xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories

Abstract: Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models. Capturing patterns both within and between temporal and multivariate components is crucial for reliable predictions. We introduce xLSTM-Mixer, a model designed to effectively integrate temporal sequences, joint time-variate information, and multiple perspectives for robust forecasting. Our approach begins with a linear forecast shared across variates, which is then refined by xLSTM blocks. These blocks serve as key elements for modeling the complex dynamics of challenging time series data. xLSTM-Mixer ultimately reconciles two distinct views to produce the final forecast. Our extensive evaluations demonstrate xLSTM-Mixer's superior long-term forecasting performance compared to recent state-of-the-art methods. A thorough model analysis provides further insights into its key components and confirms its robustness and effectiveness. This work contributes to the resurgence of recurrent models in time series forecasting.

• The paper proposes xLSTM-Mixer, which integrates time and variate mixing in recurrent architectures to enhance forecasting accuracy.
• It leverages scalar memories with exponential gating to capture complex temporal dependencies effectively.
• Evaluation demonstrates superior long-term forecasting performance, outperforming benchmarks in MSE and MAE across diverse datasets.

xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories

The paper introduces xLSTM-Mixer, a novel approach aimed at enhancing the forecasting of multivariate time series data by integrating both temporal sequences and multi-view perspectives. The model is grounded in recurrent neural network architectures, specifically extended Long Short-Term Memory (xLSTM), which are complemented by time-mixing and variate-mixing techniques.

Core Contributions

1. Time and Variate Mixing: The paper presents a thorough investigation into time and variate mixing within recurrent models, proposing that interleaved time and variate mixing can lead to superior results. The xLSTM-Mixer model first applies a linear forecast independent of the variates before an up-projection to a higher embedding dimension.
2. xLSTM Architecture: The xLSTM architecture is leveraged to model complex dynamics in time series data effectively. The paper highlights the utilization of scalar memories with exponential gating, enhancing the model’s ability to manage dependencies across multiple scalars.
3. Multi-View Forecasting: By introducing multi-view mixing, where forecasts from original and reversed embeddings are reconciled, the paper posits an innovative strategy to regularize training and improve robustness.

Evaluation and Results

The model demonstrates strong performance against contemporary benchmarks in long-term forecasting tasks across various datasets. It achieves superior results in 18 out of 28 cases for mean squared error (MSE) and 22 out of 28 cases for mean absolute error (MAE), confirming its competitive edge.

A detailed ablation study sheds light on the significance of various components of xLSTM-Mixer, affirming the critical role of time-mixing and view-mixing. Additionally, an evaluation of initial embedded tokens suggests their capability to better capture dataset-specific patterns.

Implications and Future Directions

Theoretical Implications: The resurgence of RNN-based models, as epitomized by the xLSTM-Mixer, underscores the potential of recurrent architectures in contexts where self-attention in transformers may not be optimal due to computational inefficiencies with long sequences.

Practical Implications: Practitioners in industries such as finance, logistics, and energy can leverage xLSTM-Mixer for improved forecasting abilities, possibly leading to enhanced operational efficiency and informed decision-making.

Future Developments: Further exploration could explore optimizing variate orderings and expanding multi-view mechanisms. Additionally, extending xLSTM-Mixer to other tasks like time-series classification or imputation may be fruitful.

In conclusion, the xLSTM-Mixer presents a significant contribution to multivariate time series forecasting, reinforcing the viability of recurrent architectures while introducing novel strategies for temporal and variate integration. Its implications for both theoretical expansion and practical applications make it a worthy addition to the toolkit of modern AI methodologies.