atol +- 10-6
2: Solve ODE: h(tx41) t odeint(foDe. (xx+11))
3: return h(x++1)
D Neural ODE
Gradient Computation via Adjoint Sensitivity. For end-to-end training, gradients of a loss function L with respect to the ODE parameters θODE and the initial state h(tx) are efficiently computed using the adjoint sensitivity method [40]. This involves solving a backward-in-time ODE for the adjoint state a()) aC/Oh(s))
da(s) ds
(0 (s, h():: fODE)
JODE Oh
ac
a(s), a(tN+1))
(23)
@h'(tx+1)
Gradients w.r.t parameters lODE are then computed through integrals involving a(s).
Stability Considerations. To ensure numerical stability, the dynamics function /ODE spec- trally normalized, which bounds its Lipschitz constant L. This constrains propagation during integration, yielding a bounded numerical error:
| (/oDE((N+1) hume (IN
M T,
(1) At = 1-1 IN.
(24)
where M represents the local truncation error of the ODE solver.
D.1 Theoretical Guarantees.
Our formulation satisfies the Picard-Lindelöi conditions for existence and uniqueness.
Theorem 1 (Existence and Boundedness). Let JonE spectrally normalized with maximun singular
value maxx and Lipschitz continuous with constant L = o max. Then for At tN+1 tx >> 0, the
state evolution admits a unique solution satisfying
[((x++1) h((tx)] S Fmax At maax
(25)
This bounded evolution property ensures stability for long-horizon extrapolation.
E
Pretraining Datasets
Table 7: The pre-training dataset of MIRA, which encompasses various sources.
WAVES (2023)
MIMIC-III
MIMIC-IV
Sleep-EDF (2000)
PTB-XL (2020)
Total
Source
(2016)
(2020)
Pts.
4.8B
400B
48B 10.57%
0.14B 0.03%
1.3B 0.29%
454B 100.0%
%
1.06%
88.06%
Our pretraining corpus consists of five publicly available medical time series datasets, selected for their diversity in sampling frequency. modality coverage, and clinical relevance:
MIMIC-III [73] is widely used publicly available database containing de-identified health records of over 40,000 patients admitted to intensive care units (ICUs) at the Beth Israel Deaconess Medical Center between 2001 and 2012. It includes multivariate time series of vital signs, laboratory test results, medication administrations, and clinical notes. The data exhibit irregular sampling patterns and substantial missingness, making them suitable for evaluating temporal robustness.
26

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MIMIC-IV [74] is the successor to MIMIC-III, covering ICU and emergency department admissions from 2008 to 2019. It offers expanded variable coverage, improved data standardization, and higher temporal resolution. Time series are recorded with greater granularity across broader range of hospital units, including both adult and pediatric care. Like MIMIC-III, reflects realistic clinical irregularity but with enhanced data fidelity and scale.
PTB-XL [75] is 12-lead ECG dataset sampled at 100 Hz, containing over 20,000 clinical recordings annotated with diagnostic statements, It enables robust modeling of waveform-based cardiovascular signals.
Sleep-EDF [76] contains overnight sleep EEG and respiration recordings annotated with sleep stages, collected under controlled conditions. The data are sampled 100 Hz and exhibit moderate regularity with biologically driven transitions.
WAVES [77] is pediatric waveform dataset that combines high-frequency physiological signals (ECG, PPG, respiration) from intensive care and operating room settings. It provides long continuous sequences with natural variability and noise.
F Model Configurations and Training Detail
Informed by recent scaling studies [29), we design MIRA in three model scales: MIRAsmall (73M parameters), M/RAnnse (114M), and M M/RAtarge (455M), enabling flexible deployment across different hardware constraints. All models are trained on up to eight NVIDIA 80GB A GPUs with micro-batch size of 128 and maximum sequence length of 512. We pre-trained one epoch with each training step processes approximately 65,000 time points. We consider forecast horizons of 24, 32, 48, 64 for short-term and long-term evaluation. Following standard practice, we apply an auxiliary load balancing loss with weight a 0.02 to encourage expert utilization.
G Downstream Tasks and Datasets
CinC 2012[78] originates from the PhysioNet 2012 Challenge and contains multivariate time series from ICU patients. Each record includes asynchronously sampled clinical variables such as blood pressure, heart rate, and oxygen saturation, with irregular measurement frequencies and observation patterns. The forecasting task focuses predicting future physiological values and deterioration risk based on past observations.
CDC-IHA', published by the U.S. CDC, contains weekly aggregated hospital admission metrics related to respiratory diseases across U.S. jurisdictions. includes counts for COVID-19 influenza, and RSV-reltted hospitalizations. The signals are inherently discrete and asynchronous across regions, with missing entries due to delayed or inconsistent reporting. The forecasting task involves predicting near-future hospitalization counts by location. We using below column in weekly frequency: Total Patients Hospitalized with COVID-19, Total Patients Hospitalized with Influenza, Total Patients Hos- pitalized with RSV, Total ICU Patients Hospitalized with DOVID-19,Tottl ICU Patients Hospitalized with Influenza, Total ICU Patients Hospitalized with RSV.
