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Department of Applied Mathematics and Theoretical Physics

Congratulations to the team of mathematicians, statisticians and image processing experts from Bath, Cambridge and UCL who have been awarded a large five year Programme Grant worth £3.5M by the EPSRC on ‘The mathematics of deep learning’. This Programme Grant aims to put deep learning onto a firm mathematical basis, and will combine theory, modelling, data, and computation to help unlock the next generation of deep learning.

If you are ill, would you trust a diagnosis only made by a machine without involving a doctor? Would you be happy to fly on an aeroplane designed just from looking at previous aeroplanes, or have a weather forecast made by a machine without using the laws of physics?

Huge advances in machine learning mean that all of the above are possible either now, or in the near future. Machine learning, in particular Deep Learning (DL) based on ‘neural networks’, 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, or 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 sometimes mysterious, and there is often a lack of a clear link between the data training DL algorithms, and the decisions made by these algorithms

The research work in 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, linked to and supported by industry, including medical image processing, partial differential equations and environmental problems. For example the team 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 results of the work will be presented to the public and policy makers at science festivals and many other open events.