Characterizing AlphaEarth Embedding Geometry for Agentic Environmental Reasoning

arXiv cs.AI / 4/22/2026

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Key Points

The paper studies the geometric structure of Google AlphaEarth’s 64-dimensional Earth-observation embeddings at massive US-scale coverage (12.1M samples) over 2017–2023, finding a non-Euclidean manifold with much lower effective dimensionality than the raw vector size.
It shows that local geometry varies strongly across locations (e.g., large tangent-space rotation and weak local-global alignment), and that naive linear/probing directions and vector arithmetic do not reliably yield precise compositional reasoning.
Retrieval based on local geometric properties is more effective than parametric-only approaches, with local manifold geometry predicting retrieval coherence (reported R² = 0.32) and producing physically coherent results.
The authors build an agentic environmental reasoning system using nine specialized tools that turn queries into multi-step reasoning chains over a FAISS-indexed embedding database, where ablations indicate embedding retrieval dominates answer quality.
A cross-model benchmark suggests the benefit of geometric characterization depends on the downstream model: geometric tools slightly reduce Sonnet 4.5 scores but improve Opus 4.6 scores, with Opus showing better geometric grounding.

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

|\cos\theta| = 0.17

) approaching the random baseline of 0.125. Supervised linear probes indicate that concept directions rotate across the manifold, and compositional vector arithmetic using both PCA-derived and probe-derived directions yields poor precision. Retrieval instead produces physically coherent results, with local geometry predicting retrieval coherence (

R^2 = 0.32

). Building on this characterization, we introduce an agentic system with nine specialized tools that decomposes environmental queries into reasoning chains over a FAISS-indexed embedding database. A five-condition ablation (120 queries, three complexity tiers) shows that embedding retrieval dominates response quality (

\mu = 3.79 \pm 0.90

vs.\

3.03 \pm 0.77

parametric-only; scale 1--5), with peak performance on multi-step comparisons (

\mu = 4.28 \pm 0.43

). A cross-model benchmark show that geometric tools reduce Sonnet 4.5's score by 0.12 points but improve Opus 4.6's by 0.07, with Opus achieving higher geometric grounding (3.38 vs.\ 2.64), suggesting that the value of geometric characterization scales with the reasoning capability of the consuming model.