Who Guards the Guardians? The Challenges of Evaluating Identifiability of Learned Representations
This work addresses a critical issue for researchers and practitioners in machine learning who rely on identifiability evaluation, highlighting incremental improvements in methodology.
The paper tackles the problem that standard metrics for evaluating identifiability in representation learning can fail when their implicit assumptions about data and encoders are violated, leading to misleading results, and it introduces a taxonomy and evaluation suite to address this.
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.