Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2 Background 3 Experimental Setup and 3.1 Datasets for Continued Pretraining (CPT) and Instruction Finetuning (IFT) 3 Experimental Setup and 3.1 Datasets for Continued Pretraining (CPT) and Instruction Finetuning (IFT) 3.2 Measuring Learning with Coding and Math Benchmarks (target domain evaluation) 3.2 Measuring Learning with Coding and Math Benchmarks (target domain evaluation) 3.3 Forgetting Metrics (source domain evaluation) 3.3 Forgetting Metrics (source domain evaluation) 4 Results 4.1 LoRA underperforms full finetuning in programming and math tasks 4.1 LoRA underperforms full finetuning in programming and math tasks 4.2 LoRA forgets less than full finetuning 4.2 LoRA forgets less than full finetuning 4.3 The Learning-Forgetting Tradeoff 4.3 The Learning-Forgetting Tradeoff 4.4 LoRA’s regularization properties 4.4 LoRA’s regularization properties 4.5 Full finetuning on code and math does not learn low-rank perturbations 4.5 Full finetuning on code and math does not learn low-rank perturbations 4.6 Practical takeaways for optimally configuring LoRA 4.6 Practical takeaways for optimally configuring LoRA 5 Related Work 5 Related Work 6 Discussion 6 Discussion 7 Conclusion and References 7 Conclusion and References Appendix Appendix A. Experimental Setup A. Experimental Setup B. Learning rate searches B. Learning rate searches C. Training Datasets C. Training Datasets D. Theoretical Memory Efficiency Gains with LoRA for Single and Multi-GPU Settings D. Theoretical Memory Efficiency Gains with LoRA for Single and Multi-GPU Settings 6 Discussion Does the difference between LoRA and full finetuning decrease with model size? Studies in the past have hinted at a relationship between the effectiveness of finetuning and model size (Aghajanyan et al., 2020; Hu et al., 2021; Zhuo et al., 2024). While recent studies have successfully applied LoRA to 70B parameter models (Ivison et al., 2023; Yu et al., 2023), we leave a rigorous study of these intriguing scaling properties to future work. Does the difference between LoRA and full finetuning decrease with model size? Limitations of the spectral analysis. The observation that full finetuning tends to find high rank solutions does not rule out the possibility of low-rank solutions; rather, it shows that they are not typically found. An alternative interpretation is that the rank needed to reconstruct the weight matrix is higher than the rank needed for a downstream task. Limitations of the spectral analysis. Why does LoRA perform well on math and not code? One hypothesis is that math datasets involve a smaller domain shift; they include a larger percentage of English and lead to decreased forgetting. The second hypothesis is that the GSM8K evaluation is too easy and does not capture the new college-level math learned in finetuning. Why does LoRA perform well on math and not code? 7 Conclusion This work sheds light on the downstream performance of contemporary LLMs (with 7 and 13 billion parameters) trained with LoRA. Different from most prior work, we use domain-specific datasets in code and math, associated with sensitive evaluation metrics. We show that LoRA underperforms full finetuning in both domains. We also show that LoRA keeps the finetuned model’s behavior close to that of the base model, with diminished source-domain forgetting and more diverse generations at inference time. We investigate LoRA’s regularization properties, and show that full finetuning finds weight perturbations are far from being low-rank. We conclude by analyzing LoRA’s increased sensitivity to hyperparameters and highlighting best practices. References Armen Aghajanyan, Luke Zettlemoyer, and Sonal Gupta. Intrinsic dimensionality explains the effectiveness of language model fine-tuning. arXiv preprint arXiv:2012.13255, 2020. Loubna Ben Allal, Niklas Muennighoff, Logesh Kumar Umapathi, Ben Lipkin, and Leandro von Werra. A framework for the evaluation of code generation models. https://github.com/bigcode-project/ bigcode-evaluation-harness, 2022. Sahil Chaudhary. Code alpaca: An instruction-following llama model for code generation. https://github. com/sahil280114/codealpaca, 2023. Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, Alex Ray, Raul Puri, Gretchen Krueger, Michael Petrov, Heidy Khlaaf, Girish Sastry, Pamela Mishkin, Brooke Chan, Scott Gray, Nick Ryder, Mikhail Pavlov, Alethea Power, Lukasz Kaiser, Mohammad Bavarian, Clemens Winter, Philippe Tillet, Felipe Petroski Such, Dave Cummings, Matthias Plappert, Fotios Chantzis, Elizabeth Barnes, Ariel Herbert-Voss, William Hebgen Guss, Alex Nichol, Alex Paino, Nikolas Tezak, Jie Tang, Igor Babuschkin, Suchir Balaji, Shantanu Jain, William Saunders, Christopher Hesse, Andrew N. Carr, Jan Leike, Josh Achiam, Vedant Misra, Evan Morikawa, Alec Radford, Matthew Knight, Miles Brundage, Mira Murati, Katie Mayer, Peter Welinder, Bob McGrew, Dario Amodei, Sam McCandlish, Ilya Sutskever, and Wojciech Zaremba. Evaluating large language models trained on code, 2021. Hyung Won Chung, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Yunxuan Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, et al. Scaling instruction-finetuned language models. Journal of Machine Learning Research, 25(70):1–53, 2024. Peter Clark, Isaac Cowhey, Oren Etzioni, Tushar Khot, Ashish Sabharwal, Carissa Schoenick, and Oyvind Tafjord. Think you have solved question answering? try arc, the ai2 reasoning challenge. ArXiv, abs/1803.05457, 2018. URL https://api.semanticscholar.org/CorpusID:3922816. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168, 2021. Tim Dettmers, Artidoro Pagnoni, Ari Holtzman, and Luke Zettlemoyer. Qlora: Efficient finetuning of quantized llms. Advances in Neural Information Processing Systems, 36, 2024. Yuqing Du, Alexander Havrilla, Sainbayar Sukhbaatar, Pieter Abbeel, and Roberta Raileanu. A study on improving reasoning in language models. In I Can’t Believe It’s Not Better Workshop: Failure Modes in the Age of Foundation Models, 2024. URL https://openreview.net/forum?id=tCZFmDyPFm. Yann Dubois, Chen Xuechen Li, Rohan Taori, Tianyi Zhang, Ishaan Gulrajani, Jimmy Ba, Carlos Guestrin, Percy S Liang, and Tatsunori B Hashimoto. Alpacafarm: A simulation framework for methods that learn from human feedback. Advances in Neural Information Processing Systems, 36, 2024. Leo Gao, Jonathan Tow, Baber Abbasi, Stella Biderman, Sid Black, Anthony DiPofi, Charles Foster, Laurence Golding, Jeffrey Hsu, Alain Le Noac’h, Haonan Li, Kyle McDonell, Niklas Muennighoff, Chris Ociepa, Jason Phang, Laria Reynolds, Hailey Schoelkopf, Aviya Skowron, Lintang Sutawika, Eric Tang, Anish Thite, Ben Wang, Kevin Wang, and Andy Zou. A framework for few-shot language model evaluation, 12 2023. URL https://zenodo.org/records/10256836. Bogdan Gliwa, Iwona Mochol, Maciej Biesek, and Aleksander Wawer. Samsum corpus: A human-annotated dialogue dataset for abstractive summarization. arXiv preprint arXiv:1911.12237, 2019. Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep learning. MIT press, 2016. Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. Measuring massive multitask language understanding. arXiv preprint arXiv:2009.03300, 2020. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. arXiv preprint arXiv:2103.03874, 2021. Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. Lora: Low-rank adaptation of large language models. arXiv preprint arXiv:2106.09685, 2021. Hamish Ivison, Yizhong Wang, Valentina Pyatkin, Nathan Lambert, Matthew Peters, Pradeep Dasigi, Joel Jang, David Wadden, Noah A Smith, Iz Beltagy, et al. Camels in a changing climate: Enhancing lm adaptation with tulu 2. arXiv preprint arXiv:2311.10702, 2023. Weisen Jiang, Han Shi, Longhui Yu, Zhengying Liu, Yu Zhang, Zhenguo Li, and James T. Kwok. Forwardbackward reasoning in large language models for mathematical verification, 2024. Dawid Jan Kopiczko, Tijmen Blankevoort, and Yuki Markus Asano. Vera: Vector-based random matrix adaptation. arXiv