# Charting Empirical Laws for LLM Fine-Tuning in Scientific Multi-Discipline Learning

arXiv: https://arxiv.org/abs/2602.11215 · HTML: https://mlsanity.com/paper/2602.11215/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 40 of its 68 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 30 of 40)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [LLaVA-Med: Training a Large Language-and-Vision Assistant for Biomedicine in One Day](https://mlsanity.com/paper/2306.00890/) (2023)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Cross-Task Generalization via Natural Language Crowdsourcing Instructions](https://mlsanity.com/paper/2104.08773/) (2021)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [ChatDoctor: A Medical Chat Model Fine-Tuned on a Large Language Model Meta-AI (LLaMA) Using Medical Domain Knowledge](https://mlsanity.com/paper/2303.14070/) (2023)
- [MedAlpaca -- An Open-Source Collection of Medical Conversational AI Models and Training Data](https://mlsanity.com/paper/2304.08247/) (2023)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Pushing Mixture of Experts to the Limit: Extremely Parameter Efficient MoE for Instruction Tuning](https://mlsanity.com/paper/2309.05444/) (2023)
- [A Question-Entailment Approach to Question Answering](https://mlsanity.com/paper/1901.08079/) (2019)
- [The Impact of Large Language Models on Scientific Discovery: a Preliminary Study using GPT-4](https://mlsanity.com/paper/2311.07361/) (2023)
- [HEAD-QA: A Healthcare Dataset for Complex Reasoning](https://mlsanity.com/paper/1906.04701/) (2019)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [AlpaCare:Instruction-tuned Large Language Models for Medical Application](https://mlsanity.com/paper/2310.14558/) (2023)
- [Towards Modular LLMs by Building and Reusing a Library of LoRAs](https://mlsanity.com/paper/2405.11157/) (2024)
- [K2: A Foundation Language Model for Geoscience Knowledge Understanding and Utilization](https://mlsanity.com/paper/2306.05064/) (2023)

## Built on by (most cited first, 2 of 2)

- [FirstPass: Grounding AI Scientific Judgment in Multi-Round Editorial Outcomes](https://mlsanity.com/paper/2606.20769/) (2026)
- [Token Distribution versus Data Volume: Domain Balancing in Multi-Domain Meeting Summarisation](https://mlsanity.com/paper/2608.15935/) (2026)

## Abstract (arXiv)

While large language models (LLMs) have achieved strong performance through fine-tuning within individual scientific domains, their learning dynamics in multi-disciplinary contexts remains poorly understood, despite the promise of improved generalization and broader applicability through cross-domain knowledge synergy. In this work, we present the first systematic study of multi-disciplinary LLM fine-tuning, constructing a five-discipline corpus and analyzing learning patterns of full fine-tuning, LoRA, LoRA-MoE, and LoRA compositions. Particularly, our study shows that multi-disciplinary learning is substantially more variable than single-discipline training and distills four consistent empirical laws: (1) Balance-then-Diversity: low-resource disciplines degrade performance unless mitigated via diversity-aware upsampling; (2) Merge-then-Align: restoring instruction-following ability is critical for cross-discipline synergy; (3) Optimize-then-Scale: parameter scaling offers limited gains without prior design optimization; and (4) Share-then-Specialize: asymmetric LoRA-MoE yields robust gains with minimal trainable parameters via shared low-rank projection. Together, these laws form a practical recipe for principled multi-discipline fine-tuning and provide actionable guidance for developing generalizable scientific LLMs.