# Hierarchical vs. Flat Iteration in Shared-Weight Transformers

arXiv: https://arxiv.org/abs/2604.14442 · HTML: https://mlsanity.com/paper/2604.14442/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 35 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [White-Box Transformers via Sparse Rate Reduction](https://mlsanity.com/paper/2306.01129/) (2023)
- [QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead](https://mlsanity.com/paper/2406.03482/) (2024)
- [PolarQuant: Quantizing KV Caches with Polar Transformation](https://mlsanity.com/paper/2502.02617/) (2025)
- [Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2409.09913/) (2024)

## Built on by (most cited first, 4 of 4)

- [Solve the Loop: Attractor Models for Language and Reasoning](https://mlsanity.com/paper/2605.12466/) (2026)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [CART: Context-Anchored Recurrent Transformer -- A Parameter-Efficient Architecture with Learned Stability](https://mlsanity.com/paper/2606.01495/) (2026)
- [LoopCoder-v2: Only Loop Once for Efficient Test-Time Computation Scaling](https://mlsanity.com/paper/2606.18023/) (2026)

## Abstract (arXiv)

We present an empirical study of whether hierarchically structured, shared-weight recurrence can match the representational quality of independent-layer stacking in a Transformer-based language model. HRM-LM replaces L independent Transformer layers with a two-speed recurrent pair: a Fast module operating at every step for local refinement, and a Slow module operating every T steps for global compression. This recurrent hierarchy is unrolled for M = N x T steps with shared parameters. The central and most robust finding, supported by a parameter-matched Universal Transformer ablation (UniTF, 1.2B) across five independent runs, is a sharp empirical gap between the two approaches.