MIT-BIH [79] This dataset provides annotated ECG waveform segments from patients with arrhyth- mias. The input is a regularly sampled 2-lead ECG sequence, and the forecasting task involves predicting future signal windows. We introduce synthetic missingness during evaluation to test
robustness.
JHU COVID-19 Dataset [80] This dataset aggregates daily COVID-19 cases and deaths by region. While data are reported regular intervals, inconsistencies and reporting delays motivate the use of masked evaluation. Forecasting focuses on short-term case count prediction. We using this dataset in daily frequency
CDC-IIlness [82] The CDC outpatient illness dataset tracks ILI (influenza-like illness) and other symptoms across U.S. reporting centers. Although data are uniformly weekly, mask 30% of time points to simulate partial surveillance dropout.
bptps://daaa.cdc..o/PPbbbc Health-Surveilllnce
27

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Heart Rate This dataset, sourced from the Monash Time Series Extrinsic Regression Archive [81], contains photoplethysmograpyy (PPG) sequences paired with continuous heart rate values targets. Each instance represents short PPG segment with the goal of predicting the corresponding heart rate, making a benchmark for physiological signal regression tasks.
H Baselines
Time-MoE [29]: A sparsely activated decoder-only Transformer model that incorporates a Mixture- of-Experts (MoE) architecture with token-level routing. Trained on over 300 billion real-world time points spanning nine domains, Time-MoE demonstrates strong zero-shot forecasting performance, especially in long-range and multi-resolltion prediction. uses autoregressive decoding and sliding window inference with shared expert regularization.
Moirai [28]: universal forecasting backbone that uses patch-wise tokenization and any-variate self-attention. It is trained on the LOTSA dataset comprising 27 billion time points and supports forecasting across arbitrary time steps, variable sets, and resolutions. Moirai also employs resolution- adaptive projection layers to accommodate different patch sizes during inference.
An extension of Moirai that integrates token-level MoE module into the decoder block. This allows for frequency-speciff specialization without relying on handcrafted signal partitions. Moirai-Mol achieves improved generalization across domains with limited added compute, and supports both token-aware routing and auxiliary balancing loss.
Moirai-MoF [31]:
Mi [30]: A decoder-only Transformer developed by Google Research, pre- pre-trained on 100 billion real-world time points from diverse sources including IoTT finance, and weather. It features autoregressive generation with fixed-length context windows and shows strong performance in forecasting across hundreds of benchmarks.
Chronos [33]: A family of probabilistic time series foundation models that transform numerical sequences into quantized token representations. Chronos leverages discrete latent spaces and causal language modeling for forecasting and sampling. It supports both point and probabilistic prediction.
Timer [85]: A generative time series language model trained on diverse mix of real-world and synthetic data. It uses next-token prediction and masked time-step modeling for flexible downstream adaptation. While architecture and scale details are less publicly documented, it has demonstrated competitive zero-shot accuracy on common forecasting benchmarks.
ContiFormer [19]: A continuous-time Transformer model that combines Neural ODEs with attention. uses a NeuralODE kernel for modeling value transitions between observations and a standard self-attention block for relational reasoning. It is trained end-to-end on irregularly sampled series.
T-PatchGNN [87]: A graph- based model that converts univariate time series into graph of overlap- ping time patches, using GNNs to capture local and global dependencies. It is especially effective for sparse and low-signal series and supports continuous- mittinuuus-tme time node embedding.
Neural-CDE [88]: A continuous time model based on controlled differential equations. It encodes the trajectory of observed data using Neural CDE solver and predicts future values through learned hidden dynamics. Particularly suited for datasets with asynchronous observations.
ODE-RNN [66]: Combines standard RNN encoders with ODE solvers to update latent states irregular intervals. It supports interpolation between time steps and improves temporal continuity compared to discrete RNNs.
Moment [83] presents open-source Transformer-basee models pre-trained on the Time-series Pile, a large and diverse collection of public time series data. Employing masked time series prediction task, MOMENT demonstrates strong performance across forecasting, classification, and anomaly detection tasks, particularly in low-resource settings.
Lag-Llama [86] a decoder-only Transformer model tailored for univariate probabilistic forecasting. By incorporating lagged inputs covariates and pretraining diverse corpus of time series data, Lag-I exhibits robust zero-shot generalization and state-of-the-arr performance upon fine-tuning on unseen datasets.
28

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TimeGPT [84] is introduced as the first foundation model for time series analysis, capable of generating accurate predictions across diverse datasets without additional training. Leveraging advancements in deep learning. TimeGPTTs zero-shot inference outperforms traditional statistical, machine learning, and deep learning methods in both performance and efficiency.
I Evaluation Metrics
We evaluate forecasting performance using two widely adopted metrics: Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). Both are computed over all predicted time steps and variables, averaged across evaluation windows.
Mean Absouuee Error (MAE) quantifies the average absolute deviation between predictions i and ground truth Tz:
N
1
MAE
It
2//.
(26)
N
where N denotes the number of valid (unmasked) prediction points. MAE is robust to outliers and provides a direct measure of average deviation.
Root Mean Squared Error (RMSE) emphasizes larger errors by squaring deviations before averag- ing:
1 N
RMSE
Σ xt
22)2..
