Advancing mathematics by guiding human intuition with AI.

The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures1, most famously in the Birch and Swinnerton-Dyer conjecture2, a Millennium Prize Problem3. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning-demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups4. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning.

Clinically Applicable Segmentation of Head and Neck Anatomy for Radiotherapy: Deep Learning Algorithm Development and Validation Study.

BACKGROUND: Over half a million individuals are diagnosed with head and neck cancer each year globally. Radiotherapy is an important curative treatment for this disease, but it requires manual time to delineate radiosensitive organs at risk. This planning process can delay treatment while also introducing interoperator variability, resulting in downstream radiation dose differences. Although auto-segmentation algorithms offer a potentially time-saving solution, the challenges in defining, quantifying, and achieving expert performance remain. OBJECTIVE: Adopting a deep learning approach, we aim to demonstrate a 3D U-Net architecture that achieves expert-level performance in delineating 21 distinct head and neck organs at risk commonly segmented in clinical practice. METHODS: The model was trained on a data set of 663 deidentified computed tomography scans acquired in routine clinical practice and with both segmentations taken from clinical practice and segmentations created by experienced radiographers as part of this research, all in accordance with consensus organ at risk definitions. RESULTS: We demonstrated the model's clinical applicability by assessing its performance on a test set of 21 computed tomography scans from clinical practice, each with 21 organs at risk segmented by 2 independent experts. We also introduced surface Dice similarity coefficient, a new metric for the comparison of organ delineation, to quantify the deviation between organ at risk surface contours rather than volumes, better reflecting the clinical task of correcting errors in automated organ segmentations. The model's generalizability was then demonstrated on 2 distinct open-source data sets, reflecting different centers and countries to model training. CONCLUSIONS: Deep learning is an effective and clinically applicable technique for the segmentation of the head and neck anatomy for radiotherapy. With appropriate validation studies and regulatory approvals, this system could improve the efficiency, consistency, and safety of radiotherapy pathways.

Clinically applicable deep learning for diagnosis and referral in retinal disease.

The volume and complexity of diagnostic imaging is increasing at a pace faster than the availability of human expertise to interpret it. Artificial intelligence has shown great promise in classifying two-dimensional photographs of some common diseases and typically relies on databases of millions of annotated images. Until now, the challenge of reaching the performance of expert clinicians in a real-world clinical pathway with three-dimensional diagnostic scans has remained unsolved. Here, we apply a novel deep learning architecture to a clinically heterogeneous set of three-dimensional optical coherence tomography scans from patients referred to a major eye hospital. We demonstrate performance in making a referral recommendation that reaches or exceeds that of experts on a range of sight-threatening retinal diseases after training on only 14,884 scans. Moreover, we demonstrate that the tissue segmentations produced by our architecture act as a device-independent representation; referral accuracy is maintained when using tissue segmentations from a different type of device. Our work removes previous barriers to wider clinical use without prohibitive training data requirements across multiple pathologies in a real-world setting.