Hyperbolic Time Series Forecasting with Learnable Decomposition and Manifold Dynamics

Key points

• Multiscale structure is central to time series forecasting: temporal signals contain slowly varying trends, intermediate seasonal patterns, and high-frequency residuals.1
• Traditional forecasters model this multiscale structure in Euclidean space, without representing the ordering it induces among components.1
• We model geodesic velocity through two manifold-dynamics variants: (a) autoregressive forecasting via Poincaré residual dynamics, and (b) non-autoregressive forecasting that predicts all future segments in parallel.1
• Further analysis reveals that the learned radial embeddings recover the frequency hierarchy and that hyperbolic geometry contributes substantially to forecasting performance.1

Sources (1)

• [1]Hyperbolic Time Series Forecasting with Learnable Decomposition and Manifold Dynamics
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 11, 04:40 PM

  We propose HyperForecast, the first long-term time series forecasting (LTSF) framework operating in hyperbolic space.

  Multiscale structure is central to time series forecasting: temporal signals contain slowly varying trends, intermediate seasonal patterns, and high-frequency residuals.

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