Data-Efficient Learning via Clustering-Based Sensitivity Sampling: Foundation Models and Beyond

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is Hölder continuous, our approach provably allows selecting a set of “typical” k + 1/ε^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1±ε) factor and an additive ελΦ_k, where Φ_k represents the k-means cost for the input embeddings and λ is the Hölder constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.