Code for the NeurIPS 2019 paper: Topology-Preserving Deep Image Segmentation
DMT codes for the ICLR 2021 paper: Topology-Aware Segmentation Using Discrete Morse Theory
Computing Betti numbers from simplicial complexes.
Structure-Aware Image Segmentation with Homotopy Warping
Codes for the ICLR 2022 paper: Trigger Hunting with a Topological Prior for Trojan Detection
a mathematica notebook for computing homology groups of the vietoris-rips simplicial complex over the Z_2 ring
Topological Early Warning Signals for Flash Crashes: A Proof-of-Concept using Topological Data Analysis (TDA) and Persistent Homology to detect structural market fragility and liquidity voids in Limit Order Books before a crash occurs.
Multi-agent system for automated discovery of Betti numbers and Euler characteristic from triangulated surface data. GF(2) chain-complex features + cooperative REINFORCE agents + certified Lean 4 provability oracle.
Detecting Topological Precursors to Technological Breakthroughs in the USPTO Patent Citation Network. Persistent homology applied to 8.4M patents and 118M citations.
Topology and geometry of Transformer hidden states via persistent homology. The manifold is a 1D arc (PC1=norm, r=0.999), not a torus or sphere. PC2=position, PC3=surprisal+POS. Validated up to 40B.
Betti Numbers for a Sub-Level Set of Volumetric Scalar Data
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