Critical Loci and Their Singularities in Quantum Machine Learning

Given their importance for classical models of statistical learning, we aim to analyse the role
of singularities in quantum machine learning. This will be done by a mixture of theoretical
and practical approaches. In order to make this feasible in the limited timeframe of six weeks
there will be a strong emphasis on specific examples such as mixture models or Bayesian
networks that are known to be singular from a classical perspective. On the theoretical
level we will look at natural notions of loss functions and parametrizations and try to analyse
the asymptotic behaviour of relevant generating functions. On the practical level we will
implement these examples as machine learning problems on a quantum computer with the
goal to verify the theoretical predictions.

Saleh Naghdi

The University of Melbourne

Saleh is an avid undergraduate student and a holder of the prestigious Melbourne Chancellor’s Scholarship at The University of Melbourne. Following his completion of the Victorian Certification of Education (VCE) in 2018, Saleh was recognised as one of the 23 Top All-Round VCE High-Achievers in the state by the Honourable Daniel Andrews, Premier of Victoria. He subsequently received a formal invitation to Government House for his academic achievements by the Honourable Linda Dessau, Governor of Victoria.

Now studying mathematical physics and computer science, Saleh has a strong research interest in the field of quantum computing. In his first year of undergraduate studies, Saleh interned at CQC2T under the supervision of Dr Lloyd Hollenberg in evaluating commercially available quantum software. In the summer of 2020, he also worked as a software research intern at WEHI on incorporating deep learning algorithms to simulate fluorescent microscopy. And with the onset of school closures during the COVID-19 pandemic, he and a group of university friends established a NFP tutoring organisation dubbed Student Science Squad targeted to freely tutor students in need.

Best described as a hopeless romantic, Saleh relishes the underlying beauty of physics and hopes to ultimately devote himself to research in quantum gravity – but not before pioneering large-scale quantum computers first. He is always on the lookout for research opportunities in his field of interest.

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