Earth observation embeddings are effective sub-grid descriptors for probabilistic weather downscaling

Global weather reanalyses and forecasts resolve the evolving atmospheric state on coarse grids, but site-specific applications require predictions at arbitrary locations where near-surface conditions also depend on unresolved terrain and land-surface properties. Existing probabilistic downscalers address this gap using hand-crafted topographic descriptors. We ask instead whether Earth observation foundation models can provide transferable sub-grid surface representations for probabilistic weather downscaling. We augment a convolutional conditional neural process that downscales coarse ERA5 reanalysis fields at ~25 km resolution with a learned local surface descriptor, obtained by compressing a patch of TESSERA embeddings at 10 m resolution. Although these embeddings summarise surface conditions over annual timescales, they improve downscaling of instantaneous 2 m temperature and 10 m wind speed by encoding persistent surface properties that capture a location's departure from the coarse-grid atmospheric state. Across five climatically diverse regions, the embedding improves point and probabilistic skill at stations held out in both space and time, overall improving CRPS skill by 11.5% for 2 m temperature and 6.2% for 10 m wind speed. We further analyse how its contribution differs by variable, finding that topography explains more of temperature's sub-grid structure, while TESSERA provides additional surface information for wind speed. These improvements persist when the coarse input is changed from ERA5 to forecasts from the Aurora AI forecasting model, and when predicting at newly deployed stations with no regional history. To our knowledge, this is the first evidence that long-timescale Earth-observation embeddings can support short-timescale weather downscaling where sub-grid departures are systematically structured by persistent surface properties.

From Machine Learning to Large-Scale EO Products: Best Practices for Making Maps

Recent years have seen a rapid expansion in the production of large-scale geospatial maps derived from Earth observation (EO) data, driven largely by advances in machine learning (ML) and large computing infrastructure. Although the barrier to generating such maps has dropped substantially, established best practices have yet to emerge, and design decisions made early in the pipeline can quietly propagate errors into the final product. Producing a technically sound and scientifically credible product remains challenging. Choices made at every stage are tightly coupled: preprocessing decisions shape the training signal, dataset design governs what the model can learn and how reliably its performance can be assessed, and global-scale inference introduces engineering challenges in compute and data access at scale, as well as artifact mitigation. Furthermore, uncertainty quantification and independent map validation each require dedicated methodological attention that is often underestimated. This paper presents a concise, end-to-end account of the recommended practices spanning the pipeline from satellite data to an operational map product. We organize the discussion around six interconnected themes: the EO data infrastructure landscape, data selection and preprocessing, ML dataset construction and model training, uncertainty quantification, map production and distribution, and validation. This paper is a condensed version of a longer guide that provides greater depth across all stages, accessible online at ghjuliasialelli.github.io/MLEO-Maps/.

TESSERA v2: Scaling Pixel-wise Earth Foundation Models

Pixel-wise Earth-observation (EO) foundation models are now achieving state-of-the-art performance via generated spatial embeddings. However, how these models scale and how best to spend a pretraining budget remain poorly understood. We present the largest controlled scaling study for EO to date: 395 training runs on 1,024 GH200 superchips within a fixed pixel-wise Barlow Twins family, each evaluated on 15 downstream tasks. We find that pretraining loss barely predicts downstream performance (|Pearson r| < 0.2), so selecting models by loss wastes a large share of the compute. We also find that, as the training budget grows, the encoder and the data should grow together while the projector stays fixed, which gives a simple rule for allocating compute. Using this rule, we train a family of pixel-wise models (0.5B and 1B, with a 2B model in training) and distill them into compact students for embeddings-as-data deployment. The 21-million-parameter distilled TESSERA v2-1B-M in aggregate outperforms all open and proprietary models tested, some of which are orders of magnitude larger. These students produce Matryoshka representations that are inexpensive to serve: a 16-dimensional prefix keeps 92% of the full 128-dimensional performance at 1/8 of the storage. Upon completion of training we plan to release v2 global embeddings covering 2017-2025. Together, these results give a concrete, empirically grounded recipe for scaling pixel-wise EO foundation models: train large encoders, select by downstream performance, and distil into flexible student models. All code will be released at https://github.com/ucam-eo/tessera.

