# Unifying Linear-Time Attention via Latent Probabilistic Modelling

arXiv: https://arxiv.org/abs/2402.17512 · HTML: https://mlsanity.com/paper/2402.17512/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 27 Feb 2024.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [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)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [A Survey of Transformers](https://mlsanity.com/paper/2106.04554/) (2021)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [Zoology: Measuring and Improving Recall in Efficient Language Models](https://mlsanity.com/paper/2312.04927/) (2023)
- [Transformer Quality in Linear Time](https://mlsanity.com/paper/2202.10447/) (2022)
- [Mega: Moving Average Equipped Gated Attention](https://mlsanity.com/paper/2209.10655/) (2022)
- [A Length-Extrapolatable Transformer](https://mlsanity.com/paper/2212.10554/) (2022)
- [The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry](https://mlsanity.com/paper/2402.04347/) (2024)
- [Luna: Linear Unified Nested Attention](https://mlsanity.com/paper/2106.01540/) (2021)
- [Lightning Attention-2: A Free Lunch for Handling Unlimited Sequence Lengths in Large Language Models](https://mlsanity.com/paper/2401.04658/) (2024)

## Built on by (most cited first, 1 of 1)

- [Do Vision Transformers Need All-to-All Attention? Global Communication Through Elastic Learned Cores](https://mlsanity.com/paper/2605.12491/) (2026)

## Abstract (arXiv)

Transformers have achieved state-of-the-art results across a range of domains, but their quadratic attention mechanism poses significant challenges for long-sequence modelling. Recent efforts to design linear-time attention mechanisms have yielded more scalable alternatives, yet often at the cost of performance, particularly on discrete data such as language. In this work, we revisit linear attention through the lens of probabilistic graphical models. We first show that standard linear attention can be interpreted as an undirected latent variable model, revealing a key limitation: the absence of directionality. To address this, we propose a novel directed parameterisation of linear attention that introduces an asymmetric structure, enabling an interpretation aligned with the causal and sequential nature of language. Our formulation integrates global latent-variable attention with local standard attention in a fully probabilistic framework. Additionally, we introduce a recurrent parameterisation of queries and keys that avoids reliance on relative positional encodings, often incompatible with linear attention. Experiments on language modelling benchmarks demonstrate that our model achieves competitive performance with standard attention and outperforms existing linear attention variants.