The Technical University of Denmark (DTU) - PhD scholarship in Deep Learning Theory and Differential Geometry - DTU Compute

Do you want to contribute to the understanding of modern deep learning by leveraging principles from differential geometry? 

As our new PhD student, you will study modern deep learning approaches and develop a theoretical understanding potentially based on differential geometry. In particular, deep neural networks perform surprisingly well on unseen data, a phenomenon known as generalization. However, existing machine learning theory does not fully explain this behavior, leading to the development of new approaches.

A promising explanation is that models are implicitly regularized during training, an effect attributed to the properties of the optimization technique. Intuitively, stochastic optimizers tend to converge to flatter minima in the complex loss landscape, which is believed to correlate with improved generalization. Likewise, the behavior of neural networks is influenced by architectural choices and various training techniques applied during learning, known as inductive bias.

The goal of this project is to investigate these concepts potentially based on differential geometry, providing a new theoretical framework and developing practical methodologies accordingly.

Approval and Enrolment 
The scholarship for the PhD degree is subject to academic approval, and the candidate will be enrolled in one of the general degree programmes at DTU. For information about our enrolment requirements and the general planning of the PhD study programme, please see DTU's rules for the PhD education.

Assessment
The assessment of the candidates will be made by associate professor Georgios Arvanitidis.

We offer
DTU is a leading technical university globally recognized for the excellence of its research, education, innovation and scientific advice. We offer a rewarding and challenging job in an international environment. We strive for academic excellence in an environment characterized by collegial respect and academic freedom tempered by responsibility.

Salary and appointment terms 
The appointment will be based on the collective agreement with the Danish Confederation of Professional Associations. The allowance will be agreed upon with the relevant union. 

The period of employment is 3 years. Starting date is 1 September 2025 according to the mutual agreement. The position is full-time.

You can read more about career paths at DTU here.

Further information
Further information may be obtained from Georgios Arvanitidis, gear@dtu.dk, www2.compute.dtu.dk/~gear/. 

You can read more about DTU Compute at www.compute.dtu.dk. 

If you are applying from abroad, you may find useful information on working in Denmark and at DTU at DTU – Moving to Denmark. Furthermore, you have the option of joining our monthly free seminar “PhD relocation to Denmark and startup “Zoom” seminar” for all questions regarding the practical matters of moving to Denmark and working as a PhD at DTU.

Application procedure 
Your complete online application must be submitted no later than 31 May 2025 (23:59 Danish time). Applications must be submitted as one PDF file containing all materials to be given consideration. To apply, please open the link "Apply now", fill out the online application form, and attach all your materials in English in one PDF file. The file must include:

• A letter motivating the application (cover letter)
• Curriculum vitae
• Grade transcripts and BSc/MSc diploma (in English) including official description of grading scale

You may apply prior to obtaining your master's degree but cannot begin before having received it.

Applications received after the deadline will not be considered.

All interested candidates irrespective of age, gender, disability, race, religion or ethnic background are encouraged to apply. As DTU works with research in critical technology, which is subject to special rules for security and export control, open-source background checks may be conducted on qualified candidates for the position.

DTU Compute
DTU Compute – Department of Mathematics and Computer Science – is an internationally recognised academic environment with over 400 employees and 10 research sections. We broadly cover digital technologies within mathematics, data science, computer science, and computer engineering, including artificial intelligence (AI), machine learning, internet of things (IoT), chip design, cybersecurity, human-computer interaction, social networks, fairness, and data ethics. Our research is rooted in basic research and centres on mathematical models of the physical and virtual world, as a basis for the analysis, design, and implementation of complex systems. We focus on ensuring that our research results contribute to creating a better society by supporting areas such as health, green transition, energy supply, and life science. We collaborate with universities, public and private organisations, and companies in Denmark and abroad, and through DTU’s startup ecosystem, we encourage innovation and entrepreneurship. We have a strong ethical, human, and sustainable approach that ensures integrity in our work. Therefore, we strive for and take responsibility for driving the democratisation of digital technologies, so that everyone has the opportunity to actively participate in the development, and we ensure a continued open, democratic, and inclusive society for the benefit of all. At DTU Compute, we value diversity, inclusion, and a flexible work-life balance. Read more about us at www.compute.dtu.dk.

Section for Cognitive Systems
The position is in the Section for Cognitive Systems at DTU Compute, the Technical University of Denmark, which is an internationally renowned group for machine learning research, aiming for the highest quality research. Collaboration within the group and with other international groups is encouraged. Both salary and working conditions are excellent, and the group emphasizes a healthy work/life balance, while Denmark is known for high living standards. You can find more information at Section for Cognitive Systems – DTU Compute.

Technology for people
DTU develops technology for people. With our international elite research and study programmes, we are helping to create a better world and to solve the global challenges formulated in the UN’s 17 Sustainable Development Goals. Hans Christian Ørsted founded DTU in 1829 with a clear mission to develop and create value using science and engineering to benefit society. That mission lives on today. DTU has 13,500 students and 6,000 employees. We work in an international atmosphere and have an inclusive, evolving, and informal working environment. DTU has campuses in all parts of Denmark and in Greenland, and we collaborate with the best universities around the world.

Responsibilities and qualifications
The nature of this project suggests that you should have a strong interest in the mathematical and theoretical aspects of machine learning. A solid background in mathematics (e.g., linear algebra, statistics, optimization, and calculus) is expected, along with programming experience using deep learning frameworks in Python (e.g., PyTorch). While prior knowledge of machine learning and differential geometry is appreciated, it is not strictly required. Beyond technical skills, curiosity and motivation to learn new concepts are essential.

You must have a two-year master's degree (120 ECTS points) or a similar degree with an academic level equivalent to a two-year master's degree.