Abstract
2D Matryoshka training enables a single embedding model to generate sub-network representations across different layers and embedding dimensions, offering adaptability to diverse computational and task constraints. However, its effectiveness remains well below that of individually trained models of equivalent sizes. To address this, we propose Starbucks, a new training strategy for Matryoshka-style embedding models that combines structured fine-tuning with masked autoencoder (MAE) pre-training. During fine-tuning, we compute the loss over a fixed set of layer-dimension pairs, from small to large, which significantly improves performance over randomly sampled sub-networks and matches that of separately trained models. Our MAE-based pre-training further enhances the representation quality of sub-networks, providing a stronger backbone for downstream tasks. Experiments on both in-domain (semantic similarity and passage retrieval) and out-of-domain (BEIR) benchmarks show that Starbucks con