[2405.16730] "Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2405.16730 (cs) [Submitted on 27 May 2024 ( v1 ), last revised 25 Apr 2026 (this version, v2)] Title: "Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood Authors: Peiyu Yu , Dinghuai Zhang , Hengzhi He , Xiaojian Ma , Sirui Xie , Ruiyao Miao , Yifan Lu , Yasi Zhang , Deqian Kong , Ruiqi Gao , Jianwen Xie , Guang Cheng , Ying Nian Wu View a PDF of the paper titled "Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood, by Peiyu Yu and Dinghuai Zhang and Hengzhi He and Xiaojian Ma and Sirui Xie and Ruiyao Miao and Yifan Lu and Yasi Zhang and Deqian Kong and Ruiqi Gao and Jianwen Xie and Guang Cheng and Ying Nian Wu View PDF HTML (experimental) Abstract: Noise Contrastive Estimation (NCE) has fueled major breakthroughs in representation learning and generative modeling. Yet a long-standing challenge remains: accurately estimating ratios between distributions that differ substantially, which significantly limits the applicability of NCE on modern high-dimensional and multimodal datasets. We revisit this problem from a less explored perspective: the magnitude of the noise distribution. Specifically, we show that with a virtually scaled (\ie, artificially increased) noise magnitude, the gradient of the NCE objective can closely align with that of Maximum Likelihood, enabling a trajectory-wise approximation from NCE to MLE, and faster convergence both theoretically and empirically. Building on this insight, we introduce ``Noisier'' NCE, a simple drop-in modification to vanilla NCE that incurs little to no extra computational cost, while effectively handling density-ratio estimation in challenging regimes where traditional MLE and NCE struggle. Beyond improving classical density-ratio learning, ``Noisier'' NCE proves broadly applicable: it achieves strong results across image modeling, anomaly detection, and offline black-box optimization. On CIFAR-10 and ImageNet64x64 datasets, it yields 10-step and even 1-step samplers that match or surpass state-of-the-art methods, while cutting training iterations by up to half. Comments: ICLR 2026 Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Applications (stat.AP) Cite as: arXiv:2405.16730 [cs.LG] (or arXiv:2405.16730v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2405.16730 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Peiyu Yu [ view email ] [v1] Mon, 27 May 2024 00:11:53 UTC (659 KB) [v2] Sat, 25 Apr 2026 21:17:25 UTC (1,453 KB) Full-text links: Access Paper: View a PDF of the paper titled "Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood, by Peiyu Yu and Dinghuai Zhang and Hengzhi He and Xiaojian Ma and Sirui Xie and Ruiyao Miao and Yifan Lu and Yasi Zhang and Deqian Kong and Ruiqi Gao and Jianwen Xie and Guang Cheng and Ying Nian Wu View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-05 Change to browse by: cs cs.AI stat stat.AP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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