# MeSH: Memory-as-State-Highways for Recursive Transformers

arXiv: https://arxiv.org/abs/2510.07739 · HTML: https://mlsanity.com/paper/2510.07739/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 83 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 30 of 73)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (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)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Efficient Large-Scale Language Model Training on GPU Clusters Using Megatron-LM](https://mlsanity.com/paper/2104.04473/) (2021)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)

## Built on by (most cited first, 8 of 8)

- [SpiralFormer: Looped Transformers Can Learn Hierarchical Dependencies via Multi-Resolution Recursion](https://mlsanity.com/paper/2602.11698/) (2026)
- [Universal Transformers Need Memory: Depth-State Trade-offs in Adaptive Recursive Reasoning](https://mlsanity.com/paper/2604.21999/) (2026)
- [Tying the Loop -- Tied Expert Layers in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2606.16825/) (2026)
- [LoopMTP: A looped transformer guided by latent multi-token prediction](https://mlsanity.com/paper/2608.03624/) (2026)
- [Improving Test-Time Scaling with Adaptive Looped Transformers](https://mlsanity.com/paper/2609.35748/) (2026)
- [Soft Mixture-of-Recursions: Going Deeper with Recursive Vision Transformers](https://mlsanity.com/paper/2607.00774/) (2026)
- [Storing Is Not Remembering: LSTM-UT and Bounded Gated Memory for Looped Transformers](https://mlsanity.com/paper/2609.19521/) (2026)
- [Looped Diffusion Transformer](https://mlsanity.com/paper/2609.40305/) (2026)

## Abstract (arXiv)

Recursive transformers reuse parameters and iterate over hidden states multiple times, decoupling compute depth from parameter depth. However, under matched compute, recursive models with fewer parameters often lag behind non-recursive counterparts. By probing hidden states, we trace this performance gap to two primary bottlenecks: undifferentiated computation, where the core is forced to adopt a similar computational pattern at every iteration, and information overload, where long-lived and transient information must coexist in a single hidden state. To address the issues, we introduce a Memory-as-State-Highways (MeSH) scheme, which externalizes state management into an explicit memory buffer and employs lightweight routers to dynamically diversify computation across iterations. Probing visualizations confirm that MeSH successfully resolves the pathologies by inducing functional specialization across iterations. On the Pythia suite (160M-6.9B), MeSH-enhanced recursive transformers consistently improve over recursive baselines and outperforms its larger non-recursive counterpart at the 1.4B scale, improving average downstream accuracy by +1.06% with 33% fewer non-embedding parameters. Our analysis establishes MeSH as a scalable and principled architecture for building stronger recursive models. Our code is available at https://github.com/LivingFutureLab/MeSH/ .