Measuring the alignment between representations lets us understand similarities between the feature spaces of different models, such as Vision Transformers trained under diverse paradigms. However, traditional measures for representational alignment yield only scalar values that obscure how these spaces agree in terms of learned features. To address this, we combine alignment analysis with concept discovery, allowing a fine-grained breakdown of alignment into individual concepts. This approach reveals both universal concepts across models and each representation's internal concept structure. We introduce a new definition of concepts as non-linear manifolds, hypothesizing they better capture the geometry of the featurespace. A sanity check demonstrates the advantage of this manifold-based definition over linear baselines for concept-based alignment. Finally, our alignment analysis of four different ViTs shows that increased supervision tends to reduce semantic organization in learned representations.

This work presents a data-driven approach for the indoor localization of an observer on a 2D topological map of the environment. State-of-the-art techniques may yield accurate estimates only when they are tailor-made for a specific data modality like camera-based system that prevents their applicability to broader domains. Here, we establish a modality-agnostic framework (called OT-Isomap) and formulate the localization problem in the context of parametric manifold learning while leveraging optimal transportation. This framework allows jointly learning a lowdimensional embedding as well as correspondences with a topological map. We examine the generalizability of the proposed algorithm by applying it to data from diverse modalities such as image sequences and radio frequency signals. The experimental results demonstrate decimeter-level accuracy for localization using different sensory inputs.

t-SNE has gained popularity as a dimension reduction technique, especially for visualizing data. It is well-known that all dimension reduction techniques may lose important features of the data. We provide a mathematical framework for understanding this loss for t-SNE by establishing a number of results in different scenarios showing how important features of data are lost by using t-SNE.

Nevertheless, it remains elusive that whether the Transformer-based architecture can do molecular modeling as good as equivariant GNNs.

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