Paper proposes identifiable alignment of unpaired model representations
Original title: Identifiable alignment of unpaired representations
Neural Gromov–Monge Alignment uses pullback distances, needs no pairs or labels, and beats reported baselines.
The paper argues that, under a stated form of the manifold hypothesis, the pullback of the data metric is a shared distance for any two models of one data-generating process, whether encoders, decoders or both. The alignment map preserves that distance and the representation distribution and is identifiable exactly when the data distribution breaks every symmetry of the data manifold, which the authors say holds generically. Their method, Neural Gromov–Monge Alignment, uses no pairs or labels and, they report, outperforms every unpaired and label-informed baseline, including on image models with different priors and single-cell models trained on disjoint cells where Euclidean distances fail.
Unconfirmed: Baseline outperformance is the authors’ reported comparison, not independently replicated here.
- Identifiability requires the data distribution to break every manifold symmetry.
- The coupling is the unique optimum of Gromov–Wasserstein under that condition.
- The linear program alone shares that optimum when distance distributions are distinct.
- The coupling is recovered exactly from permuted samples even without identifiability.
From the original article
1 min read at arxiv.orgAligning two models without paired data requires a distance that both share, yet existing methods use Euclidean or spherical geometry. This is either an arbitrary choice or imposed by their loss function. We show that, under a precise form of the manifold hypothesis, the pullback of the data metric gives such a distance for any two models of one data-generating process.
By Stas Syrota · arxiv.org
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