Artificial Neuroscience: metrology and engineering for Deep Learning using Linear Algebra

Synopsis: This proposal is concerned with the application of Linear Algebra in possibly the most computationally intensive and ubiquitous use of matrices today, the inner workings of Deep Neural Networks (DNNs). The Project Lead (PL) will Discipline Hop from Electronic Engineering to Mathematics to improve his understanding of Linear Algebra, including Matrix and Tensor Decomposition and Random Matrix Theory. The immersion into Mathematics paves the way for research, engineering and innovation in DNNs. The work is structured as a learning phase followed by a phase for initial studies that pave the way for a larger, follow up grant. As Deep Learning "artificial brains" continually get larger and more sophisticated, the humans that create them increasingly struggle to fully understand them. Yet, as these machines are deployed more and more in society, that understanding becomes ever more vital. As deployments and applications of DNNs diversify and spread throughout society, ways to reliably construct these artificial brains have become essential, as have improved techniques for their evaluation. This sets the context for our aims and objectives. There are two main challenges: one is concerned with creating tools to probe and understand the workings of AI's artificial brains; the other is to develop reliable engineering practices needed to democratise AI, so that its benefits can be widely applied, with confidence. This proposal addresses these needs: it explores recent literature and argues that, in order to be well positioned to prepare a comprehensive research programme (as a future, larger proposal), the PL needs to update his coding skills and learn new mathematics. This will be followed by pilot studies to prove ideas and develop research protocols for studies of this increasingly important subject. We coin the term Artificial Neuroscience (AN) to encompass techniques for the examination and understanding of the inner workings of vast systems of interacting artificial neurons. With measurement and understanding comes the capability to control and engineer DNNs, which is the bigger vision behind this proposal, and which this preliminary work prepares for. From one perspective, the proposal falls under the umbrella term Explainable AI (XAI). Yet this work is not about investigating black boxes post-hoc. Rather it is concerned first with understanding 'open' boxes, and then with re-structuring those boxes' component parts (primarily the weight matrices) to gain improved performance, increased reliability and more principled engineering. Currently, there is no capability in the UK for exploring DL models in this way that is known to the proposal team. Thus it might be argued that development of such tools is strategically important for the UK to attain its aspiration to become an AI Powerhouse. Where appropriate, the research grounds its studies in music source separation for several reasons: the PL has a solid background in this topic; there are excellent existing models, datasets and frameworks; music and audio signals exhibit strong correlations in time and frequency, this property being suggestive of compact structures in DL models. As almost all related studies to date (see Approach) are confined to toy examples, or address Computer Vision or Natural Language Processing, addressing audio should bring new insights.