(27)
is more sensitive to large prediction errors and penalizes varianer outputs.
29


Reviews:
[{"review_id": "hvy62BEu3J", "reviewer": "Reviewer_LN9n", "summary": "This paper presents MIRA, a foundation model specifically designed for medical time series forecasting. The work is motivated by the fact that real-world clinical data often exhibits irregular sampling, missing values, and heterogeneous frequencies, which pose significant challenges for standard time series models. To tackle this, the authors propose a decoder-only transformer architecture with three main contributions: a Continuous-Time Rotary Positional Encoding (CT-ROPE) to handle arbitrary time intervals, a frequency-specialized Mixture-of-Experts (MoE) layer to adapt to different temporal dynamics , and a Continuous Dynamics Extrapolation block based on Neural ODEs to enable forecasting at any future timestamp. The model is pretrained on a large corpus of over 454 billion time points, aggregated from several public medical datasets. The paper demonstrates through extensive experiments that MIRA achieves state-of-the-art zero-shot forecasting performance on a range of in-distribution and out-of-distribution clinical benchmarks, outperforming both general-purpose foundation models and specialized, fine-tuned baselines.", "questions": "1. The proposed MIRA architecture integrates several advanced components, including MoE layers and a Neural ODE solver, which are known to be computationally intensive. Could you provide a more detailed analysis of the model's computational footprint? A direct comparison of inference latency (e.g., seconds per forecast window) and memory requirements against key baselines (e.g., TimesFM and ContiFormer) would be invaluable for understanding the practical trade-offs. This information is critical for assessing the model's feasibility for deployment in real-time or resource-constrained clinical settings. \n\n2. The paper titles MIRA as a \"unified\" foundation model, but the empirical evaluation is exclusively focused on forecasting tasks. Could you elaborate on how the model's architecture and learned representations could be adapted for other critical clinical tasks, such as classification (e.g., mortality prediction on the CinC 2012 dataset) or patient phenotyping? My confidence in the paper's central claim would increase significantly if you could provide even a preliminary result showing that MIRA's embeddings can be effectively used for a non-forecasting task. \n\n3. The pre-training corpus is heavily weighted towards the MIMIC-III dataset (88.06% of time points), which originates from a single US medical center. This raises questions about potential institutional or demographic biases in the pre-trained model. To what extent do you believe this affects the model's zero-shot generalizability? To better demonstrate the value of pre-training, could you conduct an experiment where MIRA is fine-tuned on a small fraction of an out-of-distribution dataset and compare its sample efficiency against a strong baseline trained from scratch on that same small dataset? A result showing that pre-trained MIRA learns faster or better with less data would provide powerful evidence for its utility as a transferable foundation for diverse clinical settings.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- The paper addresses the highly relevant but underserved problem of creating a foundation model specifically for medical time series data. The proposed MIRA architecture is original and well-motivated, combining several components to specifically target the core challenges of irregular sampling, missing values, and heterogeneous data common in healthcare.\n\n- The quality of the empirical evaluation is a major strength. MIRA is tested against a wide range of state-of-the-art zero-shot and full-shot models on diverse clinical benchmarks. The results are strong and consistently demonstrate superior performance, which is further validated by thorough ablation studies and robustness checks against data missingness.\n\n- In addition to the model itself, the work provides two significant resources for the research community: a large, curated pre-training corpus of over 454 billion medical time points and a new, comprehensive benchmark for clinical forecasting tasks.\n\n- The paper is well-written, clearly structured, and easy to follow. The authors do an excellent job of motivating the problem and presenting their complex architecture in an understandable manner, aided by effective diagrams.\n\nWeaknesses\n\n- The paper frames MIRA as a \"unified foundation model,\" but the evaluation is exclusively focused on forecasting tasks. While the motivation mentions other clinical tasks like phenotyping and classification, the experiments do not test MIRA's capabilities on these fronts (e.g., via fine-tuning). Demonstrating its utility beyond forecasting would be necessary to fully substantiate the \"unified foundation model\" claim.\n\n-  The model architecture is inherently complex, integrating a transformer, MoE layers, and a Neural ODE solver. The use of a numerical ODE solver, in particular, can be computationally expensive. The paper lacks a detailed analysis of MIRA's inference speed, memory footprint, and training cost compared to the baselines. This information is crucial for understanding its practicality for real-time clinical applications.\n\n- The pre-training corpus is built from publicly available datasets, which is excellent for reproducibility. However, the paper could provide a more in-depth discussion of the potential demographic or institutional biases within these datasets (e.g., MIMIC-III is from a single medical center) and how such biases might impact the model's performance and fairness when deployed in different clinical environments.