Quantifying and Learning Linear Symmetry-Based Disentanglement
This work addresses a gap in evaluating disentangled representations for researchers in representation learning, though it is incremental as it builds on existing LSBD formalizations.
The paper tackles the lack of a metric to quantify Linear Symmetry-Based Disentanglement (LSBD) by proposing a mathematically sound metric and a semi-supervised learning method, showing that common VAE-based methods fail to learn LSBD representations while their method and others can with limited supervision.
The definition of Linear Symmetry-Based Disentanglement (LSBD) formalizes the notion of linearly disentangled representations, but there is currently no metric to quantify LSBD. Such a metric is crucial to evaluate LSBD methods and to compare to previous understandings of disentanglement. We propose $\mathcal{D}_\mathrm{LSBD}$, a mathematically sound metric to quantify LSBD, and provide a practical implementation for $\mathrm{SO}(2)$ groups. Furthermore, from this metric we derive LSBD-VAE, a semi-supervised method to learn LSBD representations. We demonstrate the utility of our metric by showing that (1) common VAE-based disentanglement methods don't learn LSBD representations, (2) LSBD-VAE as well as other recent methods can learn LSBD representations, needing only limited supervision on transformations, and (3) various desirable properties expressed by existing disentanglement metrics are also achieved by LSBD representations.