Epistemic Uncertainty Is Not the Reducible Kind

The standard taxonomy of predictive uncertainty defines epistemic uncertainty as the part removable by collecting more data, while the standard measure identifies it with a mutual-information term. We prove the definition and the measure are extensionally inconsistent. On an explicit construction, the measure assigns all uncertainty to the epistemic class, yet no quantity of training data reduces it. Reducibility is instead a property of the pair (uncertainty, acquisition class), and the dichotomy resolves into three parts: aleatoric, sample-reducible epistemic, and mechanism-reducible epistemic uncertainty. An exact identity for the value of an observation shows that in-distribution data never reduces mechanism-irreducible uncertainty and generically increases it. Ensemble disagreement, the deployed epistemic estimate, tracks the training procedure rather than the epistemic term. It collapses to zero beneath a positive truth under consistent training, and equals hyperparameter-scaled initialization noise under interpolation. A finite-sample falsification test and seed-swept experiments confirm the theory.

Characterizing the Representational Capacity of Neural Processes

What functions can Neural Processes represent? We analyze the representational capacity of popular NP architectures: Conditional Neural Processes (CNPs), Attentive Neural Processes (ANPs), Transformer Neural Processes (TNPs), and their latent variants. We prove these architectures form a strict hierarchy. CNP-representable functions are exactly those depending on finitely many expected features of the context distribution. ANPs strictly generalize CNPs via query-dependent reweighting, enabling kernel smoothers. ConvCNPs and ANPs are incomparable; each contains functions outside the other, separated by stationarity versus translation equivariance. TNPs with $L$ self-attention layers capture $L$-hop context interactions. For latent NPs, we show finite-dimensional latents provide coherent sampling but do not circumvent encoder limitations; matching GP posterior distributions requires latent dimension scaling with context size. These results provide a theoretical foundation for architecture selection based on task structure.

Three Costs of Amortizing Gaussian Process Inference with Neural Processes

Neural processes amortize Gaussian process inference, replacing the exact $O(n^3)$ posterior with a learned $O(n)$ map from context sets to predictive distributions. For a class of latent neural processes, we bound the Kullback--Leibler (KL) divergence between the GP and LNP predictives, decomposing it into three interpretable sources, namely label contamination as the neural process uses label values to estimate a quantity that is label-independent in the exact GP, an information bottleneck because the finite-dimensional representation cannot resolve the full context geometry, and amortization error from a single encoder network shared across all contexts. The bottleneck truncation term decays in the representation dimension $d$ as $O(e^{-cd^{2/d_x}})$ for squared-exponential kernels on $\mathbb{R}^{d_x}$ where $c > 0$ is a kernel-dependent constant and as $O(d^{-2ν/d_x})$ for Matérn-$ν$ kernels, directly linking architecture sizing to kernel smoothness and input dimension. The label contamination term is $O(1)$ in general, with only the observation-noise component decaying as $O(1/n)$, identifying a persistent cost of routing uncertainty estimation through a label-dependent representation. These results characterize the costs of amortization within the analyzed class and yield architectural recommendations to predict variance from context locations alone in the GP-amortization regime, and replace mean aggregation with second-order pooling to close the dominant amortization gap.

On the Conditioning Consistency Gap in Conditional Neural Processes

Neural processes are meta-learning models that map context sets to predictive distributions. While inspired by stochastic processes, NPs do not generally satisfy the Kolmogorov consistency conditions required to define a valid stochastic process. This inconsistency is widely acknowledged but poorly understood. Practitioners note that NPs work well despite the violation, without quantifying what this means. We address this gap by defining the conditioning consistency gap, a KL divergence measuring how much a conditional neural process's (CNP) predictions change when a point is added to the context versus conditioned upon. Our main results show that for CNPs with bounded encoders and Lipschitz decoders, the consistency gap is $O(1/n^2)$ in context size $n$, and that this rate is tight. These bounds establish the precise sense in which CNPs approximate valid stochastic processes. The inconsistency is negligible for moderate context sizes but can be significant in the few-shot regime.

