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Time-o1: Time-Series Forecasting Needs Transformed Label Alignment

Hao Wang, Licheng Pan, Zhichao Chen, Xu Chen, Qingyang Dai, Lei Wang, Haoxuan Li, Zhouchen Lin

TL;DR

Time-o1 tackles two core issues in time-series forecasting objectives: autocorrelation bias and the explosion of multitask complexity with longer horizons. It transforms the label sequence into decorrelated components ranked by significance and trains models to align the most informative components, yielding debiased training and easier optimization. The approach is theoretically justified and implemented via a unified pipeline using SVD-based projection and a mixed objective L_{α,γ}. Empirically, Time-o1 consistently improves state-of-the-art forecasts across diverse datasets and backbone models, demonstrating strong practical utility and model-agnostic applicability. The work also provides extensive ablations and generalization studies, confirming the robustness and versatility of the proposed objective.

Abstract

Training time-series forecast models presents unique challenges in designing effective learning objectives. Existing methods predominantly utilize the temporal mean squared error, which faces two critical challenges: (1) label autocorrelation, which leads to bias from the label sequence likelihood; (2) excessive amount of tasks, which increases with the forecast horizon and complicates optimization. To address these challenges, we propose Time-o1, a transformation-augmented learning objective tailored for time-series forecasting. The central idea is to transform the label sequence into decorrelated components with discriminated significance. Models are then trained to align the most significant components, thereby effectively mitigating label autocorrelation and reducing task amount. Extensive experiments demonstrate that Time-o1 achieves state-of-the-art performance and is compatible with various forecast models. Code is available at https://github.com/Master-PLC/Time-o1.

Time-o1: Time-Series Forecasting Needs Transformed Label Alignment

TL;DR

Time-o1 tackles two core issues in time-series forecasting objectives: autocorrelation bias and the explosion of multitask complexity with longer horizons. It transforms the label sequence into decorrelated components ranked by significance and trains models to align the most informative components, yielding debiased training and easier optimization. The approach is theoretically justified and implemented via a unified pipeline using SVD-based projection and a mixed objective L_{α,γ}. Empirically, Time-o1 consistently improves state-of-the-art forecasts across diverse datasets and backbone models, demonstrating strong practical utility and model-agnostic applicability. The work also provides extensive ablations and generalization studies, confirming the robustness and versatility of the proposed objective.

Abstract

Training time-series forecast models presents unique challenges in designing effective learning objectives. Existing methods predominantly utilize the temporal mean squared error, which faces two critical challenges: (1) label autocorrelation, which leads to bias from the label sequence likelihood; (2) excessive amount of tasks, which increases with the forecast horizon and complicates optimization. To address these challenges, we propose Time-o1, a transformation-augmented learning objective tailored for time-series forecasting. The central idea is to transform the label sequence into decorrelated components with discriminated significance. Models are then trained to align the most significant components, thereby effectively mitigating label autocorrelation and reducing task amount. Extensive experiments demonstrate that Time-o1 achieves state-of-the-art performance and is compatible with various forecast models. Code is available at https://github.com/Master-PLC/Time-o1.

Paper Structure

This paper contains 39 sections, 6 theorems, 23 equations, 11 figures, 12 tables, 1 algorithm.

Key Result

Theorem 3.1

Given label sequence $Y$ where $\Sigma\in\mathbb{R}^{\mathrm{T}\times\mathrm{T}}$ denotes the step-wise correlation coefficient, the TMSE in eq:tmp is biased compared to the negative log-likelihood of the label sequence, which is given by: where $\|v\|_{\Sigma^{-1}}^2=v^\top\Sigma^{-1}v$. The bias vanishes if different steps in $Y$ are decorrelated.The pioneering work wang2025iclrfredf identifies

Figures (11)

  • Figure 1: Comparison of label sequence and associated components. (a) shows the correlation volume within the label sequence (left panel) and components (right panel). (b) visualizes 8 label sequences randomly from ETTh1 (left panel) and the associated components (right panel).
  • Figure 2: The visualization of forecast sequence generated by DF and Time-o1. The left panels in (a) and (b) present label and forecast sequences, the right panels present the associated components.
  • Figure 3: Improvement of Time-o1 applied to different forecast models, shown with colored bars for means over forecast lengths (96, 192, 336, 720) and error bars for 50% confidence intervals.
  • Figure 4: The label autocorrelation in the original label sequence and the extracted components. The datasets are ETTh1, ETTh2, ETTm1, and Weather from left to right. The forecast length is set to 96.
  • Figure 5: Running cost for projection matrix calculation (left panel with varying number of samples, right panel with varying prediction length) and sequence transformation (left panel for forward pass, right panel for backward pass, with average and shaded areas for 95% confidence intervals).
  • ...and 6 more figures

Theorems & Definitions (9)

  • Theorem 3.1: Autocorrelation bias
  • Lemma 3.2: Decorrelated components
  • Lemma 3.3
  • Theorem B.1: Autocorrelation bias, Theorem \ref{['thm:bias']} in the main text
  • proof
  • Lemma B.2: Lemma \ref{['lem:svd']} in the main text
  • proof
  • Lemma B.3: Decorrelated components, Lemma \ref{['lem:decorrelation']} in the main text
  • proof