# Scaling Reasoning Hop Exposes Weaknesses: Demystifying and Improving Hop Generalization in Large Language Models

arXiv: https://arxiv.org/abs/2601.21214 · HTML: https://mlsanity.com/paper/2601.21214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 39 of its 84 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Transformers Can Achieve Length Generalization But Not Robustly](https://mlsanity.com/paper/2402.09371/) (2024)
- [Structured, flexible, and robust: benchmarking and improving large language models towards more human-like behavior in out-of-distribution reasoning tasks](https://mlsanity.com/paper/2205.05718/) (2022)
- [How to think step-by-step: A mechanistic understanding of chain-of-thought reasoning](https://mlsanity.com/paper/2402.18312/) (2024)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens](https://mlsanity.com/paper/2508.01191/) (2025)
- [Summing Up the Facts: Additive Mechanisms Behind Factual Recall in LLMs](https://mlsanity.com/paper/2402.07321/) (2024)
- [A Survey on Large Language Models with some Insights on their Capabilities and Limitations](https://mlsanity.com/paper/2501.04040/) (2025)
- [How Likely Do LLMs with CoT Mimic Human Reasoning?](https://mlsanity.com/paper/2402.16048/) (2024)
- [Real-Time Detection of Hallucinated Entities in Long-Form Generation](https://mlsanity.com/paper/2509.03531/) (2025)
- [The Curse of CoT: On the Limitations of Chain-of-Thought in In-Context Learning](https://mlsanity.com/paper/2504.05081/) (2025)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [Memory Injections: Correcting Multi-Hop Reasoning Failures during Inference in Transformer-Based Language Models](https://mlsanity.com/paper/2309.05605/) (2023)
- [Finite State Automata Inside Transformers with Chain-of-Thought: A Mechanistic Study on State Tracking](https://mlsanity.com/paper/2502.20129/) (2025)

## Built on by (most cited first, 1 of 1)

- [Every Coin Has Two Sides: On the Dual Nature of Generalization in On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2608.16647/) (2026)

## Abstract (arXiv)

Chain-of-thought (CoT) reasoning has become the standard paradigm for enabling Large Language Models (LLMs) to solve complex problems. However, recent studies reveal a sharp performance drop in reasoning hop generalization scenarios, where the required number of reasoning steps exceeds training distributions while the underlying algorithm remains unchanged. The internal mechanisms driving this failure remain poorly understood. In this work, we conduct a systematic study on tasks from multiple domains, and find that errors concentrate at token positions of a few critical error types, rather than being uniformly distributed. Closer inspection reveals that these token-level erroneous predictions stem from internal competition mechanisms: certain attention heads, termed erroneous processing heads (ep heads), tip the balance by amplifying incorrect reasoning trajectories while suppressing correct ones. Notably, removing individual ep heads during inference can often restore the correct predictions. Motivated by these insights, we propose test-time correction of reasoning, a lightweight intervention method that dynamically identifies and deactivates ep heads in the reasoning process. Extensive experiments across different tasks and LLMs show that it consistently improves reasoning hop generalization, highlighting both its effectiveness and potential.