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The divergence\ntriangle is a compact and symmetric (anti-symmetric) objective function that\nseamlessly integrates variational learning, adversarial learning, wake-sleep\nalgorithm, and contrastive divergence in a unified probabilistic formulation.\nThis unification makes the processes of sampling, inference, energy evaluation\nreadily available without the need for costly Markov chain Monte Carlo methods.\nOur experiments demonstrate that the divergence triangle is capable of learning\n(1) an energy-based model with well-formed energy landscape, (2) direct\nsampling in the form of a generator network, and (3) feed-forward inference\nthat faithfully reconstructs observed as well as synthesized data. The\ndivergence triangle is a robust training method that can learn from incomplete\ndata.","url_abs":"http://arxiv.org/abs/1812.10907v2","url_pdf":"http://arxiv.org/pdf/1812.10907v2.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":"divergence-triangle-for-joint-training-of","repo_url":"https://github.com/enijkamp/triangle","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"model","task_name":"model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1812.10907","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1812.10907"}},"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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