# CoDA: Towards Effective Cross-domain Knowledge Transfer via CoT-guided Domain Adaptation

arXiv: https://arxiv.org/abs/2604.19488 · HTML: https://mlsanity.com/paper/2604.19488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 52 of its 70 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 52)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [C-Pack: Packed Resources For General Chinese Embeddings](https://mlsanity.com/paper/2309.07597/) (2023)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [In-context Learning with Retrieved Demonstrations for Language Models: A Survey](https://mlsanity.com/paper/2401.11624/) (2024)
- [Large Language Models Can be Lazy Learners: Analyze Shortcuts in In-Context Learning](https://mlsanity.com/paper/2305.17256/) (2023)

## Abstract (arXiv)

Large language models (LLMs) have achieved substantial advances in logical reasoning, yet they continue to lag behind human-level performance. In-context learning provides a viable solution that boosts the model's performance via prompting its input with expert-curated, in-domain exemplars. However, in many real-world, expertise-scarce domains, such as low-resource scientific disciplines, emerging biomedical subfields, or niche legal jurisdictions, such high-quality in-domain demonstrations are inherently limited or entirely unavailable, thereby constraining the general applicability of these approaches. To mitigate this limitation, recent efforts have explored the retrieval of cross-domain samples as surrogate in-context demonstrations. Nevertheless, the resulting gains remain modest. This is largely attributable to the pronounced domain shift between source and target distributions, which impedes the model's ability to effectively identify and exploit underlying shared structures or latent reasoning patterns. Consequently, when relying solely on raw textual prompting, LLMs struggle to abstract and transfer such cross-domain knowledge in a robust and systematic manner. To address these issues, we propose CoDA, which employs a lightweight adapter to directly intervene in the intermediate hidden states. By combining feature-based distillation of CoT-enriched reference representations with Maximum Mean Discrepancy (MMD) for kernelized distribution matching, our method aligns the latent reasoning representation of the source and target domains. Extensive experimental results on multiple logical reasoning tasks across various model families validate the efficacy of CoDA by significantly outperforming the previous state-of-the-art baselines by a large margin.