# Latest Exact Match Attention

arXiv: https://arxiv.org/abs/2609.25802 · HTML: https://mlsanity.com/paper/2609.25802/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 101 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 30 of 41)

- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Effective Long-Context Scaling of Foundation Models](https://mlsanity.com/paper/2309.16039/) (2023)
- [Retrieval Head Mechanistically Explains Long-Context Factuality](https://mlsanity.com/paper/2404.15574/) (2024)
- [Zoology: Measuring and Improving Recall in Efficient Language Models](https://mlsanity.com/paper/2312.04927/) (2023)
- [MoBA: Mixture of Block Attention for Long-Context LLMs](https://mlsanity.com/paper/2502.13189/) (2025)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [An Empirical Study of Mamba-based Language Models](https://mlsanity.com/paper/2406.07887/) (2024)
- [MiniMax-01: Scaling Foundation Models with Lightning Attention](https://mlsanity.com/paper/2501.08313/) (2025)
- [RetrievalAttention: Accelerating Long-Context LLM Inference via Vector Retrieval](https://mlsanity.com/paper/2409.10516/) (2024)
- [Binarized Neural Networks: Training Deep Neural Networks with Weights and Activations Constrained to +1 or -1](https://mlsanity.com/paper/1602.02830/) (2016)
- [Conditional Memory via Scalable Lookup: A New Axis of Sparsity for Large Language Models](https://mlsanity.com/paper/2601.07372/) (2026)
- [InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models](https://mlsanity.com/paper/2503.06692/) (2025)
- [Masked Hard-Attention Transformers Recognize Exactly the Star-Free Languages](https://mlsanity.com/paper/2310.13897/) (2023)
- [Memory Layers at Scale](https://mlsanity.com/paper/2412.09764/) (2024)
- [Learning Transformer Programs](https://mlsanity.com/paper/2306.01128/) (2023)
- [Log-Linear Attention](https://mlsanity.com/paper/2506.04761/) (2025)
- [Neural Random-Access Machines](https://mlsanity.com/paper/1511.06392/) (2015)
- [PENCIL: Long Thoughts with Short Memory](https://mlsanity.com/paper/2503.14337/) (2025)

## Abstract (arXiv)

We introduce latest exact match attention (LEMA), an attention variant for transformers where queries and keys are binarized and each query attends only to the latest exactly matching key. We prove that LEMA transformers with chain of thought can simulate word-RAMs, as was recently shown for the less restrictive rightmost hard attention. In contrast to prior hard attention variants, the restriction to exact matches enables an efficient converse direction: word-RAMs can simulate LEMA transformers at a cost per token independent of the context length. Together, these results yield a close correspondence between the two computational models in terms of both compute and memory. Beyond the theory, we propose a training method for LEMA transformers that handles their non-differentiable operations with a straight-through estimator for the binarization and a soft attention surrogate annealed towards LEMA. On a synthetic associative recall task, LEMA models trained this way use their growing state to store and recall a large number of associations, outperforming gated DeltaNet (GDN) with its fixed state size. As a first scaling test, we train LEMA language models with up to 834 million parameters. They match softmax transformers of around half their size in loss and, on repeated rare phrases and a needle-retrieval task, remain behind softmax transformers but recall across longer distances than GDN models of comparable size. Finally, we implement dictionary-based inference for LEMA transformers and show constant generation speed comparable to GDN despite their growing state, with the dictionaries residing in main memory rather than VRAM. Code is available at https://github.com/moritzbroe/latest_exact_match_attention.