TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting

Researchers introduce TopoCast, a topology-based evaluation framework for time series forecasting that moves beyond traditional error metrics to assess structural fidelity in deep learning models. The framework uses persistent homology to detect phase shifts, oscillatory distortions, and timing errors that conventional metrics like MSE overlook, revealing that models with similar numerical accuracy can exhibit substantially different structural quality.

TopoCast addresses a critical blind spot in machine learning evaluation: the gap between numerical accuracy and structural validity. Traditional metrics like Mean Squared Error measure pointwise prediction accuracy but ignore whether forecasts preserve the underlying dynamics of time series data. A forecast can exhibit phase shifts, frequency distortions, or over-smoothing while still achieving low MSE, creating a false sense of model reliability. This matters particularly in domains like financial forecasting, weather prediction, and systems monitoring where capturing oscillatory patterns and temporal dynamics carries operational significance.

The framework leverages persistent homology, a topological data analysis technique that characterizes the intrinsic shape and recurring patterns of time series. By reconstructing phase-space representations using Takens delay embedding and analyzing persistence diagrams, TopoCast derives four complementary topological measures. The introduction of dominant cycle overlap extends this analysis into the temporal domain, capturing whether oscillatory patterns occur at the correct time points—a dimension entirely missed by conventional metrics.

Empirical validation across five Transformer architectures and three benchmark datasets demonstrates that models achieving similar forecasting errors exhibit markedly different structural fidelity profiles. This finding carries implications for model selection, particularly in applications where structural accuracy determines downstream decision-making. For practitioners developing production forecasting systems, TopoCast provides tools to identify failure modes hidden by traditional evaluation protocols.

The framework advances the broader conversation around evaluation rigor in deep learning, especially for tasks where temporal structure matters as much as point accuracy. Future adoption could reshape how researchers benchmark time series models and how practitioners validate forecasts before deployment.

• →TopoCast identifies structural failures in time series forecasts that conventional error metrics fail to detect, such as phase shifts and frequency distortions
• →Persistent homology and topological data analysis enable quantification of forecast dynamics and oscillatory pattern preservation independent of numerical accuracy
• →Experiments show Transformer models with equivalent MSE can exhibit significantly different topological fidelity profiles, revealing previously invisible failure modes
• →The Localized Topological Fidelity Score captures temporal localization of oscillatory patterns, bridging topological and temporal evaluation dimensions
• →Framework has practical implications for financial forecasting, weather prediction, and systems monitoring where dynamic structure preservation is operationally critical