{"paper":{"title":"NICE: Non-linear Independent Components Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A composition of coupling layers learns an invertible non-linear map that turns high-dimensional data into independent latent factors for exact likelihood training.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"David Krueger, Laurent Dinh, Yoshua Bengio","submitted_at":"2014-10-30T19:44:20Z","abstract_excerpt":"We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables. We parametrize this transformation so that computing the Jacobian determinant and inverse transform is"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). ... The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a composition of the proposed coupling layers (each based on a deep neural network) can represent sufficiently complex non-linear transformations while preserving trivial Jacobian determinant and inverse.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"NICE learns a composition of invertible neural-network layers that transform data into independent latent variables, enabling exact log-likelihood training and sampling for density estimation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A composition of coupling layers learns an invertible non-linear map that turns high-dimensional data into independent latent factors for exact likelihood training.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5c454cd940a3af71351344f59944b0eaa37d41de0ea1074271164448b2ade80a"},"source":{"id":"1410.8516","kind":"arxiv","version":6},"verdict":{"id":"ba08ea7d-28c9-4256-9882-3ba1dcc2df6e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T01:18:38.464346Z","strongest_claim":"We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). ... The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy.","one_line_summary":"NICE learns a composition of invertible neural-network layers that transform data into independent latent variables, enabling exact log-likelihood training and sampling for density estimation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a composition of the proposed coupling layers (each based on a deep neural network) can represent sufficiently complex non-linear transformations while preserving trivial Jacobian determinant and inverse.","pith_extraction_headline":"A composition of coupling layers learns an invertible non-linear map that turns high-dimensional data into independent latent factors for exact likelihood training."},"references":{"count":33,"sample":[{"doi":"","year":2012,"title":"J., Bergeron, A., Bouchard, N., and Bengio, Y","work_id":"b37aac9a-cbd5-4153-9c72-c29c2f40ff18","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1991,"title":"Bengio, Y. (1991). Artificial Neural Networks and their Application to Sequence Recognition . PhD thesis, McGill University, (Computer Science), Montreal, Canada","work_id":"b0a5c649-8d83-40f0-a6f4-f000ca1e52b3","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Bengio, Y. (2009). Learning deep architectures for AI . Now Publishers","work_id":"b60e0d3b-6787-42e5-b5db-1f5fd9561fe2","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"arXiv preprint arXiv:1407.7906 , year =","work_id":"3837ddfa-70a7-4a68-8bb1-309a0ba7c349","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"Bengio, Y. and Bengio, S. (2000). Modeling high-dimensional discrete data with multi-layer neural networks. In Solla, S., Leen, T., and M \\\"u ller, K.-R., editors, Advances in Neural Information Proce","work_id":"44a249e3-a243-4e1f-b78d-87517d275cd0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":33,"snapshot_sha256":"a87047053490196ab9761fbc0abf4f94a604a87b51e6079cf3e644a0453386c5","internal_anchors":5},"formal_canon":{"evidence_count":2,"snapshot_sha256":"3e8f228c2993a47a6b042b333a84addc7ba309a3a50bde468251939912614c82"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}