Data-Efficient Learning via Clustering-Based Sensitivity Sampling:
  Foundation Models and Beyond
Kyriakos Axiotis Vincent Cohen-Addad Monika Henzinger Sammy Jerome Vahab Mirrokni David Saulpic David Woodruff Michael Wunder
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 H\"older
continuous, our approach provably allows selecting a set of ``typical'' $k +
1/\varepsilon^2$ elements whose average loss corresponds to the average loss of
the whole dataset, up to a multiplicative $(1\pm\varepsilon)$ factor and an
additive $\varepsilon \lambda \Phi_k$, where $\Phi_k$ represents the $k$-means
cost for the input embeddings and $\lambda$ is the H\"older 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.