QiYao-I: A Manifold Based Foundation Model for Irregular Multivariate Time Series Forecasting

arXiv:2610.06936 · cs.LG · Submitted 2026-10-03 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "QiYao-I: A Manifold Based Foundation Model for Irregular Multivariate Time Series Forecasting".

Jane: Irregular multivariate time series forecasting is addressed by QiYao-I,

Tom: First, who's behind it and why it matters.

Title and authors: Tom: Let's look at the core idea behind this paper again. They call it a manifold based foundation model. That means they aren't just looking at raw data points; they are mapping those observations into some kind of geometric space, or manifold, where the relationships between them are smoother and easier for an AI to learn from.

Jane: Exactly. The idea is that by learning this manifold structure, the model can capture the underlying patterns in the data better than if it just treated every timestamp as an equally spaced token. They want to learn how time itself is structured, not just where the tokens are located on a sequence.

Lu: Specifically, they propose a novel sampling-conditioned temporal manifold attention mechanism. This part is key because it maps those real timestamps into this learnable temporal feature space and injects biases into the attention layers based on that manifold structure #pg1

Meng: So, it’s not just looking at the sequence order; it’s using the actual time information to shape how much attention a model pays to different parts of the data stream. That sounds like a smart way to handle uneven gaps in the data.

Lalam: It helps distinguish between two observations that might fall on the same general time interval but have very different numbers of sampled points, which is something traditional methods often get wrong >

The paper's summary: Tom: Moving into what they actually did in the paper, QiYao-I tackles irregular multivariate time series forecasting by introducing three main components. These are the Sampling-Conditioned Temporal Manifold Attention, the Learnable Irregular Spectral Representation, and the Frequency-Guided Cross-Variable Interaction.

Jane: Those three pieces work together to tackle different aspects of irregular data. The first part handles how time behaves irregularly, the second focuses on extracting meaningful frequency information from those irregular values themselves, and the third manages how variables interact across different frequencies.

Lu: The sampling-conditioned temporal manifold attention maps timestamps into that feature space and adjusts the attention biases based on manifold distances #pg1 This mechanism also uses a Gaussian-kernel descriptor to handle pairs with the same time interval but different sample counts by adapting the bandwidth of those biases

Meng: That adaptive bandwidth thing sounds important for robustness. It means two pairs of observations that look close in terms of time might get different attention weights if their sampling patterns are locally different, which makes sense for real-world data where things don't always behave perfectly predictably >

Lalam: And then you have the frequency-guided cross-variable interaction. This mechanism selects relevant patches from other variables and weights them based on how similar their local and global frequencies are, which is crucial when those variables are moving asynchronously #pg3

The paper's improvements: Tom: Now let's talk about what they claim as their main contributions. They really put forward the unified framework itself—QiYao-I—which jointly models irregular temporal dependencies and asynchronous cross-variable interactions in one go #pg3

Jane: And they highlight that novel sampling-conditioned temporal manifold time attention, which lets them capture those irregular time intervals and distinguish the same interval under different sampling structures. That’s a big win for generalization across different data collection methods.

Lu: They also propose the frequency-guided dynamic variable interaction mechanism. By grouping observations into patches, selecting the top K nearest patches from other variables based on temporal distance, and weighting their contributions using learnable spectrum projection and aggregation to emphasize information from patches with similar local and global temporal patterns #pg3

Meng: The ablation studies they ran are interesting too. They showed that adding the sampling-conditioned temporal manifold bias consistently beats standard RoPE and CT-RoPE, which proves adapting the model to local sampling structures actually helps improve things >

Lalam: And removing the cross-variable interaction or swapping out the frequency selection for a dense interaction method definitely made performance worse, so they proved that selective information exchange is really important when dealing with asynchronous variables >

Conclusion: Tom: So to wrap up on "QiYao-I: A Manifold Based Foundation Model for Irregular Multivariate Time Series Forecasting," the authors have shown this unified framework can handle irregular multivariate time series forecasting better than existing foundation models and end-to-end models.

Jane: It seems the main implication is that we can move past models that are strictly built for evenly spaced data and start building systems that are more flexible when dealing with real-world, messy, irregularly sampled data across multiple variables.

