Emergent Sparsity: How Many Effective Variables Survive Coarse-Graining in AlphaEarth Embeddings?

Key points

• Yet many scientific applications work at coarser spatial supports, for which fewer than 64 effective variables may suffice.1
• We ask whether these vectors can be reorganized into ranked global nonlinear coordinates, how many suffice at a chosen reconstruction accuracy, and whether that number decreases with spatial scale.1
• We thus describe effective dimension as a two-control surface over tolerance and spatial scale, rather than one intrinsic number.1
• At each scale, a $β$-VAE scan with a common architecture produces a rank--distortion envelope, giving the smallest retained count achieved within the scanned family at each reconstruction tolerance.1

Sources (1)

• [1]Emergent Sparsity: How Many Effective Variables Survive Coarse-Graining in AlphaEarth Embeddings?
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 18, 01:24 PM

  AlphaEarth encodes each 10 m land pixel as a 64-component vector intended to support diverse global mapping tasks.

  Yet many scientific applications work at coarser spatial supports, for which fewer than 64 effective variables may suffice.

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