# Starbucks-v2: Improved Training for 2D Matryoshka Embeddings

arXiv: https://arxiv.org/abs/2410.13230 · HTML: https://mlsanity.com/paper/2410.13230/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2024.

## Built on by (most cited first, 7 of 7)

- [Unlocking Multimodal Document Intelligence: From Current Triumphs to Future Frontiers of Visual Document Retrieval](https://mlsanity.com/paper/2602.19961/) (2026)
- [CausalEmbed: Auto-Regressive Multi-Vector Generation in Latent Space for Visual Document Embedding](https://mlsanity.com/paper/2601.21262/) (2026)
- [CSRv2: Unlocking Ultra-Sparse Embeddings](https://mlsanity.com/paper/2602.05735/) (2026)
- [Learning Retrieval Models with Sparse Autoencoders](https://mlsanity.com/paper/2603.13277/) (2026)
- [Making Large Language Models Efficient Dense Retrievers](https://mlsanity.com/paper/2512.20612/) (2025)
- [Embedding World Knowledge into Tabular Models: Towards Best Practices for Embedding Pipeline Design](https://mlsanity.com/paper/2603.17737/) (2026)
- [MM-Matryoshka: Towards Budget-Elastic Visual Document Retrieval via a 2D Multimodal Matryoshka Training Framework](https://mlsanity.com/paper/2606.07654/) (2026)

## Abstract (arXiv)

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 consistently outperforms 2D Matryoshka models and matches or exceeds the performance of individually trained models, while maintaining high efficiency and adaptability. Ablation studies confirm our loss design choices, the impact of SMAE pre-training and demonstrate the applicability of Starbucks across backbones. We further show that depth- and width-wise Starbucks variants capture complementary information, and that their hybridization yields additional performance gains with minimal latency overhead due to parallelization. Code available at https://github.com/ielab/Starbucks