DualTimesField: Rethinking Time Series as Continuous-Time Trends and Events

Effective time series representation is critical for revealing temporal dynamics in many fields. However, existing approaches encounter fundamental limitations. Discrete-time representations struggle with irregular sampling and the tradeoff of fidelity and efficiency, while traditional implicit neural representations suffer from spectral bias and frequency entanglement. To address these challenges, we conceptualize time series as the superposition of continuous trends and discrete events from a continuous-time perspective and propose DualTimesField, a framework that utilizes dual implicit neural fields. Its Continuous Time Field captures smooth trends through bandwidth-limited parameterization, while a Discrete Geometric Field models transient events using learnable Gabor atoms, gated sparsity, and coarse-to-fine scale annealing. This explicit field separation effectively overcomes both limitations. Experiments on nine real-world benchmarks demonstrate substantial improvements in representation fidelity, achieving 51.2% average MSE reduction over discrete-time baselines and competitive interpolation on irregular data. Code is available at https://github.com/WisdomTogether/DualTimesField.

Heartbeats, electricity meters, traffic flow: much of the world generates long streams of numbers over time. These streams usually mix two different patterns, a slow background that drifts along and short bursts such as spikes or jolts. Most machine learning models handle the mixture badly. They either smooth away the bursts or lose track of the drift, and they assume measurements arrive on a regular schedule, which is rarely true in practice. Our model, DualTimesField, treats the two patterns as separate jobs. One part of the network focuses only on the smooth background. A second part stays quiet until a sharp event happens, then fires off a small number of precise, wave-shaped pulses to describe it. Because the model represents time as a continuous quantity rather than a fixed grid, it works the same way on regular and irregular data. Across nine standard benchmarks our approach roughly halves the reconstruction error of the previous best method, and it ranks first on five of six datasets with uneven sampling. We also ran it on electrocardiogram recordings without telling the model anything about heart disease, and the event module on its own lit up where cardiologists would expect to find abnormal beats.