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Using techniques from matrix\nperturbation theory, we reveal a fundamental bias-variance trade-off in\ndimensionality selection for word embeddings. This bias-variance trade-off\nsheds light on many empirical observations which were previously unexplained,\nfor example the existence of an optimal dimensionality. Moreover, new insights\nand discoveries, like when and how word embeddings are robust to over-fitting,\nare revealed. By optimizing over the bias-variance trade-off of the PIP loss,\nwe can explicitly answer the open question of dimensionality selection for word\nembedding.","url_abs":"http://arxiv.org/abs/1812.04224v1","url_pdf":"http://arxiv.org/pdf/1812.04224v1.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":"on-the-dimensionality-of-word-embedding","repo_url":"https://github.com/ziyin-dl/word-embedding-dimensionality-selection","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"on-the-dimensionality-of-word-embedding","repo_url":"https://github.com/aaaasssddf/PIP-experiments","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"on-the-dimensionality-of-word-embedding","repo_url":"https://github.com/aaaasssddf/word-embedding-dimensionality-selection","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"open-question","task_name":"Open-Ended Question Answering"},{"task_slug":"word-embeddings","task_name":"Word Embeddings"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1812.04224","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1812.04224"}},"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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