Explanation: how the contrastive objective shapes the embedding space

The InfoNCE loss used here pulls together matched image-text pairs and pushes apart unmatched pairs within a batch. A few points worth making explicit:

1. Temperature (τ in Eq. 1) controls how peaked the distribution is over negatives. Lower τ → harder negatives get more gradient, but training becomes unstable.
2. Batch size as implicit negative pool: with B=32k the model sees 32k−1 negatives per positive. This is why the paper emphasizes large batches — more negatives ≈ harder task ≈ better representations.
3. Alignment vs. uniformity trade-off (Wang & Isola 2020): InfoNCE implicitly optimizes both, but batch size and τ shift the balance.

This framing helps explain why smaller-batch reproductions consistently fall short — it's not just compute, it's the negative sampling regime.