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arxiv: 2606.11510 · v1 · pith:4H2EFXMVnew · submitted 2026-06-09 · 🧬 q-bio.QM · q-bio.PE· stat.ML

Continuous biome representations from Earth observation embeddings

Maxwell B. Joseph , Fl\'avia De Souza Mendes , Dieu My T. Nguyen , Camile Sothe , Christopher B. Anderson (Planet Labs PBC) This is my paper

Pith reviewed 2026-06-27 10:21 UTC · model grok-4.3

classification 🧬 q-bio.QM q-bio.PEstat.ML
keywords continuous biome representationEarth observation embeddingsspecies occurrence predictionbiome classificationecological gradientssatellite imagery
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The pith

A linear classifier on satellite embeddings turns categorical biome maps into continuous probability vectors that improve species occurrence prediction.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Biotic communities vary gradually across space, yet standard biome maps divide them into fixed categories that erase detail at transitions. The paper fits a linear classifier to dense embeddings from Earth observation images to predict those categorical labels, then uses the softmax outputs as a vector of continuous probabilities over the biome classes. Evaluated on Brazilian forest plots, this graded representation raises mean per-species AUC for predicting occurrences of 4,672 plant species from 0.570 with discrete labels to 0.618. The gain traces specifically to the continuous probabilities rather than any shift in which label is assigned. The method keeps the named biome categories while restoring the graded ecological variation that discrete maps suppress.

Core claim

Training a linear classifier on Clay v1.5 satellite image embeddings to predict biome labels and taking the softmax as a continuous probability vector over biome classes produces representations that outperform discrete biome labels when predicting species occurrence, with mean per-species AUC rising from 0.570 to 0.618 across 10 spatial cross-validation folds on 10,015 withheld plots. The improvement is attributable to continuity in the graded output rather than label reassignment and holds at all distances from biome boundaries; the raw 1024-dimensional embedding reaches 0.646 but the continuous vector recovers most of that advantage.

What carries the argument

The softmax probability vector output by a linear classifier fitted to Earth observation embeddings, which converts discrete biome categories into a continuous graded representation over the same named classes.

If this is right

  • Continuity in the graded probability output, rather than any change in assigned labels, accounts for the predictive improvement.
  • The advantage persists across all distances from biome boundaries.
  • The continuous representation captures most but not all of the gain achieved by the raw 1024-dimensional embedding over discrete labels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same linear-classifier-plus-softmax procedure could convert other categorical ecological or land-cover maps into continuous versions without retraining the underlying embedding model.
  • Species distribution models that currently ingest discrete biome layers could substitute these probability vectors to better represent transitional communities.
  • The gap between the continuous representation and the raw embedding suggests that further post-processing of the probabilities might close the remaining performance difference.

Load-bearing premise

The reported performance gain is caused by the continuity of the probability outputs rather than label reassignment or other unmeasured factors, and the 10 spatial cross-validation folds sufficiently control for spatial structure in the withheld plots.

What would settle it

Replacing the softmax probabilities with the classifier's hard label assignments and observing no remaining AUC improvement would show that continuity is not the source of the gain.

Figures

Figures reproduced from arXiv: 2606.11510 by Camile Sothe, Christopher B. Anderson (Planet Labs PBC), Dieu My T. Nguyen, Fl\'avia De Souza Mendes, Maxwell B. Joseph.

Figure 1
Figure 1. Figure 1: Study system overview. Left: IBGE biome map of Brazil, with six biomes shown as colored polygons. Middle: First three principal components of Clay v1.5 embeddings rendered as an RGB composite, with IBGE biome boundaries overlaid. Right: Locations of 10,015 national forest inventory plots, colored by spatial cross-validation fold assignment, with biome boundaries overlaid. We develop a case study in Brazil,… view at source ↗
Figure 2
Figure 2. Figure 2: A linear layer maps a 𝐷-dimensional EO embedding to 𝐾 logits, and a softmax function produces a 𝐾- dimensional continuous representation. The model is trained with cross-entropy loss against discrete biome labels from a categorical map. Taking the argmax of the continuous representation yields a predicted label. In this study 𝐷 = 1024 (Clay v1.5) and 𝐾 = 6 (IBGE biomes). To characterize uncertainty at each… view at source ↗
Figure 3
Figure 3. Figure 3: Continuous biome representations derived from Earth observation embeddings. Left: predicted probability for each of the six IBGE biomes, with color intensity proportional to probability (saturated = near 1, white = near 0). Right: normalized Shannon entropy (𝐻/𝐻max) of the six-dimensional probability vector, shown as a sequential shading (light = low entropy, indicating confident single-biome assignment; d… view at source ↗
Figure 4
Figure 4. Figure 4: Per-species ΔAUC stratified by distance to the nearest biome boundary. Left: total advantage of the con￾tinuous representation over the map label. Middle and right: additive decomposition into continuous representation minus predicted label and predicted label minus map label; the middle and right components sum to the total shown at left. Each dot is one spatial CV fold’s mean ΔAUC across species within a… view at source ↗
read the original abstract