\n\n- The main results in Table 2 compare zero-shot MIRA against fine-tuned specialist models. While MIRA's ability to compete with or even exceed these models in a zero-shot setting is impressive, the comparison is not entirely direct. Fine-tuning MIRA on these downstream tasks would provide a more complete picture, helping to disentangle the benefits of its pre-training from its architectural advantages in a full-data scenario.", "was_revised": true, "final_justification": "Authors thoroughly answered all my questions.", "rebuttal": "We sincerely thank the reviewer for their thoughtful and constructive feedback on our submission. We are especially appreciative of your recognition of the motivation and technical contributions of MIRA in addressing the challenges of medical time series. In response to your suggestions, we have made the following updates:\n\n1. **Quantified MIRA’s computational efficiency.**\n2. **Explore the potential for adapting MIRA to classification tasks**, demonstrating its broader applicability beyond forecasting.\n3. **Investigated potential dataset imbalance and bias**, using influence score analysis and analysis of model menchinism.\n4. **Demonstrated MIRA’s sample-efficient domain adaptation**, by comparing few-shot fine-tuning with from-scratch training on an out-of-distribution dataset.\n\nWe hope these additions clarify the contributions and practical value of our work. Please see below for our point-by-point responses.\n\n---\n\n**Q1: Could you provide a detailed analysis of MIRA’s computational footprint, including inference latency (seconds per forecast window) and memory requirements, directly compared to TimesFM and ContiFormer?**\n\nA: We measured average inference latency and GPU memory consumption over 10 batches (batch size = 32) with history length 512 and prediction length 96:\n\n|  | MIRA | TimesFM | Contiformer |\n| --- | --- | --- | --- |\n| Inference Speed | 0.5119s | 1.0702s | 1.0351s |\n| Peak GPU memory | 2575.65MB | 4489.0 MB | 1072.11 MB |\n\nMIRA achieves 2× faster inference than TimesFM (500m) despite comparable model complexity, demonstrating superior parameter efficiency through sparse MoE activation. Although ContiFormer's memory usage is smaller, it requires iterative extrapolation for multi-step forecasting, significantly increasing inference time compared to the other two models.\n\n**Q2: How can MIRA’s architecture or learned embeddings be adapted to non-forecasting clinical tasks (e.g., mortality prediction on the CinC 2012 dataset or patient phenotyping), and can you share any preliminary downstream results?**\n\nA: We use HeartBeat (contains ECG-based labels for normal and abnormal rhythms) from CinC 2016 as classification dataset to evaluate whether our proposed model could be adopt to other task format. We keep the same data split and metrics reported in Time Series Library (TSLib) and baselines[1,2]. We extract the final hidden states from MIRA as sequence-level representations and pass them to a lightweight classifier (e.g., CNN variant) for training. \n\nOur results show that MIRA achieves competitive accuracy compared to specialized models. These findings suggest that MIRA’s learned embeddings retain clinically useful information and can be effectively adapted for non-forecasting tasks. We will extend this line of work to additional downstream tasks and datasets.\n\n|  | TimesNet | DLinear | Autoformer | MIRA |\n| --- | --- | --- | --- | --- |\n| ACC | 78.0 | 75.1 | 74.6 | 77.6 |\n\n**Q3.1: Could MIMIC-III’s 88% share in the pre-training corpus introduce demographic or institutional biases into MIRA’s representations?**\n\nA:  Thank you for this insightful question. While MIMIC-III play a major role in pre-training corpus, we believe the risk of demographic or institutional bias in MIRA is minimal, for the following reasons:\n\nFirst, MIRA operates solely on physiological time series (e.g., vitals, labs, ECG) and is not provided with age, sex or hospital information. This prevents the model from conditioning on potential sources of bias and encourages learning representations based only on universal temporal patterns present in the data.\n\nSecond, MIRA aim to autonomously learn latent temporal patterns from physiological signals, rather than memorizing dataset-specific artifacts. By design, the model encourages generalization across diverse domains, and the MoE architecture facilitates this by dynamically routing inputs based on their signal properties, not dataset identity. This enables MIRA to develop domain-robust representations that transfer well beyond any single data source.\n\nOur empirical results support this: For example, table 2 shows that the performance is still comparable to other datasets. If institutional bias were significant, we would expect substantial performance degradation on these datasets, which we do not observe. Additionally, please also refer to reviewer vkqd’s Q1.1, where we conduct the influence score of training dataset to quantify their impact. Result shows that although MIMIC-III constitutes a large portion of the pretraining corpus, it does not overwhelmingly influence the learned representations, suggesting that potential biases introduced by MIMIC-III are limited.\n\n**Q3.2:** **Can you provide few-shot fine-tuning results on an out-of-distribution dataset to compare MIRA’s sample efficiency against a model trained from scratch?**\n\nA: We constructed a training set with 20k samples based on MIT-BIH dataset, each having a sequence length of 256. During inference, the prediction lengths are set to 24, 36, 48, and 64, with the context length being twice the prediction length. Average RMSE performance reported. \n\nNotably, **Time-MoE required 80% of the data (~16k samples)** to reach similar RMSE levels as MIRA with 128–256 samples. This underscores MIRA’s strong few-shot performance, as well as its potential to **significantly reduce data and computational costs** in new clinical settings. \n\n| Few-shot | 16 | 32 | 64 | 128 | 256 |\n| --- | --- | --- | --- | --- | --- |\n| MIRA | 0.1224 | 0.1221 | 0.1220 | 0.1215 | 0.1211 |\n| Training Size | 20% | 50% | 60% | 70% | 80% |\n| Time-MoE | 0.2004 | 0.1559 | 0.1368 | 0.1222 | 0.1206 |\n\n[1] Wu, Haixu, et al. \"Timesnet: Temporal 2d-variation modeling for general time series analysis.