Lu: The strong generalization ability they showed in both zero-shot and few-shot settings suggests this model learns representations that aren't tied too closely to specific training datasets, which is a significant step forward for practical deployment >

Meng: From an engineering standpoint, the performance compared to end-to-end models in few-shot settings is what really matters here. It shows that having a good foundation model structure can give you a solid starting point even when you only have very little specific data to train on >

Lalam: Overall, QiYao-I demonstrates how we can use manifold learning and frequency awareness to create representations that capture complex temporal and cross-variable relationships in irregular data, which is a really useful tool for general forecasting research >

East China Normal University · Huawei Technologies Ltd.

cs.LG

Submitted: 2026-10-03

Updated: 2026-10-11

Comments: 29 pages, 5 figures, 20 tables. Preprint

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 91/100

The gist: Irregular multivariate time series forecasting is addressed by QiYao-I, a manifold based foundation model that learns transferable representations through sampling-conditioned temporal manifold

Key concepts

Sampling-Conditioned Temporal Manifold Attention: This mechanism maps irregular timestamps into a learnable feature space, injecting temporal biases into attention layers. It models temporal relationships by learning distances on this manifold and adaptively adjusts how these distances are interpreted based on the sampling structure, effectively distinguishing observations with different point counts in the same time window.
Learnable Irregular Spectral Representation: This component extracts frequency information directly from irregular data and timestamps using sine and cosine bases without resampling. It computes global frequency representations by aggregating point-level coefficients into a variable-level spectrum, summarizing periodic patterns across the historical time window.
Frequency-Guided Cross-Variable Interaction: This process selects relevant data patches from other variables based on their temporal distance and weights them using frequency similarity. This allows the model to selectively exchange information across asynchronous variables, emphasizing interactions between data points that share similar local and global temporal patterns.

Terminology

Foundation Model — 1× in this paper · explained in 3 episodes
Time Series Forecasting — 1× in this paper · explained in 3 episodes

Summary

Irregular multivariate time series forecasting is addressed by QiYao-I, a manifold based foundation model that learns transferable representations through sampling-conditioned temporal manifold attention and frequency-guided patch interaction to capture irregular temporal dependencies and asynchronous cross-variable relations.

How it works

QiYao-I is designed as a unified foundation model framework that jointly models irregular temporal dependencies and asynchronous cross-variable interactions. The architecture consists of three main components: Sampling-Conditioned Temporal Manifold Attention, Learnable Irregular Spectral Representation, and Frequency-Guided Cross-Variable Interaction.

The Sampling-Conditioned Temporal Manifold Attention mechanism maps timestamps into a learnable temporal manifold feature space and injects temporal manifold biases into attention layers. This mechanism models temporal relations by learning manifold distances and converts these distances into temporal manifold biases. Furthermore, it introduces a Gaussian-kernel descriptor to distinguish observation pairs that span the same time interval but have different numbers of sampled points by adaptively adjusting the bandwidth of these temporal manifold biases.

The Learnable Irregular Spectral Representation component extracts frequency representations directly from irregular values and timestamps through multi-source pre-training. This involves applying sine and cosine bases with learnable frequencies directly to their timestamps to obtain spectral representations without resampling the input. The model then computes global frequency representations by aggregating point-level coefficients into a variable-level spectrum to summarize periodic patterns across the historical window.

The Frequency-Guided Cross-Variable Interaction mechanism selects temporally relevant patches from other variables and weights them according to local and global frequency similarity to model asynchronous cross-variable interaction. This is achieved by grouping observations into patches, selecting the top-K nearest patches from other variables based on temporal distance, and weighting their contributions using learnable spectrum projection and aggregation to emphasize information from patches with similar local and global temporal patterns.

Main Contributions

The main contributions of QiYao-I are summarized as follows:

• We propose QiYao-I, which jointly models irregular temporal dependencies and asynchronous cross-variable interactions in a unified framework.

• We propose a novel sampling-conditioned temporal manifold time attention, which captures irregular time intervals and distinguishes the same interval under different sampling structure.

• We propose a frequency-guided dynamic variable interaction mechanism that selects patches from other variables based on temporal distance and weights their contributions by frequency similarity, enabling selective interactions across asynchronous variables.

• Extensive experiments show that QiYao-I achieves superior forecasting performance and strong generalization ability in both zero-shot and few-shot settings.

