Independent researcher working on applied algebraic topology, neural fields, and scientific computing on unified-memory hardware (AMD ROCm).
📧 nauheimer.t@gmail.com
All repositories include code and unit tests. Figures in the papers are only those reproducible from the published code; where something is still pending, the repository says so.
Spectral Inconsistency Entropy — discrete Hodge theory
A gauge-invariant entropy over the eigenspaces of the cycle-space Hodge Laplacian that measures how "spread out" the non-transitive (cyclic) part of a pairwise-comparison network is. Includes a symmetry result for complete graphs and a closed-form Dirichlet–digamma expectation under isotropic noise, checked against Monte Carlo simulation.
Cymatic Φ-NeRF — positional-encoding bandwidth in coordinate MLPs
Compares dyadic (2^k), golden-ratio (Φ^k) and Nyquist-matched frequency progressions for sinusoidal positional encodings on toy 3D fields with held-out test points (3 seeds). Main takeaway: matching the highest band to the sampling-density Nyquist limit matters most; Φ^k helps mainly because it is sub-dyadic.
Topological Barriers in GCT — algebraic geometry & complexity theory
Examines why Milnor-fiber / Betti-number comparisons of the determinant and permanent hypersurfaces do not by themselves give a separation in Geometric Complexity Theory, including the effect of padding-induced non-isolated singularities.
Plastic Transformer — test-time Hebbian plasticity
Self-attention blocks augmented with Hebbian fast-weight updates during inference for in-context adaptation.
SuperCon Zero-Copy Discovery — work in progress
Pipeline architecture for ML-guided superconductor screening on an AMD Strix Halo APU, with C++/HIP zero-copy (hipHostMallocMapped + torch::from_blob) sources and Quantum ESPRESSO v7.5 SCF inputs/outputs for five generated candidates. A measured zero-copy benchmark is pending (see the status section in the repository).