Title: EmbedDistill: A geometric knowledge distillation for information retrieval. Abstract: Large neural models (such as Transformers) achieve state-of-the-art performance for information retrieval. In this paper, we aim to improve distillation methods that pave the way for the deployment of such models in practice. The proposed distillation approach supports both retrieval and re-ranking stages and crucially leverages the relative geometry among queries and documents learned by the large teacher model. It goes beyond existing distillation methods in the information retrieval literature, which simply rely on the teacher's scalar scores over the training data, on two fronts: providing stronger signals about local geometry via embedding matching and attaining better coverage of data manifold globally via query generation. Embedding matching provides a stronger signal to align the representations of the teacher and student models. At the same time, query generation explores the data manifold to reduce the discrepancies between the student and teacher where the training data is sparse. Our distillation approach is theoretically justified and applies to both dual encoder (DE) and cross-encoder (CE) models. Furthermore, for distilling a CE model to a DE model via embedding matching, we propose a novel dual pooling-based scorer for the CE model that facilitates a more distillation-friendly embedding geometry, especially for DE student models.