Janis Keck

Lukas Silvester Barth, Fatemeh, Fahimi et al.

This work introduces IsUMap, a novel manifold learning technique that enhances data representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We present a systematic and detailed construction of a metric representation for locally distorted metric spaces that captures complex data structures more accurately than the previous schemes. Our approach addresses limitations in existing methods by accommodating non-uniform data distributions and intricate local geometries. We validate its performance through extensive experiments on examples of various geometric objects and benchmark real-world datasets, demonstrating significant improvements in representation quality.

Daniel Carlström Schad, Shrey Dixit, Janis Keck et al.

We present VIBE, a two-stage Transformer that fuses multi-modal video, audio, and text features to predict fMRI activity. Representations from open-source models (Qwen2.5, BEATs, Whisper, SlowFast, V-JEPA) are merged by a modality-fusion transformer and temporally decoded by a prediction transformer with rotary embeddings. Trained on 65 hours of movie data from the CNeuroMod dataset and ensembled across 20 seeds, VIBE attains mean parcel-wise Pearson correlations of 0.3225 on in-distribution Friends S07 and 0.2125 on six out-of-distribution films. An earlier iteration of the same architecture obtained 0.3198 and 0.2096, respectively, winning Phase-1 and placing second overall in the Algonauts 2025 Challenge.

Janis Keck, Lukas Silvester Barth, Fatemeh et al.

Fuzzy simplicial sets have become an object of interest in dimensionality reduction and manifold learning, most prominently through their role in UMAP. However, their definition through tools from algebraic topology without a clear probabilistic interpretation detaches them from commonly used theoretical frameworks in those areas. In this work we introduce a framework that explains fuzzy simplicial sets as marginals of probability measures on simplicial sets. In particular, this perspective shows that the fuzzy weights of UMAP arise from a generative model that samples Vietoris-Rips filtrations at random scales, yielding cumulative distribution functions of pairwise distances. More generally, the framework connects fuzzy simplicial sets to probabilistic models on the face poset, clarifies the relation between Kullback-Leibler divergence and fuzzy cross-entropy in this setting, and recovers standard t-norms and t-conorms via Boolean operations on the underlying simplicial sets. We then show how new embedding methods may be derived from this framework and illustrate this on an example where we generalize UMAP using Čech filtrations with triplet sampling. In summary, this probabilistic viewpoint provides a unified probabilistic theoretical foundation for fuzzy simplicial sets, clarifies the role of UMAP within this framework, and enables the systematic derivation of new dimensionality reduction methods.

Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad et al.

Many machine learning algorithms try to visualize high dimensional metric data in 2D in such a way that the essential geometric and topological features of the data are highlighted. In this paper, we introduce a framework for aggregating dissimilarity functions that arise from locally adjusting a metric through density-aware normalization, as employed in the IsUMap method. We formalize these approaches as m-schemes, a class of methods closely related to t-norms and t-conorms in probabilistic metrics, as well as to composition laws in information theory. These m-schemes provide a flexible and theoretically grounded approach to refining distance-based embeddings.