\" arXiv preprint arXiv:2210.02186 (2022).\n\n[2] Wang, Yuxuan, et al. \"Deep time series models: A comprehensive survey and benchmark.\" arXiv preprint arXiv:2407.13278 (2024).\n\n[3] Haq, Kazi T., et al. \"Demographic and methodological heterogeneity in electrocardiogram signals from guinea pigs.\" *Frontiers in physiology* 13 (2022): 925042."}, {"review_id": "GS2zEYSUcI", "reviewer": "Reviewer_vk9d", "summary": "This paper introduces MIRA, a foundation model specifically designed for medical time series forecasting. It addresses challenges inherent to medical data, including irregular sampling, heterogeneous frequencies, and missing values. The model architecture combines 1) Continuous Time Rotary Positional Encoding, to represent real-valued irregular timestamps; 2) Frequency-Specific Mixture-of-Experts layer, to specialize processing across latent temporal frequencies; and 3) Continuous Dynamics Extrapolation Block, to leverage neural ODEs for modeling trajectories over continuous time.", "questions": "Q1: The paper includes a diverse set of datasets (e.g., ICU, sleep, pediatrics). How are class proportions and sampling frequencies balanced across these domains? Are certain domain-specific signals disproportionately influencing the learned representations? Additionally, how is time alignment standardized given the heterogeneity of these datasets?\n\nQ2: For the original regular datasets, missingness is simulated via random masking. However, in real-world scenarios, missingness often follows structured patterns (e.g., block-missingness). Have such patterns been considered in the evaluation? If not, how might they affect the model's robustness?\n\nQ3: Even in zero-shot forecasting, models typically require a context window. What is the size of the context window used in your experiments? Given that patients may share similar observed histories but differ in latent characteristics (e.g., children vs. elderly), how does the model account for such underlying variability—particularly in the absence of demographic features?\n\nQ4: Regarding Table 5, it would be helpful to include statistical significance testing (e.g., confidence intervals or p-values) to assess whether the improvements in MAE and RMSE are meaningful.\n\nQ5: While the model demonstrates strong generalizability across domains, how does its performance compare to specialized, domain-specific models? It would be informative to discuss whether the general model sacrifices any accuracy relative to tailored models that may be computationally cheaper or more interpretable.", "limitations": "Yes. Authors discussed the limitations of the work.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths: The authors provide clear motivation in the paper, effectively highlighted the practical need for foundation models that can generalize across diverse, irregular medial time series. The introduced MIRA got competitive results consistently outperforms baselines including Time-MoE, Moirai, TimesFM, Chronos. Additionally, they release the curated datasets and code and provide a comprehensive benchmark for further research. \n\nWeaknesses: In healthcare, the interpretability of the model usually matters a lot. There are no methods provided to make forecasts understandable to clinicians, which is vital for deployment in real-world settings.", "was_revised": true, "final_justification": "The rebuttal satisfactorily addressed my concerns with new analyses on dataset balance, time alignment, and block-missingness, as well as added statistical significance testing. The discussion on domain-specific trade-offs and interpretability was also helpful. While clinician-facing interpretability remains for future work, I am satisfied with the responses and have adjusted my final rating.", "rebuttal": "We thank the reviewer for their insightful comments and for highlighting the clear motivation behind our work. In response to your insightful questions, we have made the following additions and clarifications:\n\n1. **Quantified potential dataset imbalance and domain dominance** by analyzing cross-dataset attribution using influence score analysis.\n2. **Explain the standardization of time alignment**, by outlining our model architecture and modelling mechanism.\n3. **Evaluated MIRA under realistic block-missingness patterns**\n4. **Report context window configurations**\n5. **Added statistical significance testing** to validate the contributions of each architectural component.\n6. **Discuss model performance and interpretability** with domain-specific models. \n\nWe appreciate your thoughtful feedback and hope our responses address your concerns clearly. Please see below for point-by-point replies.\n\n---\n\n**Q1.1: How did you balance differences in class distributions and sampling rates across ICU, sleep, and pediatric datasets? Are certain domain-specific signals disproportionately influencing the learned representations?** \n\nA:  Rather than manually resampling or reweighting datasets to correct for size or sampling-rate imbalance, we rely on the scale and heterogeneity of our corpus and the MoE architecture to learn domain-robust representations.\n\nTo quantify whether certain datasets dominate the learning process, we conducted an influence score analysis using the data attribution techniques, i.e. gradient dot product (Grad-Dot) method [1,2]. This method measures how much each training sample contributes to the test loss gradient, allowing us to estimate the relative importance of different training sources.