PhD Position on Geometry and Physics-Based Inductive Bias for Robust and Explainable Foundational Models

PhD Position: Geometry and physics-based inductive bias for robust and explainable foundational models– AI4I

Deadline

December 17th 2025 at 12 (noon – CET)

Curriculum

Hostile and Unstructured Environments (CODE 11660), Topic number 2

Hosting Institution

AI4I – The Italian Institute of Artificial Intelligence

Department

PHI Lab

Supervisor

Leonel Rozo

Contacts

Funding Scheme

This doctorate grant is fully funded by The Italian institute of Artificial Intelligence (AI4I) in collaboration with
Università degli Studi di Genova

Scholarship Amount

Fascia 4: 19,500 €/year

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

1. A. Testa et al. "Geometric Contact Flows: Contactomorphisms for Dynamics and Control", ICML, 2025.

2. N. He, et al. "Beyond Euclidean: Foundation Models Should Embrace Non-Euclidean Geometries", arXiv, 2025.

3. H. Ding et al. "Fast and Robust Visuomotor Riemannian Flow Matching Policy", Transactions on Robotics, 2025.

Number of Positions Available

1

Application Documents

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

Main Research Site

AI4I –
The Italian Institute of Artificial Intelligence

Corso Castelfidardo 22, 10129 Torino, Italy

What We Offer

• Joint supervision between
  AI4I
  and
  Università degli Studi di Genova.
• 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 conference and Winter/Summer schools.

Start Date

1st March 2026

How to Apply

Applications for this position are managed by
Università degli Studi di Genova
.

Please apply via the university's official PhD admissions portal:

For More Information

https://drim.i-

About AI4I

AI4I – The Italian Research Institute for Artificial Intelligence

AI4I 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.