Dresden 2026 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 14: Focus Session: Physics of AI I (joint session SOE/DY)
SOE 14.3: Vortrag
Donnerstag, 12. März 2026, 10:15–10:30, GÖR/0226
How to describe high-dimensional statistics by diagrammatic expansions around non-Gaussian theories — •Tobias Kühn, Gabriel Mahuasa, and Ulisse Ferrari — stitut de la Vision, Sorbonne Université, CRNS, INSERM, 17 rue Moreau, 75012 Paris, France
Approximations for entropies and free energies are at the core of many techniques for the analysis of high-dimensional data, for example message-passing algorithms. For the problem of extensive- rank matrix factorization, e.g., the corresponding free energy has recently been computed by means of a high-temperature expansion around a non-Gaussian theory (Maillard et al. 2022). Their results, however, were partly inconclusive, notably because the structure of the perturbative series was not entirely clear. Feynman diagrams are designed to solve this problem, however, non-Gaussianity has mostly prevented their use. We lift this restriction in our novel framework (Kühn & Helias 2018, Kühn & van Wijland 2023, Kühn 2026).
Our first application are spins (with, in general, non-Gaussian statistics) coupled by rotationally invariant matrices (Maillard et al. 2019). We exactly compute their free energy in the thermodynamic limit as a high-temperature expansion in small couplings (Kuehn 2026), proving a conjecture from (Maillard et al. 2019). Second, we estimate the mutual-information rates transmitted by spiking neurons. Here we use that for probability distributions from the exponential family, often employed in statistics, the free energy equals the entropy - a quantity that is notoriously difficult to estimate reliably in the realm of limited data. We solve this problem by applying approximations derived by means of our diagrammatic approach (Kuehn, Mahuas, Ferrari 2025, Mahuas et al. 2023).