Who Guards the Guardians? The Challenges of Evaluating Identifiability of Learned Representations

TL;DR

This paper critically examines the limitations of current metrics for evaluating the identifiability of learned representations, revealing their assumptions and failure modes, and provides tools for more robust assessment.

Contribution

It introduces a taxonomy of assumptions underlying identifiability metrics, analyzes their validity domains, and offers an evaluation suite for stress testing these metrics.

Findings

Metrics can produce false positives and negatives when assumptions are violated.

Existing metrics are valid only under specific structural conditions.

A new evaluation suite enables reproducible stress testing of identifiability metrics.

Abstract

Identifiability in representation learning is commonly evaluated using standard metrics (e.g., MCC, DCI, R^2) on synthetic benchmarks with known ground-truth factors. These metrics are assumed to reflect recovery up to the equivalence class guaranteed by identifiability theory. We show that this assumption holds only under specific structural conditions: each metric implicitly encodes assumptions about both the data-generating process (DGP) and the encoder. When these assumptions are violated, metrics become misspecified and can produce systematic false positives and false negatives. Such failures occur both within classical identifiability regimes and in post-hoc settings where identifiability is most needed. We introduce a taxonomy separating DGP assumptions from encoder geometry, use it to characterise the validity domains of existing metrics, and release an evaluation suite for reproducible stress testing and comparison.