Sparsity May Be All You Need: Sparse Random Parameter Adaptation

Full fine-tuning of large language models for alignment and task adaptation has become prohibitively expensive as models have grown in size. Parameter-Efficient Fine-Tuning (PEFT) methods aim at significantly reducing the computational and memory resources needed for fine-tuning these models by only training on a small number of parameters instead of all model parameters. Currently, the most popular PEFT method is the Low-Rank Adaptation (LoRA), which freezes the parameters of the model to be fine-tuned and introduces a small set of trainable parameters in the form of low-rank matrices. We propose simply reducing the number of trainable parameters by randomly selecting a small proportion of the model parameters to train on. In this paper, we compare the efficiency and performance of our proposed approach with PEFT methods, including LoRA, as well as full parameter fine-tuning.

Robust Partially-Compressed Least-Squares

Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investigate compressed least-squares problems and propose new models and algorithms that address the issue of error and noise introduced by compression. While maintaining computational efficiency, our models provide robust solutions that are more accurate--relative to solutions of uncompressed least-squares--than those of classical compressed variants. We introduce tools from robust optimization together with a form of partial compression to improve the error-time trade-offs of compressed least-squares solvers. We develop an efficient solution algorithm for our Robust Partially-Compressed (RPC) model based on a reduction to a one-dimensional search. We also derive the first approximation error bounds for Partially-Compressed least-squares solutions. Empirical results comparing numerous alternatives suggest that robust and partially compressed solutions are effectively insulated against aggressive randomized transforms.