\n\nResults across five target test datasets (see table below) show that while MIMIC-III has the largest share, its average influence scores are not disproportionately dominant. In fact, other datasets also show consistent, non-negligible influence, indicating that MIRA internally balances its attention across domains rather than overfitting to dataset size.\n\n|  | Mimic-iii | Mimic-iv | WAVES | PTB-XL | Sleep-EDF |\n| --- | --- | --- | --- | --- | --- |\n| Heart | 0.4426 | 0.1802 | 0.1449 | 0.1277 | 0.1046 |\n| MIT-BIH | 0.5769 | 0.1640 | 0.1733 | 0.0521 | 0.0338 |\n| CDC-IHA | 0.3836 | 0.2924 | 0.1645 | 0.1032 | 0.0563 |\n| COVID-19 | 0.4314 | 0.2002 | 0.1898 | 0.0694 | 0.1092 |\n| ILI | 0.5335 | 0.1913 | 0.1431 | 0.1065 | 0.0256 |\n\n**Q1.2: How is time alignment standardized given the heterogeneity of these datasets?**\n\nA: Similar to other foundation models like Chronos [3] , which implicitly handles this by quantizing arbitrary-length sequences in a fixed number of bins, our method handles the heterogeneous sampling frequencies through a unified token-by-token input approach, where our MoE architecture automatically learns to process different temporal scales without explicit frequency standardization.\n\nEach data point becomes a token with its associated timestamp, regardless of original sampling rate. Our time quantization procedure (Appendix A) standardizes absolute timestamps into relative time intervals while preserving temporal ordering. This enables CT-RoPE to directly encode continuous-time relationships across variable intervals. In addition, the MoE routing mechanism learns to specialize different experts for distinct temporal regimes. As evidenced in Appendix L Figure 3 (right), high-frequency datasets (MIT-BIH) activate different expert combinations compared to low-frequency datasets (COVID-19), demonstrating automatic adaptation to temporal characteristics.\n\n**Q2:Have you tested MIRA’s robustness to block‐missingness patterns, and how might such structured gaps impact its performance compared to your random‐masking experiments?**\n\nWe evaluated MIRA under both random (scattered) and structured (block) missingness at 30% and 50%  masking rates at illness dataset. As shown below, MIRA performs robustly across both settings, consistently outperforming Moirai. Specifically, MIRA shows minimal performance degradation between the two settings. In contrast, Moirai exhibits more pronounced deterioration under block missingness, which shows that block-missingness removes contiguous segments of input, making interpolation harder due to the lack of nearby temporal anchors, showing the meaning of developing an irregular TS foundation model.\n\n|  | 30%-scattered | 30%-block | 50%-scattered | 50%-block |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| MIRA | 1.114 | 1.113 | 1.238 | 1.255 |  |  |\n| Moirai | 1.501 | 1.537 | 1.593 | 1.624 |  |  |\n\n**Q3.1: What is the size of the context window used in your experiments?**\n\nA:  During training, we used a context window of 512 time steps. This length balances computational efficiency with our need to process parallel value and timestamp sequences, and proved sufficient to capture the temporal dependencies in our tasks.\n\nWhen it comes to inference, we follow each benchmark’s established protocol. For example, Illness dataset are {24, 36, 48, and 60} [4]**.** We’ll include a summary table of all testset context window sizes in the revised manuscript for full clarity.\n\n**Q3.2:How does the model account for underlying variability  (e.g., children vs. elderly), particularly in the absence of demographic features?**\n\nA:  Our model is designed to learn generalizable temporal patterns that can transfer across demographic groups without requiring explicit demographic features. The model implicitly learns to capture demographic-related temporal dynamics directly from the signals themselves. For instance, pediatric patients typically exhibit higher heart rates and different baseline ranges [5], which are naturally encoded in the time series data. Our MoE architecture enables the model to route different types of physiological patterns to specialized experts, potentially allowing adaptation to demographic-specific characteristics without explicit labels. Our model's performance well on pediatric data (WAVES) despite representing only 1% of training data, demonstrates that the model successfully generalizes across age groups and demographic variations.\n\n**Q4: Can you add confidence intervals or p-values for the MAE/RMSE gains in Table 5?**\n\nA:  We conducted paired t-tests based on results from five independent runs for each ablation variant. The results show that all ablated variants exhibit statistically significant degradation compared to the full model, with p-values of 0.025 (w/o CT-RoPE), 0.022 (w/o MoE Block), and 0.004 (w/o Extrapolation Block), respectively (p < 0.05 in all cases). We will add this in next revision.\n\n|  | MIRA | w/o CT-RoPE | w/o MoE Block | w/o Extrapolation |\n| --- | --- | --- | --- | --- |\n| RMSE | 0.156 ± 0.002 | 0.158 ± 0.001 | 0.158 ± 0.002 | 0.161 ± 0.002 |\n\n**Q5: How does its performance compare to specialized, domain-specific models?  Does MIRA trade off any accuracy, efficiency, or interpretability compared to domain-specific models?**\n\nA: Thank you for this insightful question. While there are limited specialized models specifically designed for irregular medical time series forecasting, we provide comprehensive comparisons against irregular time series models (ContiFormer, T-PatchGNN, Neural-CDE, ODE-RNN) trained in a full-shot manner on specific medical datasets (Table 2).\n\n**Accuracy**: MIRA may achieve slightly lower accuracy than full-shot specialized models on some datasets, but significantly outperforms zero/few-shot alternatives while providing consistent cross-domain performance without requiring domain-specific training or fine-tuning. This competitive performance is achieved through our CT-RoPE and Neural ODE-based extrapolation block, which enable effective modeling of irregular temporal patterns across diverse medical domains.