International Postdoc Programme (CROP) will recruit researchers with a recent PhD degree (see Eligibility criteria below) for a full 18-month employment contract.

Candidates should prepare their own research proposal from the topics offered . Application form should be filled and all required documents uploaded using the dedicated electronic form.\nhelpdesk: Eligibility criteria

Experience:

PhD degree at the time of beginning of the contract\nApplicants who are close to the defense of their doctoral thesis will also be considered eligible to
maximum of 8 years experience in research, from the date of the award of their PhD degree till the time of the Call opening (June 1, 2026). Years of experience outside research and career breaks will not count towards the above maximum.
previous studies compatible with the project they intend to with

Mobility:

applicants must not have resided or carried out their main activity in the Czech Republic for more than 12 months in the 3 years prior to the Calls' deadline (career breaks not counted). Benefits and Conditions Gross monthly salary of 83 531 CZK/month

\nFamily allowance 9044 CZK/month (for applicants with dependent family members)\nTravel support for conferences and secondments\nResearch costs
The gross monthly salary CZK is under the standard scheme in the Czech Republic and includes mandatory social and health insurance.

Therefore, the gross salary contains an employee contribution to social and health insurance of 11% and it is standardly taxable (15 % rate). Some tax discounts are given to e.g. employees with children.

Example:

a single researcher would get 61 813 CZK as net salary The offered salary is equivalent to the standard MSCA individual postdoc award, and it is highly competitive (double the average salary in Czechia, the typical salary of an Associate professor) Required documents to be uploaded to the Application form webpage CV including a list of a) Invited presentations to conferences and/or international advanced schools,\nb) Organisation of International conferences (membership in the steering and/or programme committee),\nc) Prizes, Awards, and Scholarships\nd) Projects funded and/or active participation,\ne) Examples of participation in industrial innovation, if any.

List of publications:

Journal papers first, conference papers second, followed by patents.

Research proposal:

Select one of the topics offered, describe the scope, objectives and foreseen research and training activities, including cooperation with the Associated partner.

Required sections:

1) Excellence, 2) Impact incl. expected outputs of the project, 3) Quality and Efficiency of the Implementation 4), Personal motivation: description of career goals, foreseen advancement in research and professional skills of the Applicant. Consult your proposal with the respective Mentor. You are encouraged to communicate with the mentor before you submit the application. PhD diploma (or certificate of defense) Applicants should select one topic from the List of topics and prepare their own Research proposal.\nIt is recommended that the applicants contact the Mentor of the relevant topic and consult their proposal in advance. The Application form is open for modifications until the deadline. ================================================ The description of the research topic\n\"Mathematical foundations of approximation by (deep) neural networks\"\nis as follows. Recently, the extensive use of (deep) artificial neural networks reached most of the areas of society and technology. However, the theoretical understanding of their properties (and also possible limits) is unsatisfactory. With the use of neural networks also in critical applications, like security, military, health care, traffic control, finance and other areas, this represents a serious threat. The aim of this topic is to develop our understanding of artificial neural networks and of their success in high-dimensional tasks but also to explore their limitations. This modern area of mathematics is nowadays booming worldwide, attracting attention of many research communities. To be more specific, we plan

to study the approximation rates of functions from Sobolev, Besov, Barron and other function classes;
to identify new classes of functions, which allow tractable approximation by neural networks;
to study the role of fixed and adaptive architecture of neural networks for approximation of functions;
to study the identification of parameters of an existing neural network from a limited number of samples;
to employ modern tools from different areas of mathematics, like the Maurey probabilistic argument, Vapnik-Chervonenkis dimension, entropy and covering numbers to obtain also lower bounds for approximation rates achievable by neural networks.

Jan Vybíral is a full professor at the Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague. He obtained a Ph.D. degree in mathematics from Friedrich-Schiller University Jena in 2005, then he worked as postdoc at Johann Radon Institute for Computational and Applied Mathematics in Linz (Austria), at Technical University Berlin (Germany) and as Assistant Professor and Associated Professor at Charles University in Prague. He was a Guest Professor at the Faculty of Mathematics of Technical University in Munich (Germany) in 2022. He was a vice-dean for international affairs in 2021-2026. He serves as a Senior Editor of Journal of Complexity and as an Editor of Constructive Approximation and of Mathematische Nachrichten.

Publications:

60 journal papers, over 1700 citations in WoS, h-index=19 Advising experience: supervised 1 PhD student, >15 student projects and theses Main research topics: Functional analysis, numerical analysis, approximation theory, high-dimensional probability theory, mathematical aspects of machine learning, compressed sensing

Secondment:

Univ

Prof.

Dr. Philipp Grohs (University of Vienna, Faculty of Mathematics, Mathematical Data Science, Austria)

WoS:

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Mathematical foundations of approximation by (deep) neural networks