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Oral
Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss
Jeff Z. HaoChen · Colin Wei · Adrien Gaidon · Tengyu Ma

Wed Dec 08 08:40 AM -- 08:55 AM (PST) @
in Oral Session 3: Deep Learning »

Recent works in self-supervised learning have advanced the state-of-the-art by relying on the contrastive learning paradigm, which learns representations by pushing positive pairs, or similar examples from the same class, closer together while keeping negative pairs far apart. Despite the empirical successes, theoretical foundations are limited -- prior analyses assume conditional independence of the positive pairs given the same class label, but recent empirical applications use heavily correlated positive pairs (i.e., data augmentations of the same image). Our work analyzes contrastive learning without assuming conditional independence of positive pairs using a novel concept of the augmentation graph on data. Edges in this graph connect augmentations of the same data, and ground-truth classes naturally form connected sub-graphs. We propose a loss that performs spectral decomposition on the population augmentation graph and can be succinctly written as a contrastive learning objective on neural net representations. Minimizing this objective leads to features with provable accuracy guarantees under linear probe evaluation. By standard generalization bounds, these accuracy guarantees also hold when minimizing the training contrastive loss. In all, this work provides the first provable analysis for contrastive learning where the guarantees can apply to realistic empirical settings.

Keywords: Theory · Deep Learning · Self-Supervised Learning · Graph Learning · Contrastive Learning · Representation Learning

Author Information

Jeff Z. HaoChen (Stanford University)
Colin Wei (Stanford University)
Adrien Gaidon (Toyota Research Institute)
Tengyu Ma (Stanford University)

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