Title: SENSE: $\underline{\text{SEN}}$sing Similarity $\underline{\text{SE}}$eing Structure
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Privacy Preserving, Distributed Learning, Federated Learning, Contrastive Neighbor Embedding, Hyperbolic Embedding, Matrix Completion

Abstract: Dimensionality reduction is widely used to visualize and analyze high-dimensional data, but most methods assume centralized access to all pairwise similarities, which is infeasible in privacy-sensitive, decentralized settings. We introduce $\textbf{SENSE}$, a geometry-aware framework for privacy-preserving decentralized representation learning. SENSE reconstructs global structure from sparse, locally observed distances via structured matrix completion, requiring no raw data sharing or iterative communication. It supports both Euclidean and hyperbolic geometries, adapts to flat and hierarchical structures, and operates under four deployment regimes reflecting real-world data availability. By design, SENSE safeguards raw features while producing faithful embeddings. Our theoretical analysis establishes formal privacy guarantees, and experiments on diverse benchmark datasets show that SENSE matches centralized baselines while remaining efficient and privacy-preserving.

TL;DR: SENSE is a privacy-preserving framework that builds high-quality global embeddings across decentralized clients without sharing raw data, working in both Euclidean and hyperbolic spaces.