# Beyond In-Distribution Success: Scaling Curves of CoT Granularity for Language Model Generalization

arXiv: https://arxiv.org/abs/2502.18273 · HTML: https://mlsanity.com/paper/2502.18273/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 62 references that are in the map.
- First posted on arXiv 25 Feb 2025.

## Builds on (most cited first, 30 of 53)

- [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)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022)
- [Pretrained Transformers Improve Out-of-Distribution Robustness](https://mlsanity.com/paper/2004.06100/) (2020)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [ShowUI: One Vision-Language-Action Model for GUI Visual Agent](https://mlsanity.com/paper/2411.17465/) (2024)
- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [Exploring Length Generalization in Large Language Models](https://mlsanity.com/paper/2207.04901/) (2022)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Aria-UI: Visual Grounding for GUI Instructions](https://mlsanity.com/paper/2412.16256/) (2024)
- [Investigating the Limitations of Transformers with Simple Arithmetic Tasks](https://mlsanity.com/paper/2102.13019/) (2021)

## Built on by (most cited first, 5 of 5)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Theoretical Framework for OOD Robustness in Transformers using Gevrey Classes](https://mlsanity.com/paper/2504.12991/) (2025)
- [The Imitation Game: Turing Machine Imitator is Length Generalizable Reasoner](https://mlsanity.com/paper/2507.13332/) (2025)
- [Understanding Chain-of-Thought in Large Language Models via Topological Data Analysis](https://mlsanity.com/paper/2512.19135/) (2025)
- [Agri-R1: Agricultural Reasoning for Disease Diagnosis via Automated-Synthesis and Reinforcement Learning](https://mlsanity.com/paper/2601.04672/) (2026)

## Abstract (arXiv)

Generalization to novel compound tasks under distribution shift is important for deploying transformer-based language models (LMs). This work investigates Chain-of-Thought (CoT) reasoning as a means to enhance OOD generalization. Through controlled experiments across several compound tasks, we reveal three key insights: (1) While QA-trained models achieve near-perfect in-distribution accuracy, their OOD performance degrades catastrophically, even with 10000k+ training examples; (2) the granularity of CoT data strongly correlates with generalization performance; finer-grained CoT data leads to better generalization; (3) CoT exhibits remarkable sample efficiency, matching QA performance with much less (even 80%) data. Theoretically, we demonstrate that compound tasks inherently permit shortcuts in Q-A data that misalign with true reasoning principles, while CoT forces internalization of valid dependency structures, and thus can achieve better generalization. Further, we show that transformer positional embeddings can amplify generalization by emphasizing subtask condition recurrence in long CoT sequences. Our combined theoretical and empirical analysis provides compelling evidence for CoT reasoning as a crucial training paradigm for enabling LM generalization under real-world distributional shifts for compound tasks.