preprint arXiv:2310.11454, 2023. Timothée Lesort, Vincenzo Lomonaco, Andrei Stoian, Davide Maltoni, David Filliat, and Natalia DíazRodríguez. Continual learning for robotics: Definition, framework, learning strategies, opportunities and challenges. Information fusion, 58:52–68, 2020. Timothée Lesort, Oleksiy Ostapenko, Diganta Misra, Md Rifat Arefin, Pau Rodríguez, Laurent Charlin, and Irina Rish. Challenging common assumptions about catastrophic forgetting. arXiv preprint arXiv:2207.04543, 2022. Chunyuan Li, Heerad Farkhoor, Rosanne Liu, and Jason Yosinski. Measuring the intrinsic dimension of objective landscapes. arXiv preprint arXiv:1804.08838, 2018. Raymond Li, Loubna Ben Allal, Yangtian Zi, Niklas Muennighoff, Denis Kocetkov, Chenghao Mou, Marc Marone, Christopher Akiki, Jia Li, Jenny Chim, et al. Starcoder: may the source be with you! arXiv preprint arXiv:2305.06161, 2023. Shih-Yang Liu, Chien-Yi Wang, Hongxu Yin, Pavlo Molchanov, Yu-Chiang Frank Wang, Kwang-Ting Cheng, and Min-Hung Chen. Dora: Weight-decomposed low-rank adaptation. arXiv preprint arXiv:2402.09353, 2024. Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. Roberta: A robustly optimized bert pretraining approach. arXiv preprint arXiv:1907.11692, 2019. Ziyang Luo, Can Xu, Pu Zhao, Qingfeng Sun, Xiubo Geng, Wenxiang Hu, Chongyang Tao, Jing Ma, Qingwei Lin, and Daxin Jiang. Wizardcoder: Empowering code large language models with evol-instruct. arXiv preprint arXiv:2306.08568, 2023. Jekaterina Novikova, Ondřej Dušek, and Verena Rieser. The e2e dataset: New challenges for end-to-end generation. arXiv preprint arXiv:1706.09254, 2017. Keiran Paster, Marco Dos Santos, Zhangir Azerbayev, and Jimmy Ba. Openwebmath: An open dataset of high-quality mathematical web text. arXiv preprint arXiv:2310.06786, 2023. Samyam Rajbhandari, Jeff Rasley, Olatunji Ruwase, and Yuxiong He. Zero: Memory optimizations toward training trillion parameter models. In SC20: International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 1–16. IEEE, 2020. Prajit Ramachandran, Barret Zoph, and Quoc V Le. Searching for activation functions. arXiv preprint arXiv:1710.05941, 2017. Sebastian Raschka. Practical tips for finetuning llms using lora (low-rank adaptation), 2023. URL https://magazine.sebastianraschka.com/p/practical-tips-for-finetuning-llms# %C2%A7enable-lora-for-more-layers. Baptiste Roziere, Jonas Gehring, Fabian Gloeckle, Sten Sootla, Itai Gat, Xiaoqing Ellen Tan, Yossi Adi, Jingyu Liu, Tal Remez, Jérémy Rapin, et al. Code llama: Open foundation models for code. arXiv preprint arXiv:2308.12950, 2023. Keisuke Sakaguchi, Ronan Le Bras, Chandra Bhagavatula, and Yejin Choi. Winogrande: An adversarial winograd schema challenge at scale, 2019. Thomas Scialom, Tuhin Chakrabarty, and Smaranda Muresan. Fine-tuned language models are continual learners. arXiv preprint arXiv:2205.12393, 2022. Noam Shazeer. Glu variants improve transformer. arXiv preprint arXiv:2002.05202, 2020. Ying Sheng, Shiyi Cao, Dacheng Li, Coleman Hooper, Nicholas Lee, Shuo Yang, Christopher Chou, Banghua Zhu, Lianmin Zheng, Kurt Keutzer, Joseph E. Gonzalez, and Ion Stoica. S-lora: Serving thousands of concurrent lora adapters, 2023. Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew Y Ng, and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp. 1631–1642, 2013. Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1): 1929–1958, 2014. Fan-Keng Sun, Cheng-Hao Ho, and Hung-Yi Lee. Lamol: Language modeling for lifelong language learning. arXiv preprint arXiv:1909.03329, 2019. Simeng Sun, Dhawal Gupta, and Mohit Iyyer. Exploring the impact of low-rank adaptation on the performance, efficiency, and regularization of rlhf, 2023. Rohan Taori, Ishaan Gulrajani, Tianyi Zhang, Yann Dubois, Xuechen Li, Carlos Guestrin, Percy Liang, and Tatsunori B Hashimoto. Stanford alpaca: An instruction-following llama model, 2023. Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288, 2023. Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R Bowman. Glue: A multitask benchmark and analysis platform for natural language understanding. arXiv preprint arXiv:1804.07461, 2018. Liyuan Wang, Xingxing Zhang, Hang Su, and Jun Zhu. A comprehensive survey of continual learning: Theory, method and application, 2024. Yuxiang Wei, Zhe Wang, Jiawei Liu, Yifeng Ding, and Lingming Zhang. Magicoder: Source code is all you need. arXiv preprint arXiv:2312.02120, 2023. Yixuan Weng, Minjun Zhu, Fei Xia, Bin Li, Shizhu He, Shengping Liu, Bin Sun, Kang Liu, and Jun Zhao. Large language models are better reasoners with self-verification. arXiv preprint arXiv:2212.09561, 2022. Adina Williams, Nikita Nangia, and Samuel R Bowman. A broad-coverage challenge corpus for sentence understanding through inference. arXiv preprint arXiv:1704.05426, 2017. Wenhan Xia, Chengwei Qin, and Elad Hazan. Chain of lora: Efficient fine-tuning of language models via residual learning. arXiv preprint arXiv:2401.04151, 2024. Longhui Yu, Weisen Jiang, Han Shi, Jincheng Yu, Zhengying Liu, Yu Zhang, James T Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. Metamath: Bootstrap your own mathematical questions for large language models. arXiv preprint arXiv:2309.12284, 2023. Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. Hellaswag: Can a machine really finish your sentence?, 2019. Jiawei Zhao, Zhenyu Zhang, Beidi Chen, Zhangyang Wang, Anima Anandkumar, and Yuandong Tian. Galore: Memory-efficient llm training by gradient low-rank projection. arXiv preprint arXiv:2403.03507, 2024a. Justin Zhao, Timothy Wang, Wael Abid, Geoffrey Angus, Arnav Garg, Jeffery Kinnison, Alex Sherstinsky, Piero Molino, Travis Addair, and Devvret Rishi. Lora land: 310 fine-tuned llms that rival gpt-4, a technical report. arXiv preprint arXiv:2405.00732, 2024b. Victor Zhong, Caiming Xiong, and Richard Socher. Seq2sql: Generating structured queries from natural language using reinforcement learning. arXiv preprint arXiv:1709.00103, 2017. Terry Yue Zhuo, Armel Zebaze, Nitchakarn Suppattarachai, Leandro von Werra, Harm de Vries, Qian Liu, and Niklas Muennighoff. Astraios: Parameter-efficient instruction tuning code large language models. arXiv preprint arXiv:2401.00788, 2024. Authors:
(1) Dan Biderman, Columbia University and Databricks Mosaic AI (db3236@columbia.edu);
(2) Jose Gonzalez Ortiz, Databricks Mosaic AI (j.gonzalez@databricks.com);
(3) Jacob Portes, Databricks Mosaic AI (jportes@databricks.com);
(4) Mansheej Paul, Databricks Mosaic AI (mansheej.paul@databricks.com);
(5) Philip Greengard, Columbia University (pg2118@columbia.edu);
(6) Connor Jennings, Databricks Mosaic AI (connor.jennings@databricks.com);
(7) Daniel King, Databricks Mosaic AI (daniel.king@databricks.com);
(8) Sam Havens, Databricks Mosaic AI (sam.havens@databricks.com);
(9) Vitaliy Chiley, Databricks Mosaic AI (vitaliy.chiley@databricks.com);
(10) Jonathan Frankle, Databricks Mosaic AI (jfrankle@databricks.com);
(11) Cody Blakeney, Databricks Mosaic AI (cody.blakeney);
(12) John P. Cunningham, Columbia University (jpc2181@columbia.edu). Authors: Authors: (1) Dan Biderman, Columbia University and Databricks Mosaic AI (db3236@columbia.edu); (2) Jose Gonzalez Ortiz, Databricks Mosaic AI (j.gonzalez@databricks.com); (3) Jacob Portes, Databricks Mosaic AI (jportes@databricks.com); (4) Mansheej Paul, Databricks Mosaic AI (mansheej.paul@databricks.com); (5) Philip Greengard, Columbia University (pg2118@columbia.edu); (6) Connor Jennings, Databricks Mosaic AI (connor.jennings@databricks.com); (7) Daniel King, Databricks Mosaic AI (daniel.king@databricks.com); (8) Sam Havens, Databricks Mosaic AI (sam.havens@databricks.com); (9) Vitaliy Chiley, Databricks Mosaic AI (vitaliy.chiley@databricks.com); (10) Jonathan Frankle, Databricks Mosaic AI (jfrankle@databricks.com); (11) Cody Blakeney, Databricks Mosaic AI (cody.blakeney); (12) John P. Cunningham, Columbia University (jpc2181@columbia.edu). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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