Albert Kjøller Jacobsen

Johanna Marie Gegenfurtner, Albert Kjøller Jacobsen, Naima Elosegui Borras et al.

Modern generative models can produce realistic samples, however, balancing memorisation and generalisation remains an open problem. We approach this challenge from a Bayesian perspective by focusing on the parameter space of flow matching and diffusion models and constructing a predictive posterior that better captures the variability of the data distribution. In particular, we capture the geometry of the loss using a Riemannian metric and leverage a flexible approximate posterior that adapts to the local structure of the loss landscape. This approach allows us to sample generative models that resemble the original model, but exhibit reduced memorisation. Empirically, we demonstrate that the proposed approach reduces memorisation while preserving generalisation. Further, we provide a theoretical analysis of our method, which explains our findings. Overall, our work illustrates how considering the geometry of the loss enables effective use of the parameter space, even for complex high-dimensional generative models.

Albert Kjøller Jacobsen, Leo Uhre Jakobsen, Johanna Marie Gegenfurtner et al.

The minima of modern neural network loss functions are typically not isolated, rather they form connected components of reparameterization invariant solutions on the training data. Analytically characterizing these solutions is a hard problem, but sampling approaches are feasible. By construction, existing methods either spread over low-loss regions, and thus do not sample reparameterization invariant solutions exactly, or are inherently local, which limits exploration of other minima valleys. We propose sampling such reparameterization invariant models using a dynamical system based on kinetic energy, subject to a gravitational pull and a friction term that dissipates energy from the system. Our proposed sampler, DiMS, is guaranteed to sample exactly from the minimum level sets and depends on physically motivated hyperparameters which allows control over the exploration capabilities of the sampler. We consider uncertainty quantification in Bayesian inference as the motivating problem and observe improved performance compared to previously proposed approaches.

Albert Kjøller Jacobsen, Georgios Arvanitidis

Recent studies on deep neural networks show that flat minima of the loss landscape correlate with improved generalization. Sharpness-aware minimization (SAM) efficiently finds flat regions by updating the parameters according to the gradient at an adversarial perturbation. The perturbation depends on the Euclidean metric, making SAM non-invariant under reparametrizations, which blurs sharpness and generalization. We propose Monge SAM (M-SAM), a reparametrization invariant version of SAM by considering a Riemannian metric in the parameter space induced naturally by the loss surface. Compared to previous approaches, M-SAM works under any modeling choice, relies only on mild assumptions while being as computationally efficient as SAM. We theoretically argue that M-SAM varies between SAM and gradient descent (GD), which increases robustness to hyperparameter selection and reduces attraction to suboptimal equilibria like saddle points. We demonstrate this behavior both theoretically and empirically on a multi-modal representation alignment task.