# SpikF-GO: Spiking Fourier Graph Operators for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2606.13901 · HTML: https://mlsanity.com/paper/2606.13901/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 28 of 28)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [SpikingJelly: An open-source machine learning infrastructure platform for spike-based intelligence](https://mlsanity.com/paper/2310.16620/) (2023)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Efficient Neuromorphic Signal Processing with Loihi 2](https://mlsanity.com/paper/2111.03746/) (2021)
- [Integer-Valued Training and Spike-Driven Inference Spiking Neural Network for High-performance and Energy-efficient Object Detection](https://mlsanity.com/paper/2407.20708/) (2024)
- [Scaling Spike-driven Transformer with Efficient Spike Firing Approximation Training](https://mlsanity.com/paper/2411.16061/) (2024)
- [QKFormer: Hierarchical Spiking Transformer using Q-K Attention](https://mlsanity.com/paper/2403.16552/) (2024)
- [An Analytical Estimation of Spiking Neural Networks Energy Efficiency](https://mlsanity.com/paper/2210.13107/) (2022)
- [Spiking Transformer with Spatial-Temporal Attention](https://mlsanity.com/paper/2409.19764/) (2024)
- [Spike2Former: Efficient Spiking Transformer for High-performance Image Segmentation](https://mlsanity.com/paper/2412.14587/) (2024)
- [Neuromorphic Principles for Efficient Large Language Models on Intel Loihi 2](https://mlsanity.com/paper/2503.18002/) (2025)
- [TS-LIF: A Temporal Segment Spiking Neuron Network for Time Series Forecasting](https://mlsanity.com/paper/2503.05108/) (2025)
- [Time-coded Spiking Fourier Transform in Neuromorphic Hardware](https://mlsanity.com/paper/2202.12650/) (2022)
- [Advancing Spiking Neural Networks for Sequential Modeling with Central Pattern Generators](https://mlsanity.com/paper/2405.14362/) (2024)

## Abstract (arXiv)

Spiking Neural Networks (SNNs) have emerged as an energy-efficient alternative to conventional neural networks, demonstrating strong performance in computer vision and robotics. More recently, SNNs have been applied to time series forecasting (TSF), with methods exploring spiking temporal backbones, spike-compatible positional encodings, Fourier-domain processing, and redesigned neuron dynamics. However, existing SNN forecasting approaches process variables independently, lacking explicit mechanisms for modeling inter-variable dependencies. This is a critical limitation in multivariate settings, where cross-variable correlations carry substantial predictive information. We propose Spiking Fourier Graph Operators (SpikF-GO), which addresses this gap by combining a hypervariate graph formulation in which every scalar observation becomes a graph node with spike-driven spectral processing. SpikF-GO introduces a Hard Concrete frequency gate for learnable sparse frequency selection and a Complex LIF gate that applies independent spiking neurons to real and imaginary Fourier components, preserving binary, event-driven computation throughout the spectral domain. We further present a variant incorporating Central Pattern Generator-based positional encodings for stronger long-range temporal modeling. Evaluated on eight benchmarks under a unified experimental protocol, SpikF-GO achieves the best average rank among all SNN methods and outperforms its ANN counterpart, FourierGNN, at reduced energy cost. SpikF-GO maintains competitive accuracy even at substantially smaller embedding dimensions, thereby achieving significant energy reductions. To our knowledge, this is among the first works to bring graph-based multivariate modeling into the spiking domain for TSF and the first to provide a unified comparison across SNN forecasting architectures under a common experimental protocol.