# The Impossibility Triangle of Long-Context Modeling

arXiv: https://arxiv.org/abs/2605.05066 · HTML: https://mlsanity.com/paper/2605.05066/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 65 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 30 of 54)

- [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)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [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)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [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)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [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)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [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)
- [Ring Attention with Blockwise Transformers for Near-Infinite Context](https://mlsanity.com/paper/2310.01889/) (2023)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)

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

- [Three Tokens Force Exponential Feature Rank in Nonnegative Kernel Attention](https://mlsanity.com/paper/2608.11427/) (2026)

## Abstract (arXiv)

We identify and prove a fundamental trade-off governing long-sequence models: no model can simultaneously achieve (i) per-step computation independent of sequence length (Efficiency), (ii) state size independent of sequence length (Compactness), and (iii) the ability to recall a number of historical facts proportional to sequence length (Recall). We formalize this trade-off within an Online Sequence Processor abstraction that unifies Transformers, state space models, linear recurrent networks, and their hybrids. Using the Data Processing Inequality and Fano's Inequality, we prove that any model satisfying Efficiency and Compactness can recall at most O(poly(d)/log V) key-value pairs from a sequence of arbitrary length, where d is the model dimension and V is the vocabulary size. We classify 52 architectures published before March 2026 into the triangle, showing that each achieves at most two of the three properties and that hybrid architectures trace continuous trajectories in the interior. Experiments on synthetic associative recall tasks with five representative architectures validate the theoretical bound: empirical recall capacity lies strictly below the information-theoretic limit, and no architecture escapes the triangle.