Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting

Conference: ICLR 2026
arXiv: 2602.21498
Code: Available
Area: Time Series
Keywords: Irregular Time Series, Multi-scale Modeling, Recursive Splitting, Sampling Pattern Preservation, Forecasting

TL;DR

The authors propose ReIMTS, which preserves the original sampling patterns of irregular multivariate time series (IMTS) through period-based recursive splitting (rather than resampling). Combined with an irregularity-aware representation fusion mechanism for multi-scale modeling, it achieves an average improvement of 27.1% across six IMTS backbones as a plug-in.

Background & Motivation

Background: Irregular multivariate time series (IMTS) are ubiquitous in scenarios such as healthcare and meteorology, characterized by non-uniform observation intervals and misaligned observation timestamps across different variables.

Limitations of Prior Work: The sampling pattern itself contains crucial information; for example, in an ICU, the transition from intensive monitoring to sparse monitoring reflects a patient recovering from a critical to a stable condition. Existing multi-scale approaches face two core issues: - Methods for regular time series (e.g., Scaleformer, TimeMixer, Pathformer) assume uniform sampling, making them inapplicable to IMTS. - IMTS-specific multi-scale methods (e.g., Warpformer, Hi-Patch, HD-TTS) rely on resampling to obtain coarse-grained sequences, which destroys original sampling patterns. For instance, in PhysioNet'12, the "dense-to-sparse" sampling pattern of Bilirubin is disrupted after downsampling.

Key Insight: Sampling pattern information (e.g., the shift between urgent and routine monitoring) is vital for clinical decisions and should be preserved.

Method

Overall Architecture

ReIMTS is a plug-and-play multi-scale framework compatible with most encoder-decoder IMTS models. At each scale level, it recursively splits samples into sub-samples with shorter periods based on time intervals while keeping the original timestamps of all observations intact. Global and local representations are injected layer-by-layer from top to bottom using level-specific backbone encoders and an irregularity-aware fusion module, providing a multi-scale perspective without destroying sampling patterns. The data flow follows a top-down chain: "Recursive Splitting → Layer-wise Encoding and Shape Alignment → IARF Fusion (Recursive Injection) → Concatenated Decoding."

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    IN["Irregular Multivariate Time Series<br/>(Original Timestamps)"] --> SPLIT["Period-based Recursive Splitting<br/>Split into P^n sub-samples by T^n<br/>Zero-padding alignment, timestamps unchanged"]
    SPLIT --> ENC["Multi-scale Representation Learning<br/>Independent backbone encoding per layer + Shape alignment<br/>(Time/Obs splitting, Variable replication)"]
    ENC --> IARF["Irregularity-Aware Representation Fusion (IARF)<br/>Masking padding + Adaptive weight α<br/>G = E + α·H"]
    IARF -->|"Top-down layer-wise injection<br/>Recursive into next scale"| ENC
    IARF --> DEC["Concatenate G^n from all layers<br/>One-shot decoding"]
    DEC --> OUT["Multi-scale forecasting results"]

Key Designs

1. Period-based Recursive Splitting: Preserving Sampling Patterns vs. Resampling

Design Motivation: Existing IMTS multi-scale methods use resampling (downsampling) to obtain coarse-grained sequences, which erases semantically meaningful sampling patterns. ReIMTS adopts splitting based on time periods: at scale level \(n\), samples are divided into \(P^n = T^1/T^n\) sub-samples according to a time period \(T^n\). The key is that splitting is based on real-world time durations (e.g., 12 hours, 24 hours) rather than the number of observations. Splitting by observation count would cause sub-samples to correspond to inconsistent real-time spans, disrupting temporal semantics. By splitting by time periods, original timestamps are fully preserved, using only zero-padding for alignment. For example, in PhysioNet'12, Level 1 covers the full 48 hours, Level 2 splits it into two 24-hour sub-samples, and Level 3 into four 12-hour sub-samples, forming a global-to-local multi-scale perspective while keeping the sampling time of each observation constant.

2. Multi-scale Representation Learning: Independent Encoding and Downward Shape Alignment

Mechanism: Each scale level utilizes an independent backbone encoder \(\mathcal{F}^n_{\text{enc}}\) to encode its sub-samples, resulting in \(\mathbf{E}^n = \mathcal{F}^n_{\text{enc}}(\mathbf{S}^n)\). Encoded latent representations are categorized into three types: temporal representations \(\mathbf{E}^n_{\text{time}} \in \mathbb{R}^{P^n \times L^n \times D}\), variable representations \(\mathbf{E}^n_{\text{var}} \in \mathbb{R}^{P^n \times V \times D}\), and observation representations \(\mathbf{E}^n_{\text{obs}} \in \mathbb{R}^{P^n \times L^n \times V \times D}\). To inject the global representation \(\mathbf{H}^n\) from the previous layer into the next, shape matching is required: splitting operations are applied to temporal/observation representations, and replication is used for variable representations. This transforms \(\mathbf{H}^n\) into a shape aligned with the local representation \(\mathbf{E}^{n+1}\) of the subsequent layer.

