Title: Interpretable Representation Evaluation — A Spectral Principle for Probe Reliability
Primary area: interpretability and explainable AI
Keywords: probe reliability, interpretability, representation evaluation, spectral analysis, eigengap, Fisher information

Abstract: Linear probes are widely used to interpret and evaluate learned representations, yet their reliability is often questioned: probes can appear accurate in some regimes but collapse unpredictably in others. We identify the spectral mechanism behind this phenomenon and develop a spectral identifiability principle that serves as a practical diagnostic. Specifically, when the Fisher information spectrum maintains a nontrivial eigengap separating the discriminative subspace, the estimated subspace concentrates and probe accuracy remains stable; when the gap vanishes, accuracy collapses in a phase-transition manner. Our analysis connects eigengap geometry, sample size, and probe reliability through finite-sample reasoning, but framed as an interpretable criterion rather than a generic error bound. Controlled synthetic studies confirm the predicted transitions, and the framework highlights how eigenspectrum inspection can warn of unreliable probe evaluations before they mislead downstream model assessment.

TL;DR: Probe reliability follows spectral separation: clear gaps ensure trust, gap closure signals failure.