Biotic communities vary continuously across space, yet biome maps impose categorical boundaries that compress this variation, particularly at ecotones where transitional communities are ecologically distinct. Could Earth observation (EO) foundation models, which encode spectral, spatial, and temporal information with dense embeddings, convert discrete biome maps into continuous representations that better capture ecological variation? Here, we fit a linear classifier on Clay v1.5 satellite image embeddings to predict biome labels from a categorical map. The softmax output yields a continuous probability vector whose dimensions correspond to named biome classes. We evaluate this approach using six Brazilian biomes, 1.3 million embeddings, and 10,015 withheld forest inventory plots spanning 4,672 plant species. The continuous biome representation outperforms discrete biome labels for predicting species occurrence (mean per-species AUC 0.618 vs. 0.570 across 10 spatial cross-validation folds). Decomposing this gain shows that continuity in the graded probability output, rather than label reassignment, accounts for the improvement; the pattern holds across all distances from biome boundaries. The raw 1024-dimensional embedding remains the strongest predictor we tested (mean AUC 0.646 vs. 0.618), but the continuous representation recovers most of the embedding's gain over discrete labels. This simple approach provides a probabilistic replacement for categorical map labels, preserving their meaning while encoding graded variation that discrete maps suppress.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that training a linear classifier on Clay v1.5 Earth observation embeddings to predict categorical biome labels yields softmax probability vectors that serve as continuous biome representations; these outperform discrete biome labels when predicting occurrence of 4,672 plant species across 10,015 withheld plots (mean per-species AUC 0.618 vs. 0.570) under 10 spatial cross-validation folds, with the gain attributed to graded probabilities rather than label reassignment, and the raw 1024-d embeddings performing best (AUC 0.646).

Significance. If the central comparison holds, the method supplies an interpretable, probabilistic substitute for categorical biome maps that recovers most of the predictive value of dense EO embeddings while retaining named biome classes; this could improve modeling of transitional communities at ecotones. The use of independent species-occurrence data for evaluation and the explicit continuity-vs-reassignment decomposition are strengths.

major comments (2)
  1. [spatial cross-validation procedure] The spatial cross-validation procedure (abstract and results): the reported AUC comparison relies on 10 spatial folds separating the 10,015 plots, yet no details are given on fold construction (minimum inter-plot distance, clustering radius, or blocking method). Because Clay embeddings encode spatial context and species exhibit strong spatial autocorrelation, inadequate separation risks leakage that could inflate the 0.048 AUC difference; this is load-bearing for the claim that continuity drives the improvement.
  2. [results decomposition] Decomposition isolating continuity (results): the assertion that 'continuity in the graded probability output, rather than label reassignment, accounts for the improvement' and that the pattern holds 'across all distances from biome boundaries' requires the exact baseline construction and distance-binned analysis to be specified; without these, the attribution cannot be verified as isolating the continuity effect.
minor comments (2)
  1. Clarify the relationship between the 1.3 million embeddings used for classifier fitting and the 10,015 evaluation plots (abstract).
  2. The abstract states the continuous representation 'recovers most of the embedding's gain'; provide the exact numerical breakdown of the three AUC values in a table for direct comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. The two major comments identify areas where the manuscript would benefit from greater methodological transparency. We address each point below and commit to revisions that strengthen the presentation without altering the core claims.

read point-by-point responses

  1. Referee: The spatial cross-validation procedure (abstract and results): the reported AUC comparison relies on 10 spatial folds separating the 10,015 plots, yet no details are given on fold construction (minimum inter-plot distance, clustering radius, or blocking method). Because Clay embeddings encode spatial context and species exhibit strong spatial autocorrelation, inadequate separation risks leakage that could inflate the 0.048 AUC difference; this is load-bearing for the claim that continuity drives the improvement.

    Authors: We agree that explicit details on fold construction are required to allow readers to assess the risk of spatial leakage. In the revised manuscript we will add a dedicated subsection describing the spatial blocking procedure, including the clustering algorithm, the radius used to define blocks, the minimum inter-plot distance enforced between folds, and the resulting distribution of plot-to-fold assignments. This addition will enable direct evaluation of whether the reported 0.048 AUC gain can be attributed to continuity rather than residual spatial dependence. revision: yes

  2. Referee: Decomposition isolating continuity (results): the assertion that 'continuity in the graded probability output, rather than label reassignment, accounts for the improvement' and that the pattern holds 'across all distances from biome boundaries' requires the exact baseline construction and distance-binned analysis to be specified; without these, the attribution cannot be verified as isolating the continuity effect.

    Authors: We accept that the current description of the continuity-versus-reassignment decomposition is insufficiently specified. In revision we will expand the relevant results section to state the precise baseline construction (i.e., how the discrete-label comparator was generated from the same embeddings), the distance metric used to compute distance from biome boundaries, the binning procedure, and the per-bin AUC differences. These additions will make the claim that graded probabilities, rather than label reassignment, drive the improvement verifiable from the reported figures and tables. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical AUC comparison on independent species data

full rationale

The paper trains a linear classifier on Clay embeddings to predict categorical biome labels from a map, then uses the resulting softmax probability vector as a continuous representation. This vector is evaluated for its ability to predict species occurrence on 10,015 withheld inventory plots (4,672 species) under 10 spatial CV folds. The reported mean per-species AUC (0.618 vs. 0.570) is measured on a downstream task whose labels are independent of the biome training data; the performance metric therefore cannot reduce to the fitted biome classifier by construction. No self-definitional equations, fitted-input-as-prediction steps, or load-bearing self-citations appear in the derivation chain. The decomposition into continuity vs. reassignment is likewise an empirical contrast on the held-out species data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Approach rests on pre-trained Clay embeddings and a fitted linear classifier; no new physical entities or ad-hoc constants beyond standard ML fitting are introduced.

free parameters (1)
  • linear classifier weights
    Weights fitted to map embeddings to biome class logits before softmax.
axioms (1)
  • domain assumption Clay v1.5 embeddings encode spectral, spatial, and temporal information sufficient for biome discrimination.
    Invoked when treating the embeddings as direct input features for the linear classifier.

pith-pipeline@v0.9.1-grok · 5805 in / 1211 out tokens · 25373 ms · 2026-06-27T10:21:06.253498+00:00 · methodology

discussion (0)

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Reference graph

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