Reproduce “Spectral Identifiability for Interpretable Probe Geometry” on OpenResearch
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About this paper
William Hao-Cheng Huang
A new framework called the Spectral Identifiability Principle (SIP) was developed to predict the reliability of linear probes for neural network interpretability before deployment. It establishes a verifiable spectral condition by linking the geometry of feature representations, specifically eigengaps, to finite-sample estimation errors and probe misclassification risk.
Key insights
- Probe instability stems from a lack of spectral identifiability, occurring when the estimation error of the feature covariance matrix (Fisher operator) exceeds its eigengap.
- A critical phase transition in probe misclassification risk is observed when the estimation error crosses the spectral gap threshold.
- Data preprocessing, specifically an optimal clipping quantile, can effectively stabilize Fisher estimation and improve probe reliability in heavy-tailed data distributions.
Summary by alphaXiv.
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