arXiv:2604.14211v1 Announce Type: cross
Abstract: This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserstein Distance and optimal transport theory. We present some of the major results and proofs that connect Ollivier-Ricci curvature with classical Ricci curvature of Riemannian manifolds, including extensions of various theoretical bounds and theorems such as Bonnet-Myers and Levy-Gromov. Then we shift to results introduced by Lin-Lu-Yau on an extension of Ollivier-Ricci curvature on graphs, as well as the work of Jost-Liu on proving various combinatorial bounds for graph Ollivier-Ricci curvature. At the end of this thesis we present novel ideas and proofs regarding extensions of these results to directed graphs, and finally applications of graph-based Ollivier-Ricci curvature to various algorithms in network science and graph machine learning.
Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control
arXiv:2604.19018v1 Announce Type: cross Abstract: Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods,



