PhD Position on Geometry and Physics-Based Inductive Bias for Robust and Explainable Foundational Models
Join to apply for the PhD Position on Geometry and Physics-Based Inductive Bias for Robust and Explainable Foundational Models role at AI4I.
Deadline
December 17th 2025 at 12 (noon – CET)
Hosting Institution
AI4I – The Italian Institute of Artificial Intelligence
Department
PHI Lab
Funding Scheme
This doctorate grant is fully funded by the Italian Institute of Artificial Intelligence (AI4I) in collaboration with Università degli Studi di Genova.
Position Description
The Italian Institute of Artificial Intelligence (AI4I), in collaboration with Università degli Studi di Genova, invites applications for a PhD position in Geometry and physics-based inductive bias as part of the PhD Programme in Hostile and Unstructured Environments.
Recent research highlights the promising potential of geometry-aware and physics-informed attention mechanisms, as well as the power of differential geometry in the analysis and refinement of foundational models. In this PhD thesis, we will study the properties of Riemannian embeddings in large multimodal models, and the role of different curvatures for accommodating and associating inter-connected tokens. We will design geometry-, physics- and control-based attention mechanisms to capture complex underlying perception-action interactions. These advancements may help develop new models that leverage physics-aware and curved spaces to better abstract and disentangle the information coming from multimodal perception systems in foundational models. The developed methods will be applied to general foundational models, vision-action large models for robotics, among others.
Requirements
Must have skills:

Excellent Master’s degree in computer science, physics, mathematics, electrical or mechatronics engineering, or a related field
Strong background in machine learning and robotics
Good programming skills in Python
Fluent in spoken and written English
A team player, but also can work autonomously
Experience with scientific writing

Good to have skills:

Background on (applied) differential geometry
Publication of peer-reviewed research papers

References

A. Testa et al. “Geometric Contact Flows: Contactomorphisms for Dynamics and Control”, ICML, 2025.
N. He, et al. “Beyond Euclidean: Foundation Models Should Embrace Non-Euclidean Geometries”, arXiv, 2025.
H. Ding et al. “Fast and Robust Visuomotor Riemannian Flow Matching Policy”, Transactions on Robotics, 2025.

Number of Positions Available
1
Application Documents

One-page cover letter including a short (two-paragraph) research proposal related to the PhD topic and aligned with your professional interests.
Bachelor’s and Master’s diplomas with transcripts and grades.

Main Research Site
AI4I – The Italian Institute of Artificial Intelligence
What We Offer

Access to high-performance computing resources and advanced research infrastructure.
Opportunities for international collaboration and contributions to high-impact publications.
A dynamic and interdisciplinary research environment.
Financial support for attending international conferences and Winter/Summer schools.

Start Date
1st March 2026
How to Apply
Please apply via the university’s official PhD admissions portal.
For More Information
https://drim.i-rim.it/en/admission/
About AI4I
AI4I – The Italian Research Institute for Artificial Intelligence has been founded to perform transformative, application-oriented research in Artificial Intelligence.
AI4I is set to engage and empower gifted, entrepreneurial, young researchers who commit to producing an impact at the intersection of science, innovation, and industrial transformation.
Highly competitive pay, bonus incentives, access to dedicated high-performance computing, state-of-the-art laboratories, industrial collaborations, and an ecosystem tailored to support the initiation and growth of startups stand out as some of the distinctive features of AI4I, bringing together people in a dynamic international environment.
AI4I is an Institute that aims to enhance scientific research, technological transfer, and, more generally, the innovation capacity of the Country, promoting its positive impact on industry, services, and public administration. To this end, the Institute contributes to creating a research and innovation infrastructure that employs artificial intelligence methods, with particular reference to manufacturing processes, within the framework of the Industry 4.0 process and its entire value chain. The Institute establishes relationships with similar entities and organizations in Italy and abroad, including Competence Centers and European Digital Innovation Hubs (EDIHs), so that the center may become an attractive place for researchers, companies, and start-ups.
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