# Bidirectional Linear Recurrent Models for Sequence-Level Multisource Fusion

arXiv: https://arxiv.org/abs/2504.08964 · HTML: https://mlsanity.com/paper/2504.08964/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 72 of its 114 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 30 of 72)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [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)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [Bidirectional LSTM-CRF Models for Sequence Tagging](https://mlsanity.com/paper/1508.01991/) (2015)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)

## Abstract (arXiv)

Sequence modeling is a critical yet challenging task with wide-ranging applications, especially in time series forecasting for domains like weather prediction, temperature monitoring, and energy load forecasting. Transformers, with their attention mechanism, have emerged as state-of-the-art due to their efficient parallel training, but they suffer from quadratic time complexity, limiting their scalability for long sequences. In contrast, recurrent neural networks (RNNs) offer linear time complexity, spurring renewed interest in linear RNNs for more computationally efficient sequence modeling. In this work, we introduce BLUR (Bidirectional Linear Unit for Recurrent network), which uses forward and backward linear recurrent units (LRUs) to capture both past and future dependencies with high computational efficiency. BLUR maintains the linear time complexity of traditional RNNs, while enabling fast parallel training through LRUs. Furthermore, it offers provably stable training and strong approximation capabilities, making it highly effective for modeling long-term dependencies. Extensive experiments on sequential image and time series datasets reveal that BLUR not only surpasses transformers and traditional RNNs in accuracy but also significantly reduces computational costs, making it particularly suitable for real-world forecasting tasks. Our code is available here.