3. Irregularity-Aware Representation Fusion (IARF): Distinguishing Observations from Padding

Function: After shape alignment, temporal/observation representations still contain zero-padded positions. Direct addition would treat padding noise as signal. IARF utilizes a binary mask \(\mathbf{M}^{n+1}\) to identify real observations versus padding in the lower scale. For temporal/observation representations, padding is masked via \(\mathbf{H}^n_{\text{IMTS}} = \mathbf{H}^n \cdot \mathbf{M}^{n+1}\). For variable representations, since irregularity information is already encoded by the IMTS backbone, \(\mathbf{H}^n_{\text{IMTS}} = \mathbf{H}^n\) is used directly. An adaptive weight \(\alpha = \text{ReLU}(\text{FF}(\mathbf{H}^n_{\text{IMTS}}))\) is calculated via a lightweight scoring layer to fuse global information: \(\mathbf{G}^{n+1} = \mathbf{E}^{n+1} + \alpha \mathbf{H}^n_{\text{IMTS}}\). This ensures global context only affects real observations, preventing padding values from contaminating lower-level representations.

Loss & Training

At the lowest scale level \(N\), the decoder concatenates all fused representations for one-shot decoding, \(\hat{\mathbf{Z}} = \mathcal{F}_{\text{dec}}(\text{Concat}(\{\mathbf{G}^n\}_{n=1}^N))\). This allows final predictions to leverage information from global to local scales. The model is trained using MSE loss, calculated only for the \(Y_Q\) prediction queries within the prediction window: \(\mathcal{L} = \frac{1}{Y_Q} \sum_{j=1}^{Y_Q} (\hat{z_j} - z_j)^2\). Optimization runs for a maximum of 300 epochs with an early stopping patience of 10.

Key Experimental Results

Main Results

Evaluated across 5 IMTS datasets (MIMIC-III/IV, PhysioNet'12, Human Activity, USHCN) and 26 baseline methods.

Backbone Model	Original MSE (×10⁻¹)	+ReIMTS MSE (×10⁻¹)	Avg. Gain
PrimeNet	9.04/6.25/7.93/26.84/4.57	4.76/3.58/3.01/0.82/1.71	↑62.3%
mTAN	8.51/5.09/3.75/0.89/5.65	6.37/4.04/3.51/0.89/1.70	↑24.3%
TimeCHEAT	4.41/2.50/3.27/0.68/1.73	4.40/2.02/2.90/0.52/1.62	↑12.1%
GRU-D	4.75/5.97/3.25/1.76/2.42	4.67/3.91/3.25/0.51/1.89	↑25.8%
GraFITi	4.08/2.39/2.85/0.43/1.71	4.07/1.79/2.83/0.42/1.66	↑6.3%

Comparison with other multi-scale IMTS methods (using GraFITi as backbone):

Method	MIMIC-III	MIMIC-IV	PhysioNet'12	Human Activity	USHCN
Warpformer	4.09	2.42	2.88	0.54	1.77
HD-TTS	4.17	2.36	2.83	0.50	1.66
Hi-Patch	4.35	2.36	3.11	0.48	2.34
Ours (ReIMTS)	4.07	1.79	2.83	0.42	1.66

Ablation Study

Variant	MIMIC-III	MIMIC-IV	PhysioNet'12	Human Activity	USHCN
ReIMTS (Full)	4.07	1.79	2.83	0.42	1.66
rp sample (No splitting)	4.99	1.92	2.83	0.45	1.69
rp split (Split by obs count)	5.02	2.36	3.20	0.61	2.31
rp IARF (Fusion -> Addition)	4.20	1.84	2.79	0.47	1.89
w/o IARF (No fusion)	4.77	2.07	3.06	0.54	1.69

Key Findings

• Period-based splitting (ReIMTS) significantly outperforms splitting by observation count (rp split), with a gap as high as 0.65 on USHCN.
• Classic models (e.g., mTAN, GRU-D) can outperform more recent models when augmented with ReIMTS.
• Efficiency: When using the GraFITi backbone, ReIMTS achieves the fastest training speed and lowest GPU memory consumption, outperforming Warpformer, HD-TTS, and Hi-Patch.

Highlights & Insights

1. Pattern-Preserving Multi-Scale Design: Instead of resampling, it uses period-based recursive splitting, which is simple yet effective.
2. Plug-and-Play Compatibility: Highly versatile, adapting to most encoder-decoder IMTS models.
3. Revitalizing Older Methods: Improvements of 62.3% for PrimeNet and 25.8% for GRU-D suggest that multi-scale modeling was a critical missing piece for these architectures.
4. Efficiency Advantage: By leveraging lightweight backbones like GraFITi, it achieves both optimal accuracy and efficiency.

Limitations & Future Work

• Lack of theoretical explanation when combining ODE-based models with ReIMTS.
• The fusion mechanism is not directly compatible with the noisy latent representations of diffusion models.
• Choice of period lengths requires manual specification (dataset settings are provided in the appendix); adaptive selection is a potential direction.
• Only forecasting tasks were validated; other downstream tasks like classification remain unexplored.

Related Work & Insights

• Relation to tPatchGNN and PrimeNet: These can be viewed as single-scale special cases of ReIMTS.
• Multi-scale methods for regular time series like Scaleformer destroy sampling information due to resampling.
• Insight: For other tasks involving irregular data (e.g., event sequences, point processes), multi-scale approaches that preserve original temporal information may be equally beneficial.

Rating

• Novelty: ⭐⭐⭐⭐ (The period-based splitting concept is simple and effective; IARF fusion is well-designed.)
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ (5 datasets, 26 baselines, 6 backbones, complete ablation and efficiency analysis.)
• Writing Quality: ⭐⭐⭐⭐ (Motivation is clear, diagrams are intuitive, and comparisons are detailed.)
• Value: ⭐⭐⭐⭐ (Plug-and-play design is highly practical; open-sourced in PyOmniTS.)

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