{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/deep-contrastive-learning-is-provably-almost","title":"Understanding Deep Contrastive Learning via Coordinate-wise Optimization","arxiv_id":"2201.12680","date":"2022-01-29","proceeding":null,"authors":["Yuandong Tian"],"abstract":"We show that Contrastive Learning (CL) under a broad family of loss functions (including InfoNCE) has a unified formulation of coordinate-wise optimization on the network parameter $\\boldsymbol{\\theta}$ and pairwise importance $\\alpha$, where the \\emph{max player} $\\boldsymbol{\\theta}$ learns representation for contrastiveness, and the \\emph{min player} $\\alpha$ puts more weights on pairs of distinct samples that share similar representations. The resulting formulation, called $\\alpha$-CL, unifies not only various existing contrastive losses, which differ by how sample-pair importance $\\alpha$ is constructed, but also is able to extrapolate to give novel contrastive losses beyond popular ones, opening a new avenue of contrastive loss design. These novel losses yield comparable (or better) performance on CIFAR10, STL-10 and CIFAR-100 than classic InfoNCE. Furthermore, we also analyze the max player in detail: we prove that with fixed $\\alpha$, max player is equivalent to Principal Component Analysis (PCA) for deep linear network, and almost all local minima are global and rank-1, recovering optimal PCA solutions. Finally, we extend our analysis on max player to 2-layer ReLU networks, showing that its fixed points can have higher ranks.","url_abs":"https://arxiv.org/abs/2201.12680v7","url_pdf":"https://arxiv.org/pdf/2201.12680v7.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"deep-contrastive-learning-is-provably-almost","repo_url":"https://github.com/facebookresearch/luckmatters","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"contrastive-learning","task_name":"Contrastive Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[{"method_slug":"contrastive-learning","method_name":"Contrastive Learning"},{"method_slug":"infonce","method_name":"InfoNCE"},{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2201.12680","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2201.12680"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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