aiqbench analysis
This paper proposes HyperForecast, a long-term time series forecaster that embeds decomposed signal components in hyperbolic (Poincaré ball) space, with low-frequency components near the origin and high-frequency ones near the boundary. The reported gains, including a 58% MSE reduction at long horizons on 9 of 11 benchmarks, are benchmark-specific, and the authors' ablation claim that hyperbolic geometry drives much of the improvement is the key result to verify. Practitioners should check whether the gains hold against strong, well-tuned Euclidean baselines and on non-benchmark data.
Hyperbolic Time Series Forecasting with Learnable Decomposition and Manifold Dynamics
arXiv:2610.15760v1 Announce Type: cross Abstract: Multiscale structure is central to time series forecasting: temporal signals contain slowly varying trends, intermediate seasonal patterns, and high-frequency residuals. Traditional forecasters model this multiscale structure in Euclidean space, without representing the ordering it induces among components. We identify that cascaded decomposition orders components by their characteristic frequencies, forming a natural frequency hierarchy. This hierarchy aligns with the exponential volume growth of hyperbolic space, which provides increasing representational capacity with radius and naturally accommodates nested hierarchies. We propose HyperForecast, the first long-term time series forecasting (LTSF) framework operating in hyperbolic space. HyperForecast embeds decomposed temporal segments on the Poincar\'e ball where radial distance captures this nested structure, from low-frequency components near the origin to high-frequency components near the boundary. We model geodesic velocity through two manifold-dynamics variants: (a) autoregressive forecasting via Poincar\'e residual dynamics, and (b) non-autoregressive forecasting that predicts all future segments in parallel. HyperForecast consistently outperforms existing and state-of-the-art baselines on 9 of 11 long-term forecasting benchmarks, achieving up to 58% lower mean squared error at long horizons. Further analysis reveals that the learned radial embeddings recover the frequency hierarchy and that hyperbolic geometry contributes substantially to forecasting performance.
Abstract:Multiscale structure is central to time series forecasting: temporal signals contain slowly varying trends, intermediate seasonal patterns, and high-frequency residuals. Traditional forecasters model this multiscale structure in Euclidean space, without representing the ordering it induces among components. We identify that cascaded decomposition orders components by their characteristic frequencies, forming a natural frequency hierarchy. This hierarchy aligns with the exponential volume growth of hyperbolic space, which provides increasing representational capacity with radius and naturally accommodates nested hierarchies. We propose HyperForecast, the first long-term time series forecasting (LTSF) framework operating in hyperbolic space. HyperForecast embeds decomposed temporal segments on the Poincaré ball where radial distance captures this nested structure, from low-frequency components near the origin to high-frequency components near the boundary. 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. HyperForecast consistently outperforms existing and state-of-the-art baselines on 9 of 11 long-term forecasting benchmarks, achieving up to 58% lower mean squared error at long horizons. Further analysis reveals that the learned radial embeddings recover the frequency hierarchy and that hyperbolic geometry contributes substantially to forecasting performance.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.15760 [cs.LG]
(or arXiv:2610.15760v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.15760 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 288 words
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