The Mathematics of Deep Learning

深度学习的数学

• 批准号: EP/V026259/1
• 负责人: Chris Budd
• 金额: $ 427.81万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV026259%2F1
• 关键词: Mathematics; Deep; Learning; Mathematics; Deep; Learning

Machine learning (ML), in particular Deep Learning (DL) is one of the fastest growing areas of modern science and technology, which has potentially enormous and transformative impact on all areas of our life. The applications of DL embrace many disciplines such as (bio-)medical sciences, computer vision, the physical sciences, the social sciences, speech recognition, gaming, music and finance. DL based algorithms are now used to play chess and GO at the highest level, diagnose illness, drive cars, recruit staff and even make legal judgements. The possible applications in the future are almost unlimited. Perhaps DL methods will be used in the future to predict the weather and climate, of even human behaviour. However, alongside this explosive growth has been a concern that there is a lack of explainability behind DL and the way that DL based algorithms make their decisions. This leads to a lack of trustworthiness in the use of the algorithms. A reason for this is that the huge successes of deep learning is not well understood, the results are mysterious, and there is a lack of a clear link between the data training DL algorithms (which is often vague and unstructured) and the decisions made by these algorithms. Part of the reason for this is that DL has advanced so fast, that there is a lack of understanding of its foundations. According to the leading computer scientist Ali Rahimi at NIPS 2017: 'We say things like "machine learning is the new electricity". I'd like to offer another analogy. Machine learning has become alchemy!'Indeed, despite the roots of ML lying in mathematics, statistics and computer science there currently is hardly any rigorous mathematical theory for the setup, training and application performance of deep neural networks. We urgently need the opportunity to change machine learning from alchemy into science. This programme grant aims to rise to this challenge, and, by doing so, to unlock the future potential of artificial intelligence. It aims to put deep learning onto a firm mathematical basis, and will combine theory, modelling, data, computation to unlock the next generation of deep learning.The grant will comprise an interlocked set of work packages aimed to address both the theoretical development of DL (so that it becomes explainable) and the algorithmic development (so that it becomes trustworthy). These will then be linked to the development of DL in a number of key application areas including image processing, partial differential equations and environmental problems. For example we will explore the question of whether it is possible to use DL based algorithms to forecast the weather and climate faster and more accurately than the existing physics based algorithms.The investigators on the grant will be doing both theoretical investigations and will work with end-users of DL in many application areas. Mindful that policy makers are trying to address the many issues raised by DL, the investigators will also reach out to them through a series of workshops and conferences. The results of the work will also be presented to the public at science festivals and other open events.

机器学习（ML），尤其是深度学习（DL）是现代科学和技术增长最快的领域之一，它对我们生活的所有领域都具有巨大和变革性的影响。 DL的应用包括许多学科，例如（生物 - ）医学科学，计算机视觉，物理科学，社会科学，语音识别，游戏，音乐和金融。现在，基于DL的算法被用来下棋并以最高水平诊断疾病，驾驶汽车，招聘人员，甚至做出法律判断。将来可能的应用几乎是无限的。也许将来将使用DL方法来预测人类行为的天气和气候。但是，与这种爆炸性增长一起，人们一直担心DL背后缺乏解释性以及基于DL的算法做出决定的方式。这导致使用算法缺乏可信赖性。这样做的原因是，深度学习的巨大成功尚不清楚，结果是神秘的，并且数据培训DL算法（通常是模糊且非结构化的）与这些算法做出的决定之间缺乏明确的联系。这样做的一部分原因是，DL进步如此之快，以至于对其基础缺乏了解。根据NIPS 2017年领先的计算机科学家阿里·拉希米（Ali Rahimi）的说法：“我们说“机器学习就是新电”之类的东西。我想提供另一个类比。机器学习已经变成了炼金术！”的确，尽管ML的根源在数学，统计学和计算机科学上，但目前几乎没有任何严格的数学理论来设置，培训和应用深度神经网络。我们迫切需要机会将机器学习从炼金术转变为科学。该计划的赠款旨在提高这一挑战，并这样做，以释放人工智能的未来潜力。它的目的是将深度学习置于牢固的数学基础上，并将理论，建模，数据，计算结合起来，以解锁下一代深度学习。该赠款将构成一组互锁的工作包，旨在解决DL的理论发展（以便可以解释）和算法发展（因此它变得可信赖）。然后，这些将与许多关键应用领域的DL的开发有关，包括图像处理，部分微分方程和环境问题。例如，我们将探讨是否可以使用基于DL的算法来比现有的基于物理的算法更快，更准确地预测天气和气候的问题。赠款的研究人员将同时进行理论研究，并将在许多应用领域与DL的最终用户合作。请注意，决策者正试图解决DL提出的许多问题，调查人员还将通过一系列的研讨会和会议与他们联系。这项工作的结果还将在科学节和其他开放活动上向公众展示。