# Fighter: Unveiling the Graph Convolutional Nature of Transformers in Time Series Modeling

arXiv: https://arxiv.org/abs/2510.17106 · HTML: https://mlsanity.com/paper/2510.17106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 42 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [Time Series Prediction using Deep Learning Methods in Healthcare](https://mlsanity.com/paper/2108.13461/) (2021)
- [Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Version](https://mlsanity.com/paper/2204.13767/) (2022)
- [Machine Learning Advances for Time Series Forecasting](https://mlsanity.com/paper/2012.12802/) (2020)
- [Mechanics of Next Token Prediction with Self-Attention](https://mlsanity.com/paper/2403.08081/) (2024)
- [Transformers are Graph Neural Networks](https://mlsanity.com/paper/2506.22084/) (2025)
- [Graph Neural Tangent Kernel: Convergence on Large Graphs](https://mlsanity.com/paper/2301.10808/) (2023)
- [Uncertainty-Aware Deep Ensembles for Reliable and Explainable Predictions of Clinical Time Series](https://mlsanity.com/paper/2010.11310/) (2020)
- [Nonparametric Teaching for Multiple Learners](https://mlsanity.com/paper/2311.10318/) (2023)
- [Nonparametric Teaching for Graph Property Learners](https://mlsanity.com/paper/2505.14170/) (2025)

## Abstract (arXiv)

Transformers have achieved remarkable success in time series modeling, yet their internal mechanisms remain opaque. This work demystifies the Transformer encoder by establishing its fundamental equivalence to a Graph Convolutional Network (GCN). We show that in the forward pass, the attention distribution matrix serves as a dynamic adjacency matrix, and its composition with subsequent transformations performs computations analogous to graph convolution. Moreover, we demonstrate that in the backward pass, the update dynamics of value and feed-forward projections mirror those of GCN parameters. Building on this unified theoretical reinterpretation, we propose Fighter (Flexible Graph Convolutional Transformer), a streamlined architecture that removes redundant linear projections and incorporates multi-hop graph aggregation. This perspective yields an explicit and interpretable representation of temporal dependencies across different scales, naturally expressed as graph edges. Experiments on standard forecasting benchmarks confirm that Fighter achieves competitive performance while providing clearer mechanistic interpretability of its predictions.