人工知能で人間の直感を導くことで数学を発展させる
Alex Davies1, Petar Veličković2, Lars Buesing2
1DeepMind, London, UK. adavies@deepmind.com.
Nature
|December 2, 2021
まとめ
機械学習は,パターンを特定し,推測の形成を導くことで,数学者が新しい定理を発見するのを助けます. このAIによるアプローチは 純粋な数学の研究の進歩を加速します
科学分野:
- 純粋な数学
- 人工知能
背景:
- 数学は伝統的に推測や定理のパターン発見に依存している.
- コンピューターは1960年代から パターンの発見と推測の形成に 数学者たちを支援してきた.
- 注目すべき例は,ミレニアム賞問題であるバーチとスウィナートン・ダイヤー推論である.
研究 の 目的:
- 新しい仮説や定理を発見する数学者を支援する機械学習の方法を実証する.
- 数学的直感と発見を導くために 機械学習の枠組みを提案する.
主な方法:
- 数学的なオブジェクト間の潜在的なパターンと関係を特定するために機械学習を使用します.
- 発見したパターンを理解するために アトリビューションのテクニックを使います
- 人間の直感を導くために これらの洞察を活用し 新しい数学的推測を策定します
主要な成果:
- 機械学習によるフレームワークを純粋な数学における現在の研究課題に適用する.
- 結び目の代数学的構造と 幾何学的構造の間の新しいつながりの発見
- シンメトリックグループに対するコンビネトリアルインヴァリアンス推測によって予測された候補アルゴリズムの識別.
結論:
- 機械学習は 純粋な数学における 基本的な結果の発見に 大きく役立ちます
- 提案された枠組みは,数学者と人工知能 (AI) の間の協力を促進します.
- この協同的なアプローチは 驚くような意味のある数学問題への貢献につながります
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