# Scaling Laws for Linear Complexity Language Models

arXiv: https://arxiv.org/abs/2406.16690 · HTML: https://mlsanity.com/paper/2406.16690/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Unified Scaling Laws for Routed Language Models](https://mlsanity.com/paper/2202.01169/) (2022)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)
- [Simple Hardware-Efficient Long Convolutions for Sequence Modeling](https://mlsanity.com/paper/2302.06646/) (2023)
- [Toeplitz Neural Network for Sequence Modeling](https://mlsanity.com/paper/2305.04749/) (2023)
- [Various Lengths, Constant Speed: Efficient Language Modeling with Lightning Attention](https://mlsanity.com/paper/2405.17381/) (2024)

## Built on by (most cited first, 19 of 19)

- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [Forgetting Transformer: Softmax Attention with a Forget Gate](https://mlsanity.com/paper/2503.02130/) (2025)
- [MoM: Linear Sequence Modeling with Mixture-of-Memories](https://mlsanity.com/paper/2502.13685/) (2025)
- [A Systematic Analysis of Hybrid Linear Attention](https://mlsanity.com/paper/2507.06457/) (2025)
- [MetaLA: Unified Optimal Linear Approximation to Softmax Attention Map](https://mlsanity.com/paper/2411.10741/) (2024)
- [Native Hybrid Attention for Efficient Sequence Modeling](https://mlsanity.com/paper/2510.07019/) (2025)
- [Essential-Web v1.0: 24T tokens of organized web data](https://mlsanity.com/paper/2506.14111/) (2025)
- [Fast and Simplex: 2-Simplicial Attention in Triton](https://mlsanity.com/paper/2507.02754/) (2025)
- [Statistical Advantage of Softmax Attention: Insights from Single-Location Regression](https://mlsanity.com/paper/2509.21936/) (2025)
- [On the Expressivity of Selective State-Space Layers: A Multivariate Polynomial Approach](https://mlsanity.com/paper/2502.02209/) (2025)
- [Autoregressive Image Generation with Linear Complexity: A Spatial-Aware Decay Perspective](https://mlsanity.com/paper/2507.01652/) (2025)
- [xLSTM Scaling Laws: Competitive Performance with Linear Time-Complexity](https://mlsanity.com/paper/2510.02228/) (2025)
- [Sliced ReLU attention: Quasi-linear contextual expressivity via sorting](https://mlsanity.com/paper/2512.11411/) (2025)
- [Unified Neural Scaling Laws](https://mlsanity.com/paper/2605.26248/) (2026)
- [Small transformer architectures for task switching](https://mlsanity.com/paper/2508.04461/) (2025)
- [The Hamilton-Jacobi Theory of Deep Learning](https://mlsanity.com/paper/2605.28983/) (2026)
- [Orthros: Phase-Aware Heterogeneous Attention for Efficient Transformers](https://mlsanity.com/paper/2610.13735/) (2026)
- [Compute-Optimal Scaling Laws for Spiking Language Models](https://mlsanity.com/paper/2610.15146/) (2026)

## Abstract (arXiv)

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.