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Speaker 1: Rishi Dev Jha (Cornell Tech) Title 1: All AI Models Might Be the Same: Harnessing the Universal Geometry of Embeddings Abstract 1: AI models transform inputs like images and text into high-dimensional vectors called embeddings. Influenced by factors such as architecture, training data, and input modality, these embeddings are model-specific and not directly interoperable. In this talk, we show that—despite these fundamental differences—embeddings across models share significant common geometric structure. We then introduce vec2vec, a method that translates between embedding spaces by learning a universal semantic representation without paired training data or predefined mappings. This shared structure provides empirical support for the Platonic Representation Hypothesis and enables black-box inversion: reconstructing original inputs from vector representations alone. Speaker 2: Nora Wagner (University of Vienna) Title 2: Clustering in Semi-Metric Spaces for Identifying Nearby Stellar Populations in Gaia DR3 Abstract 2: Stars form in clustered environments, sharing similar initial positions and velocities. As these systems evolve, many dissolve into the Galactic field, erasing most direct evidence of their common origin. Recovering such coeval groups is essential for reconstructing the recent star-formation history and for establishing robust age benchmarks for objects that are otherwise difficult to date (e.g., brown dwarfs and exoplanet hosts), enabling tests of planet-formation and early-evolution timescales. Gaia has enabled the discovery of thousands of clusters via density-based methods in five-parameter astrometry; however, in the immediate Solar neighborhood, projection effects smear tangential-velocity overdensities. Clustering in full six-dimensional phase space would largely remove this limitation, but it requires precise radial velocities, which exist for only a minority of Gaia sources. In this talk, I present two complementary approaches to recover clusters within 100 pc. First, for each stellar pair we infer optimal radial velocities via a minimization scheme, yielding a semi-metric estimate of their minimal 3D velocity separation that can be used as a proximity constraint even when RVs are missing. Building on these constraints, a constrained autoencoder combines Gaia observables with the velocity-separation information to infer an approximate 6D phase-space representation, enabling density-based clustering beyond the RV-complete subset. Second, we interpret the resulting pairwise distance matrix as a weighted graph, sparsify it by pruning unlikely connections, and identify groups via community detection. I will show results on controlled synthetic data (injections/ablations) and discuss a path toward a new census of nearby dissolving clusters.