A Proofs 421 A.1 Proof of Theorem 4.5

In the next step, we prove the uniqueness of the optimal solution. Then we construct the generalization guarantee of tri-contrastive learning. Following the proof of Theorem 4.5, we know that the optimal solutions learned by triCL are With lemma A.1, we have Based on the proof of Theorem 4.5, we know that the We first extend the augmentation graph to an asymmetric form. We adopt ResNet-18 as the backbone. And for SCL, we randomly choose 20 dimensions.