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In practice, they yield strongly differing embeddings and can suggest conflicting interpretations of the same data. The fundamental reasons for this and, more generally, the exact relationship between $t$-SNE and UMAP have remained unclear. In this work, we uncover their conceptual connection via a new insight into contrastive learning methods. Noise-contrastive estimation can be used to optimize $t$-SNE, while UMAP relies on negative sampling, another contrastive method. We find the precise relationship between these two contrastive methods and provide a mathematical characterization of the distortion introduced by negative sampling. Visually, this distortion results in UMAP generating more compact embeddings with tighter clusters compared to $t$-SNE. We exploit this new conceptual connection to propose and implement a generalization of negative sampling, allowing us to interpolate between (and even extrapolate beyond) $t$-SNE and UMAP and their respective embeddings. Moving along this spectrum of embeddings leads to a trade-off between discrete / local and continuous / global structures, mitigating the risk of over-interpreting ostensible features of any single embedding. We provide a PyTorch implementation.","url_abs":"https://arxiv.org/abs/2206.01816v2","url_pdf":"https://arxiv.org/pdf/2206.01816v2.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":"contrastive-learning-unifies-t-sne-and-umap","repo_url":"https://github.com/hci-unihd/cl-tsne-umap","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"contrastive-learning-unifies-t-sne-and-umap","repo_url":"https://github.com/berenslab/contrastive-ne","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"contrastive-learning-unifies-t-sne-and-umap","repo_url":"https://github.com/sdamrich/cl-tsne-umap","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"contrastive-learning","task_name":"Contrastive Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"bottleneck-residual-block","method_name":"Bottleneck Residual Block"},{"method_slug":"colorjitter","method_name":"ColorJitter"},{"method_slug":"contrastive-learning","method_name":"Contrastive Learning"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"feedforward-network","method_name":"Feedforward Network"},{"method_slug":"global-average-pooling","method_name":"Global Average Pooling"},{"method_slug":"infonce","method_name":"InfoNCE"},{"method_slug":"kaiming-initialization","method_name":"Kaiming Initialization"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"nt-xent","method_name":"NT-Xent"},{"method_slug":"random-gaussian-blur","method_name":"Random Gaussian Blur"},{"method_slug":"random-resized-crop","method_name":"Random Resized Crop"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"residual-block","method_name":"Residual Block"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"simclr","method_name":"SimCLR"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2206.01816","atlas_url":"https://app.syntology.ai/?focus=2206.01816","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.01816"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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