講演情報
[8a-N102-10]Geometric Stability as a Reliability Criterion for AI-Assisted Spectroscopic Inference: From Mössbauer Spectroscopy to Geometric Identifiability Theory
〇Sonia Sharmin1, Chiharu Mitsumata1, Eiji Kita1, Hideto Yanagihara1 (1.Appl. Phys., Sci. & Eng., Univ. Tsukuba)
キーワード：
Measurement Informatics、Explainable Machine Learning、Principal Component Analysis
Reliable parameter estimation challenges automated spectroscopic inference: inverse problems can become unreliable while standard goodness-of-fit metrics still indicate a good fit. We present a geometric reliability framework based on the stability of the spectral manifold. Spectra are embedded in a fixed reference frame from clean data, and noise-induced deformation is quantified by the subspace rotation angle θ—the principal angle between the sensitivity directions of parameter recovery. Crucially, θ needs neither a nonlinear fit nor ground-truth parameters: it comes directly from the embedded data in one linear-algebra step, ~600× faster than the least-squares fit it diagnoses (≈0.1 ms vs ≈60 ms), enabling real-time, high-throughput screening.Using Mössbauer spectroscopy as a model inverse problem, θ exposes parameter instability hidden from residual-based metrics: at fixed signal-to-noise the spectral residual stays at the noise floor while per-spectrum recovery error spans over two decades. Across additive Gaussian and Poisson noise, θ scales linearly with noise amplitude (inverse-square-root in total counts), and a critical threshold θ*≈0.36° separates stable from unstable inversion regimes, a calibrated basis for adaptive acquisition.We relate θ to Jacobian conditioning, Fisher-information eigenspectra, and perturbative manifold deformation. The recovery error reaches the Cramér–Rao bound, which itself diverges as the Fisher information becomes singular—confirming the instability is intrinsic to the inverse problem, not an optimizer artifact. PCA, kernel PCA, diffusion-map, and UMAP embeddings recover the same θ* and noise scaling, so the simplest, fastest (linear PCA) suffices. Geometric instability grows with inverse-problem complexity. These results establish geometric stability as an embedding-independent, interpretable measure of identifiability and a low-cost reliability criterion for automated spectroscopic inference.