Approximation in Contrastive Representation Learning
Contrastive representation learning (CRL) is a fundamental paradigm for learning transferable representations. Recent work identifies its population target as the pointwise mutual information (PMI) $\log\frac{p(x,y)}{p_X(x)p_Y(y)}$ between two modalities $X,Y$, where $p$ is the joint density function and $p_X,p_Y$ are the marginals. However, it remains unclear why standard inner-product scores $f(x)^\top g(y)$ can effectively approximate a generally nonseparable population target PMI. In this paper, we address this question from the aspect of approximation for CRL. By linking PMI to a compact operator, we show that $D$-dimensional inner-product models perform rank-$D$ spectral approximati...
| Authors | Yuanfan Li, Zihan Zhang, Yiming Ying et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 October 2026 |
| Last updated at source | 11 October 2026 |
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