Title: MeSH: Memory-as-State-Highways for Recursive Transformers
Primary area: foundation or frontier models, including LLMs
Keywords: Recursive Transformer, Language Model, Parameter Sharing, Parameter Efficiency

Abstract: 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 **Me**mory-as-**S**tate-**H**ighways **(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–1.4B), 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.

TL;DR: We diagnose why recursive transformers underperform and propose a targeted solution for building stronger recursive backbones.