Leonel Aguilar

Leonel Aguilar, Jan Nagler, Christoph Hoelscher et al.

Successful deep neural networks discover salient features of data. We show when and why they fail to learn out-of-distribution (OOD)-relevant representations from an in-distribution (ID) training window. This requires decoupling feature learning from data-generating-process (DGP) identifiability. From a single training window, OOD extrapolation is non-identifiable: infinitely many DGPs are $\varepsilon$-observationally equivalent on the training data but diverge arbitrarily outside it, and no in-distribution criterion alone reliably breaks the tie. A structural commitment, the feature map, label map, and model class $(φ, ψ, \mathcal{M})$, dictates the assumed DGP and governs OOD generalization while leaving ID performance essentially unchanged. When architecture, pretraining, augmentation, input formats, or domain knowledge implicitly inject the missing commitment, the model succeeds. When it cannot infer OOD-relevant structure from ID evidence, it fails. Changing only the representation can make the same architecture, at the same in-distribution loss, differ by ${\sim}520\times$ out of distribution. When the commitment is correct and identifiable, OOD error vanishes. For example, Fourier coordinates turn periodic extrapolation into interpolation on $\mathbb{S}^1$. The same mechanism predicts outcomes in three natural-science settings (mass-action chemistry; Kepler's-third-law exoplanet prediction, $n=2{,}362$; and cross-species coding-DNA detection) and in a 264-run positional-encoding study across Transformer, Mamba, and S4D. Finally, a controlled study shows: correct features are necessary but not sufficient. The model class must express the target, and the transformed training data must cover the relevant representation space.

Jascha Grübel, Tyler Thrash, Leonel Aguilar et al.

Smart Cities already surround us, and yet they are still incomprehensibly far from directly impacting everyday life. While current Smart Cities are often inaccessible, the experience of everyday citizens may be enhanced with a combination of the emerging technologies Digital Twins (DTs) and Situated Analytics. DTs represent their Physical Twin (PT) in the real world via models, simulations, (remotely) sensed data, context awareness, and interactions. However, interaction requires appropriate interfaces to address the complexity of the city. Ultimately, leveraging the potential of Smart Cities requires going beyond assembling the DT to be comprehensive and accessible. Situated Analytics allows for the anchoring of city information in its spatial context. We advance the concept of embedding the DT into the PT through Situated Analytics to form Fused Twins (FTs). This fusion allows access to data in the location that it is generated in an embodied context that can make the data more understandable. Prototypes of FTs are rapidly emerging from different domains, but Smart Cities represent the context with the most potential for FTs in the future. This paper reviews DTs, Situated Analytics, and Smart Cities as the foundations of FTs. Regarding DTs, we define five components (Physical, Data, Analytical, Virtual, and Connection environments) that we relate to several cognates (i.e., similar but different terms) from existing literature. Regarding Situated Analytics, we review the effects of user embodiment on cognition and cognitive load. Finally, we classify existing partial examples of FTs from the literature and address their construction from Augmented Reality, Geographic Information Systems, Building/City Information Models, and DTs and provide an overview of future direction