\n\n**Efficiency:** While MIRA incurs higher upfront pretraining costs compared to individual domain-specific models, it provides substantially higher deployment efficiency in zero/few-shot scenarios (please refer to Reviewer LN9n's Q1). Once pretrained, MIRA applies immediately to new tasks without retraining. Additionally, during inference, our model only activates approximately half of the model parameters, significantly reducing computational overhead while maintaining performance. This efficiency gain is enabled by our frequency-specific mixture-of-experts architecture that learns generalizable temporal specializations during pretraining.\n\n**Interpretability:** MIRA's MoE architecture provides superior cross-domain interpretability through expert activation patterns (Figure 3), offering insights into temporal frequency specialization that narrow specialized models cannot provide.\n\n[1] Charpiat, G., Girard, N., Felardos, L., et al. (2019). \"Input similarity from the neural network perspective,\" *Advances in Neural Information Processing Systems, 32*.\n\n[2] Wei, D., Padhi, I., Ghosh, S., et al. (2024). \"Final-Model-Only Data Attribution with a Unifying View of Gradient-Based Methods,\" *arXiv preprint arXiv:2412.03906*.\n\n[3] Ansari, Abdul Fatir, et al. \"Chronos: Learning the language of time series.\" arXiv preprint arXiv:2403.07815 (2024).\n\n[4] TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis\n\n[5] Fleming, Susannah, et al. \"Normal ranges of heart rate and respiratory rate in children from birth to 18 years of age: a systematic review of observational studies.\" The Lancet 377.9770 (2011): 1011-1018."}, {"review_id": "5RKMwghyKx", "reviewer": "Reviewer_CKRd", "summary": "The paper proposes a novel foundation model for health data. The architecture proposed has multiple novel components: CT-RoPE for temporal encoding, a temporal Mixture-of-Experts layer, and an extrapolation block based on Neural ODE. The method was evaluated on a large set of datasets combined and compared to relevant foundation model baselines. The results obtained are relevant as they achieve significant improvement in zero-shot forecasting.", "questions": "- The zero-shot forecasting improvements are significant. Beyond the metrics, what do these results tell us about the model's learned representations? Can the authors provide a deeper analysis or qualitative examples that illustrate why MIRA succeeds where baselines fail? This would move the discussion from what the results are to what they mean.\n\n- Foundation models are often computationally intensive. Could you comment on the resources required to train MIRA compared to baselines and its efficiency at inference time? This would be valuable for assessing its practical applicability.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\n- The paper introduces MIRA, a novel foundation model for medical time series, distinguished by several innovative architectural components (CT-RoPE, a temporal Mixture-of-Experts layer, and a Neural ODE-based extrapolation block).\n- The empirical evaluation is thorough and convincing, testing the model across a diverse set of real-world health datasets against relevant and strong baselines.\n- The work is very well-written, and the inclusion of code is a significant contribution to reproducibility.\n\n\nWeaknesses:\n- The primary weakness is the underdeveloped discussion section. Section 5 largely omits a critical analysis. The paper would be significantly strengthened by a deeper discussion that interprets why the proposed components lead to performance gains.", "was_revised": true, "final_justification": "I will be maintaining my original score for this paper.\n\nThe discussion has confirmed my initial assessment of the work's contributions and limitations. Since the rebuttal reinforced my original evaluation without uncovering reasons to change it, I am confident that my current score accurately reflects the paper's merits.", "rebuttal": "We sincerely thank the reviewer for their thoughtful and constructive feedback. We are particularly grateful for your recognition of MIRA’s architectural innovations. In response to your valuable comments, we have taken the following steps to further strengthen our submission:\n\n1. **Provided detailed reasoning for each architectural component**, clarifying why CT-RoPE, temporal MoE, and CD-Extrapolation lead to performance gains through ablation comparisons and theoretical justifications.\n2. **Offered deeper qualitative insights** to illustrate how MIRA captures clinically meaningful temporal dynamics beyond what baseline models can achieve, especially under irregular sampling conditions.\n3. **Quantified MIRA’s computational efficiency.**\n\nWe hope these additions clarify the rationale behind MIRA’s design and its practical utility. Please find our detailed responses below.\n\n---\n\n**Q1: Lacks a critical analysis explaining why the proposed components yield the observed performance gains.** \n\nA:  We provide comprehensive ablation studies (Table 5) demonstrating each component's contribution. Here we explain why each component yields performance gains and what alternatives were used in ablation studies:\n\nCT-RoPE vs. Standard Positional Encoding: In our ablation, we replaced CT-RoPE with standard learned positional embeddings. Standard approaches treat irregular timestamps as discrete indices, losing crucial temporal distance information. For example, a 5-minute gap and 2-seconds gap between measurements would be treated identically. CT-RoPE's continuous encoding (θᵢ(t) = ωᵢ · t) preserves actual temporal relationships, enabling the attention mechanism to appropriately weight recent vs. distant observations based on real time differences rather than sequence positions.