Alex O. Davies
Publications
Demographically-Informed Heat-Mortality Risk Curves via Risk Graph Neural Networks
Estimating heat-related mortality risk is a core task in environmental epidemiology, typically addressed with Distributed Lag Non-linear Models (DLNMs); interpretable exposure-response surfaces fitted to temperature-mortality time series. DLNMs are effective but ignore demographic and geographic context, despite well-established relevance to heat vulnerability. We propose Risk Graph Neural Networks (RGNNs), a hierarchical GNN encoder that uses granular census features to optimise DLNM coefficient vectors, preserving interpretable risk curve outputs while substantially improving predictive calibration. Evaluated across 10 regions of England and Wales on two unprecedented heat years, RGNN variants maintain both lower point-errors and near-nominal uncertainty coverage during the 2022 heatwave where baselines collapse.
AI Co-Mathematician: Accelerating Mathematicians with Agentic AI
We introduce the AI co-mathematician, a workbench for mathematicians to interactively leverage AI agents to pursue open-ended research. The AI co-mathematician is optimized to provide holistic support for the exploratory and iterative reality of mathematical workflows, including ideation, literature search, computational exploration, theorem proving and theory building. By providing an asynchronous, stateful workspace that manages uncertainty, refines user intent, tracks failed hypotheses, and outputs native mathematical artifacts, the system mirrors human collaborative workflows. In early tests, the AI co-mathematician helped researchers solve open problems, identify new research directions, and uncover overlooked literature references. Besides demonstrating a highly interactive paradigm for AI-assisted mathematical discovery, the AI co-mathematician also achieves state of the art results on hard problem-solving benchmarks, including scoring 48% on FrontierMath Tier 4, a new high score among all AI systems evaluated.
Mind the Gap? A Distributional Comparison of Real and Synthetic Priors for Tabular Foundation Models
Tabular foundation models are pre-trained on one of three classes of corpus: curated datasets drawn from benchmark repositories, tables harvested at scale from the web, or synthetic tables sampled from a parametric generative prior. Despite the centrality of pre-training data to model performance, little is known about how these corpora relate to one another in distribution, and the impact this has on downstream performance. In this work we take three canonical, archetypal datasets used to train tabular foundation models; the T4 dataset represents web-scraped corpora, the TabFM dataset curated tables from Kaggle, and the TabICL dataset as the only well-used synthetic prior with publicly available parameters. We characterise each corpus using aggregate features over whole tables, columns and correlations, and compare them using discriminator AUCs and k-NN coverage metrics. We find that the TabICL synthetic prior occupies a narrow region of the space of real tables, that this mismatch cannot be closed by optimising prior hyper-parameters across more than 86 thousand configurations, and that curated and web-scraped corpora are broadly interchangeable on a distributional level in feature space. Surprisingly, the distributional gap between synthetic pre-training data and real tables has a clearly detectable effect on performance under neither feature-based proximity measures or TabICL's own internal representations, suggesting that coverage of the real-data distribution is not the primary driver of TabICL's generalisation.