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Formula to calculate Cross Domain Contrastive Loss

cdcl

For each target anchor $x$$t$$i$ with a pseudo-label $\hat{y}$$t$$i$ in a mini-batch, loss $L$$CDC$$t,i$ is calculated using the above formula.

  • $Z$$t$$i$ represents the flattened representation of the target anchor obtained from encoder + projection network.

  • $τ$ is the temperature hyper-parameter

  • $P$$s$($\hat{y}$$t$$i$) is the set of positive samples, i.e. samples from source domain with same label as the pseudo label of target anchor.

  • $Z$$s$$p$ reppresents the flattened representation of a positive sample from source domain obtained from encoder + projection network

  • $I$$s$ is the set of all samples whether positive or negative in the mini-batch.

  • The encircled formula shown below represents the Cosine-Similarity between the flattened vectors in both numerator and denominator.

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