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.

Why Is RLHF Alignment Shallow? A Gradient Analysis

Why is safety alignment in LLMs shallow? We prove that gradient-based alignment inherently concentrates on positions where harm is decided and vanishes beyond. Using a martingale decomposition of sequence-level harm, we derive an exact characterization of alignment gradients. The gradient at position $t$ equals the covariance between the conditional expected harm and the score function. This implies that positions beyond the harm horizon where the output's harmfulness is already determined receive zero gradient signal during training. This explains empirical observations that KL divergence between aligned and base models concentrates on early tokens. Consequently, standard alignment objectives cannot produce deep alignment, regardless of optimization quality. We introduce the concept of harm information $I_t$, which quantifies each position's influence on harm, and prove that equilibrium KL divergence tracks this quantity. Finally, we derive an objective based on recovery penalties that creates gradient signal at all positions, providing theoretical grounding for empirically successful data augmentation techniques.

Why Does RLAIF Work At All?

Reinforcement Learning from AI Feedback (RLAIF) enables language models to improve by training on their own preference judgments, yet no theoretical account explains why this self-improvement seemingly works for value learning. We propose the latent value hypothesis, that pretraining on internet-scale data encodes human values as directions in representation space, and constitutional prompts elicit these latent values into preference judgments. We formalize this intuition under a linear model where the constitution acts as a projection operator selecting value-relevant directions. Our analysis yields several results. RLAIF improves alignment when the constitution-activated direction correlates with true values better than the model's default generation direction thus explaining the generation-judgment gap; the ceiling on RLAIF quality is determined by how well representations encode values, which scales with model capacity; and adversarial constitutions exist that can activate anti-social value directions encoded from harmful pretraining data. Our account unifies scattered empirical findings including the refusal direction, low-rank safety subspaces, and RLAIF scaling behavior.

Calibrated Probabilistic Interpolation for GEDI Biomass

Reliable wall-to-wall biomass mapping from NASA's GEDI mission requires interpolating sparse LiDAR observations across heterogeneous landscapes. While machine learning approaches like Random Forest and XGBoost are standard for this task, they treat spatial predictions of GEDI observations from multispectral or SAR remote sensing data as independent without adapting to the varying difficulty of heterogeneous landscapes. We demonstrate these approaches generally fail to produce calibrated prediction intervals. We identify that this stems from conflating ensemble variance with aleatoric uncertainty and ignoring local spatial context. To resolve this, we introduce Attentive Neural Processes (ANPs), a probabilistic meta-learning framework that explicitly conditions predictions on local observation sets and geospatial foundation model embeddings. Unlike static ensembles, ANPs learn a flexible spatial covariance function, allowing uncertainty estimates to expand in complex landscapes and contract in homogeneous areas. We validate this approach across five distinct biomes ranging from Tropical Amazonian forests to Boreal and Alpine ecosystems, demonstrating that ANPs achieve competitive accuracy while maintaining near-ideal uncertainty calibration. We demonstrate the operational utility of the method through few-shot adaptation, where the model recovers most of the performance gap in cross-region transfer using minimal local data. This work provides a scalable, theoretically rigorous alternative to ensemble variance for continental scale earth observation.

What is Harm? Baby Don't Hurt Me! On the Impossibility of Complete Harm Specification in AI Alignment

"First, do no harm" faces a fundamental challenge in artificial intelligence: how can we specify what constitutes harm? While prior work treats harm specification as a technical hurdle to be overcome through better algorithms or more data, we argue this assumption is unsound. Drawing on information theory, we demonstrate that complete harm specification is fundamentally impossible for any system where harm is defined external to its specifications. This impossibility arises from an inescapable information-theoretic gap: the entropy of harm H(O) always exceeds the mutual information I(O;I) between ground truth harm O and a system's specifications I. We introduce two novel metrics: semantic entropy H(S) and the safety-capability ratio I(O;I)/H(O), to quantify these limitations. Through a progression of increasingly sophisticated specification attempts, we show why each approach must fail and why the resulting gaps are not mere engineering challenges but fundamental constraints akin to the halting problem. These results suggest a paradigm shift: rather than pursuing complete specifications, AI alignment research should focus on developing systems that can operate safely despite irreducible specification uncertainty.

Token Democracy: The Architectural Limits of Alignment in Transformer-Based Language Models

Modern language models paradoxically combine unprecedented capability with persistent vulnerability in that they can draft poetry yet cannot reliably refuse harmful requests. We reveal this fragility stems not from inadequate training, but from a fundamental architectural limitation: transformers process all tokens as equals. Transformers operate as computational democracies, granting equal voice to all tokens. This is a design tragically unsuited for AGI, where we cannot risk adversarial "candidates" hijacking the system. Through formal analysis, we demonstrate that safety instructions fundamentally lack privileged status in transformer architectures, that they compete with adversarial inputs in the same computational arena, making robust alignment through prompting or fine-tuning inherently limited. This "token democracy" explains why jailbreaks bypass even extensively safety-trained models and why positional shifts erode prompt effectiveness. Our work systematizes practitioners' tacit knowledge into an architectural critique, showing current alignment approaches create mere preferences, not constraints.

Who's Driving? Game Theoretic Path Risk of AGI Development

Who controls the development of Artificial General Intelligence (AGI) might matter less than how we handle the fight for control itself. We formalize this "steering wheel problem" as humanity's greatest near-term existential risk may stem not from misaligned AGI, but from the dynamics of competing to develop it. Just as a car crash can occur from passengers fighting over the wheel before reaching any destination, catastrophic outcomes could arise from development competition long before AGI exists. While technical alignment research focuses on ensuring safe arrival, we show how coordination failures during development could drive us off the cliff first. We present a game theoretic framework modeling AGI development dynamics and prove conditions for sustainable cooperative equilibria. Drawing from nuclear control while accounting for AGI's unique characteristics, we propose concrete mechanisms including pre-registration, shared technical infrastructure, and automated deterrence to stabilize cooperation. Our key insight is that AGI creates network effects in safety: shared investments become more valuable as participation grows, enabling mechanism designs where cooperation dominates defection. This work bridges formal methodology and policy frameworks, providing foundations for practical governance of AGI competition risks.