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 C Training Datasets C.1 MetaMathQA (Math IFT) The MetaMathQA dataset (Yu et al. (2023), https://huggingface.co/datasets/meta-math/MetaMathQA) contains 395,000 samples that are bootsrapped from the GSM (Cobbe et al., 2021) and Math (Hendrycks et al., 2021) training sets. These samples are augmented by GPT-3.5 using the following methods: • Answer Augmentation (155k samples, Yu et al. (2023)): this method proposed by the MetaMathQA authors generates multiple reasoning paths for a given mathetical question and filters for generated reasoning paths that contain the correct final answer. • Rephrasing (130k samples, (Yu et al., 2023)): this method proposed by the MetaMathQA authors uses GPT-3.5 to rephrase questions. They check for the correctness of rephrased questions by using few-shot Chain of Thought prompting to compare reasoning chains and proposed answers with ground truth answers. Both Self-Verification (Weng et al., 2022) and FOBAR (Jiang et al., 2024) fall under the category of “backward reasoning,” where the question starts with a given condition and requires reasoning backwards to solve for an unknown variable. In order to generate new mathematical questions, a numerical value in the original question is masked as a variable X, and the question is rephrased accordingly. MetaMathQA samples are organized by 4 columns: type, original_question, query and response. We include two full examples below: C.2 Magicoder-Evol-Instruct-110k (Code IFT) C.3 Starcoder Python (Code CPT) C.4 OpenWebMath (Math CPT) 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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