{"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/a-mathematical-theory-of-semantic-development","title":"A mathematical theory of semantic development in deep neural networks","arxiv_id":"1810.10531","date":"2018-10-23","proceeding":null,"authors":["Andrew M. Saxe","James L. McClelland","Surya Ganguli"],"abstract":"An extensive body of empirical research has revealed remarkable regularities\nin the acquisition, organization, deployment, and neural representation of\nhuman semantic knowledge, thereby raising a fundamental conceptual question:\nwhat are the theoretical principles governing the ability of neural networks to\nacquire, organize, and deploy abstract knowledge by integrating across many\nindividual experiences? We address this question by mathematically analyzing\nthe nonlinear dynamics of learning in deep linear networks. We find exact\nsolutions to this learning dynamics that yield a conceptual explanation for the\nprevalence of many disparate phenomena in semantic cognition, including the\nhierarchical differentiation of concepts through rapid developmental\ntransitions, the ubiquity of semantic illusions between such transitions, the\nemergence of item typicality and category coherence as factors controlling the\nspeed of semantic processing, changing patterns of inductive projection over\ndevelopment, and the conservation of semantic similarity in neural\nrepresentations across species. Thus, surprisingly, our simple neural model\nqualitatively recapitulates many diverse regularities underlying semantic\ndevelopment, while providing analytic insight into how the statistical\nstructure of an environment can interact with nonlinear deep learning dynamics\nto give rise to these regularities.","url_abs":"http://arxiv.org/abs/1810.10531v1","url_pdf":"http://arxiv.org/pdf/1810.10531v1.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":"a-mathematical-theory-of-semantic-development","repo_url":"https://github.com/bhoov/ngd-vis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"semantic-similarity","task_name":"Semantic Similarity"},{"task_slug":"semantic-textual-similarity","task_name":"Semantic Textual Similarity"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1810.10531","atlas_url":"https://app.syntology.ai/?focus=1810.10531","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}