Experimental Results

Extensive experiments on real-world irregular multivariate forecasting benchmarks demonstrate that QiYao-I achieves superior performance compared to both time series foundation models and end-to-end irregular forecasting models. In comparison to other foundation models, QiYao-I achieves the best or second-best average results on most datasets, demonstrating cross-dataset generalization ability. Furthermore, QiYao-I achieves 10 best results among 15 end-to-end irregular time series models in few-shot settings.

Model Analysis

Ablation studies show that adding the sampling-conditioned temporal manifold bias consistently outperforms standard RoPE and CT-RoPE, demonstrating the benefit of adapting temporal relations to local sampling structures. Removing cross-variable interaction or replacing frequency-guided selection with dense interaction also degrades performance, confirming the importance of selective information exchange across asynchronous variables.

Conclusion

QiYao-I is a manifold based foundation model for irregular multivariate time series forecasting that learns transferable representations through sampling-conditioned temporal manifold attention and frequency-guided patch interaction to capture irregular temporal dependencies and asynchronous cross-variable relations. Extensive experiments demonstrate strong zero-shot generalization and few-shot adaptation. The model's code is available at https://anonymous.4open.science/r/QiYao-I-0053/. The paper focuses on methodological research for irregular multivariate time series forecasting. The proposed method is intended for general-purpose forecasting research, and we are not aware of any direct ethical risks arising from the methodology itself. The model architecture of QiYao-I are described in Section 3, with experimental settings, dataset details, and implementation provided in Appendix A. The source code is available at https://anonymous.4open.science/r/QiYao-I-0053/ and necessary scripts will be released. The research questions, methodology, experimental design, analysis, and scientific claims were developed independently by the authors. The paper is 2610.06936. The gist is that QiYao-I jointly models irregular temporal dependencies and asynchronous cross-variable interactions in a unified framework. The paper is 2610.06936.

Improvements for AI systems

textbfSampling-Conditioned Temporal Manifold Attention for Irregular Time Intervals: "This mechanism maps scalar timestamps into a learnable temporal manifold feature space and injects temporal manifold biases into attention layers, enabling the model to capture both irregular time intervals and local sampling structures." This allows the model to handle heterogeneous IMTS data without relying on dataset-specific interpolation, enhancing generalization across different sampling structures.
textbf Dynamic Variable Interaction Mechanism with Frequency Awareness: We therefore use learnable spectrum projection and aggregation to extract patch-level and global-level frequency features directly from irregular values and timestamps. This enables the model to capture periodic patterns by weighting interactions based on local and global frequency similarity, allowing selective cross-variable message passing across asynchronous observations.
textbf Adaptive Bandwidth Mechanism: The effective bandwidth is βl,r p r l,r u r l,r w. This mechanism adjusts the penalty derived from manifold distance based on the local sampling structure (Sampling-conditioned bandwidth), meaning two pairs with the same manifold distance can receive different attention biases when their local sampling structures differ, making temporal dependencies more robust.
textbf Unified Foundation Model Framework: QiYao-I, a unified foundation model framework designed for irregular multivariate time series. This architecture jointly models irregular temporal dependencies and asynchronous cross-variable interactions in a unified framework, providing a single system capable of handling both aspects simultaneously.

Abstract

Irregular multivariate time series forecasting is a challenging yet important problem in real-world applications, where observations are often irregularly sampled and asynchronously recorded across variables. Existing time series foundation models are mostly built on regularly sampled sequences, making them difficult to generalize to irregular time intervals and asynchronous cross-variable dependencies. To address these challenges, we propose QiYao-I, a manifold based foundation model for irregular multivariate time series forecasting. Specifically, we introduce a novel sampling-conditioned temporal manifold attention mechanism that maps real timestamps into a learnable temporal manifold feature space and injects temporal manifold biases into attention layers, enabling the model to capture both irregular time intervals and local sampling structures. Further, we propose a dynamic variable interaction mechanism with frequency awareness. It selectively performs cross-variable message passing under asynchronous observations. Extensive experiments on real-world irregular multivariate forecasting benchmarks demonstrate that QiYao-I achieves superior performance compared with both time series foundation models and end-to-end irregular forecasting models, showing strong generalization ability in zero-shot and few-shot settings.