# LayerRoPE: Dynamic Depth-wise Magnitude & Angular Superposition

arXiv: https://arxiv.org/abs/2610.09179 · HTML: https://mlsanity.com/paper/2610.09179/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 42 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 26 of 26)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [mHC: Manifold-Constrained Hyper-Connections](https://mlsanity.com/paper/2512.24880/) (2025)
- [Attention Residuals](https://mlsanity.com/paper/2603.15031/) (2026)
- [The Curse of Depth in Large Language Models](https://mlsanity.com/paper/2502.05795/) (2025)
- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding](https://mlsanity.com/paper/2410.01405/) (2024)
- [Peri-LN: Revisiting Normalization Layer in the Transformer Architecture](https://mlsanity.com/paper/2502.02732/) (2025)
- [On the Residual Scaling of Looped Transformers: Stability and Transferability](https://mlsanity.com/paper/2606.18524/) (2026)
- [Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models](https://mlsanity.com/paper/2605.26895/) (2026)
- [Dissecting Outlier Dynamics in LLM NVFP4 Pretraining](https://mlsanity.com/paper/2602.02047/) (2026)

## Abstract (arXiv)

As data propagates through a Transformer, the norm of its hidden states grows by orders of magnitude with depth, a phenomenon framed as 'curse of depth' and nearly universally treated as a pathology to be suppressed. We take the opposite view. Across 16 pre-trained LLMs from 9 families, spanning dense, mixture-of-experts and hybrid architectures and Pre-, Peri- and Post-Norm designs, we find that this growth reflects an emergent depth-positional encoding, carried by the only learned per-layer gain on the residual stream, the normalization weight γ: with depth, γ grows in magnitude and rotates in direction, jointly encoding the layer index. We make this depth-conditioned encoding explicit with LayerRoPE, an implicit analog of RoPE along the depth axis, which replaces all layerwise γ vectors with a single shared vector and depth-conditioned scalars, at a net reduction in parameters and <0.02% change in FLOPs. Across a model ladder scaled up to 100B+ tokens, LayerRoPE consistently outperforms Pre-, Post- and Peri-Norm and Layer-Norm Scaling, reaching Pre-Norm's 1.3B loss with 3.4× less compute; LayerRoPE is the only approach that shows strong convergence and improves near monotonically as depth scales to 512 layers. It improves learning-rate sensitivity by 3-10×, and transfers naively to and consistently improves looped latent models and Vision Transformers. Inspecting its learned schedule inverts the prevailing premise: LayerRoPE does not shrink the residual stream but widens it, damping what each block reads while amplifying what it writes. Depth stability, our results suggest, calls not for suppressing the residual stream, but for depth-conditioned regulation of the computational blocks it feeds.