Below-ground Fungal Biodiversity Can be Monitored Using Self-Supervised Learning Satellite Features

Mycorrhizal fungi are vital to terrestrial ecosystem functioning. Yet monitoring their biodiversity at landscape scales is often unfeasible due to time and cost constraints. Current predictions suggest that 90\% of mycorrhizal diversity hotspots remain unprotected, opening questions of how to broadly and effectively map underground fungal communities. Here, we show that self-supervised learning (SSL) applied to satellite imagery can predict below-ground ectomycorrhizal fungal richness across diverse environments. Our models explain over half the variance in species richness across ~12,000 field samples spanning Europe and Asia. SSL-derived features prove to be the single most informative predictor, subsuming the majority of information contained in climate, soil, and land cover datasets. Using this approach, we achieve a 10,000-fold increase in spatial resolution over existing techniques, moving from 1km landscape averages to 10m habitat-scale observations with nearly no systematic bias. As satellite observations are dynamic rather than static, this enables temporal monitoring of below-ground biodiversity at landscape scales for the first time. We analyze multi-year trends in predicted fungal richness across UK National Park woodlands, finding that ancient forests may be losing ectomycorrhizal diversity at disproportionate rates. These results establish SSL satellite features as a scalable tool for extending sparse field observations to continuous, high-resolution biodiversity maps for monitoring the invisible half of terrestrial ecosystems.

Spatiotemporal Interpolation of GEDI Biomass with Calibrated Uncertainty

Monitoring deforestation-driven carbon emissions requires both spatially explicit and temporally continuous estimates of aboveground biomass density (AGBD) with calibrated uncertainty. NASA's Global Ecosystem Dynamics Investigation (GEDI) provides reliable LIDAR-derived AGBD, but its orbital sampling causes irregular spatiotemporal coverage, and occasional operational interruptions, including a 13-month hibernation from March 2023 to April 2024, leave extended gaps in the observational record. Prior work has used machine learning approaches to fill GEDI's spatial gaps using satellite-derived features, but temporal interpolation of biomass through unobserved periods, particularly across active disturbance events, remains largely unaddressed. Moreover, standard ensemble methods for biomass mapping have been shown to produce systematically miscalibrated prediction intervals. To address these gaps, we extend the Attentive Neural Process (ANP) framework, previously applied to spatial biomass interpolation, to jointly sparse spatiotemporal settings using geospatial foundation model embeddings. We treat space and time symmetrically, empirically validating a form of space-for-time substitution in which observations from nearby locations at other times inform predictions at held-out periods. Our results demonstrate that the ANP produces well-calibrated uncertainty estimates across disturbance regimes, supporting its use in Measurement, Reporting, and Verification (MRV) applications that require reliable uncertainty quantification for forest carbon accounting.

Knowledge Divergence and the Value of Debate for Scalable Oversight

AI safety via debate and reinforcement learning from AI feedback (RLAIF) are both proposed methods for scalable oversight of advanced AI systems, yet no formal framework relates them or characterizes when debate offers an advantage. We analyze this by parameterizing debate's value through the geometry of knowledge divergence between debating models. Using principal angles between models' representation subspaces, we prove that the debate advantage admits an exact closed form. When models share identical training corpora, debate reduces to RLAIF-like where a single-agent method recovers the same optimum. When models possess divergent knowledge, debate advantage scales with a phase transition from quadratic regime (debate offers negligible benefit) to linear regime (debate is essential). We classify three regimes of knowledge divergence (shared, one-sided, and compositional) and provide existence results showing that debate can achieve outcomes inaccessible to either model alone, alongside a negative result showing that sufficiently strong adversarial incentives cause coordination failure in the compositional regime, with a sharp threshold separating effective from ineffective debate. We offer the first formal connection between debate and RLAIF, a geometric foundation for understanding when adversarial oversight protocols are justified, and connection to the problem of eliciting latent knowledge across models with complementary information.