What does this equation mean?

Radford and colleagues’ 2021 paper, “Learning Transferable Visual Models From Natural Language Supervision,” is usually remembered simply as CLIP, and the compression loses the specific thing that made it a turning point rather than an incremental improvement. The method itself is not exotic: encode an image, encode its paired caption, and train both encoders so that the true pairing scores higher than every mismatched pairing drawn from the same batch. For a batch of B image-text pairs with normalised image embedding $u_i$ , text embedding $v_i$ , and a learned temperature $\tau$ , the symmetric form of the objective is $\mathcal{L} = -\frac{1}{2B}\sum_{i=1}^{B}\left[\log\frac{\exp(\langle u_i, v_i\rangle/\tau)}{\sum_{j=1}^{B}\exp(\langle u_i, v_j\rangle/\tau)} + \log\frac{\exp(\langle u_i, v_i\rangle/\tau)}{\sum_{j=1}^{B}\exp(\langle u_j, v_i\rangle/\tau)}\right]$. an image-to-text and a text-to-image cross-entropy averaged together, each treating every other pairing in the batch as a negative. Nothing in that objective is architecturally new; matching objectives had been used for retrieval before CLIP. What changed was scale, and what the scale was spent on: 400 million image-text pairs collected from the public internet, with no hand-assigned category label anywhere in the pipeline [ 5 ] .