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.