\n\nMoE vs. Standard FFN: Medical signals exhibit vastly different temporal scales (e.g. ECG operates at milliseconds while lab values change over hours). A single FFN must compromise between these scales, diluting its effectiveness. MoE routing allows specialized experts: some optimized for high-frequency cardiac rhythms, others for slow-varying metabolic trends. This specialization prevents interference between temporal regimes.\n\nCD-Extrapolation vs. Standard Autoregressive: Traditional approaches can only predict at the next sequence position (i.e. next-token prediction), limiting clinical utility where prediction times are irregular (e.g., predicting patient status at discharge time). Our Neural ODE approach evolves hidden states continuously, enabling predictions at clinically relevant timestamps rather than fixed intervals.\n\n**Q2: Beyond metric gains, can you provide qualitative examples or deeper analysis illustrating why MIRA succeeds where baselines fail?**\n\nA:  Beyond metrics, our results reveal that MIRA learns fundamentally different representations from baselines:\n\nMIRA learns \"physiological continuity\", understanding that biological processes evolve continuously even when measurements are discrete. Through expert activation patterns (Appendix L), we observe frequency-specific specialization: high-frequency datasets (MIT-BIH) activate different experts than low-frequency data (CDC-IHA), suggesting learned temporal hierarchy decomposition.\n\nAs a example, consider a cardiac patient with arrhythmia where we need to predict the next ECG values:\n\n**Input sequence (with missing values)**:\n[0.8, –, –, 1.2, –, –, –, 0.4, –] at timestamps [0, 1, 2, 3, 4, 5, 6, 7, 8]\n\n**Target prediction**:\nNext 3 values should be [–, 1.0, –] at timestamps [9, 10, 11]\n\n**Baseline approach**:\n\n- First interpolates: [0.8, 0.9, 1.0, 1.2, 1.1, 0.9, 0.7, 0.4, 0.5]\n- Then predicts: [0.6, 0.7, 0.8] (smooth progression, missing sharp jump)\n\n**MIRA prediction**:\n\n- **CT-RoPE** encodes irregular timestamps [0, 3, 7] directly, capturing temporal relationships without interpolation\n- **Neural ODE** models continuous dynamics: dh(s)/ds = f(s-t₇, h(s); θ), where h(t₇) = h₀.₄ evolves from timestamp 7 to 10\n- The ODE solver integrates: h(t₁₀) = h₀.₄ + ∫₇¹⁰ f(s-7, h(s); θ)ds, enabling extrapolation to arbitrary timestamps\n- Predicts: [–, 0.98, –] (captures physiological jump pattern, 0.98≈1.0)\n\nThe baseline’s interpolation smooths out abrupt voltage drops, masking key signs of arrhythmia (Please also refer to Reviewer vk9d’s Q2 for different type of missing data’s imapct).  In contrast, MIRA's continuous-time modeling preserves the underlying arrhythmic dynamics through its ODE formulation, enabling more accurate and clinically meaningful forecasting under irregular sampling \n\n**Q3: Please comment on training resources and inference efficiency compared to the baselines.**\n\nA:  We appreciate this important question about computational efficiency. We provide detailed analysis in our response to Reviewer Lv9n Q1, and summarize the key findings here:\nMIRA achieves 2× faster inference than TimesFM with 2.5× fewer activated parameters (~200M vs 500M), demonstrating superior parameter efficiency through sparse MoE activation. While ContiFormer uses significantly less memory (1072.1MB vs 2575.65MB), its iterative extrapolation approach significantly increases inference time for multi-step forecasting."}]

Author rebuttal:

Meta-review: The paper presents MIRA, a novel foundation model tailored for medical time series data, and it stands out for its originality and relevance. The authors tackle a pressing challenge in healthcare AI: handling irregular, heterogeneous, and incomplete time series data. MIRA’s architecture is thoughtfully designed, integrating components like CT-RoPE, temporal Mixture-of-Experts (MoE), and Neural ODEs to address these issues. The empirical evaluation is particularly strong, with MIRA outperforming several state-of-the-art models across diverse benchmarks. The inclusion of a massive pre-training corpus and a new benchmark suite further enhances the paper’s contribution to the field. Moreover, the clarity of writing and the availability of code and datasets support reproducibility and accessibility for future research. The paper in its first submission suffered several limitations. While MIRA is positioned as a “unified foundation model,” its evaluation is narrowly focused on forecasting tasks. This leaves its broader applicability, such as classification or phenotyping, unexplored, weakening the claim of generality. The architecture’s complexity, especially the use of Neural ODEs, raises concerns about computational efficiency, yet the paper lacks a detailed analysis of inference speed, memory usage, and training cost. This omission is critical given the real-time demands of clinical settings. Additionally, although the pre-training data is publicly available, the paper does not sufficiently address potential biases stemming from sources like MIMIC-III, which could affect fairness and generalizability. Another notable gap is the lack of interpretability tools, essential for clinical adoption, since clinicians need to understand and trust model outputs. Finally, the discussion section is underdeveloped; it misses an opportunity to critically analyze why MIRA’s components lead to performance gains, which would have added depth to the paper’s insights.
However, the rebuttals were very clear and answered point by point to criticisms from the reviewers, that all recognized their concerns were all fully solved after the rebuttal from the authors and the subsequent highly engaging discussion. All reviewers confirmed they were fully satisfied with the discussion.
Decision: Accept (poster)