Post-Doctoral Research Visit F/M Structured matrices for geometric computations

About the HeKa team at PariSanté Campus

This postdoctoral position will be hosted within the HeKA team at PariSanté Campus and supervised by the KeOps development team: Jean Feydy (Inria, HeKA), Joan Glaunès (Université Paris Cité, MAP5) and Benjamin Charlier (INRAE, MIAT).

Based at PariSanté Campus, the HeKA team is a multidisciplinary group specializing in biomedical informatics, biostatistics, and applied mathematics for clinical decision support. The team brings together researchers, clinician-scientists, and faculty members from Inria, Inserm, Université Paris Cité, and AP-HP. It also collaborates closely with several departments of the European Hospital Georges Pompidou, Necker Hospital, and the Imagine Institute.

Benefits package

• Subsidized meals

• Comfortable budget for travel costs

• Partial reimbursement of public transport costs

• Approximately 9 weeks of paid time off per year: 7 weeks of annual leave + 10 extra days off thanks to to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)

• Possibility of teleworking and flexible organization of working hours

• Professional equipment available (videoconferencing, loan of computer equipment, etc.)

• Social, cultural and sports events and activities

• Access to vocational training

• Contribution to mutual insurance (subject to conditions)

• Gross Salary : 3,362 € per month

Scientific context

Massively parallel accelerators such as Graphics Processing Units (GPUs) now provide significant computational power at a fraction of the cost of a high-performance cluster. Providing user-friendly libraries that leverage these capabilities while remaining compatible with high-level development environments is essential for developping new methodological approach to analyze real-world datasets.

The KeOps library (https://kernel-operations.io/) (1M+ downloads) follows this approach and focuses on geometric computations based on the manipulation of distance and kernel matrices. These are widely used to compute interactions between large collections of samples, with applications that range from 3D shape processing to machine learning and computational physics.

KeOps introduces a high-level abstraction based on symbolic matrices (LazyTensors), offering a memory- and compute-efficient, transparent framework that is fully compatible with Python (NumPy, PyTorch) and R. We refer to this discussion (https://www.kernel-operations.io/keops/introduction/why_using_keops.html) for more details.

The current implementation of KeOps provides efficient acceleration for dense, tensor-like operators. However, recent advances in biological and medical imaging, such as spatial omics, are producing a new class of high-dimensional datasets with strong underlying structures, including sparsity patterns. The goal of this postdoctoral project is therefore to move beyond bruteforce dense computations and leverage these structures to enable efficient processing of high-dimensional data.

Several research directions are possible, each tied to a specific application context. Depending on your scientific profile and interests, we will be able to focus on one or more of the following:

Strategy 1: sparse neighborhood and spatial structures: generalize block-wise reduction schemes to handle sparse matrices which have few non-zero coefficients per row. Combined with the symbolic engine of the KeOps library, this could lead to very efficient routines for geometry processing.

Strategy 2: sparse, high-dimensional features: Address the computational limitations associated to high intrinsic dimensionality by developing sparse variants of the core operations used to process such datasets. A particular emphasis will be placed on efficient GPU implementations within the KeOps framework. Applications to spatial omics data can be found in [1].

Strategy 3: low rank kernel approximation: Investigate scalable approaches to kernel matrix-vector multiplication that rely on low-rank approximations, such as the Fast and Free Memory method explored in [2].

[1] xIV-LDDMM Toolkit: A Suite of Image-Varifold Based Technologies for Representing and Mapping 3D Imaging and Spatial-omics Data Simultaneously Across Scales. K. M. Stouffer et al. Nature Commun Biol

[2] Giga-scale Kernel Matrix-Vector Multiplication on GPU. R. Hu et al. NeurIps 2022

Main activities :

• Research work
• Software development
• Software documentation

• Thoroughness, with attention paid to details.

• Willingness to engage in cross-disciplinary research.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage