Fatemeh

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.

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.

Fatemeh, Nourzad, Amirhossein Roknilamouki et al.

Aligning Large Language Models (LLMs) with human values often involves balancing multiple, conflicting objectives such as helpfulness and harmlessness. Training these models is computationally intensive, and centralizing the process raises significant data privacy concerns. Federated Learning (FL) offers a compelling alternative, but existing Federated Multi-Objective Optimization (FMOO) methods face severe communication bottlenecks as their reliance on transmitting multiple gradients to a server is unscalable for large models. We introduce FIRM (Federated In-client Regularized Multi-objective alignment), a novel algorithm that achieves both client disagreement drift mitigation and communication efficiency. In FIRM, each client locally solves a regularized multi-objective optimization problem. By directly mitigating client disagreement drift through in-client regularization, our method eliminates the need for the multi-gradient transmissions common in prior works. Consequently, clients need only to transmit a single set of adapted parameters, maintaining high communication efficiency. We prove that our algorithm converges to Pareto-stationary points and, to our knowledge, provide the first finite-time convergence guarantees for this federated multi-objective alignment setting. Empirically, we show that FIRM leads to smoother training dynamics, reduced client disagreement drift, and improved reward trade-offs compared to baselines. We further propose a method to incorporate a preference over the objectives and report empirical Pareto plots, demonstrating that FIRM can smoothly adapt trade-offs between objectives in response to specified preferences.