Characterizing AlphaEarth Embedding Geometry for Agentic Environmental Reasoning
Mashrekur Rahman, Samuel J. Barrett, Christina Last

TL;DR
This paper explores the geometric structure of Earth observation embeddings, revealing their non-Euclidean nature and how this understanding enhances environmental reasoning through an agentic system leveraging retrieval and specialized tools.
Contribution
It characterizes the manifold geometry of AlphaEarth embeddings and develops an agentic reasoning system that improves environmental query responses using geometric insights.
Findings
Embedding manifold is non-Euclidean with effective dimensionality 13.3.
Retrieval-based methods outperform parametric-only responses in environmental reasoning.
Geometric understanding improves reasoning performance, especially in complex, multi-step queries.
Abstract
Earth observation foundation models encode land surface information into dense embedding vectors, yet the geometric structure of these representations and its implications for downstream reasoning remain underexplored. We characterize the manifold geometry of Google AlphaEarth's 64-dimensional embeddings across 12.1 million Continental United States samples (2017--2023) and develop an agentic system that leverages this geometric understanding for environmental reasoning. The manifold is non-Euclidean: effective dimensionality is 13.3 (participation ratio) from 64 raw dimensions, with local intrinsic dimensionality of approximately 10. Tangent spaces rotate substantially, with 84\% of locations exceeding 60\textdegree{} and local-global alignment (mean) approaching the random baseline of 0.125. Supervised linear probes indicate that concept directions rotate across…
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