Emmanuel Abbé

Anand Choudhary, Xiaowu Sun, Thabo Mahendiran et al.

Invasive Coronary Angiography (ICA) is the clinical gold standard for the assessment of coronary artery disease. However, its interpretation remains subjective and prone to intra- and inter-operator variability. In this work, we introduce ODySSeI: an Open-source end-to-end framework for automated Detection, Segmentation, and Severity estimation of lesions in ICA images. ODySSeI integrates deep learning-based lesion detection and lesion segmentation models trained using a novel Pyramidal Augmentation Scheme (PAS) to enhance robustness and real-time performance across diverse patient cohorts (2149 patients from Europe, North America, and Asia). Furthermore, we propose a quantitative coronary angiography-free Lesion Severity Estimation (LSE) technique that directly computes the Minimum Lumen Diameter (MLD) and diameter stenosis from the predicted lesion geometry. Extensive evaluation on both in-distribution and out-of-distribution clinical datasets demonstrates ODySSeI's strong generalizability. Our PAS yields large performance gains in highly complex tasks as compared to relatively simpler ones, notably, a 2.5-fold increase in lesion detection performance versus a 1-3\% increase in lesion segmentation performance over their respective baselines. Our LSE technique achieves high accuracy, with predicted MLD values differing by only $\pm$ 2-3 pixels from the corresponding ground truths. On average, ODySSeI processes a raw ICA image within only a few seconds on a CPU and in a fraction of a second on a GPU and is available as a plug-and-play web interface at swisscardia.epfl.ch. Overall, this work establishes ODySSeI as a comprehensive and open-source framework which supports automated, reproducible, and scalable ICA analysis for real-time clinical decision-making.

Kirill Brilliantov, Etienne Bamas, Emmanuel Abbé

We introduce a code-based challenge for automated, open-ended mathematical discovery based on the $k$-server conjecture, a central open problem in competitive analysis. The task is to discover a potential function satisfying a large graph-structured system of simple linear inequalities. The resulting evaluation procedure is sound but incomplete: any violated inequality definitively refutes a candidate, whereas satisfying all inequalities does not by itself constitute a proof of the corresponding conjecture's special case. Nevertheless, a candidate that passes all constraints would be strong evidence toward a valid proof and, to the best of our knowledge, no currently known potential achieves this under our formulation in the open $k=4$ circle case. As such, a successful candidate would already be an interesting contribution to the $k$-server conjecture, and could become a substantial theoretical result when paired with a full proof. Experiments on the resolved $k=3$ regime show that current agentic methods can solve nontrivial instances, and in the open $k=4$ regime they reduce the number of violations relative to existing potentials without fully resolving the task. Taken together, these results suggest that the task is challenging but plausibly within reach of current methods. Beyond its relevance to the $k$-server community, where the developed tooling enables researchers to test new hypotheses and potentially improve on the current record, the task also serves as a useful \emph{benchmark} for developing code-based discovery agents. In particular, our $k=3$ results show that it mitigates important limitations of existing open-ended code-based benchmarks, including early saturation and the weak separation between naive random baselines and more sophisticated methods.