Bringing Generative Learning to Representation Learning: Self-Supervised Transfer Learning as Distribution Matching

arXiv:2502.14424v3 Announce Type: replace-cross Abstract: Most self-supervised learning objectives defend against collapse but leave the target representation law unspecified. We formulate representation learning as Distribution Matching (DM), learning an augmentation-invariant encoder whose induced law matches an explicit geometric reference. The reference law specifies what the learned representation distribution should look like, whereas a separately chosen discrepancy determines how deviations from this target are measured; here we use Mallows distance. The DM framework reveals a directional inverse: generative learning maps a tractable reference to data, whereas representation learning maps data to a designed reference law. We connect the population objective to class-centre separation and classification error and prove a non-asymptotic neural-sieve guarantee. Simulations and image benchmarks show manifold rectification, fine-grained structure and transfer across label spaces.

Abstract:Most self-supervised learning objectives defend against collapse but leave the target representation law unspecified. We formulate representation learning as Distribution Matching (DM), learning an augmentation-invariant encoder whose induced law matches an explicit geometric reference. The reference law specifies what the learned representation distribution should look like, whereas a separately chosen discrepancy determines how deviations from this target are measured; here we use Mallows distance. The DM framework reveals a directional inverse: generative learning maps a tractable reference to data, whereas representation learning maps data to a designed reference law. We connect the population objective to class-centre separation and classification error and prove a non-asymptotic neural-sieve guarantee. Simulations and image benchmarks show manifold rectification, fine-grained structure and transfer across label spaces.

70 pages, 5 figures, and 6 tables. Substantially revised version with a new title, an explicit distribution-matching formulation linking generative learning and representation learning, expanded theoretical treatment, additional transfer experiments, and appendices integrated into the main file. Code is available at this https URL

Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME)

arXiv:2502.14424 [stat.ML]

(or arXiv:2502.14424v3 [stat.ML] for this version)

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Bringing Generative Learning to Representation Learning: Self-Supervised Transfer Learning as Distribution Matching

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