# On the Runway Cascade of Transformers for Language Modeling

arXiv: https://arxiv.org/abs/2601.14522 · HTML: https://mlsanity.com/paper/2601.14522/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 42 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 30 of 39)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [ConceptNet 5.5: An Open Multilingual Graph of General Knowledge](https://mlsanity.com/paper/1612.03975/) (2016)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Large Language Models are Zero-Shot Rankers for Recommender Systems](https://mlsanity.com/paper/2305.08845/) (2023)
- [When Attention Sink Emerges in Language Models: An Empirical View](https://mlsanity.com/paper/2410.10781/) (2024)
- [Exphormer: Sparse Transformers for Graphs](https://mlsanity.com/paper/2303.06147/) (2023)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [Why do LLMs attend to the first token?](https://mlsanity.com/paper/2504.02732/) (2025)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [Understanding Oversquashing in GNNs through the Lens of Effective Resistance](https://mlsanity.com/paper/2302.06835/) (2023)
- [Transformers need glasses! Information over-squashing in language tasks](https://mlsanity.com/paper/2406.04267/) (2024)
- [Expander Graph Propagation](https://mlsanity.com/paper/2210.02997/) (2022)
- [On the Emergence of Position Bias in Transformers](https://mlsanity.com/paper/2502.01951/) (2025)
- [How does over-squashing affect the power of GNNs?](https://mlsanity.com/paper/2306.03589/) (2023)

## Abstract (arXiv)

In decoder-only (causal) transformers, the computation graph created by causal masking routes information through both direct-path attention and indirect paths formed by intermediate tokens. We denote these indirect paths between token pairs as their runways. We argue that certain failure modes of causal transformers as observed by a growing body of recent works are likely exacerbated by a misalignment between these two information propagation modes. We formalize runway cascade as a phenomenon whereby this misalignment results in redundancies and irrelevant information cascading to token representations despite adequately learned attention patterns. As a solution, we propose runway-aware rewiring as a more explicit way of incorporating runway context directly into each token's direct-path attention. This mechanism re-wires the attention pattern for each token based on a summary of its runway landscape, enabling awareness of accumulating representational influences and allowing for more balanced information propagation. Our proposed methodology introduces no additional parameters and can seamlessly be integrated into standard attention mechanism. Empirically, our rewired transformer results in steady improvements in general language modeling as well as noticeably stronger information retrieval and extrapolation abilities compared to standard transformers.