Trio: Learning Time-Series Forecasting with Temporal-Spatial-Sample Attention and Structural Causal Priors

2026-06-05

AI Summary

Multivariate time series forecasting faces challenges in modeling temporal dynamics, capturing inter-variable dependencies, and effectively leveraging historical input–output pairs, while existing synthetic tasks often lack transferability. This work proposes Trio, a novel architecture that explicitly organizes and reuses sample-level historical input–output pairs, introducing a time–space–sample triple attention mechanism to jointly model intra-window dynamics, cross-variable dependencies, and relevant historical samples. Additionally, the authors introduce a Temporal Structural Causal Model (TS-SCM) to generate synthetic tasks incorporating dynamic lags and distribution shifts, injecting structural causal priors to guide Prior-Data Fitted Networks (PFNs). Experiments demonstrate significant performance gains across synthetic, industrial, and public benchmark datasets, with zero-shot results validating the efficacy of the TS-SCM–derived structural priors and advancing the applicability of PFNs in time series forecasting.

Abstract

Multivariate time-series forecasting requires models to reason over temporal dynamics, cross-variable dependencies, and historical input-output correspondences. Recent Prior-Data Fitted Networks (PFNs) suggest that synthetic tasks can be useful for learning transferable inference behavior. However, directly transferring this paradigm to time-series forecasting remains difficult, since temporal order, dynamic lags, and recurring historical patterns are not naturally captured by ordinary tabular priors. Motivated by this observation, we propose Trio, a sample-aware time-series forecasting architecture based on Temporal-Spatial-Sample attention. Temporal attention captures within-window dynamics, spatial attention models inter-variable dependencies, and sample attention retrieves relevant historical lookback-future pairs to guide the current prediction. Rather than claiming a fully general PFN-style forecaster, our goal is to study how historical input-output examples can be explicitly organized and reused within a forecasting model. We further introduce a Time-Series Structural Causal Model (TS-SCM) generator to create structured synthetic forecasting tasks with dynamic lags, cross-variable interactions, noise, feedback, and distributional drift. Experiments on synthetic, industrial, and public benchmarks show that the proposed architecture improves forecasting performance. Exploratory zero-shot experiments further suggest that TS-SCM-generated tasks may provide useful structural priors, while fully general PFN-style time-series forecasting remains an open problem.

Problem

• time-series forecasting
• multivariate time-series
• historical input-output correspondence
• structural causal model
• dynamic lags

Innovation

• Temporal-Spatial-Sample Attention
• Structural Causal Model
• Time-Series Forecasting
• Prior-Data Fitted Networks
• Synthetic Task Generation