When Does Dense Retrieval Need Asymmetric Geometry? A Bias-Variance Theory of Shared and Dual Projections

arXiv:2609.32488 · cs.IR, cs.LG · Submitted 2026-09-26 · Read on arXiv

cs.IR, cs.LG

Submitted: 2026-09-26

Updated: 2026-09-26

Terminology

• Regret — 20× in this paper · explained in 3 episodes
• Embeddings — 18× in this paper · explained in 2 episodes
• Accuracy — 9× in this paper · explained in 1 episode
• Calibration — 4× in this paper · explained in 7 episodes
• Contrastive Learning — 3× in this paper · explained in 5 episodes
• Adaptation — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Cross-fitted Asymmetry Risk Selector — 2× in this paper
• Ambient Dimension — 1× in this paper · explained in 1 episode
• Anisotropy — 1× in this paper · explained in 3 episodes
• Data Augmentation — 1× in this paper · explained in 7 episodes
• Distribution Shift — 1× in this paper · explained in 6 episodes
• Domain Adaptation — 1× in this paper · explained in 5 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Matrix Completion — 1× in this paper · explained in 4 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Riemannian optimization — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Towards General Text Embeddings with Multi-stage Contrastive Learning
• Text Embeddings by Weakly-Supervised Contrastive Pre-training

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