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Theory

Forecasting with TiRex builds on the powerful xLSTM (Extended Long Short-Term Memory) architecture — a next-generation recurrent model designed to combine the efficiency and interpretability of classic RNNs with the long-range modeling capabilities of Transformers. This section provides a conceptual overview of how TiRex performs forecasting, followed by detailed descriptions of its input and output handling.

Architectural Foundations​

At its core, xLSTM introduces several innovations beyond classical LSTMs:

  • Expanded Memory Dynamics: xLSTM extends the traditional LSTM cell with additional multiplicative interactions and normalization mechanisms that improve temporal credit assignment over long horizons.

  • Hierarchical Temporal Abstraction: Time series often contain information at multiple scales (daily, weekly, seasonal). xLSTM layers in TiRex are designed to process signals at these varying frequencies efficiently using frequency-aware resampling (based on FFT-derived periodicity).

  • Parameter Efficiency: Compared to Transformers, xLSTM achieves similar or superior accuracy with far fewer parameters and lower latency, making it suitable for Edge and industrial deployments.

  • Zero-Shot Forecasting Capability: TiRex models are trained on a broad mixture of time series domains, allowing them to generalize to unseen datasets without fine-tuning. This enables rapid deployment across diverse tasks such as demand, energy, or environmental forecasting.

Conceptual Summary​

TiRex’s forecasting process can be viewed as a sequence of transformations:

  1. Input normalization → Ensure consistent scale and alignment of the input series.

  2. Frequency-based resampling → Automatically adjust temporal resolution to align dominant frequencies with model patch size.

  3. xLSTM-based sequence modeling → Encode long- and short-term dependencies in a compact representation.

  4. Probabilistic decoding → Generate multiple quantile forecasts representing the predictive distribution.

Together, these steps enable accurate, data-efficient, and generalizable forecasting across time series of varying lengths, domains, and sampling rates.

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