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Advancing mathematics by guiding human intuition with AI.

ABSTRACT: 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.

SUBMITTER: Davies A

PROVIDER: S-EPMC8636249 | biostudies-literature | 2021 Dec

REPOSITORIES: biostudies-literature

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Advancing mathematics by guiding human intuition with AI.

Davies Alex A Veličković Petar P Buesing Lars L Blackwell Sam S Zheng Daniel D Tomašev Nenad N Tanburn Richard R Battaglia Peter P Blundell Charles C Juhász András A Lackenby Marc M Williamson Geordie G Hassabis Demis D Kohli Pushmeet P

Nature 20211201 7887

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 ...[more]

PMID: 34853458

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Project description:Artificial intelligence (AI) provides considerable opportunities to assist human work. However, one crucial challenge of human-AI collaboration is that many AI algorithms operate in a black-box manner where the way how the AI makes predictions remains opaque. This makes it difficult for humans to validate a prediction made by AI against their own domain knowledge. For this reason, we hypothesize that augmenting humans with explainable AI improves task performance in human-AI collaboration. To test this hypothesis, we implement explainable AI in the form of visual heatmaps in inspection tasks conducted by domain experts. Visual heatmaps have the advantage that they are easy to understand and help to localize relevant parts of an image. We then compare participants that were either supported by (a) black-box AI or (b) explainable AI, where the latter supports them to follow AI predictions when the AI is accurate or overrule the AI when the AI predictions are wrong. We conducted two preregistered experiments with representative, real-world visual inspection tasks from manufacturing and medicine. The first experiment was conducted with factory workers from an electronics factory, who performed [Formula: see text] assessments of whether electronic products have defects. The second experiment was conducted with radiologists, who performed [Formula: see text] assessments of chest X-ray images to identify lung lesions. The results of our experiments with domain experts performing real-world tasks show that task performance improves when participants are supported by explainable AI with heatmaps instead of black-box AI. We find that explainable AI as a decision aid improved the task performance by 7.7 percentage points (95% confidence interval [CI]: 3.3% to 12.0%, [Formula: see text]) in the manufacturing experiment and by 4.7 percentage points (95% CI: 1.1% to 8.3%, [Formula: see text]) in the medical experiment compared to black-box AI. These gains represent a significant improvement in task performance.

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Advancing mathematics by guiding human intuition with AI.

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Advancing mathematics by guiding human intuition with AI.

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