My recent research consists of three main pillars.
One of these focuses on Topological Data Analysis (TDA) and its industrial applications. I have been working on a fine-grained topological framework based on modeling domain-specific features using Cellular Sheaves and Cosheaves, which has theoretically established. Within this framework, counterfactual inconsistencies are exposed through the conjugation of higher topological invariants.
A presentation will be held during the event running from January 19 to January 21, 2026. Please check below for further information.
| Dates | January 19–21, 2026 (The exact schedule for my specific session is currently pending). |
| Official information | https://sites.google.com/view/finland-japan-workshop-iam/information |
| Location | At Tokyo Kioicho Campus of Josai University |
| Title | Spectral Identification of Logical Defects: An Inverse Problem on Cellular Sheaves |
| Abstract | In industrial systems ranging from supply chain networks to generative causal models, the “Direct Problem” is well-understood: given a consistent set of mechanisms (laws) and initial conditions, data flows harmonically across the network. The corresponding “Inverse Problem”—detecting and localizing structural contradictions (defects) based solely on noisy observed data—remains ill-posed and computationally challenging. I propose a robust topological framework for solving this inverse problem using Persistent Spectral Sheaf Theory. I model the system as a cellular sheaf over a graph, where restriction maps encode local consistency constraints (mechanisms). While standard approaches treat inconsistency as a binary satisfiability failure, I redefine it as a continuous spectral obstruction in the 1st Sheaf Cohomology group (  ), together with the 0th. I introduce the concept of “Spectral Witnesses”—eigenvectors of the Persistent Sheaf Laplacian (PSL) that localize the source of global inconsistency.Analogous to how boundary measurements in impedance tomography identify internal physical voids, the harmonic modes of the PSL identify “logical voids”—cycles where local consistency fails to integrate globally. By filtrating over a tolerance parameter, I separate transient measurement noise from persistent structural impossibilities. I demonstrate the efficacy of this method in identifying “impossible” states in counterfactual causal inference, effectively solving the inverse problem of validating complex relational data. |